Eugene L. Fleeman Tactical Missile Design E-Mail: [email protected] Web Site

Eugene L. Fleeman Tactical Missile Design E-Mail: Genefleeman@Msn.Com Web Site

ProfessionalProfessional DevelopmentDevelopment ShortShort CourseCourse onon

TacticalTactical MissileMissile DesignDesign

Eugene L. Fleeman Tactical Missile Design E-mail: [email protected] Web Site: http://genefleeman.home.mindspring.com

2/24/2008 ELF 1 OutlineOutline

Introduction / Key Drivers in the Design Process Aerodynamic Considerations in Tactical Missile Design Propulsion Considerations in Tactical Missile Design Weight Considerations in Tactical Missile Design Flight Performance Considerations in Tactical Missile Design Measures of Merit and Launch Platform Integration Sizing Examples Development Process Summary and Lessons Learned References and Communication Appendices ( Homework Problems / Classroom Exercises, Example of Request for Proposal, Nomenclature, Acronyms, Conversion Factors, Syllabus ) 2/24/2008 ELF 2 EmphasisEmphasis IsIs onon Physics-Based,Physics-Based, AnalyticalAnalytical SizingSizing ofof AerodynamicAerodynamic ConfigurationConfiguration Area Emphasis Aero Configuration Sizing Aero Stability & Control Aero Flight Performance Propulsion Structure Weight Warhead Miss Distance Cost Additional Measures of Merit Launch Platform Integration Primary Emphasis Seeker, Sensors, and Electronics Secondary Emphasis Power Supply Tertiary Emphasis Safe, Arm, and Fuzing - Not Addressed - 2/24/2008 ELF 3 TacticalTactical MissilesMissiles AreAre DifferentDifferent fromfrom FighterFighter AircraftAircraft

Tactical Missile Example of Comparison With Characteristics State-of-the-Art Fighter Aircraft Axial Acceleration AGM-88 Maneuverability AA-11 Speed / altitude SM-3 Dynamic pressure PAC-3 Size Javelin Weight FIM-92 Production cost GBU-31 Observables AGM-129 Range AGM-86 – Kills per use Storm Shadow – Target acquisition LOCAAS –

Superior Better Comparable – Inferior

2/24/2008 ELF 4 AeroAero ConfigurationConfiguration SizingSizing ParametersParameters EmphasizedEmphasized inin ThisThis CourseCourse

Propulsion Sizing / Propellant or Fuel Diameter Stabilizer Nose Fineness Geometry / Size Wing Geometry / Size Thrust Profile

Flight Conditions ( α, M, h )

Flight Control Length Geometry / Size

2/24/2008 ELF 5 CConceptualonceptual DesignDesign ProcessProcess RequiresRequires EvaluationEvaluation ofof AlternativesAlternatives andand IterationIteration

• Mission / Scenario Update Definition Initial Revised

• Weapon Trades / Eval Effectiveness / Eval Requirements, Trade Studies Initial Alt Baseline and Sensitivity Reqs Concepts Selected Analysis • Launch Platform Initial Carriage / Iteration Integration Launch Refine Weapons Req

• Weapon Concept Alternate Concepts ⇒ Select Preferred Design ⇒Eval / Refine Design Synthesis

• Technology Initial Tech Initial Revised Assessment and Tech Trades Roadmap Roadmap Dev Roadmap Note: Typical conceptual design cycle is 3 to 9 months. House of Quality may be used to translate customer requirements to engineering characteristics. DOE may be used to efficiently evaluate the broad range of design solutions. 2/24/2008 ELF 6 MissileMissile ConceptConcept SynthesisSynthesis RequiresRequires EvaluationEvaluation ofof AlternativesAlternatives andand IterationIteration Define Mission Requirements Alt Mission Establish Baseline Alt Baseline Aerodynamics

Propulsion

Weight Resize / Alt Config / Subsystems / Tech

Trajectory

Meet No Performance?

Yes No Measures of Merit and Constraints

Yes

2/24/2008 ELF 7 ExamplesExamples ofof AiAirr-Launched-Launched MissileMissile MissionsMissions // TypesTypes

Air-to-air Example SOTA 10 feet

• Short range ATA. AA-11. Maneuverability

• Medium range ATA. AIM-120. Performance / weight

• Long range ATA. Meteor. Range

Air-to-surface • Short range ATS. AGM-114. Versatility • Medium range ATS. AGM-88. Speed • Long range ATS. Storm Shadow. Modularity

Surface-to-surface Example SOTA 10 feet • Short range STS. Javelin. Size

• Medium range STS. MGM-140. Modularity

• Long range STS. BGM-109. Range

Surface-to-air • Short range STA. FIM-92. Weight • Medium range STA. PAC-3. Accuracy • Long range STA. SM-3. High altitude

Permission of Missile.Index. Copyright 1997©Missile.Index All Rights Reserved 2/24/2008 ELF 9 AeroAero ConfigurationConfiguration SizingSizing HasHas HighHigh ImpactImpact onon MissionMission RequirementsRequirements

Impact on Weapon Requirement Aero Measures of Merit Other Measures of Merit Constraint Aero Configuration Range / Time to Robust- Miss Observ- Launch Sizing Parameter Weight Maneuver Target ness Lethality Distance ables Survivability Cost Platform

Nose Fineness

Diameter

Length

Wing Geometry / Size

Stabilizer Geometry / Size

Flight Control Geometry / Size

Propellant / Fuel

Thrust Profile

Flight Conditions ( α, M, h )

Very Strong Strong Moderate– Relatively Low

2/24/2008 ELF 10 ExampleExample ofof AssessmentAssessment ofof AlternativesAlternatives toto EstablishEstablish FutureFuture MissionMission RequirementsRequirements

Measures of Merit

Alternatives for Precision Strike Number of Cost per Launch Platforms TCT Shot Required Effectiveness Future Systems

Standoff platforms / hypersonic missiles

Overhead loitering UCAVs / hypersonic missiles

Overhead loitering UCAVs / light weight PGMs

Current Systems

Penetrating aircraft / subsonic PGMs – –

Standoff platforms / subsonic missiles –

Note: Superior Good Average– Poor

Note: C4ISR targeting state-of-the-art for year 2010 projected to provide sensor-to-shooter / weapon connectivity time of less than 2 m and target location error ( TLE ) of less than 1 m for motion suspended target.

2/24/2008 ELF 11 C4ISRC4ISR TacticalTactical SatellitesSatellites andand UAVsUAVs HaveHave HighHigh ImpactImpact onon MissionMission CapabilityCapability LaunchLaunch Platforms Platforms Off-boardOff-board Sensors Sensors •Fighter Aircraft •Fighter Aircraft •Tactical•Tactical Satellite Satellite •Bomber •Bomber •UAV•UAV •Ship•Ship / Submarine/ Submarine •UCAV•UCAV PrecisionPrecision Strike Strike Weapons Weapons •Hypersonic•Hypersonic SOW SOW •Subsonic•Subsonic PGM PGM •Subsonic•Subsonic CM CM

TimeTime Critical Critical Targets Targets •TBM•TBM / TEL/ TEL •SAM•SAM •C3•C3 •Other•Other Strategic Strategic Note: C4ISR targeting state-of-the-art for year 2010 projected to provide sensor-to-shooter / weapon connectivity time of less than 2 m and target location error ( TLE ) of less than 1 m for motion suspended target. 2/24/2008 ELF 12 EExamplexample ooff SSystem-oystem-off--SystemsSystems AAnalysisnalysis toto DevelopDevelop FutureFuture MissionMission RequirementsRequirements 1. Compare Targeting of Subsonic Cruise Missile 3. Alt / Speed / RCS Required 5. Campaign Model Weapons Versus Hypersonic Missile For Survivability Mix ( CM, Hypersonic

t0 t1 t2 t 100 Missile ) Results 3 RCS1 RCS2 > RCS1 80 ( eg., Korean Scenario ) TBM Launch Hypersonic HM Intercept 60 Launch Pt Rcvd Missile Launch at XXX nm Selected For All: 40 • Value of Speed / 20 Range Altitude – 1000 ft 0 • Time Urgent Targets Cruise Missile Launch 0 2000 4000 6000 • High Threat Average Speed to Survive, fps 1 Environments - 2 -3 3 - 2 4 • Buried Targets 2. Time To Target -5 4. Lethality 4 • Launch Platform Alternatives 120 W/H W > W Range 3 > R2 3 2 • Operating and W/H W > W 100 Range 2 > R1 50 2 1 Attrition Cost in

80 Range 1 40 Warhead W1 Campaign • Weapon Cost in 60 30 Campaign Time, Min 40 20 • Mix of Weapons in 20 Penetration ( ft ) Penetration 10 Campaign 0 Lethality / Concrete • Cost Per Target Kill 0 1000 2000 3000 4000 5000 0 • C4ISR Interface Average Speed, fps 0 1000 2000 3000 4000 Impact Velocity, fps

2/24/2008 ELF 13 ExampleExample ofof TechnologicalTechnological SurpriseSurprise DrivingDriving ImmediateImmediate MissionMission RequirementsRequirements

Sidewinder AIM-9L ( IOC 1977 ) Performance •+/- 25 deg off boresight •6.5 nm range Archer AA-11 / R-73 ( IOC 1987 ) Performance •> +/- 60 deg off boresight •20 nm range New Technologies •TVC •Split canard •Near-neutral static margin •+/- 90 deg gimbal seeker •Helmet mounted sight

Note: AIM-9L maneuverability shortfall compared to Archer drove sudden development of AIM-9X. 2/24/2008 ELF 14 MissileMissile ConceptConcept SynthesisSynthesis RequiresRequires EvaluationEvaluation ofof AlternativesAlternatives andand IterationIteration

Define Mission Requirements Alt Mission Establish Baseline Alt Baseline Aerodynamics

Propulsion

Weight Resize / Alt Config / Subsystems / Tech

Trajectory

Meet No Performance?

Yes No Measures of Merit and Constraints

Yes

2/24/2008 ELF 15 BaselineBaseline DesignDesign BenefitsBenefits andand GuidelinesGuidelines

Benefits of Baseline Design Allows simple, conceptual design methods to be used with good accuracy Well documented benchmark / configuration control / traceability between cause and effect Balanced subsystems Gives fast startup / default values for design effort Provides sensitivity trends for changing design Baselines can cover reasonable range of starting points Baselines can normally be extrapolated to ±50% with good accuracy Guidelines Don’t get locked-in by baseline Be creative Project state-of-the-art ( SOTA ) if baseline has obsolete subsystems Sensors and electronics almost always need to be updated

2/24/2008 ELF 16 ExampleExample ofof MissileMissile BaselineBaseline DataData

Configuration Drawing Weight / Geometry Flow Path Geometry

( C ) = ( C ) x ( 1 - A / S ) Sta 150.3 Inlet D0 Nose Corrected D0 Nose Uncorrected c REF 11.6 Conical forebody angle, deg 17.7 37° Ramp wedge angle, deg 8.36 A Inlet capture area 2 Component Weight, lb CG Sta, In. c 2 Capture area, ft 0.52 Ac = 114 in 11.5 2 A Inlet throat area Throat area, ft Nose0.29 15.9 15.7 IT Body SRef Reference area Forebody 42.4 33.5 120° 16.5 Length, inGuidance 171.0 129.0 33.5 A5 Nozzle throat area Diameter, in 20.375 Payload Bay 64.5 60.0 Isp Specific impulse Boost Nozzle Fineness ratioWarhead 8.39 510.0 60.0 φ Equivalence ratio – operating fuel / air ratio divided by fuel / air ratio for stochiometric combustion 20.375 dia Volume, ft3 28.33 Wetted area, ft2 Midbody68.81 95.2 101.2 2 Inlet 103.0 80.0 Ramjet Fuel Base area, ft ( cruise )Electrical 0.58 30.0 112.0 Guidance Warhead Boost Propellant Boattail fineness ratioHydraulic N/A 20.0 121.0 Ramjet Engine Station Identification Booster, and Nose half angle, degFuel 15.0 Distribution 5.0 121.0 Chin Ramjet Engine Transport Air Duct Aftbody 44.5 142.5 Inlet Tail ( Exposed ) Engine 33.5 142.5 Sta 0. 23.5 43.5 76.5 126.0 Area ( 2 panels ), ft2 Tailcone2.24 31.6 165.0 2 Nose Fore-body Payload Bay Mid-body Aft-body Tail Cone Wetted area ( 4 panels ), ft Exit Duct8.96 31.0 165.0 Aspect ratio ( exposed )Controls 1.64 37.0 164.0 159.0 171.0 Taper ratioFins ( 4 ) 0.70 70.0 157.2 0 1 23 4 5 6 Root chord, in 16.5 End of Cruise 1,262.6 81.8 Free Stream Inlet Throat Span, in. ( exposed ) 23.0 3 Subscripts Ramjet Fuel ( 6.9 ft ) 476.0 87.0 2 2 Note: Dimensions are in inches L.E. sweep, deg 37.0 0 Free stream conditions ( Ramjet Baseline A0 = 75.4 in at Mach 4, α = 0 deg, Note: AC = 114 in ) Start of Cruise 1,738.6 83.2 2 M.A.C., in 14.2 1 Inlet throat ( Ramjet Baseline A1 = AIT = 41.9 in ) Boost Nozzle ( Ejected ) 31.0 164.0 2 Thickness ratio 0.04 2 Diffuser exit ( Ramjet Baseline A2 = 77.3 in ) Frangible Port 11.5 126.0 2 X MAC, in 150.5 3 Flame holder plane ( Ramjet Baseline A3 = 287.1 in ) End of Boost 1,781.1 84.9 2 Y MAC, in ( from root chord ) 5.4 4 Combustor exit ( Ramjet Baseline A4 = 287.1 in ) 2 20.375 in diameter Boost Propellant 449.0 142.5 5 Nozzle throat ( Ramjet Baseline A5 = 103.1 in ) Reference values: 2 Source: Bithell, R.A. and Stoner, R.C. “Rapid Approach for Missile Synthesis”, Vol. II, Air-breathing 2 Booster Ignition 2,230.1 96.5 6 Nozzle exit ( A6 = 233.6 in ) Reference area, ft 2.264 Ref Reference Area ( Ramjet Baseline Body Cross-sectional Area, S = 326 in2 ) Synthesis Handbook, AFWAL TR 81-3022, Vol. II, March 1982. Reference length, ft 1.698 Ref Aerodynamics Ramjet Propulsion Rocket Propulsion

-.4 2 SRef = 2.264 ft LRef = DRef = 1.698 ft 30 Xcg @ Sta 82.5 in. 1,500 20,000 ( ISP )Booster = 250 sec + .4 .4 2 -.2 SRef = 2.264 ft ~ per deg 20 L = D = 1.698 ft δ Ref Ref • • .3 h = SL

m • C m Xcg @ Sta 82.5 in. • 0 2 SRef = 2.264 ft 1,000 • Note: 15,000 • 10 LRef = Dref = 1.698 ft • • 0 C D 0 .2 φ = 1 Xcg @ Sta 82.5 in. •

4.0 1000 lbs Thrust ~Boost .10 .40

-.4 N 0 .1A Mach Mach 1.2 h = 20K ft 01.02.03.04.05.0 6.0 3.0 • • .30 1.2 1.5 500 • 10,000 Time ~ sec Mach 2.0 Note: Note: Constant altitude flyout .05 0 1.5 •

4.0 , Specific Impulse, sec ~ per deg per ~ 3.0 -.8 01234 3.0

δ 2.0 2.0 4.0 sp φ = 1 • 2.0 M = 0.80 .20 I L

C N M, Mach Number 3.0 constant altitude flyout

3.0 T, Net Thrust, lb 4.0 h = 40K ft 0 .10 1.0 5,000 1.0 012 34-1.2 • • 2.5 M, Mach Number •

Axial Force Coefficient, C Coefficient, Force Axial 2.0 0 Pitching Moment Coefficient, C

Normal Force Coefficient, C 0 12 34 • 0 0 • h = 60K ft 04812161.5 0481216 M, Mach Number • • • Boost Range~ nm 0 • Burnout Mach Number -1.6 α, Angle of Attack ~ deg α, Angle of Attack ~ deg h = 80K ft 0204060 2.0 1.2 • 0204060 0 h, Altitude 1,000 ft 80 04 81216 01234 h, Altitude 1,000 ft α, Angle of Attack ~ deg M, Mach Number Flight Performance House of Quality Paredo Sensitivity for DOE

1.5 500 1 400 60,000 ft 0.5 300 0 to Parameter Range ~ nm 200 ISP Fuel Thrust CD0, Zero- CLA, Lift- Inert Weight Lift Drag Curve- Weight 40,000 ft -0.5 Coefficient Slope 100 Coefficient

20,000 ft Nondimensional RangeSensitivity -1 Note: h = SL Parameter • ML = 0.8, Constant Altitude Flyout 0 Example: 01 2 34 • Breguet Range for Mach 3 / 60 Kft flyout: M, Mach Number Sea Level Flyout at Mach 2.3 20 Kft Flyout at Mach 2.5 Rmax = V ISP ( L / D )Max ln [ WBC / ( WBC - Wf )] = 2901 ( 950 ) ( 3.15 ) ln ( 1739 / ( 1739 - 476 )) = 2,777,192 ft or 457 nm 40 Kft Flyout at Mach 2.8 60 Kft Flyout at Mach 3.0 2/24/2008 ELF 17 BaselineBaseline DesignDesign DataData AllowsAllows CorrectionCorrection ofof ComputedComputed ParametersParameters inin ConceptualConceptual DesignDesign

PCD, C = ( PB, C / PB, U ) PCD, U

PCD, C Parameter of conceptual design, corrected

PB, C Parameter of baseline, corrected ( actual data )

PB, U Parameter of baseline, uncorrected ( computed )

PCD, U Parameter of conceptual design, uncorrected (computed ) Example • Ramjet Baseline with RJ-5 fuel ( heating value = 11,300,000 ft-lbf / lbm ) • Advanced Concept with slurry fuel ( 40% JP-10 / 60% boron carbide = 18,500,000 ft-lbf / lbm ) • Flight conditions: Mach 3.5 cruise, 60k ft altitude, combustion temperature 4,000 R

• Calculate specific impulse ( ISP )CD,C for conceptual design, based on corrected baseline data

– ( ISP )B, C = 1,120 s – ( ISP )B, U = 1387 s – ( ISP )CD, U = 2,271 s – ( ISP )CD, C = [( ISP )B, C / ( ISP )B, U ] ( ISP )CD, U = [( 1120 ) / ( 1387 )] ( 2271 ) = 0.807 ( 2271 ) = 1,834 s 2/24/2008 ELF 18 SummarySummary ofof ThisThis ChapterChapter

Overview of Missile Design Process Examples Tactical missile characteristics Conceptual design process SOTA of tactical missiles Aerodynamic configuration sizing parameters Processes that establish mission requirements Process for correcting design predictions Discussion / Questions? Classroom Exercise

2/24/2008 ELF 19 IntroductionIntroduction ProblemsProblems

1. The missile design team should address the areas of mission / scenario definition, weapon requirements, launch platform integration, design, and t______a______. 2. The steps to evaluate missile flight performance require computing aerodynamics, propulsion, weight, and flight t______. 3. Air-to-air missile characteristics include light weight, high speed, and high m______. 4. Air-to-surface missiles are often versatile and m______. 5. Four aeromechanics measures of merit are weight, range, maneuverability, and t___ to target. 6. The launch platform often constrains the missile span, length, and w_____. 7. An enabling capability for hypersonic strike missiles is fast and accurate C____. 8. An enabling capability for large off boresight air-to-air missiles is a h_____ m______sight. 9. A baseline design improves the accuracy and s____ of the design process. 2/24/2008 ELF 20 OutlineOutline

Define Mission Requirements Alt Mission Establish Baseline Alt Baseline Aerodynamics

Propulsion

Weight Resize / Alt Config / Subsystems / Tech

Trajectory

Meet No Performance?

Yes No Measures of Merit and Constraints

Yes

2/24/2008 ELF 22 MissileMissile DiameterDiameter TradeoffTradeoff

Drivers toward Small Diameter • Decrease drag • Launch platform diameter constraint Drivers toward Large Diameter • Increase seeker range and signal-to-noise, better resolution and tracking • Increase blast frag and shaped charge warhead effectiveness ( larger diameter ⇒ higher velocity fragments or higher velocity jet ) • Increase body bending frequency • Subsystem diameter packaging • Launch platform length constraint Typical Range in Body Fineness Ratio 5 < l / d < 25 • Man-portable anti-armor missiles are low l / d ( Javelin l / d = 8.5 ) • Surface-to-air and air-to-air missiles are high l / d ( AIM-120 l / d = 20.5 )

2/24/2008 ELF 23 SmallSmall DiameterDiameter MissilesMissiles HaveHave LowLow DragDrag

2 D = CD q SRef = 0.785 CD q d 100000 Note: D = drag in lb, CD = drag coefficient, q = dynamic pressure in psf, d = diameter ( reference length ) in ft

10000 Dynamic Pressure = 1,000 psf 1000 Dynamic Pressure = 5,000 psf Dynamic Pressure = 10,000 psf 100 Example for Rocket Baseline:

D / CD, Drag / Drag Coefficient, lb d = 8 in = 0.667 ft 10 Mach 2, h = 20k ft, ( C ) = 0.95 D0 Powered 4 8 12 16 20 q = 1/2 ρ V2 = 1/2 ρ ( M a )2 2 d, Diameter, in = 1/2 ( 0.001267 ) [( 2 ) ( 1037 )] = 2,725 psf D / C = 0.785 ( 2725 ) ( 0.667 )2 = 952 0 D0

D0 = 0.95 ( 952 ) = 900 lb

2/24/2008 ELF 24 LargeLarge DiameterDiameter RadarRadar SeekerSeeker ProvidesProvides LongerLonger DetectionDetection RangeRange andand BetterBetter ResolutionResolution R = { πσn3/4 / [ 64 λ2 K T B F L ( S / N ) ]}1/4 P 1/4 d Assumptions: Negligible clutter, interference, and D t atmospheric attenuation; non-coherent radar ( only 100 θ = 1.02 λ / d, θ in rad signal amplitude integrated ); uniformly illuminated 3dB 3dB circular aperture; receiver sensitivity limited by thermal noise Symbols:

10 σ = Target radar cross section, m2 n = Number of pulses integrated λ = Wavelength, m K = Boltzman’s constant = 1.38 x 10-23 J / K T = Receiver temperature, K B = Receiver bandwidth, Hz 1 F = Receiver noise factor 0 5 10 15 20 L = Transmitter loss factor d, Diameter, Inches S / N = Signal-to-noise ratio for target detection Pt = Transmitted power, W Example Seeker Range for Transmitted Power Pt = 100 W, nm d = Antenna diameter Example Seeker Range for Transmitted Power Pt = 1,000 W, nm Example: Rocket Baseline

Example Seeker Range for Transmitted Power Pt = 10,000 W, nm d = 8 in = 0.20 m, Pt = 1000 W, λ = 0.03 m ( f = 10 GHz ) 3/4 Example Seeker Beam Width, deg RD = Target detection range = { π ( 10 ) ( 100 ) / [ 64 ( 0.03 )2 ( 1.38 x 10-23 ) ( 290 ) ( 106 ) ( 5 ) ( 5 )( 10 )]}1/4 ( Note for figure: σ = 10 m2, n = 100, λ = 0.03 m ( f = Transmitter 1000 )1/4 ( 0.203 ) = 13,073 m or 7.1 nm 9 6 -6 frequency = 10 x 10 Hz ), T = 290 K, B = 10 Hz ( 10 s pulse ), F θ3dB = 3-dB beam width = 1.02 ( 0.03 ) / 0.203 = 0.1507 = 5, L = 5, S / N = 10 rad or 8.6 deg

2/24/2008 ELF 25 LargeLarge DiameterDiameter IRIR SeekerSeeker ProvidesProvides LongerLonger DetectionDetection RangeRange andand BetterBetter ResolutionResolution

R = { ( I ) η A { D* / [( Δf )1/2 ( A )1/2 ]} ( S / N ) -1 }1/2 R = Target detection range, m 100 D T Δλ a o p d D D ( IT )Δλ = Target radiant intensity between λ1 and λ2= ε IFOV = dp / [ ( f-number ) do ] Lλ ( λ2 - λ1 ) AT, W / sr ηa = Atmospheric transmission 2 Ao = Optics aperture area, m 10 D* = Specific detectivity, cm Hz1/2 / W

Δfp = Pixel bandwidth, Hz 2 Ad = Detectors total area, cm ( S / N )D = Signal-to-noise ratio required for detection 1 ε = Emissivity coefficient 0246810 4 Lλ = Spectral radiance ( Planck’s Law ) = 3.74 x 10 / { 4 do, Optics Diameter, Inches λ5 { e[ 1.44 x 10 / ( λ TT )] – 1 }}, W cm-2 sr-2 μm-1

λ2 = Upper cutoff wavelength for detection, μm Example Seeker Range for Exo-atmospheric, km λ1 = Lower cutoff wavelength for detection, μm Example Seeker Range for Humidity at 7.5 g / m3, km 2 AT = Target planform area, cm Example Seeker Range for Rain at 4 mm / hr, km λ = Average wavelength, μm Example Seeker IFOV, 10-5 rad TT = Target temperature, K IFOV = Instantaneous field-of-view of pixel, rad Example: do = 5 in = 0.127 m, exo-atmospheric 4 5 { 1.44 x 104 / [ 4 ( 300 ) ]} -2 -2 f-number = d / ( 2.44 λ ) Lλ = 3.74 x 10 / { 4 { e – 1 }} = 0.000224 W cm sr spot -1 d = Pixel diameter, either μm μm , ( IT )Δλ = 0.5 ( 0.000224 ) ( 4.2 – 3.8 ) 2896 = 0.1297 W / sr, Ad = p 2 2 256 x 256 x ( 20 μm ) = 0.262 cm , f-number = 20 / [ 2.44 ( 4 ) ] = 2.05 dspot = Spot resolution if diffraction limited = dp, μm 11 1/2 1/2 -1 RD = { 0.1297 ( 1 ) ( 0.01267 ) { 8 x 10 / [( 250 ) ( 0.262 ) ]} ( 1 ) Figure: d = 2 ft ( 60.96 cm ), T = 300 K, λ = 3.8 μm, }1/2 = 12, 740 m T T 1 λ2 = 4.2 μm, ε = 0.5, λ = 4 μm, FPA ( 256 x 256, 20 μm IFOV = 0.000020 / [ 2.05 ( 0.127 )] = 0.0000769 rad 11 1/2 ), D* = 8 x 10 cm Hz / W, ( S / N )D = 1, Δfp = 250 Hz. 2/24/2008 ELF 26 MissileMissile FinenessFineness RatioRatio MayMay BeBe LimitedLimited byby ImpactImpact ofof BodyBody BendingBending onon FlightFlight ControlControl Assumes body cylinder structure, thin skin, high 1/2 ωBB = 18.75 { E t / [ W ( l / d ) ]} fineness ratio, uniform weight distribution, free-free 10000 motion. Neglects bulkhead, wing / tail stiffness.

ωBB = First mode body bending frequency, rad / s E = Modulus of elasticity in psi t = Thickness in inches W = Weight in lb l / d = Fineness ratio E t / W = 1,000 per in 1000 E t / W = 10,0000 per in E t / W = 100,000 per in

Example for Rocket Baseline: l / d = 18 6 EAVG = 19.5 x 10 psi tAVG = 0.12 in W = 500 lb First Mode Body Bending Frequency, rad / s First Mode Body Bending Frequency, 100 E t / W = 19.5 x 106 ( 0.12 ) / 500 = 4680 per in ω = 18.75 ( 4680 / 18 )1/2 = 302 rad / sec = 48 Hz 0102030BB ωActuator = 100 rad / sec = 16 Hz ω / ω = 302 / 100 = 3.02 > 2 l / d, length / diameter BB Actuator

Derived from: AIAA Aerospace Design Engineers Guide, American Institute of Aeronautics and Astronautics, 1993. 2/24/2008 ELF 27 NoseNose FinenessFineness TradeoffTradeoff

High Nose Fineness Superior Aerodynamically, Low Observables

Example: lN / d = 5 tangent ogive

Low Nose Fineness Ideal Electromagnetically, High Propellant Length / Volume

Example: lN / d = 0.5 ( hemisphere ) d

Moderate Nose Fineness Compromise Dome

Examples: lN / d = 2 tangent ogive lN / d = 2 faceted lN / d = 2 window lN / d = 2 multi-lens d ow Wind

2/24/2008 ELF 28 FacetedFaceted andand FlatFlat WindowWindow DomesDomes CanCan HaveHave LowLow DomeDome ErrorError Slope,Slope, LowLow Drag,Drag, andand LowLow RCSRCS

Firestreak

Mistral

SLAM-ER Faceted Dome ( Mistral ) Video

JASSM

THAAD

2/24/2008 ELF 29 SupersonicSupersonic BodyBody DragDrag DrivenDriven byby NoseNose FinenessFineness whilewhile SubsonicSubsonic DragDrag DrivenDriven byby WettedWetted AreaArea ( C ) = (C ) +( C ) + ( C ) D0 Body D0 Body,Friction D0 Base D0 Body, Wave (C ) = 0.053 ( l / d ) [ M / ( q l )]0.2. Based on Jerger reference, turbulent boundary layer, q in psf, l in ft. D0 Body,Friction ( C ) = 0.25 / M, if M > 1 and (C ) = ( 0.12 + 0.13 M2 ), if M < 1 D0 Base,Coast D0 Base,Coast ( C ) = ( 1 – A / S ) ( 0.25 / M ), if M > 1 and ( C ) = ( 1 – A / S ) ( 0.12 + 0.13 M2 ), if M < 1 D0 Base,Powered e Ref D0 Base,Powered e Ref ( C ) = ( 1.59 + 1.83 / M2 ) { tan-1 [ 0.5 / ( l / d )]}1.69, for M > 1. Based on Bonney reference, tan-1 in rad. D0 Body, Wave N Note: ( C ) = body zero-lift wave drag coefficient, ( C ) = body base drag coefficient, ( C ) = body skin D0 Body,Wave D0 Base D0 Body, Friction friction drag coefficient, ( CD )Body = body zero-lift drag coefficient, lN = nose length, d = missile diameter, l = missile body 0 -1 length, Ae = nozzle exit area, SRef = reference area, q = dynamic pressure, tan [ 0.5 / ( lN / d )] in rad. 10 Example for Rocket Baseline: ( C ) ( C ) ( C ) (CD0)Body,Wave; D0 Body, Wave D0 Body, Friction D Base lN / d = 0.5 1 (CD0)Body,Wave; 2 2 lN / d = 2.4, Ae = 11.22 in , SRef = 50.26 in , M = lN / d = 1 2, h = 20k ft, q = 2725 psf, l / d = 18, l = 12 ft (CD0)Body,Wave; ( C ) = 0.053 ( 18 ) { ( 2 ) / [( 2725 ) 0.1 D0 Body, Friction lN / d = 2 ( 12 ) ]}0.2 = 0.14 (CD0)Body,Wave; ( C ) = 0.25 / 2 = 0.13 lN / d = 5 D Base Coast 0.01 ( C ) = ( 1 - 0.223 ) ( 0.25 / 2 ) = 0.10 (CD)Base,Coast D Base Powered 012345 ( C ) = 0.14 D0 Body, Wave M, Mach Number ( C ) = 0.14 + 0.13 + 0.14 = 0.41 D0 Body, Coast ( C ) = 0.14 + 0.10 + 0.14 = 0.38 D0 Body, Powered 2/24/2008 ELF 30 ModerateModerate NoseNose TipTip BluntnessBluntness CausesCauses aa NegligibleNegligible ChangeChange inin SupersonicSupersonic DragDrag

Steps to Calculate Wave Drag of a Blunted Nose 1. Relate blunted nose tip geometry to pointed nose tip geometry

dNoseTip dRef

2. Compute (C ) for sharp nose, based on the body reference area D0 Wave,SharpNose ( C ) , = ( 1.59 + 1.83 / M2 ) { tan-1 [ 0.5 / ( l / d )]}1.69 D0 Wave SharpNose N

3. Compute ( CD )Wave,Hemi of the hemispherical nose tip ( lNoseTip / dNoseTip = 0.5 ), based on the nose tip area 0 ( C ) = ( 1.59 + 1.83 / M2 ) {[ tan-1 ( 0.5 / ( 0.5 )]}1.69 = 0.665 ( 1.59 + 1.83 / M2 ) D0 Wave,Hemi 4. Finally, compute ( C ) of the blunt nose, based on the body reference area D0 Wave,BluntNose ( C ) = ( C ) ( S -S ) / S + ( C ) S / S D0 Wave,BluntNose D0 Wave,SharpNose Ref NoseTip Ref D0 Wave,Hemi NoseTipi Ref

Example Rocket Baseline ( dRef = 8 in ) with 10% Nose Tip Bluntness at Mach 2 • ( C ) = [ 1.59 + 1.83 / ( 2 )2 ] [ tan-1 ( 0.5 / 2.4)]1.69 = 0.14 D0 Wave,SharpNose • dNoseTip = 0.10 ( 8 ) = 0.8 in 2 2 2 2 • SNoseTip = π dNoseTip / 4 = 3.1416 ( 0.8 ) / 4 = 0.503 in = 0.00349 ft • ( C ) = 0.665 [ 1.59 + 1.83 / ( 2 )2 ] = 1.36 D0 Wave,Hemi • ( C ) = 0.14 ( 0.349 - 0.003 ) / 0.349 + ( 1.36 ) ( 0.003 ) / ( 0.349 ) = 0.14 + 0.01 = 0.15 D0 Wave,BluntNose 2/24/2008 ELF 31 BoattailBoattail DecreasesDecreases BaseBase PressurePressure DragDrag AreaArea

Base Pressure Drag Area

Without Boattail dRef

During Motor Burn After Motor Burnout θBT

With Boattail dBT

Note: Boattail angle θBT and boattail diameter dBT limited by propulsion nozzle packaging, tail flight control packaging, and flow separation Reference: Chin, S. S., Missile Configuration Design, McGraw-Hill Book Company, New York, 1961

2/24/2008 ELF 32 BoattailingBoattailing ReducesReduces DragDrag forfor SubsonicSubsonic MissilesMissiles

0.45 Boattail 0.40 Nose Center body 3.00 6.00 1.50 0.35 10.50

0.30

0.25

0.20 dBT / dRef = 1.0 d / d = 0.9 0.15 BT Ref d / d = 0.8

, Example Zero-Lift Drag Coefficient BT Ref Note: O

D dBT / dRef = 0.6 d = Boattail Diameter C 0.10 d / d = 0.4 BT BT Ref dRef = Body Reference Diameter 0.05 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 M∞ Note: Boatail half angle should be less than 10 deg, to avoid flow separattion. Source: Mason, L.A., Devan, L. and Moore, F.G., “Aerodynamic Design Manual for Tactical Weapons,” NSWC TR 81-156, July 2/24/20081981 ELF 33 LiftingLifting BodyBody HasHas HigherHigher NormalNormal ForceForce

2 2 2 ⏐ CN ⏐ = [⏐( a / b ) cos φ + ( b / a ) sin φ⏐] [⏐ sin ( 2α ) cos ( α / 2 ) ⏐ + 2 ( l / d ) sin α ]

Note:

150 If α negative, CN negative Based on slender body theory ( Pitts, et al ) and cross flow theory ( Jorgensen ) references Valid for l / d > 5 Example l / d = length / diameter = 20 a / b = 3 d = 2 ( a b )1/2 CN, 100 φ = 0° Example CN Normal 2b a / b = 2 Force Coefficient φ 50 2a for l / d = 20 a / b = 1

0 020406080100 α, Angle of Attack, Deg

2/24/2008 ELF 34 LL // DD IsIs ImpactedImpacted byby CCDD00,, BodyBody Fineness,Fineness, andand LiftingLifting BodyBody CrossCross SectionSection GeometryGeometry

L / D = CL / CD = ( CN cos α –CD0 sin α ) / ( CN sin α + CD0 cos α ) 2 2 2 For a lifting body, ⏐ CN ⏐ = [⏐( a / b ) cos ( φ ) + ( b / a ) sin ( φ ) ⏐] [⏐ sin ( 2α ) cos ( α / 2 ) ⏐ + 2 ( l / d ) sin α ] 4

3 High drag, low fineness body ( a / b = 1, l / d = 10, C = 0.5 ) L / D, DO Low drag nose ( a / b = 1, l / d = 10, CDO = 0.2 ) Lift / Drag High fineness, low drag ( a / b = 1, l / d = 20, C = 0.2 ) 2 DO Lifting body, high fineness, low drag ( a / b = 2 @ φ = 0°, l / d = 20, CD = 0.2 ) O 2b 1 CN

0 φ 020406080100 2a Note: α, Angle of Attack, Deg • If α negative, L / D negative •d = 2 ( a b )1/2 •Launch platform span constraints ( e.g., VLS launcher ) and length constraints ( e.g., aircraft compatibility ) may limit missile aero configuration enhancements

2/24/2008 ELF 35 LiftingLifting BodyBody RequiresRequires FlightFlight atat LowLow DynamicDynamic PressurePressure toto AchieveAchieve HighHigh AeroAero EfficiencyEfficiency

L / D = CL / CD = ( CN cos α –CDO sin α ) / ( CN sin α + CDO cos α ) 2 2 2 ⏐ CN ⏐ = [⏐( a / b ) cos ( φ ) + ( b / a ) sin ( φ ) ⏐] [⏐ sin ( 2α ) cos ( α / 2 ) ⏐ + 2 ( l / d ) sin α ]

4 Example: q = 500 psf 3 •a / b = 1 ⇒ L / D = 2.40 2 •a / b = 2 ⇒ L / D = 3.37 q = 5,000 psf 1 •a / b = 1 ⇒ L / D = 0.91 •a / b = 2 ⇒ L / D = 0.96 Example L / D, Lift / Drag / Lift D, L / Example 0 100 1000 10000 100000 q, Dynamic Pressure, lb / ft2

Circular Cross Section ( a / b = 1 ) Lifting Body ( a / b = 2 )

Note. Example figure based on following assumptions: Body lift only ( no surfaces ), cruise flight ( lift = weight ), W = L = 2,000 lb, d = 2 ( a b )1/2, S = 2 ft2,

l / d = 10, CD0 = 0.2 2/24/2008 ELF 36 Trade-offTrade-off ofof LowLow ObservablesObservables andand (( LL // DD ))MaxMax VersusVersus VolumetricVolumetric EfficiencyEfficiency

6 Tailored Advantages: • ( L / D ) Weapons Max • Low RCS Lower Max 5 Advantages: Conventional • Payload Weapons • Launch Platform

, ( Lift / Drag ) ( circular Integration

Max cross section ) 4

( L / D ) Radar Cross Section

2 Circular 4 6 8 10 Cross Section Body Planform Area ( Body Volume )2/3

2/24/2008 ELF 37 ΔΔ CCmm // ΔΔ αα andand StaticStatic MarginMargin DefineDefine StaticStatic StabilityStability xAC xAC Statically Stable: ΔCm / Δα < 0, Statically Unstable: ΔCm / Δα > 0, with xac behind xcg with xac in front of xcg xCG xCG

δ1 Cm Cm δ2

α α

δ1 δ2 Non-oscillatory Divergent

Non-oscillatory α Convergent α

t t Oscillatory Oscillatory Convergent Divergent Note: Statically unstable missile requires high bandwidth autopilot. Autopilot negative rate feedback provides stability augmentation. 2/24/2008 ELF 38 BBodyody AAerodynamicerodynamic CCenterenter IIss aa FFunctionunction ooff AAnglengle ofof Attack,Attack, NoseNose Fineness,Fineness, andand BodyBody LengthLength

2 2 ( xAC )B / lN = 0.63 ( 1 - sin α ) + 0.5 ( lB /lN ) sin α 5 c

4 total length of body / length of nose = 1 3 total length of body / length of nose = 2 total length of body / 2 length of nose = 5 total length of body / 1 length of nose = 10 Center / Length of Nose 143.9 Example: 19.2 Distance to Aerodynami Body 0 Rocket Baseline Body

020406080100lB /lN = 143.9 / 19.2 = 7.49 α = 13 deg Angle of Attack, Deg ( xAC )B / lN = 0.81

Note: Based on slender body theory ( Pitts, et al ) and cross flow theory ( Jorgensen ) references. No flare.

( xAC )B = Location of body aerodynamic center, lN = length of nose, α= angle of attack, lB = total length of body. 2/24/2008 ELF 39 FlareFlare IncreasesIncreases StaticStatic StabilityStability

( C ) CN = ( CN )B + ( CN )F ( C ) Nα B α α α Nα F

+M 9 d d +α F

x = 0 ( xac )B l x x N AC CG xF lB ( xac )F Based on Slender Body Theory: 2 ( CNα )F = 2 [( dF / d ) –1 ] ( xac )F = xF + 0.33 lF [ 2 ( dF / d ) + 1 ] / [ ( dF / d ) + 1 ] ( C ) = 2 per rad Nα B ( xac )B = 0.63 lN ΣM = 0 at Aerodynamic Center. For a Body-Flare: ( C ) {[ x –( x ) ] / d } + ( C ) [ x –( x ) ] / d = - [( C ) + ( C ) ] Nα B CG AC B Nα F CG AC F Nα B Nα F [( xAC –xCG ) / d ] Static Margin for a Body-Flare

( xAC –xCG ) / d = - {( CN )B {[ xCG –( xAC )B ] / d } + ( CN )F {[ xCG –( xAC )F ] / d }} / [( C ) + ( C ) ] α α Nα B Nα F

2/24/2008 ELF 40 FlareFlare IncreasesIncreases StaticStatic StabilityStability (( contcont ))

Example of Static Margin for THAAD ( Statically Unstable Missile ) C = ( C ) ( C ) ( CN )B Nα Nα B + Nα F α ( CNα )F

9 14.6 18.7 in

( xac )B = 57.7 91.5 146.9 230.9 242.9 xAC = 140.9 ( xac )F = 237.1

2 2 ( CNα )F = 2 [( 18.7 / 14.6 ) – 1 ] = 2 [(1.28) – 1 ] = 1.28 per rad ( xac )F = 230.9 + 0.33 ( 12.0 )[ 2 ( 18.7 / 14.6 ) + 1 ] / [ ( 18.7 / 14.6 ) + 1 ] = 237.1 in

( xac )B = 0.63 ( 91.5 ) = 57.7 in xCGLaunch = 146.9 in ( xAC –xCG )Launch / d = - { 2 {[ 146.9 – 57.7 ] / 14.6 } + 1.28 {[ 146.9 – 237.1 ] / 14.6 }} / [ 2 + 1.28 ] = - 0.41

2/24/2008 ELF 41 TailTail StabilizersStabilizers HaveHave LowerLower DragDrag WhileWhile FlaresFlares HaveHave LowerLower AeroAero HeatingHeating andand StabilityStability ChangesChanges

Type Stabilizer Drag Span Heating C Tail Control Δ Nα Flare ( e.g., THAAD )

– –

Tails ( e.g., Standard Missile )

– –

Note: Superior Good Average– Poor

2/24/2008 ELF 42 WingWing SizingSizing TradesTrades

Advantages of Small Wing / Strake / No Wing • Range in high supersonic flight / high dynamic pressure • Max angle of attack • Launch platform compatibility • Lower radar cross section • Volume and weight for propellant / fuel Advantages of Larger Wing • Range in subsonic flight / low dynamic pressure • Lower guidance time constant* • Normal acceleration* • High altitude intercept* • Less body bending aeroelasticity ( wing stiffens body ) • Less seeker error due to dome error slope ( lower angle of attack ) • Less wipe velocity for warhead ( lower angle of attack ) • Lower gimbal requirement for seeker

*Based on assumption of aerodynamic control and angle of attack below wing stall 2/24/2008 ELF 43 MostMost SupersonicSupersonic MissilesMissiles AreAre WinglessWingless

Stinger FIM-92 Grouse SA-18 Grison SA-19 ( two stage ) Gopher SA-13

Starburst Mistral Kegler AS-12 Archer AA-11

Gauntlet SA-15 Magic R550 Python 4 U-Darter

Python 5 Derby / R-Darter Aphid AA-8 Sidewinder AIM-9X

ASRAAM AIM-132 Grumble SA-10 / N-8 Patriot MIM-104 Starstreak

Gladiator SA-12 PAC-3 Roland ( two stage ) Crotale

Hellfire AGM-114 ATACM MGM-140 Standard Missile 3 ( three stage ) THAAD

Permission of Missile Index. Copyright 1997©Missile.Index All Rights Reserved 2/24/2008 ELF 44 Wings,Wings, Tails,Tails, andand CanardsCanards withwith LargeLarge AreaArea andand atat HighHigh AngleAngle ofof AttackAttack HaveHave HighHigh NormalNormal ForceForce

2 1/2 2 2 1/2 ⏐( CN )Surface ⏐ = [ 4⏐sin α’cos α’⏐ / ( M –1 ) + 2 sin α’] ( SSurface / SRef ), if M > { 1 + [ 8 / ( π A )] } 2 2 1/2 ⏐( CN )Surface ⏐ = [ ( π A / 2) ⏐sin α’cosα’⏐ + 2 sin α’] ( SSurface / SRef ), if M < { 1 + [ 8 / ( π A )] } Note: Linear wing theory applicable if M > { 1 + [ 8 / ( π A )]2 }1/2, slender wing theory applicable if M < { 1 + [ 8 / ( π A )]2 }1/2,

A = Aspect Ratio < 3, SSurface = Surface Planform Area, SRef = Reference Area M < 1.35, based on slender wing theory + Newtonian impact theory Example for Rocket Baseline M = 2, based on linear wing theory + Newtonian impact theory Wing M = 5, based on linear wing theory + Newtonian impact theory AW = 2.82

, 4 2 W SW = 2.55 ft

/ S 2 SRef = 0.349 ft

REF 3 δ = 13 deg, α = 9 deg S M = 2 Wing ) { 1 +[ 8 / ( π A )]2 }1/2 = 1.35

N 2 Since M > 1.35, use linear wing ( C for Rocket Baseline theory + Newtonian theory 1 α’= αW = α + δ = 22°

Wing Normal Force Coefficient Wing Normal Force ( CN )Wing SRef / SW = 4 sin 22° cos 22° / ( 22 –1 )1/2 + 2 sin2 22° 0 = 1.083 ( C ) = 1.08 ( 2.55 ) / 0.349 = 0306090N Wing 7.91

α’= αW = α + δ , Wing Effective Angle of Attack for Rocket Baseline, Deg 2/24/2008 ELF 45 AerodynamicAerodynamic CenterCenter ofof aa ThinThin SurfaceSurface (( e.g.,e.g., Wing,Wing, Tail,Tail, CanardCanard )) VariesVaries withwith MachMach NumberNumber

2 1/2 2 1/2 ( xAC / cMAC )Surface = [ A ( M –1 ) – 0.67 ] / [ 2A ( M –1 ) – 1 ], if M > ~ 2 Note: Based on linear wing theory ( x / c ) = 0.25, if M < ~ 0.7 AC MAC Surface Thin wing ⇒ M ( t / c ) << 1

( xAC )Surface = Surface aerodynamic 0.5 center distance from leading

edge of ( cMAC )Surface cMAC = Mean aerodynamic chord 0.4 A = Aspect ratio = b2 / S

0.3 A = 1 A = 2 0.2 A = 3 Example: Rocket Baseline Wing Aerodynamic Center Aerodynamic 0.1 x c A = 2.82 MAC MAC xAC XAC / CMAC, Surface Non-dimensional Surface CMAC, / XAC c = 13.3 in 0 MAC ( xMAC )Wing = 67.0 in 012345M = 2

M, Mach Number ( xAC / cMAC )Wing = 0.481

( xAC )Wing = 6.4 in from mac leading edge = 73.4 in from nose tip 2/24/2008 ELF 46 HingeHinge MomentMoment IncreasesIncreases withwith DynamicDynamic PressurePressure andand EffectiveEffective AngleAngle ofof AttackAttack

Note: Based on linear wing HM = NSurface ( xAC -xHL )Surface theory, slender wing theory, q = 436 psf ( M = 0.8 ) q = 1242 psf ( M = 1.35 ) and thin wing ( M ( t / c ) << 1 )

q = 2725 psf ( M = 2 ) q = 17031 psf ( M = 5 ) NSurface = Normal force on surface ( two panels )

30000 ( xAC -xHL )W = distance from surface aerodynamic center to hinge line of surface 25000 Example for Rocket Baseline Wing Control x NW 20000 AC cmac = 13.3 in x HL xHL = 0.25 cmac c ma 15000 2 c SRef = 0.349 ft 2 SW = 2.55 ft 10000 δ = 13 deg, α = 9 deg

α’= αW = α + δ = 22° M = 2, h = 20k ft, q = 2725 psf HM, Example Hinge Moment, in - lb 5000

NW = [ CN ( SRef / SW )] qSW = 1.083 ( 2725W ) ( 2.55 ) = 7525 lb 0 x / c = 0.48 0102030AC mac α’= αW = α + δ , Wing Effective Angle of Attack of Rocket Baseline, Deg HM = 7525 ( 0.48 – 0.25 ) ( 13.3 ) = 23019 in – lb for two panels 2/24/2008 ELF 47 Wings,Wings, Tails,Tails, andand CanardsCanards UsuallyUsually HaveHave GreaterGreater SkinSkin FrictionFriction DragDrag ThanThan ShockShock WaveWave DragDrag ( C ) = n { 0.0133 [ M / ( q c )]0.2 } ( 2 S / S ), q in psf, c in ft D0 Surface,Friction Surface mac Surface Ref mac ( C ) = n ( 1.429 / M 2 ){( 1.2 M 2 )3.5 [ 2.4 / ( 2.8 M 2 – 0.4 )]2.5 –1 } sin2 δ cos Λ DO Surface,Wave Surface ΛLE ΛLE ΛLE LE LE tmac b / SRef , based on Newtonian impact theory nSurfaces = number of surface planforms ( cruciform = 2 ) ( CD )Surface = ( CD )Surface,Wave + ( CD )Surface,Friction O O O q = dynamic pressure in psf 0.4 cmac = length of mean aero chord in ft γ = Specific heat ratio = 1.4 M = M cos Λ = Mach number ⊥ leading edge 0.3 ΛLE LE

δLE = leading edge section total angle

ΛLE = leading edge sweep angle Surface,Friction

) 0.2 t = max thickness of mac

0 mac D b = span Example for Rocket Baseline Wing: 0.1 n = 2, M = 2, h = 20k ft ( q = 2,725 psf ), c = 1.108 Example ( C W mac 2 2 ft, SRef = 50.26 in , SW = 367 in , δLE = 10.01 deg, ΛLE = 45 deg, t = 0.585 in, b = 32.2 in, M = 1.41 ( M = 2 ) mac ΛLE 0 M / ( q cmac ) = 2 / [ 2725 ( 1.108 )] = 0.000662 ft / lb 0 1020304050 n SSurface / SRef = 2 ( 367 ) / 50.26 = 14.60 n SSurface / SRef ( C ) = 0.090 DO Wing,Friction M / ( q cmac ) = 0.00001 ft / lb M / ( q cmac ) = 0.0001 ft / lb ( CD )Wing,Wave = 0.024 M / ( q cmac ) = 0.001 ft / lb M / ( q cmac ) = 0.01 ft / lb 0 ( C ) = 0.024 + 0.090 = 0.11 DO Wing 2/24/2008 ELF 48 ExamplesExamples ooff Wing,Wing, Tail,Tail, andand CCanardanard PanelPanel GeometryGeometry AlternativesAlternatives

Triangle Aft Swept LE Double Parameter ( Delta ) Trapezoid Bow Tie Swept LE Rectangle – Variation xAC Bending Moment / Friction – – Supersonic Drag – RCS – Span Constraint – Stability & Control Aeroelastic Stab. –

λ = Taper ratio = cT / cR 2 Note: Superior Good Average Poor A = Aspect ratio = b / S = 2 b / [( 1 + λ ) cR ] yCP = Outboard center-of-pressure = ( b / 6 ) ( 1 + 2 λ ) / ( 1 + λ ) – c = Mean aerodynamic chord = ( 2 / 3 ) c ( 1 + λ + λ 2 ) / ( 1 + λ ) Based on equal surface area and equal span. MAC R Surface area often has more impact than geometry. 2/24/2008 ELF 49 EExamplesxamples ooff SSurfaceurface AArrangementrrangement anandd AerodynamicAerodynamic ControlControl AlternativesAlternatives Four Two Panels Three ( Cruciform ) Six* Eight* ( Mono-Wing ) ( Tri-Tail )

Folded Wraparound Extended Balanced Actuation Flap Control Control

Interdigitated In-line

Note: More than four tails are usually free-to-roll pitch / yaw stabilizers, for low induced roll. 2/24/2008 ELF 50 MMostost MiMissilesssiles UUsese FFourour CControlontrol SSurfacesurfaces wwithith CombinedCombined PitchPitch // YawYaw // RollRoll ControlControl IntegrationIntegration

Control Integ Control Surfaces Example Control Effect Cost Packaging Pitch / Yaw 2 Stinger FIM-92 –

Pitch / Roll 2 ALCM AGM-86 –

Pitch / Yaw / Roll 3 SRAM –

Pitch / Yaw / Roll 4 Adder AA-12

Pitch + Yaw + Roll 5 Kitchen AS-4 – –

Pitch / Yaw + Roll 6 Derby / R-Darter – –

Note: Superior Good Average– Poor

2/24/2008 ELF 51 ThereThere AreAre ManyMany FlightFlight ControlControl ConfigurationConfiguration AlternativesAlternatives Control Design Fixed Surface Control Alternatives Alternatives Tail Cruciform ( 4 ) Wingless Tri-tail ( 3 ) Wing Not Compressed Strake / Canard Folded In Line with Controls Wraparound Interdigitated with Controls Switchblade Number ( 2, 3, 4 ) Canard Above Tail ( 3, 4, 6, 8 ) Rolling Airframe ( 2 ) Tail + Wing In Line with Controls Interdigitated with Controls Wing Above Tail ( 3, 4, 6, 8 ) Strake / Canard & Tail In Line with Controls Interdigitated with Controls TVC or Movable Nozzle Tail ( 3, 4, 6, 8 ) Reaction Jet Jet Tab Tail + Canard / Strake Jet Vane Control Tail + Wing Axial Plate Secondary Injection Normal Jet / JI Spanwise Jet / JI 2/24/2008 ELF 52 TailTail ControlControl IsIs EfficientEfficient atat HighHigh AngleAngle ofof AttackAttack

CN Trim ( assumed statically stable ) CN at δ = 0

C at δ = 0 V∞ cg NC

ΔC Negative δ CNC N

☺ Efficient Packaging Decreased Lift at Low α if ☺ Low Hinge Moment / Actuator Statically Stable Torque ☺ Low Induced Rolling Moment ☺ Efficient at High α

2/24/2008 ELF 53 TailTail ControlControl IsIs MoreMore EffectiveEffective ThanThan ConventionalConventional CanardCanard ControlControl atat HighHigh AngleAngle ofof AttackAttack • Assumed static stability • Assumed static stability • Control surface local • Control surface local angle of attack α’= α + δ angle of attack α’= α – δ + δ • Panel stalled at high α* α • Panel not stalled at high α

α V∞

V∞ – δ Conventional Canard Control Tail Control

1.0 1.0 = 0° = 0° α α ) ) δ δ l m Ø= 0° Conven ( C Conven ( C / / Canard Tail Canard Tail δ l δ C m Control Control Control Control C ☺ ☺ 0 0 10 – 20° 20 – 30° 10 – 15° 15 – 30° α ~ Angle of Attack ( deg ) α ~ Angle of Attack ( deg ) *Note: Additional forward fixed surfaces ( such as Python 4 ) in front of movable canards alleviate stall at high α. Free-to-roll tails ( such as Python 4 ) alleviate induced roll from canard control at high α. 2/24/2008 ELF 54 AboutAbout 70%70% ofof TailTail ControlControl MissilesMissiles AlsoAlso HaveHave WingsWings

JASSM AGM-158 Maverick AGM-65 CALCM JSOW AGM-154

Tomahawk BGM-109 Taurus KEPD 350 Storm Shadow / Scalp Popeye AGM-142

Exocet MIM40 TOW2-BGM71D AMRAAM AIM-120 Sunburn SS-N-22

Standard RIM-66 / 67 RBS-70 / 90 Shipwreck SS-N-19 Super 530

Sea Dart ( two stage ) FSAS Aster R-37 ( AA-X-13 ) Mica

Adder AA-12 Rapier 2000 SD-10 / PL-12 Seawolf

Permission of Missile Index. Copyright 1997©Missile.Index All Rights Reserved 2/24/2008 ELF 55 TTailail CControlontrol AltAlternatives:ernatives: CConventionalonventional BBalancedalanced ActuationActuation Fin,Fin, Flap,Flap, andand LatticeLattice FinFin Control Hinge Type of Tail Control Effectiveness Drag Moment RCS Balanced Actuation Fin ( Example: ASRAAM AIM-132 )

Flap ( Example: Hellfire AGM-114 ) –

Lattice Fin ( Example: Adder AA-12 / R-77 ) –

Note: Superior Good Average– Poor

2/24/2008 ELF 56 LatticeLattice FinsFins HaveHave AdvantagesAdvantages forfor LowLow SubsonicSubsonic andand HighHigh SupersonicSupersonic MissilesMissiles

Advantages High control effectiveness at low subsonic and high supersonic Mach number Low hinge moment Short chord length Disadvantages High RCS ( cavities, normal leading edges ) High drag at transonic Mach number ( choked flow )

Low Subsonic Transonic Low Supersonic High Supersonic ☺ ☺ 2/24/2008 ELF 57 ConventionalConventional CanardCanard ControlControl IsIs EfficientEfficient atat LowLow AngleAngle ofof AttackAttack ButBut StallsStalls atat HighHigh AlphaAlpha

δ CN Trim ( assumed statically stable ) ΔCN C N C CN at δ = 0 α

cg V∞

☺ Efficient Packaging Stall at High α if ☺ Simplified Statically Stable Manufacturing Induced Roll ☺ Increased Lift at Low α *Note: Additional forward fixed surface in Note: = CNC at δ = 0° front of movable canard alleviates stall at if Statically Stable high α. Free-to-roll tails alleviate induced roll at high α. Dedicated roll control = CNC at δ = δ surfaces avoid roll control saturation and simplify autopilot design.

2/24/2008 ELF 58 CCanardanard CControlontrol MiMissilesssiles AArere WiWinglessngless anandd MMostost AreAre SupersonicSupersonic

Stinger FIM-92 Grouse SA-18 Grison SA-19 ( two-stage ) Gopher SA-13

Starburst Gauntlet SA-15 Mistral AIM-9L

Archer AA- 11 Magic R 550 Python 4 U-Darter

Python 5 Derby / R-Darter Aphid AA-8 Kegler AS-12

GBU-12 GBU-22 GBU-27 GBU-28 Permission of Missile Index. Copyright 1997©Missile.Index All Rights Reserved 2/24/2008 ELF 59 MissilesMissiles withwith SplitSplit CanardsCanards HaveHave EnhancedEnhanced ManeuverabilityManeuverability atat HighHigh AngleAngle ofof AttackAttack

ΔCN C N α’~α C α α ’ ~ δ

Note: α’ = Local angle of attack

Kegler AS-12 Archer AA-11 Aphid AA-8

Magic R 550 Python 4 U-Darter

Note: Forward fixed surface reduces local angle-of-attack for movable canard, providing higher stall angle of attack. Forward surface also provides a fixed, symmetrical location for vortex shedding from the body. Python 4 also has free-to-roll tails and separate roll control ailerons. 2/24/2008 ELF 60 WingWing CControlontrol RequiresRequires LessLess BodyBody RotationRotation ButBut HasHas HighHigh HingeHinge Moment,Moment, InducedInduced RollRoll andand StallStall

Δ CN ~ CN Trim

V δ ( α small ) cg

☺ Low Body α / Dome Error Slope Poor Actuator Packaging ☺ Fast Response ( if skid-to-turn ) Large Hinge Moment Larger Wing Size Induced Roll Wing Stall 2/24/2008 ELF 61 WingWing ControlControl MissileMissile SusceptibleSusceptible toto HighHigh VortexVortex SheddingShedding

Strong vortices from wing interact with tail

Video of Vortices from Delta Wing at High Angle of Attack

Source: University of Notre Dame web site: Source: Nielsen Engineering & Research ( NEAR ) web site: http://www.nd.edu/~ame/facilities/SubsonicTunnels.html http://www.nearinc.com/near/project/MISDL.htm

2/24/2008 ELF 62 WingWing ControlControl MissilesMissiles AreAre OldOld TechnologyTechnology

Sparrow AIM-7: IOC 1956

Skyflash: IOC 1978

Alamo AA-10 / R-27: IOC 1980

HARM AGM-88: IOC 1983

Aspide: IOC 1986

2/24/2008 ELF 63 TVCTVC andand ReactionReaction JetJet FlightFlight ControlControl

Liquid Injection Hot Gas Injection Jet Vane* ± 12° ± 7° ± 10°

Note: Jet vanes provide roll control and share

actuators with aero control, but have reduced ISP Axial Plate Jet Tab Movable Nozzle ± 15° ± 20° ± 7°

Note: •TVC and reaction jet flight control provide high maneuverability at low dynamic pressure Reaction Jet •TVC usually has lower time constant and miss distance than aero control M ∞ Jet Flow •Reaction jets usually have lower time constant and miss distance than TVC •Reaction jets can be either impulse jets or controlled duration jets Jet inter. Thrust Jet interaction 2/24/2008 ELF 64 MostMost TacticalTactical MissilesMissiles withwith TVCTVC oror ReactionReaction JetJet ControlControl AlsoAlso UseUse AeroAero ControlControl Jet Vane + Aero Control: Mica Sea Sparrow RIM-7 AIM-9X

Sea Wolf GWS 26 IRIS-T A-Darter Javelin Jet Tab + Aero Control: Archer AA-11 Reaction Jet + Aero Control: PAC-3 Movable Nozzle + Aero Control + Reaction Jet: SM-3 Standard Missile Aster FSAF 15 Movable Nozzle + Reaction Jet: THAAD Reaction Jet: LOSAT

2/24/2008 ELF Example Video of TVC ( FSAF-15 and Javelin ) 65 Skid-to-TurnSkid-to-Turn IsIs thethe MostMost CommonCommon ManeuverManeuver LawLaw

Skid-To-Turn ( STT ) • Advantage: Fast response STT • Features S LO – Does not require roll commands from autopilot Target – Works best for axisymmetric cruciform missiles Maneuver w / o Roll Command Bank-To-Turn ( BTT ) • Advantage: Provides higher maneuverability for planar BTT ( with wing, noncircular / lifting bodies, and airbreathers Planar Wing ) • Disadvantages S LO Target – Time to roll Step 1: Roll Until – Requires fast roll rate Wing ⊥ LOS – May have higher dome error slope • Features – Roll attitude commands from autopilot – Small sideslip S LO Target Rolling Airframe ( RA ) • Advantage: Requires only two sets of gyros / Step 2: Maneuver @ Roll Rate = 0 and Wing ⊥ LOS accelerometers / actuators ( packaging for small missile ) • Disadvantages for aero control – Reduced maneuverability for aero control RA – Requires high rate gyros / actuators S LO Target – Requires precision geometry and thrust alignment • Features Maneuver with Bias Roll – Bias roll rate and roll moment Moment – Can use impulse steering ( e.g., PAC-3, LOSAT ) Bias Roll Rate ( e.g., 3 Hz ) 2/24/2008 – Compensates for thrust offset ELF 66 AsymmetricAsymmetric InletsInlets RequireRequire Bank-to-TurnBank-to-Turn ManeuveringManeuvering Examples of Twin Inlet Missiles with Bank-to-Turn

Twin Side Inlets Ramjet: ASMP

Twin Cheek Inlets Ducted Rocket: HSAD

Twin Cheek Inlets Ducted Rocket: Meteor

Examples of Single Inlet Missiles with Bank-to-Turn

Chin Inlet Ramjet: ASALM

Bottom Inlet Turbojet: BGM-109 Tomahawk

Bottom Inlet Turbojet: Storm Shadow / Scalp

Top Inlet Turbofan: AGM-86 ALCM Note: Bank-to-turn maneuvering maintains low sideslip for better inlet efficiency. 2/24/2008 ELF 67 XX RollRoll OrientationOrientation IsIs UsuallyUsually BetterBetter ThanThan ++ RollRoll OrientationOrientation + Roll Orientation with Four Tail Surfaces Control of Pitch / Yaw / Roll, Looking Forward from Base

Fin 1

Fin 4 Fin 2 Trailing edge deflection Pitch Up Yaw Right Roll Right

Fin 3

X Roll Orientation with Four Tail Surfaces Control of Pitch / Yaw / Roll, Looking Forward from Base 4 1

Pitch Up Yaw Right Roll Right

3 2 Note: + roll orientation usually has lower trim drag, less static stability and control effectiveness in pitch and yaw, and

statically unstable roll moment derivative ( Clφ > 0 ). X roll orientation has better launch platform compatibility, higher L / D, higher static stability and control

effectiveness in pitch and yaw, and statically stable roll moment derivative ( Clφ < 0 ). 2/24/2008 ELF 68 TrimmedTrimmed NormalNormal ForceForce IsIs DefinedDefined atat ZeroZero PitchingPitching MomentMoment

δ = δ Trim for either statically unstable tail

N control or statically stable canard control δ = 0

δ = δ Trim for either statically stable tail control or statically unstable canard control Normal Force, C

Angle of Attack ( Deg ) m

δ = δ Max αTrim @ Cm = 0 Angle of Attack ( Deg )

Pitching Moment, C δ = 0

2/24/2008 ELF 69 RelaxedRelaxed StaticStatic MarginMargin AllowsAllows HigherHigher TrimTrim AngleAngle ofof AttackAttack andand HigherHigher NormalNormal ForceForce

Note: Rocket Baseline XCG = 75.7 in. Mach 2 ( α + δ ) = 21.8 deg, ( C ) Max NTrim Max 16 α / δ = 0.75, ( Static Margin = 0.88 Diam ) α / δ = 1.5, ( SM = 0.43 Diam ) α / δ = ∞, ( SM = 0 ) 12 ( CN, Trim )max, Max Trimmed Normal Force Coefficient of Rocket Baseline 8

0 0 4 8 12 16 20 24

( αTrim )max, Μax Trim Angle of Attack, deg

2/24/2008 ELF 70 TailsTails AreAre SizedSized forfor DesiredDesired StaticStatic MarginMargin

C ( C ) Nα Nα W ( CN )T ( C ) α Nα B +M

+ α

x = lN

( xAC )B x = lB x = 0 ( x ) AC W ( xAC )T xCG xAC ΣM = 0 at aerodynamic center ( C ) {[ x –( x ) ] / d } + ( C ) {[ x –( x ) ] / d } S / S + ( C ) {[ x –( x ) ] / d } S / S Nα B CG AC B Nα W CG AC W W Ref Nα T CG AC T T Ref = - [( C ) + ( C ) S / S + ( C ) S / S ] [( x –x ) / d ] Nα B Nα W W Ref Nα T T Ref AC CG

Static margin for a specified tail area is

( xAC –xCG ) / d = - {( CN )B {[ xCG –( xAC )B ] / d } + ( CN )W {[ xCG –( xAC )W ] / d } SW / SRef + ( CN )T {[ xCG –( xAC )T ] / d } ( ST / SRef )} / [(C ) + (C ) S / Sα + ( C ) S / S ] α α Nα B Nα W W Ref Nα T T Ref

Required tail area for a specified static margin is

ST / SRef = ( CN )B {[ xCG –( xAC )B ] / d } + ( CN )W {[ xCG –( xAC )W ] / d } ( SW / SRef ) + {[( CN )B + ( CN )W SW / SRef ][( xAC –xCG ) / d ]} / {( C ) [( x α) –x ] / d - ( x –x ) / d } α α α Nα T AC T CG AC CG 2/24/2008 ELF 71 LLargerarger TTailail AArearea IIss RRequiredequired fforor NNeutraleutral SStabilitytability atat HighHigh MachMach NumberNumber

(ST)Neutral / SRef = { (CNα)B [ xCG –(xAC)B ] / d + (CNα)W {[ xCG –(xAC)W ]/ d } ( SW / SRef )} / {{[ (xAC)T –xCG ] / d } (CNα)T } 5 Assumptions for figure: 0.2 3 ) = ef •XCG ≈ l / 2, (XAC)B ≈ d, ( XAC )T ≈ l – d / S R S W •α < 6 deg, turbulent boundary layer } ( / l ] 0 •(CN ) = 2 per rad ) W ) = α B C f x A ) S Re 2 1/2 –( ing / •(CNα)T = (CNα)W = 4 / [ M –1 ] , if M x CG w S W 2 1/2 {[ rd }( > { 1 + [ 8 / ( π A )] } wa / l 2 or ] ( f ) W •(CN ) = (CN ) = π A / 2, if M < { 1 + (x AC .25 α T α W – - 0 [ 8 / ( π A )]2 }1/2 x CG ) = {[ f / S Re Example Rocket Baseline: S W l }( 2 ] / l = 144 in, d = 8 in, SW = 2.55 ft , SRef = ) W 2 C 0.349 ft , A = 2.82, (c ) = 13.3 in, Reference Area x A W MAC W 1 – ( x = 67.0 in from nose tip, burnout G ) MAC x C g {[ in ( xCG = 76.2 in from tip ), Mmax = 3 ft w ( a (xAC)W = 0.49 ( 13.3 ) = 6.5 in from leading edge of MAC

(ST)Neutral / SRef, Neutral StabilityTail Area / (xAC)W = 6.5 + 67.0 = 73.5 in from nose

0 {[ xCG –(xAC)W ] / l } ( SW / SRef ) = 0.14 012345( forward wing )

(ST)Neutral / SRef = 1.69 provides neutral M, Mach Number stability 2 (ST)Neutral = 1.69 ( 0.349 ) = 0.59 ft 2/24/2008 ELF 72 StabilityStability andand ControlControl DerivativesDerivatives ConceptualConceptual DesignDesign CriteriaCriteria

| Clδr / Clδa | < 0.3 ( Roll Due to Rudder Deflection ) | Clφ / Clδa | < 0.5 ( Roll Due to Roll Angle ) x x C C C C lδr lδa lφ lδa y y z z

| Cnδa / Cnδr | < 0.2 ( Yaw Due to Aileron Deflection ) | Cmα / Cmδ | < 1 ( Pitch Due to α ) x x Cnδ a Cmα Cnδ r Cmδ y z z y

| Clβ / Clδa | < 0.3 ( Roll Due to Sideslip ) | Cnβ / Cnδr | < 1 ( Yaw Due to Sideslip ) x x C C C nβ lβ lδa Cnδ r y z y z Note: The primary control derivative ( larger bold font ) should be larger than the undesirable stability and control derivative. 2/24/2008 ELF 73 MostMost ooff thethe RocketRocket BaselineBaseline BodyBody BuildupBuildup NormalNormal ForceForce IsIs ProvidedProvided byby thethe WingWing

( CN )Total = ( CN )Wing-Body-Tail ≅ ( CN )Body + ( CN )Wing + ( CN )Tail

15 Body + Wing + Tail

10 Body + Wing CN, Normal Force Coefficient of Rocket Baseline 5

Body

0 0 5 10 15 20 25 α, Angle of Attack, Deg Note for figure: M = 2, δ = 0 Note: ( C ) = ( C ) ≅ ( C ) + ( C ) + ( C ) D0 Total D0 Wing-Body-Tail D0 Body D0 Wing D0 Tail

( Cm )Total = ( Cm )Wing-Body-Tail ≅ ( Cm )Body + ( Cm )Wing + ( Cm )Tail 2/24/2008 ELF 74 SummarySummary ofof AerodynamicsAerodynamics

Conceptual Design Prediction Methods of Bodies and Surfaces Normal force coefficient Drag coefficient Aerodynamic center / pitching moment coefficient / hinge moment Design Tradeoffs Diameter Nose fineness Boattail Lifting body versus axisymmetric body Wings versus no wings Tails versus flares Surface planform geometry Flight control alternatives Maneuver alternatives Roll orientation Static margin / time to converge or diverge Tail sizing 2/24/2008 ELF 75 SummarySummary ofof AerodynamicsAerodynamics (( contcont ))

Stability and Control Design Criteria Static stability Control effectiveness Cross coupling Body Buildup New Aerodynamics Technologies Faceted / window / multi-lens domes Bank-to-turn maneuvering Lifting body airframe Forward swept surfaces Neutral static margin Lattice fins Split canard control Free-to-roll tails Discussion / Questions? Classroom Exercise

2/24/2008 ELF 76 AerodynamicsAerodynamics ProblemsProblems

1. Missile diameter tradeoffs include consideration of seeker range, warhead lethality, structural mode frequency, and d___. 2. Benefits of a high fineness nose include lower supersonic drag and lower r____ c____ s______. 3. Three contributors to drag are base drag, wave drag, and s___ f______drag. 4. To avoid flow separation, a boatail or flare angle should be less than __ deg. 5. A lifting body is most efficient at a d______p______of about 700 psf. 6. At low angle of attack the aerodynamic center of the body is on the n___. 7. Subsonic missiles often have w____ for enhanced range. 8. The aerodynamic center of the wing is between 25% and 50% of the m___ a______c____. 9. Hinge moment increases with the local flow angle due to control surface deflection and the a____ o_ a_____. 10. Increasing the surface area increases the s___ f______d___.

2/24/2008 ELF 77 AerodynamicsAerodynamics ProblemsProblems (( contcont ))

11. Leading edge sweep reduces drag and r____ c____ s______. 12. A missile with six control surfaces, four surfaces providing combined pitch / yaw control plus two surfaces providing roll control, has an advantage of good c______e______. 13. A missile with two control surfaces providing only combined pitch / yaw control has advantages of lower c____ and good p______. 14. A tail control missile has larger trim normal force if it is statically u______. 15. Lattice fins have low h____ m_____. 16. Split canards allow higher maximum angle of attack and higher m______. 17. Two types of unconventional control are thrust vector control and r______j__ control. 18. The most common type of TVC for tactical missiles is j__ v___ control. 19. Three maneuver laws are skid to turn, bank to turn, and r______a______. 20. Bank to turn maneuvering is usually required for missiles with a single wing or with a______inlets. 2/24/2008 ELF 78 AerodynamicsAerodynamics ProblemsProblems (( contcont ))

21. A missile is statically stable if the aero center is behind the c_____ o_ g______. 22. Tail stabilizers have low drag while a f____ stabilizer has low aero heating and a relatively small shift in static stability. 23. If the moments on the missile are zero the missile is in t___. 24. Total normal force on the missile is approximately the sum of the normal forces on the surfaces ( e.g., wing, tail, canard ) plus normal force on the b___. 25. Increasing the tail area increases the s_____ m______.

2/24/2008 ELF 79 OutlineOutline

Define Mission Requirements Alt Mission Establish Baseline Alt Baseline Aerodynamics

Propulsion

Weight Resize / Alt Config / Subsystems / Tech

Trajectory

Meet No Performance?

Yes No Measures of Merit and Constraints

Yes

2/24/2008 ELF 81 HighHigh SpecificSpecific ImpulseImpulse IsIs IndicativeIndicative ofof LowerLower FuelFuel // PropellantPropellant ConsumptionConsumption

4,000

Turbojet: ISP typically constrained by turbine temperature limit 3,000 / ( Fuel or Propellant 2,000 Ramjet: ISP typically constrained by combustor insulation temperature limit

Scramjet: ISP typically constrained by thermal choking Weight Flow Rate ), S 1,000

Ducted Rocket Solid Rocket: ISP typically constrained by safety , Specific Impulse, Thrust SP I 0 02 4 6 81012 Mach Number

2/24/2008 ELF 82 CruiseCruise RangeRange IsIs DrivenDriven byby L/D,L/D, IIspsp,, Velocity,Velocity, andand PropellantPropellant oror FuelFuel WeightWeight FractionFraction

R = ( L / D ) Isp V In [ WL / ( WL –WP )] , Breguet Range Equation

Typical Value for 2,000 lb Precision Strike Missile

Subsonic Turbojet Liquid Fuel Hydrocarbon Fuel Parameter Missile Ramjet Missile Scramjet Missile Solid Rocket

L / D, Lift / Drag 10 5 3 5

Isp, Specific Impulse 3,000 s 1,300 s 1,000 s 250 s

VAVG , Average Velocity 1,000 ft / s 3,500 ft / s 6,000 ft / s 3,000 ft / s

WP / WL, Cruise Propellant or 0.3 0.2 0.1 0.4 Fuel Weight / Launch Weight R, Cruise Range 1,800 nm 830 nm 310 nm 250 nm

Note: Ramjet and Scramjet missiles booster propellant for Mach 2.5 to 4 take-over speed not included in WP for cruise. Rockets require thrust magnitude control ( e.g., pintle, pulse, or gel motor ) for effective cruise. Max range for a rocket is usually a semi-ballistic flight profile, instead of cruise flight. Multiple stages may be required for rocket range greater than 200 nm. 2/24/2008 ELF 83 SolidSolid RocketsRockets HaveHave HighHigh AccelerationAcceleration CapabilityCapability

1,000 Max Solid Rocket . TMax = 2 Pc At = m Ve

100 , ( Thrust / Weight ) Max 10 Ramjet Turbojet T = (π / 4 ) d2 ρ V 2 [( V / V ) - ( T / W ) Max 0 0 e 0 2 2 TMax = (π / 4 ) d ρ0 V0 [( Ve / V0 ) - 1 ] 1 ] 1 012 34 5 M, Mach Number Note: . Pc = Chamber pressure, At = Nozzle throat area, m = Mass flow rate d = Diameter, ρ0 = Free stream density, V0 = Free stream velocity, Ve = Nozzle exit velocity ( Turbojet: Ve ~ 2,000 ft / s, Ramjet: Ve ~ 4,500 ft / s, Rocket: Ve ~ 6,000 ft / s ) 2/24/2008 ELF 84 TurbojetTurbojet NomenclatureNomenclature

Inlet Compressor Combustor Turbine Nozzle

0 Free Stream

2 3 5 Compressor Entrance Compressor Exit Turbine Exit 1 4 Inlet Entrance Turbine Entrance

2/24/2008 ELF 85 HiHighgh TTemperatureemperature CCompressorsompressors AArere RRequiredequired toto AchieveAchieve HighHigh PressurePressure RatioRatio atat HighHigh SpeedSpeed 2 ( γ - 1 ) / γ T3 ≈ T0 { 1 + [( γ0 - 1 ) / 2 ] M0 }( p3 / p2 ) 3 3 -0.0007 T p3 / p2 = 1 γ0 = 1.4, γ3 ≈ 1.29 + 0.16 e 3 R 3000 Note: Ideal inlet; ideal compressor; low subsonic, p3 / p2 = 2 isentropic flow p3 / p2 = 5 p3 / p2 = 10 2000

1000 Example:

M0 = 2, h = 60k ft ( T0 = 398 R )

p3 / p2 = 5 ⇒ T3 = 1118 R, γ3 = 1.36

T3, Compressor Exit Temperature, 0 01234 M0, Free Stream Mach Number

T3 = Compressor exit temperature in Rankine, T0 = free stream temperature in Rankine, γ = specific heat ratio, M0 = free stream Mach number, p3 = compressor exit pressure, p2 = compressor entrance pressure 2/24/2008 ELF 86 HighHigh TurbineTurbine TemperatureTemperature IsIs RequiredRequired forfor HighHigh SpeedSpeed TurbojetTurbojet MissilesMissiles

T4 ≈ T3 + ( Hf / cp ) f / a, T in R 0.109 T3 = 500 R cp4 ≈ 0.122 T4 , cp in BTU / lb / R R 5000 T3 = 1000 R T3 = 2000 R 4000 T3 = 4000 R

3000

T4 2000 Example:

M0 = 2, h = 60K ft ( T0 = 398 R ), p3 / p2 = 5 ⇒ T3 = 1118 R 1000 RJ-5 fuel ( Hf = 14,525 BTU / lb ), cp = 0.302 BTU / lb / R , f / a = 0.067 ( stochiometric ) ⇒ T4 = T4,TurbojetTurbine Temperature, 0 1118 + ( 14525 / 0.302 ) 0.067 = 4,340 R 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 f / a, Fuel-to-Air Ratio

T4 = Turbojet turbine entrance temperature in Rankine, T3 = compressor exit temperature in Rankine, Hf = heating value of fuel, cp = specific heat at constant pressure, f / a = fuel-to-air ratio 2/24/2008 ELF 87 TurbineTurbine MaterialMaterial TemperatureTemperature LimitLimit IsIs aa ConstraintConstraint forfor aa HighHigh SpeedSpeed TurbojetTurbojet MissileMissile

Max Short Turbine Material Temperature Constrained ISP for Mach Duration Temp Turbines for Mach 4 Cruise 4 Cruise ≈ 3,000R Nickel Super Alloys Very Highly Constrained Turbojet, ≈ 1,000 s Air Turbo Rocket, Turbo Ramjet ≈ 3,000R Titanium Aluminides ( lighter Very Highly Constrained Turbojet, ≈ 1,000 s weight than nickel super alloys ) Air Turbo Rocket, Turbo Ramjet ≈ 3,500R Single Crystal Nickel Highly Constrained Turbojet ≈ 1,200 s Aluminides ≈ 4,000R Ceramic Matrix Composites Moderately Constrained Turbojet ≈ 1,500 s

≈ 4,500R Rhenium Alloys Moderately Constrained Turbojet ≈ 2,000 s

≈ 5,000R Tungsten Alloys Slightly Constrained Turbojet ≈ 2,500 s

Note: Constrained turbojet for Mach 4 cruise imposes a limit on turbine temperature that is less than ideal. Constraints could consist of a combination of: • Constraint on compressor pressure ratio to limit turbine temperature • Constraint on fuel-to-air ratio to limit turbine temperature • Use of afterburner to limit turbine temperature 2/24/2008 ELF 88 TurbinTurbinee-Based-Based MissilesMissiles AreAre CapableCapable ofof SubsonicSubsonic toto SupersonicSupersonic CruiseCruise Turbojet

SS-N-19 Shipwreck

Firebee II Turbo Ramjet Regulus II

SR-71 Air Turbo Rocket

2/24/2008 ELF 89 CCompressorompressor PressurePressure RatioRatio fforor MaximumMaximum ThrustThrust TurbojetTurbojet IsIs LimitedLimited byby TurbineTurbine TemperatureTemperature 1/2 2 γ / ( γ -1 ) ( p3 / p2 )@Tmax ≈ {( T4 / T0 ) / { 1 + [( γ0 - 1 ) / 2 ] M0 }} 4 4 Assumptions: Ideal turbojet ( isentropic inlet, compressor, turbine, nozzle; low subsonic and constant pressure combustion; exit pressure = free stream pressure ) 100

10 Example: ( p3 / p2 )@Tmax / p2 p3 ( M0 = 2.0, h = 60k ft (T0 = 390 R ) , T4 = 3,000 R, γ4 = 1.31 1/2 ( p3 / p2 )@Tmax = {{ ( 3000 / 390 ) / { 1 + [( 1.4 - 1 ) / 2 ] 2.02 }}1.31/ ( 1.31 – 1 ) = 6.31 1 Note: 00.511.522.533.54 T0 = Free stream temperature M0, Mach Number T4 = Turbine entrance temperature T4 = 2000 R T4 = 3000 R γ = Specific heat ratio T4 = 4000 R T4 = 5000 R

Source: Ashley, H., Engineering Analysis of Flight Vehicles, Dover Publications, Inc., New York, 1974 2/24/2008 ELF 90 TurbojetTurbojet ThrustThrust IsIs LimitedLimited byby TurbineTurbine MaximumMaximum AllowableAllowable TemperatureTemperature . Note: TIdealMax / ( p0 A0 ) = ( γ0 M0 / a0 ) ( T / m )IdealMax . Assumption: Ideal turbojet ( T / m )IdealMax = Ve –V0 20 V = { 2 c T [ 1 – ( p / p )( γ5 - 1 ) / γ5 ]}1/2 e p 5t 0 5t T ≈ T –T + T 5t 4 3 2 T ≈ T ( p / p )( γ3 - 1 ) / γ3 15 3 2 3 2 ) T ≈ T { 1 + [( γ - 1 ) / 2 ] M 2 } 1 2 0 0 0 = 2 γ / ( γ -1 ) p p ≈ p ( T / T ) 4 4 / 5t 4 5 4 3 10 p ( p4 = p3 t Thrust je 2 γ / ( γ -1 ) m p ≈ p { 1 + [( γ - 1 ) / 2 ] M } 0 0 a 2 0 0 0 R p = Free stream static pressure 5 0 A0 = Free stream flow area into inlet

T4 = Turbine entrance temperature Tmax / [( p0 ) ( A0 )], Nondimensional A0 )], ( ) p0 Maximum /Tmax [( 0 Example: M0 = 2, h = 60 k ft ( T0 = 390 R, p0 = 1.047 psi ), T = 3,000 R, γ = 1.31, ( p / 01234 4 4 3 p2 )@Tmax = 6.31, p2 = 8.19 psi, p3 = 51.7 psi, 2 M0, Mach Number A0 = 114 in , T2 = 702 R, T3 = 1133 R, γ3 = 1.36 T4 = 2000 R T4 = 3000 R T = 2569 R, γ = 1.32, p = 23.0 psi, V = 5t 5 . 5t e T4 = 4000 R T4 = 5000 R 4524 ft / s, ( T / m )IdealMax = 2588 ft / s, TIdealMax / p0 A0 = 7.49

TIdealMax = 7.49 ( 1.047 ) ( 114 ) = 894 lb 2/24/2008 ELF 91 TurbojetTurbojet SpecificSpecific ImpulseImpulse DecreasesDecreases withwith SupersonicSupersonic MachMach NumberNumber

( ISP )Ideal@Tmax gc cp T0 / ( a0 Hf ) = TIdealMax T0 / [( p0 A0 γ0 M0 ) ( T4 –T3 )] Assumptions: Ideal turbojet ( isentropic inlet, compressor, turbine, nozzle; flow, low subsonic, constant pressure combustion; exit pressure = free stream pressure), max thrust 0.8 Example:

M0 = 2, h = 60k ft ( T0 = 390 R, a0 = 968 ft / s ), RJ-5 fuel ( Hf = 14,525 BTU / lbm ), T4 = 3,000 R, c = 0.293 BTU / lbm / R, γ = 1.4 0.6 p 0 Ram jet Calculate ( ISP )Ideal@T gc cp T0 / ( a0 Hf ) = ( p 0.559 max 3 / p 2 = 1 ( I ) = 0.559 ( 968 ) ( 14525 ) / [ 32.2 0.4 ) SP Ideal@Tmax ( 0.293 ) ( 390 )] = 2136 s Note:

0.2 gc = Gravitational constant = 32.2

cp = Specific heat at constant pressure Nondimensional Impulse Ideal Specific ( ISP )Ideal ( gc ) ( cp ) ( T0) / [ ( a0 ) ( Hf )], T0 = Free stream temperature 0 a0 = Free stream speed of sound 01234 Hf = Heating value of fuel M0, Mach Number TIdealMax = Ideal maximum thrust T4 = 2000 R T4 = 3000 R γ = Specific heat ratio

T4 = 4000 R T4 = 5000 R T4 = Combustor exit temperature

T3 = Compressor exit temperature 2/24/2008 ELF 92 TacticalTactical MissileMissile RamjetRamjet PropulsionPropulsion AlternativesAlternatives

Liquid Fuel Ramjet

Rocket Boost Inboard Profile

Ramjet Sustain Inboard Profile

Note: Booster Propellant Solid Fuel Ramjet Fuel

Boost

Sustain

Solid Ducted Rocket

Boost

Sustain

2/24/2008 ELF 93 HighHigh SpecificSpecific ImpulseImpulse forfor aa RamjetRamjet OccursOccurs UsingUsing HighHigh HeatingHeating ValueValue FuelFuel atat MachMach 33 toto 44 2 1/2 2 ( ISP )Ideal gc cp T0 / ( a0 Hf ) = { M0 {{( T4 / T0 ) / { 1 + [( γ0 - 1 ) / 2 ] M0 }} - 1 } / {{ 1 + [( γ0 - 1 ) / 2 ] M0 } {( T4 / T0 ) / { 2 1 + [( γ0 - 1 ) / 2 ] M0 }} – 1 } Assumptions: Ideal ramjet, isentropic inlet and nozzle, low subsonic and constant pressure combustion, exit pressure = free stream pressure, φ≤1 0.6 Example for Ramjet Baseline:

M = 3.5, h = 60k ft ( T0 = 390 R, a0 = 968 ft / s ), RJ-5 fuel ( Hf = 14,525 BTU / lbm ), T4 = 4,000 R, cp = 0.302 BTU / lbm / R, γ0 = 1.4

0.4 Calculate ( ISP )Ideal gc cp T0 / ( a0 Hf ) = { 3.5 {{( 4000 / 390 ) / { 1 + [( 1.4 - 1 ) / 2 ] 3.52 }}1/2 - 1 } / {{ 1 + [( 1.4 - 1 ) / 2 ] 3.52 } {( 4000 / 390 ) / { 1 + [( 1.4 - 1 ) / 2 ] 3.52 }} – 1 } = 0.372

( ISP )Ideal = 0.372 ( 968 ) ( 14525 ) / [ 32.2 ( 0.302 ) ( 0.2 390 ) = 1387 s Note:

gc = Gravitational constant = 32.2 Nondimensional Ideal Specific Impulse Specific Ideal Nondimensional

( ISP )Ideal( ISP ( gc ) ( cp ) ( T0) [ ( a0 / ) ( Hf )], c = Specific heat at constant pressure 0 p 012345T0 = Free stream temperature a = Free stream speed of sound M0, Free Stream Mach Number 0

Hf = Heating value of fuel T4 / T0 = 3 T4 / T0 = 5 γ = Specific heat ratio T4 / T0 = 10 T4 / T0 = 15 T4 = Combustor exit temperature Source: Ashley, H., Engineering Analysis of Flight Vehicles, Dover Publications, Inc., New York, 1974 2/24/2008 ELF 94 HighHigh ThrustThrust fforor aa RamjetRamjet OOccursccurs ffromrom MachMach 33 toto 55 withwith HighHigh CombustionCombustion TemperatureTemperature 2 2 1/2 TIdeal / ( φ p0 A0 ) = γ0 M0 {{[ T4 / T0 ] / { 1 + [( γ0 - 1 ) / 2 ] M0 }} -1 } Assumptions: Ideal ramjet, isentropic inlet and nozzle, low subsonic and constant pressure combustion, exit pressure = free stream pressure, φ≤1 25 Note: T4 and T0 in R Example for Ramjet Baseline:

M0 = 3.5, α = 0 deg, h = 60k ft ( T0 = 390 R, p0 = 20 1.047 psi ), T4 = 4,000 R, ( f / a ) = 0.055, φ = 2 0.82, A0 = 114 in , γ0 = 1.4 2 TIdeal / ( φ p0 A0 ) = 1.4 ( 3.5 ) {{[ 4000 / 390 ] / { 1 15 + [( 1.4 – 1 ) / 2 ] ( 3.5 )2 }}1/2 – 1 } = 12.43

TIdeal = 12.43 ( 0.82 ) ( 1.047 ) ( 114 ) = 1216 lb Thrust 10 Note:

( T )Ideal = Ideal thrust

5 p0 = Free stream static pressure

A0 = Free stream flow area into inlet T / [ ( PHI p0 ) (A0 ) ], Nondimimensional 0 γ0 = Free stream specific heat ratio

012345M0 = Free stream Mach number

M0, Free Stream Mach Number T4 = Combustor exit temperature

T0 = Free stream temperature T4 / T0 = 3 T4 / T0 = 5 φ = Equivalence ratio = fuel-to-air ratio / T4 / T0 = 10 T4 / T0 = 15 stochiometric fuel-to-air ratio Source: Ashley, H., Engineering Analysis of Flight Vehicles, Dover Publications, Inc., New York, 1974 2/24/2008 ELF 95 RamjetRamjet CombustorCombustor TemperatureTemperature IncreasesIncreases withwith MachMach NumberNumber andand FuelFuel FlowFlow 2 T4 ≈ T0 { 1 + [( γ0 - 1 ) / 2 ] M0 } + ( Hf / cp ) ( f / a ) Assumptions: Low subsonic combustion. No heat transfer through inlet ( isentropic flow ). φ≤1.

T4 = combustor exit temperature in Rankine, T0 = free stream temperature in Rankine, γ = specific heat ratio, M0 = free stream Mach number, Hf = heating value of fuel, cp = 6000 specific heat at constant pressure, f / a = fuel-to-air ratio.

Example:

4000 •M0 = 3.5

•h = 60k ft ( T0 = 390 R )

•RJ-5 fuel ( Hf = 14,525 BTU / lb / R ) •f / a = 0.055 Fuel, Rankine Fuel, 2000

•γ0 = 1.4 0.109 •cp = 0.122 T BTU / lbm / R.

Note: cp ≈ 0.302 +/- 5% if 2500 R < T < 5000 R

T4, Combustor Exit Temperature for RJ-5 RJ-5 for Temperature Exit Combustor T4, 0 2 •Then T4 = 390 { 1 + [( 1.4 – 1 ) / 2 ] ( 3.5 ) } + 012345[( 14525 ) / ( 0.302 )] 0.055 = 3,991 R M0, Free Stream Mach Number

f / a = 0.01 f / a = 0.03 f / a = 0.05 f / a = 0.067

Note: ( f / a )φ = 1 ≈ 0.067 for stochiometric combustion of liquid hydrocarbon fuel, e.g., RJ-5. 2/24/2008 ELF 96 RamjetRamjet CCombustorombustor EntranceEntrance MachMach NumberNumber ShouldShould BeBe Low,Low, toto AvoidAvoid ThermalThermal ChokingChoking 2 2 1/2 2 1/2 ( M3 )TC = {{ - b + [ b –4 γ3 ] } / ( 2 γ3 )} b = 2 γ + ( T / T )( 1 + γ )2 / {( 1 + 0.2 M 2 )[ 1 + ( γ – 1 ) / 2 ]} 3 4t 0 4 0 4 2 Assumptions: Constant area combustion, [( γ 3 – 1 ) / 2 ] M3 << 1, isentropic inlet Example: 0.4 M = 2, h = 60k ft ( T = 390 R ), T = 4,000 R, γ = 1.4 0 0 4t 0 -0.0007 ( 4000 ) γ4 = 1.29 + 0.16 e = 1.300 0.3 T = ( 1 + 0.2 M 2 ) T = 702 R 0t 0 0 -0.0007 ( 702 ) γ 3 = 1.29 + 0.16 e = 1.388 b = 2 ( 1.388 ) + ( 4000 / 390 )( 1 + 1.300 )2 / {( 1 + 0.2 0.2 ( 22 )[ 1 + ( 1.300 – 1 ) / 2 ]} = - 24.211 2 2 ( M3 )TC = {{ 24.211 + [( -24.211 ) – 4 ( 1.388 ) ]1/2 } / [ 2 ( 1.3882 )]}1/2 = 0.204 0.1 Note: Number with Thermal Choking Thermal with Number

( M3 )TC, Combustor Entrance Mach ( M3 )TC = Combustor entrance Mach number with 0 thermal choking ( M4 = 1 )

012345γ3 = Specific heat ratio at combustor entrance

M0, Free Stream Mach Number M0 = Free stream Mach number T = Combustor exit total temperature 4t T4t / T0 = 3 T4t / T0 = 5 T0 = Free stream static temperature T4t / T0 = 10 T4t / T0 = 15 γ4 = Specific heat ratio in combustion 2/24/2008 ELF 97 AA RamjetRamjet CCombustorombustor withwith aa LowLow EntranceEntrance MachMach NumberNumber RequiresRequires aa SmallSmall InletInlet ThroatThroat AreaArea

( γ + 1 ) / [ 2 ( γ - 1 )] 2 -( γ + 1 ) / [ 2 ( γ -1 )] 2 -3 AIT / A3 = [( γ + 1 ) / 2 ] M3 {[ 1 + ( γ - 1 ) / 2 ] M3 } = ( 216 / 215 ) M3 ( 1 + M3 / 5 )

Assumptions:1 Isentropic inlet, MIT = 1, γ = 1.4

Note: A = Inlet throat area 0.8 IT A3 = Combustor entrance area

M3 = Combustor entrance Mach number 0.6 γ = Specific heat ratio Example: Ramjet Baseline 0.4 2 AIT = 41.9 in 2 A3 = 287 in A / A = 41.9 / 287 = 0.1459 0.2 IT 3 Assume sonic flow ( M = 1 ) at AIT M3, Combustor Entrance Mach Number Mach Entrance Combustor M3,

M3 = 0.085

0 M3 = 0.085 < ( M3 )TC = 0.204 0 0.2 0.4 0.6 0.8 1 ( A )IT / A3, Inlet Throat Area to Combustor Area Ratio

2/24/2008 ELF 98 TTypicalypical RRamjetamjet HHasas NNearlyearly CConstantonstant PPressureressure CombustionCombustion

Assume Rayleigh Flow, with Heat Addition at Constant Area Negligible Friction Pressure Loss in Combustor is Given by 2 2 p4 / p3 = ( 1 + γ3 M3 ) / ( 1 + γ4 M4 ) Mach Number Increase in Combustor Is Given by 2 2 2 2 2 2 T4t / T0 = [( 1 + γ3 M3 ) / ( 1 + γ4 M4 )] ( M4 / M3 ) { 1 + [( γ4 – 1 ) / 2 ] M4 } / { 1 + [( γ3 – 1 ) / 2 ] M3 } From Prior Example M0 = 2, h = 60k ft ( T0 = 390 R ), T4t = 4,000 R, γ0 = 1.4, γ4 = 1.300, and γ 3 = 1.388 Assume Ramjet Baseline with Sonic Inlet Throat

AIT / A3 = 41.9 / 287 = 0.1459 ⇒ M3 = 0.085 Solving Above Equations

M4 = 0.304

p4 / p3 = 0.902 Assumption of Nearly Constant Pressure Combustion Is Reasonably Accurate 10% error

2/24/2008 ELF 99 MinimumMinimum LengthLength forfor thethe CombustorCombustor IsIs aa FunctionFunction ofof CombustionCombustion VelocityVelocity

( lcomb )min = tcomb Vcomb 10 t

tcomb = 0.001 s 1 tcomb = 0.002 s tcomb = 0.004 s

Example for tcomb = 0.002 s and Subsonic Combustion Ramjet:

Minimum Combustor Length, f •Vcomb = 200 ft / s

0.1 •( lcomb )min = 0.002 ( 200 ) = 0.4 ft Example for t = 0.002 s and 100 1000 10000 comb Scramjet:

Vcomb, Combustion Velocity, ft / s •Vcomb = 3,000 ft / s

•( lcomb )min = 0.002 ( 3000 ) = 6.0 ft

2/24/2008 ELF 100 RamjetRamjet EngineEngine // BoosterBooster IntegrationIntegration OptionsOptions

Fuel Low Cruise Drag ( Modern Ramjets ) Boost Propellant Integral-Rocket Ramjet ( IRR ) Aft Drop-off Booster

Forward Booster Podded Drop-off Booster

High Cruise Drag Podded Ramjet Podded IRR

Podded Ramjet, Aft Drop-off Booster

Source: Kinroth, G.D. and Anderson, W.R., “Ramjet Design Handbook,” CPIA Pub. 319, June 1980 2/24/2008 ELF 101 RamjetRamjet EngineEngine // BoosterBooster IntegrationIntegration TradesTrades

Selection Factors Length Diameter Weight Ejectables Cruise Drag Carry Drag Cost Cycle Compatibility Inlet Compatibility

Integral Rocket – Ramjet ( IRR )

Aft Booster ( Drop-off ) – –

Forward Booster –

Podded Booster ( Drop-off ) – –

Podded Ramjet – –– Podded IRR – – –

Podded Ramjet ––– – – Aft Booster ( Drop-off ) – Superior Above Average Average – Below average

Source: Kinroth, G.D. and Anderson, W.R., “Ramjet Design Handbook,” CPIA Pub. 319, June 1980

2/24/2008 ELF 102 RamjetsRamjets withwith InternalInternal BoostersBoosters andand NoNo WingsWings HaveHave LowLow DragDrag

• Podded Ramjet 1.2 C = D / ( q S ), Zero-Lift Drag • Podded IRR D0 O REF • Podded Ramjet, Aft Drop Coefficient Off Booster • IRR With Wings 0.8 • Aft Drop Off Booster • Forward Booster C D0 • Podded Drop Off Booster Without Wings • IRR 0.4 • Aft Drop-off Booster • Forward Booster • Podded Drop-off Booster 0 Note: Nose Fineness Ratio ≥ 2.25 2345 Nose Bluntness Ratio ≤ 0.20 M, Mach Number

Source: Kinroth, G.D. and Anderson, W.R., “Ramjet Design Handbook,” CPIA Pub. 319, June 1980 2/24/2008 ELF 103 RamjetRamjet InletInlet OptionsOptions

Type Inlet Sketch Placement

Nose Nose-full axisymmetric Forward underside in nose compression field- Chin partial axisymmetric Forward Cruciform Forward in nose compression field-cruciform ( four ) Axisymmetric axisymmetric Aft Cruciform Aft-cruciform ( four ) axisymmetric Axisymmetric Under Wing Axisymmetric In planar wing compression field-twin axisymmetric

Twin Two-dimensional Aft-twin cheek-mounted two dimensional

Underslung Axisymmetric Aft underside-full axisymmetric

Underslung Two- Aft underside-belly mounted two dimensional dimensional Cruciform Two-dimensional Aft-cruciform ( four ) two dimensional

Source: Kinroth, G.D. and Anderson, W.R., “Ramjet Design Handbook,” CPIA Pub. 319, June 1980.

2/24/2008 ELF 104 RamjetRamjet InletInlet ConceptConcept TradesTrades

Selection Factors

Type Inlet Pressure Recovery Carriage Envelope Alpha Capability Weight Drag Warhead Shrouding inlet Cost Preferred Steering Preferred Control Prime Mission Suitability

– STT W, C ATS, STA BTT T ATS, ATA, STA – – – STT T ATS, ATA, STA STT T ATS – BTT T ATS, ATA, STA BTT T ATS, ATA, STA – BTT T ATS – – BTT T ATS, ATA, STA – STT T ATS Note: BTT = Bank to Turn STT = Skid to Turn W = Wing C = Canard Superior Above Average Average – Below average T = Tail

Source: Kinroth, G.D. and Anderson, W.R., “Ramjet Design Handbook,” CPIA Pub. 319, June 1980 2/24/2008 ELF 105 CurrentCurrent SupersonicSupersonic AiAir-breathingr-breathing MissilesMissiles HaveHave EitherEither aa NoseNose InletInlet oror AxisymmetricAxisymmetric AftAft InletsInlets

United Kingdom Sea Dart GWS-30 France ASMP ANS Russia AS-17 / Kh-31 Kh-41 SS-N-22 / 3M80

SA-6 SS-N-19 SS-N-26 China C-101 C-301 Taiwan Hsiung Feng III India BrahMos

• Aft inlets have lower inlet volume and do not degrade lethality of forward located warhead. • Nose Inlet may have higher flow capture, pressure recovery, smaller carriage envelope, and lower drag. 2/24/2008 ELF 106 ShockShock onon InletInlet CowlCowl LipLip PreventsPrevents SpillageSpillage

Inlet w/o External Compression Inlet Swallows 100% of the Free Stream Flow External Compression Required for Efficient Pressure Recovery if Mach Number > 2 and Inlet Start at Low Supersonic Mach number

Spillage External Compression Inlet ( with Spillage ) Shocks Shocks Converge Outside Inlet Lip ( Results in Spillage Air )

External Compression Inlet ( w/o Spillage ) Shocks Inlet Swallows 100% of the Free Stream Flow Shocks Converge at Inlet Lip ( Inlet Captures Maximum Free Stream Flow ) 2/24/2008 ELF 107 ShShockock WWaveave AAnglengle IIncreasesncreases wwithith DDeflectioneflection AngleAngle andand DecreasesDecreases withwith MachMach NumberNumber 2 2 2 2 tan ( α + δ ) = 2 cot θ2D ( M sin θ2D – 1 ) / [ 2 + M ( γ + 1 – 2 sin θ2D )] , for 2D flow, perfect gas

Note: θ2D = 2D shock wave angle, M = Mach number, α = angle of attack, δ = body deflection angle, γ = specific heat ratio, θconical ≈ 0.81 θ2D 50

40 Example for Ramjet Baseline:

30 α δ θ 20 1.4, Degrees 1.4, δ = 17.7 deg, M = 3.5, α = 0 deg, γ = 1.4 ⇒θ = 32 deg 10 2D θconical ≈ 0.81 θ2D = 0.81 ( 32 ) = 26 deg

Theta, 2D Shock Wave Angle @ Gamma = = Gamma @ Wave Angle Shock 2D Theta, 0 Approximate estimate of θ: -1 0 5 10 15 20 θ2D ≈μ+ α + δ = sin ( 1 / M ) + α + δ -1 Alpha + Delta, Deflection Angle, Degrees θconical ≈ 0.81 θ2D = 0.81 [ sin ( 1 / M ) + α + δ ] Mach 2 ( Deltamax = 23 deg ) Mach 3 ( Deltamax = 34 deg ) Mach 5 ( Deltamax = 41 deg )

2/24/2008 ELF 108 CaptureCapture EfficiencyEfficiency ofof anan InletInlet IncreasesIncreases withwith MachMach NumberNumber

( A0 / Ac )conical = ( h / l ) ( 1 + δ M + αM ) / [( 1 – 0.23δM + αM )( δ + h / l )] , conical nose with forward inlet

( A0 / Ac )2D = ( h / l ) ( 1 + δ M + αM ) / [( 1 + αM )( δ + h / l )] , 2D nose with forward inlet

Note: A0 / Ac ≤ 1, AC = inlet capture area, A0 = free stream flow area, δ = defection angle in rad, h = inlet height, l = distance from nose tip to inlet 1 α nose body δ A 0 streamline stream 0.8 line h inlet Ac streamline stre amline oblique shock 0.6

Example for baseline ramjet ( conical

Efficiency 0.4 nose ) h = 3 in 0.2 l = 23.5 in h / l = 0.1277 A0 / Ac, Baseline Ramjet Inlet Capture 2 0 AC = 114 in 012345δ = 17.7 deg ( 0.3089 rad ) M, Mach Number M = 3.5, α = 0 deg A / A = 0.81 ⇒ A = 92 in2 Alpha = 0 Deg Alpha = 10 Deg 0 c 0 2 Spillage = Ac -A0 = 114 - 92 = 22 in

2/24/2008 ELF 109 IsentropicIsentropic CompressionCompression AllowsAllows InletInlet StartStart atat LowerLower MachMach NumberNumber 2 -3 AIT / A0 = 1.728 ( MIE )start [ 1 + 0.2 ( MIE )start ) , Assumptions: 2-D inlet, Isentropic flow through inlet ( n = ∞ ), γ = 1.4 2 2 3.5 2 2.5 AIT / A0 = ( MIE )start {[ 0.4 ( MIE )start + 2 ] / [ 2.4 ( MIE )start ] }{[2.8 ( MIE )start – 0.4 ] / 2.4 } {[ 1.2 / ( 1 + 0.2 ( 2 3 MIE )start ]} , Assumptions: 2-D inlet, single normal shock ( n = 1 ), γ = 1.4

Note: AIT = inlet throat area, A0 = free stream flow area, ( MIE )start = inlet entrance start Mach number, γ = specific heat ratio, n = number of shocks 4 Example for ramjet baseline 2 AIT = 0.29 ft n = ∞ n = 1 2 2 3 Ac = 114 in = 0.79 ft ⇒ AIT / Ac = 0.367 Process: 1. Assume ( M ) 2 IE start 2. Compute capture efficiency A / A Number IT 0

3. Compute ( MIE )start and compare with 1 assumed ( MIE )start 4. Iterate until convergence ( M )IE, Inlet( M )IE, Entrance Start Mach Limit for isentropic compression 0 - From Prior Figure, A / A = 0.53 0 0.2 0.4 0.6 0.8 1 0 c - Compute A / A = ( A / A ) / ( A / A ) = AIT / A0 IT 0 IT c 0 c 0.367 / 0.53 = 0.69 ⇒ ( MIE )start = 1.8 Inlet Start for Isentropic Compression Ramjet baseline has mixed compression with n = 5. Actual inlet start Mach Inlet Start for Single Normal Shock number is ( MIE )start > 1.8 2/24/2008 ELF 110 ForebodyForebody Shock Shock CompressionCompression ReducesReduces thethe InletInlet EntranceEntrance MachMach NumberNumber 4 2 2 2 2 2 2 2 2 2 1/2 ( MIE )2D = {{ 36 M0 sin θ2D -5 [ M0 sin θ2D - 1 ][ 7 M0 sin θ2D + 5 ]} / {[ 7 M0 sin θ2D -1 ][ M0 sin θ2D + 5 ]}} 2 2 2 2 tan ( α + δ ) = 2 cot θ2D ( M0 sin θ2D – 1 ) / [ 2 + M0 ( 2.4 – 2 sin θ2D )] Assumptions: 2D flow, perfect gas, γ = specific heat ratio = 1.4

Note: MIEt= inlet entrance Mach number, M0 = free stream Mach number, θ = oblique shock angle, α = angle of attack, δ = body deflection angle 4 Example for ramjet baseline

3 δ = 17.7 deg

( MIE )start = 1.8 ( from prior example ) 2 Compute M0 = 2.55 Note: Ramjet baseline forebody is conical, not 2D 1 ( M )IE, Inlet Entrance Mach Number Mach Entrance Inlet )IE, M ( 0 0 10203040 Alpha + Delta, Local Angle of Attack at Inlet Entrance, Deg

M0 = 2 M0 = 3 M0 = 5

2/24/2008 ELF 111 OOptimumptimum FForebodyorebody D Deflectioneflection AAngle(sngle(s)) fforor BBestest PressurePressure RecoveryRecovery IncreasesIncreases withwith MachMach NumberNumber

Note: δTotal = Total deflection angle, First External Shock nd δ1 = 1st deflection angle, δ2 = 2 Second External Shock deflection, δ3 = 3rd deflection. Optimum deflection angle provides equal loss in total pressure across each shock wave. δ2 δTotal Optimum deflection angles are δ 60 1 nearly equal for M > 4. 12.1, 15.2, 19.4 11.1, 13.0, 15.5 40 16.1, 22.1 15.0, 18.8

7.6, 8.2, 8.2 10.4, 11.2 20 Example: Optimum forebody deflection angles for double wedge ( n = 3 ) at Mach 2: δ1 = 10.4 deg, δ2 = 11.2 deg ⇒δtotal = 10.4 + 11.2 = 21.6 deg

Optimum Total Deflection Angle, Deg Angle, Deflection Total Optimum 0 01234 M0, Free Stream Mach Number

n = 1 n = 2 n = 3 n = 4 Isentropic Compression

Reference: “Technical Aerodynamics Manual,” North American Rockwell Corporation, DTIC AD 723823, June 1970. 2/24/2008 ELF 112 OObliqueblique SShockshocks PriorPrior toto thethe InletInlet NormalNormal SShockhock AreAre RequiredRequired toto SatisfySatisfy MIL-E-5008BMIL-E-5008B MIL-E-5008B Requirement: p / p = 1 –0.075 ( M –1 )1.35 tInlet t0 1 n = 1 ( Normal Shock )

n = 2 ( 1 Optimum Oblique Shock + Normal Shock ) n = 3 ( 2 Opt Oblique Shocks + Normal Shock ) 0.1

Ratio n = 4 ( 3 Opt Oblique Shocks + Normal Shock Ideal Isentropic Inlet

MIL-E-5008B PtInlet / pt0, Inlet Total Pressure 0.01 Note: 2D flow assumed 012345p = Inlet total pressure tInlet M, Mach Number p = Free stream total pressure t0

Example: MIL-E-5008B requirement for Mach 3.5 ( pt / pt = ηinlet = 0.74 ) can be satisfied only if there are more than three oblique shocks prior to inlet normal shock.Inlet 0

Source for Optimum 2D Shocks: Oswatitsch, K.L., “Pressure Recovery for Missiles with Reaction Propulsion at High Supersonic Speeds”, NACA TM - 1140, 1947. 2/24/2008 ELF 113 HighHigh DensityDensity FuelsFuels ProvideProvide HigherHigher VolumetricVolumetric PerformancePerformance butbut HaveHave HigherHigher ObservablesObservables Volumetric Density, Performance, Low Type Fuel lb / in3 BTU / in3 Observables

Turbine ( JP-4, JP-5, JP-7, JP-8, JP-10 ) ~ 0.028 559

Liquid Ramjet ( RJ-4, RJ-5, RJ-6, RJ-7 ) ~ 0.040 581

HTPB ~ 0.034 606

Slurry ( 40% JP-10 / 60% carbon ) ~ 0.049 801

Solid Carbon ( graphite ) ~ 0.075 1132 –

Slurry ( 40% JP-10 / 60% aluminum ) ~ 0.072 866 –

Slurry ( 40% JP-10 / 60% boron carbide ) ~ 0.050 1191 –

Solid Mg ~ 0.068 1200 –

Solid Al ~ 0.101 1300 –

Solid Boron ~ 0.082 2040 –

Superior Above average Average– Below average 2/24/2008 ELF 114 DuctedDucted RocketRocket DesignDesign ImplicationsImplications

Excess Fuel from Gas Generator ~ 30 % ⇒ Behaves more like a rocket ( higher burn rate, higher burn temperature, lower ISP ) ~ 70 % ⇒ Behaves more like a ramjet ( higher ISP, lower burn rate, lower burn temperature ) Choice of Fuel

Metal ( e.g., B, Al, Mg ) ⇒ Higher ISP, higher density, deposits, higher observables Carbon based ( e.g., C, HTPB ) ⇒ Lower observables, higher reliability, lower ISP Choice of Oxidizer AP ⇒ Higher burn rate, lower hazard, HCl contrail Min Smoke ( e.g., HMX, RDX ) ⇒ Lower Observables, lower heating value, lower burn rate, hazardous Thrust Magnitude Control Approaches Pintle or valve in gas generator throat Retractable wires in grain

2/24/2008 ELF 115 HighHigh PropellantPropellant FractionFraction IncreasesIncreases BurnoutBurnout VelocityVelocity 5000 ΔV = -gc Isp ln (1 - Wp / Wi) Assumption: T >> D, T >> W sin γ, γ = const

4000

Isp = 250 s

3000 ΔV, Missile Isp = 200 s Incremental Burnout Velocity, ft / s 2000

Example: Rocket Baseline

Wi,boost = WL = 500 lb, Wp, boost = 84.8 lb 1000 ISP, boost = 250 s WP, boost / Wi = 84.8 / 500 = 0.1696 ΔV = -32.2 ( 250 ) ln ( 1 - 0.1696 ) = 1496 ft / s 0 0 0.1 0.2 0.3 0.4 0.5

WP / Wi, Propellant Weight / Initial Missile Weight

2/24/2008 ELF 116 HighHigh SpecificSpecific ImpulseImpulse RequiresRequires HighHigh ChamberChamber PressurePressure andand OptimumOptimum NozzleNozzle ExpansionExpansion 2 ( γ + 1 ) / ( γ -1 ) ( γ - 1 ) / γ 1/2 ISP = cd {{[ 2 γ / ( γ - 1 )] [ 2 / ( γ + 1 )] [ 1 – ( pe / pc ) ]} + ( pe / pc ) ε -( p0 / pc ) ε } c* / gc . T = w p ISP = ( gc / c* ) pc At ISP 1/ ( γ -1 ) 1/2 1 / γ ( γ -1 ) /γ 1/2 ε = {[ 2 / ( γ + 1 )] [( γ -1 ) / ( γ + 1 )] } / {( pe / pc ) [ 1 - ( pe / pc ) ] } 300 Note: ε = nozzle expansion ratio

pe = exit pressure pc = chamber pressure p0 = atmospheric pressure . w P = propellant weight flow rate At = nozzle throat area ( minimum, sonic, choked ) 250 γ = specific heat ratio = 1.18 in figure

cd = discharge coefficient = 0.96 in figure c* = characteristic velocity = 5,200 ft / s in figure

h = 20k ft, p0 = 6.75 psi in figure Example for Rocket Baseline: 2 ε = Ae / At = 6.2 ⇒ pe / pc = 0.02488, At = 1.81 in

Isp, Specific Impulse of Rocket Baseline, s Baseline, Rocket of Impulse Specific Isp, 200 ( pc )boost = 1769 psi, pe = 44 psi, ( ISP )boost = 257 s 0102030 ( ISP )ε = 6.2 / ( ISP )ε = 1 = 257 / 200 = 1.29 Nozzle Expansion Ratio ( T )boost = ( 32.2 / 5200 ) ( 1769 ) (1.81 )( 257 ) = 5096 lb ( p ) = 301 psi, p = 7.49 psi, ( I ) = 239 s pc = 300 psi pc = 1000 psi c sustain e SP sustain pc = 2000 psi pc = 3000 psi ( ISP )ε = 6.2 / ( ISP )ε = 1 = 240 / 200 = 1.20

( T )sustain = ( 32.2 / 5200 ) ( 301 ) (1.81 )( 240 ) = 810 lb 2/24/2008 ELF 117 HighHigh PropellantPropellant WeightWeight FlowFlow RateRate RequiresRequires HighHigh ChamberChamber PressurePressure andand LargeLarge NozzleNozzle ThroatThroat

. w p = gc pc At / c* 100000

10000 c* = 4800 ft / s c* = 5200 ft / s c* = 5600 ft / s 1000 Throat Area, lb lb Area, Throat Rocket Baseline At for Boost: c* = 5200 ft / s

( pc )boost = 1,769 psi . (pc)At, Chamber Pressure x Nozzle 100 w p = Wp / tb = 84.8 / 3.69 = 23.0 lb / s . 1 10 100 pc At = c* w p / gc = 5200 ( 23.0 ) / 32.2 = 3,714 lb 2 Propellant Weight Flow Rate, lb / s At = 3714 / 1769 = 2.10 in

. Note: At = nozzle throat area, c* = characteristic velocity, w p = propellant weight flow rate, gc = gravitational constant, pc = chamber pressure 2/24/2008 ELF 118 HighHigh ChamberChamber PressurePressure RequiresRequires LargeLarge PropellantPropellant BurnBurn AreaArea andand SmallSmall NozzleNozzle ThroatThroat

Example Ab for Rocket Ab = gc pcAt / ( ρc*r ) Baseline: 600 r = r ( p / 1000 )n A = 1.81 in2 pc=1000 psi c t ρ = 0.065 lb / in3 n = 0.3

rp = 1000 psi = 0.5 in / s 400 c c* = 5,200 ft / s

Tatmosphere = 70 °F

For sustain ( pc = 301 psi ): •r = 0.5 ( 301 / 1000 )0.3 = 0.35 200 in / s 2 •Ab = 149 in

For boost ( pc = 1,769 psi ) •r = 0.59 in / s

Ab, Rocket Baseline Propellant Burn Area, in2 Area, Burn Propellant Baseline Rocket Ab, 2 0 •Ab = 514 in 0 500 1000 1500 2000 Pc, Rocket Baseline Motor Chamber Pressure, psi

Note: Ab = propellant burn area, gc = gravitation constant, At = nozzle throat area, ρ = density of propellant, c* = characteristic velocity, r = propellant burn rate, r = propellant burn rate at p = 1,000 psi, p = chamber pressure, n = burn rate exponent pc=1000 psi c c 2/24/2008 ELF 119 ConceptualConceptual DesignDesign SizingSizing ProcessProcess forfor aa RocketRocket MotorMotor 1. Define Altitude and Required Thrust-time New Value ( s )

2. Assume Propellant ( Characteristic Velocity, Nominal Burn Rate, Burn Rate Exponent ), Chamber Pressure, Burn New Value ( s ) Area, and Nozzle Geometry ( Expansion Ratio, Throat Area )

3. Compute ISP and Thrust

OK? No Yes 4. Compute Propellant Weight Flow Rate and Propellant Used

OK? No Yes

5. Determine Diameter and Length to Satisfy wp and Ae

OK? No Yes 2/24/2008 ELF 120 ConventionalConventional SolidSolid RocketRocket Thrust-TimeThrust-Time DesignDesign AlternativesAlternatives withwith PropellantPropellant Cross-SectionCross-Section

Example Mission Thrust Profile Example Web Cross Section / Volumetric Loading •≈ Cruise Constant ~ 82% ~95% ~90% Thrust

Thrust ( lb ) Burning Time ( s ) •Dive at ≈ End Burner Radial Slotted Tube constant Regressive ~ 79% dynamic Thrust

pressure Thrust ( lb ) Burning Time ( s ) •Climb at ≈ constant ~ 87% dynamic Progressive pressure Thrust Thrust ( lb ) Burning Time ( s ) •Fast launch – Production of Star Web Propellant. ≈ cruise Boost-Sustain ~ 85% Photo Courtesy of BAE Thrust ( lb ) •Fast launch – Burning Time ( s ) ≈ cruise – high Boost-Sustain-Boost speed terminal ~ 85% Thrust ( lb ) Burning Time ( s ) Medium Burn Rate Propellant Note: High thrust and chamber pressure require large surface burn area. High Burn Rate Propellant 2/24/2008 ELF 121 ConventionalConventional RocketRocket HasHas FixedFixed BurnBurn whilewhile ThrustThrust MagnitudeMagnitude ControlControl CanCan VaryVary BurnBurn IntervalInterval Conventional Fixed Burn Interval ( Boost )

End Burning Radial Burning Conventional Fixed Burn Interval ( Boost – Sustain )

Radial Boost Concentric Radial Burning End Burning Sustain High Burn Rate Boost Simultaneous Burning Low Burn Rate Sustain Pulse Motor TMC Variable Burn Interval ( Boost – Coast – Boost / Sustain - Coast )

1st Pulse: Radial Boost 1st Pulse: Radial Boost 2nd Pulse: End Burning Sustain 2nd Pulse: Radial Sustain / Boost Separate Burning ( Pulsed Motor ) Separate Burning ( Pulsed Motor ) Boost Propellant Note: Each pulse increases motor cost approximately 40%. Sustain Propellant 2/24/2008 ELF 122 TacticalTactical RocketRocket MotorMotor ThrustThrust MagnitudeMagnitude ControlControl AlternativesAlternatives

Solid Pulse Motor

☺ High ISP Limited Pulses Solid Pintle Motor ☺ Continuously Select Up to Thermal or Mechanical Barriers 40:1 Variation in Thrust ☺ Reduce MEOP on Hot Day

Good ISP Only If Burn Rate Exponent n → 1 Bi-propellant Gel Motor Pintle Pressurization Gelled Oxidizer Gelled Fuel Combustion ☺ High ISP Chamber ☺ Duty Cycle Thrust ☺ Insensitive Munition Lower Max Thrust Toxicity 2/24/2008 ELF 123 SolidSolid RocketRocket PropellantPropellant AlternativesAlternatives

Burn ISP, ρ, Rate @ Specific Density, 1,000 psi, Type Impulse, s lb / in3 in / s Safety Observables • Min Smoke. No Al fuel or AP – – – oxidizer. Either Composite with 220 - 255 0.055 - 0.062 0.25 - 2.0 Nitramine Oxidizer ( CL-20, ADN, HMX, RDX ) or Double Base. Very low

contrail (H2O).

• Reduced Smoke. No Al ( binder fuel ). AP oxidizer. Low contrail ( HCl ). 250 - 260 0.062 0.1 - 1.5

• High Smoke. Al fuel. AP oxidizer. –

High smoke ( Al2O3 ). 260 - 265 0.065 0.1 - 3.0

Superior Above Average Average – Below Average

2/24/2008 ELF 124 SteelSteel isis thethe MostMost CommonCommon MotorMotor CaseCase MaterialMaterial

Airframe / Temper- Volumetric Launcher Type ature Efficiency Weight IM Attachment Cost

Steel

Aluminum – –

Strip Steel / – Epoxy Laminate

Composite – – –

Titanium – –

Superior Above Average Average – Below Average

2/24/2008 ELF 125 HeatHeat TransferTransfer DrivesDrives RocketRocket NozzleNozzle Materials,Materials, Weight,Weight, andand CostCost Dome Closeout Exit Cone Housing Throat

Rocket Nozzle Element High Heating ( High Chamber Low Heating ( Low Chamber Pressure or Long Burn ) ⇒ Pressure or Short Burn ) ⇒ High Cost / Heavy Nozzle Low Cost / Light Weight Nozzle

♦ Housing Material ♦ Steel ♦ Cellulose / Phenolic Alternatives ♦ Aluminum

♦ Throat Material ♦ Tungsten Insert ♦ Cellulose / Phenolic Insert Alternatives ♦ Rhenium Insert ♦ Silica / Phenolic Insert ♦ Molybdenum Insert ♦ Graphite Insert ♦ Carbon – Carbon Insert

♦ Exit Cone, Dome Closeout, ♦ Silica / Phenolic Insert ♦ No Insert and Blast Tube Material ♦ Graphite / Phenolic Insert ♦ Glass / Phenolic Insert Alternatives ♦ Silicone Elastomer Insert

2/24/2008 ELF 126 SummarySummary ofof PropulsionPropulsion

Emphasis Turbojet propulsion Ramjet propulsion Rocket propulsion Conceptual Design Prediction Methods Thrust Specific impulse Design Trades Turbojet turbine material, compressor ratio, and cycle Ramjet engine / booster / inlet integration Ramjet fuel Propellant burn area requirement Nozzle throat area Nozzle expansion ratio Rocket motor grain Thrust magnitude control

2/24/2008 ELF 127 SummarySummary ofof PropulsionPropulsion (( contcont ))

Design Trades ( cont ) Solid propellant alternatives Motor case material alternatives Nozzle materials New Propulsion Technologies Hypersonic turbojet Ramjet / ducted rocket Scramjet Combined cycle propulsion High temperature turbine materials High temperature combustor Oblique shock airframe compression Mixed compression inlet Low drag inlet High density fuel / propellant Endothermic fuel

2/24/2008 ELF 128 SummarySummary ofof PropulsionPropulsion (( contcont ))

New Propulsion Technologies ( cont ) Solid rocket thrust magnitude control High burn exponent propellant Low observable fuel / propellant Discussion / Questions? Classroom Exercise ( Appendix A )

2/24/2008 ELF 129 PropulsionPropulsion ProblemsProblems

1. An advantage of turbojets compared to ramjets is s_____ thrust. 2. The specific impulse of a turbojet is often limited by the maximum allowable temperature of the t______. 3. The specific impulse of a ramjet is often limited by the maximum allowable temperature of the c______. 4. Ducted rockets are based on a fuel-rich g__ g______. 5. A safety advantage of solid rocket propulsion over liquid propulsion is less t______. 6. A rocket boost to a take-over Mach number is required by ramjets and s______. 7. Parameters that enable the long range of subsonic cruise turbojet missiles are high lift, low drag, available fuel volume, and high s______i______. 8. High thrust and high acceleration are achievable with s____ r_____ propulsion. 9. In a turbojet the power to drive the compressor is provided by the t______.

2/24/2008 ELF 130 PropulsionPropulsion ProblemsProblems (( contcont ))

10. The compressor exit temperature is a function of the flight Mach number and the compressor p______r____. 11. Compressor exit temperature, fuel heating value, and fuel-to-air ratio determine the turbojet t______temperature. 12. Three types of turbine based propulsion are turbojet, turbo ramjet, and a__ t____ r_____. 13. Mach number and fuel-to-air ratio determine the ramjet c______temperature. 14. An example of a ramjet with low drag and light weight is an i______r_____ ramjet. 15. Russia, France, China, United Kingdom, Taiwan, and India are the only countries with currently operational r_____ missiles. 16. 100% inlet capture efficiency occurs when the forebody shock waves intercept the i____ l__. 17. Excess air that does not flow into the inlet is called s______air.

2/24/2008 ELF 131 PropulsionPropulsion ProblemsProblems (( contcont ))

18. Starting a ramjet inlet at lower supersonic Mach number requires a larger area of the inlet t_____. 19. Optimum pressure recovery across shock waves is achieved when the total pressure loss across each shock wave is e____. 20. The specific impulse and thrust of a ramjet are a function of the efficiency of the combustor, nozzle, and i____. 21. High density fuels have high payoff for v_____ limited missiles. 22. The specific impulse of a ducted rocket with large excess fuel from the gas generator can approach that of a r_____. 23. High speed rockets require large p______weight. 24. At the throat, the flow area is minimum, sonic, and c_____ . 25. For an optimum nozzle expansion the nozzle exit pressure is equal to the a______pressure. 26. High thrust and chamber pressure are achievable through a large propellant b___ area.

2/24/2008 ELF 132 PropulsionPropulsion ProblemsProblems (( contcont ))

27. Three approaches to solid rocket thrust magnitude control are pulse motor, pintle motor, and g__ motor. 28. A high burn exponent propellant allows a large change in thrust with only a small change in chamber p______. 29. Three tradeoffs in selecting a solid propellant are safety, observables, and s______i______. 30. A low cost motor case is usually based on steel or aluminum material while a light weight motor case is usually based on c______material. 31. Rockets with high chamber pressure or long burn time may require a t______throat insert.

2/24/2008 ELF 133 OutlineOutline

2/24/2008 ELF 134 MissileMissile ConceptConcept SynthesisSynthesis RequiresRequires EvaluationEvaluation ofof AlternativesAlternatives andand IterationIteration

Define Mission Requirements Alt Mission Establish Baseline Alt Baseline Aerodynamics

Propulsion

Weight Resize / Alt Config / Subsystems / Tech

Trajectory

Meet No Performance?

Yes No Measures of Merit and Constraints

Yes

2/24/2008 ELF 135 DesigningDesigning LightLight WeightWeight MissileMissile HasHas HighHigh PayoffPayoff

Production cost

Logistics cost

Size

Firepower

Observables

Mission flexibility

Expeditionary warfare

2/24/2008 ELF 136 FlightFlight PerformancePerformance (( Range,Range, Speed,Speed, ManeuverabilityManeuverability )) SensitiveSensitive toto SubsystemSubsystem WeightWeight

Dome - Seeker - Guidance and Propulsion Wings Stabilizers Control -

Structure Power Warhead Insulation Data Flight Supply Link - Control

High Sensitivity Low Sensitivity - Minor Sensitivity

2/24/2008 ELF 137 MissileMissile RangeRange isis aa FunctionFunction ofof LaunchLaunch Weight,Weight, PropellantPropellant Weight,Weight, andand SpecificSpecific ImpulseImpulse Assumptions: ΔV ≈ -gc Isp ln ( 1 - WPropellant / Wi ) θ = Launch Incidence Angle = 45 deg for max 1000 2 I R ≈ V sin ( 2θi ) / gc range Thrust Greater Than Drag and Weight Flat, Non-rotating Earth

For Two-Stage Missile with ( Wi )Min : ΔV1 = ΔV2 Example: Two-Stage Missile with Minimum Weight and R = 200 nm = 1.216 x 106 ft 100 max

Assume ISP = 250 sec, WPayload = 500 lb, WInert = 0.2 WPropellant V = [( 32.2 ) ( 1.216 x 106 )]1/2 = 6251 ft / s Rmax, Maximum Range, nm Range, Maximum Rmax, ΔV1 = ΔV2 = V / 2 = 3125 ft / s

Wi,SecondStage = WPayload + WInert + WPropellant = 814 lb W =W + W = 85 + 427 = 512 lb 10 i, FirstStage Inert Propellant 100 1000 10000 Wi = Wi,FirstStage + Wi,SecondStage = 1326 lb Wi, Example Initial Launch Weight, lb Compare: Single-Stage Missile, R = 200 nm ΔV = 6251 = - 32.2 ( 250 ) ln [ 1 – W / ( Single-Stage Missile Two-Stage Missile Propellant WPropellant + 0.2 WPropellant + 500 )] ⇒ Wp = 767 ⇒ Wi = 1420 lb 2/24/2008 ELF 138 MiMissilessile WWeighteight IIss aa FFunctionunction ooff DiDiameterameter anandd LengthLength 2 WL = 0.04 l d 10000 Units: WL( lb ), l ( in ), d ( in )

1000

100 WL, Missile LaunchWL, Weight, lb 10 100 1000 10000 100000 1000000 ld2, Missile Length x Diameter2, in3

FIM-92 SA-14 Javelin RBS-70 Starstreak Mistral HOT Trigat LR LOCAAS AGM-114 Roland RIM-116 Crotale AIM-132 AIM-9M Magic 2 Mica AA-11 Python 3 AIM-120C AA-12 Skyflash Aspide AIM-9P Super 530F Super 530D AGM-65G PAC-3 AS-12 AGM-88 Penguin III AIM-54C Armat Sea Dart Sea Eagle Kormoran II AS34 AGM-84H MIM-23F ANS MM40 AGM-142 AGM-86C SA-10 BGM-109C MGM-140 SSN-22 Kh-41

2/24/2008 ELF 139 MMostost SSubsystemsubsystems fforor TTacticalactical MiMissilesssiles HHaveave aa DensityDensity ofof aboutabout 0.050.05 lblb // inin33

Guidance: Flight Control: Warhead: Propellant: Data Link: 0.04 lb / in3 0.04 lb / in3 0.07 lb / in3 0.06 lb / in3 0.04 lb / in3

Dome Material: Structure and Motor Case: Aero Surfaces: 3 3 0.1 lb / in 0.10 ( Al ) to 0.27 ( steel ) lb / in 0.05 ( built-up Al ) to 0.27 ( solid steel ) lb / in3

2/24/2008 ELF 140 ModelingModeling Weight,Weight, Balance,Balance, andand Moment-oMoment-off-Inertia-Inertia IsIs BasedBased onon aa Build-upBuild-up ofof SubsystemsSubsystems

Example Missile Configuration Wing Section Inlet Section With Fuel With Fuel Engine

Fuel Nose G&C Warhead Plug Inlet

Model +z

Assume Uniform Weight Distribution For a Given Segment Legend Structure and Subsystems Engine Structure and Subsystems Warhead and Structure Fuel Inlet Structure and Subsystems Aero Surfaces

xCG = Σ ( xsubsystem1 Wsubsystem1 + xsubsystem2 Wsubsystem2 + … ) / Wtotal 2 2 IY = Σ [ ( Iy,subsystem1 )local + Wsubsystem1 ( xsubsystem1 -xCG ) / gc + ( Iy,subsystem2 )local + Wsubsystem2 ( xsubsystem2 -xCG ) / gc + … ] 2/24/2008 ELF 141 Moment-oMoment-off-Inertia-Inertia IsIs HigherHigher forfor HighHigh FinenessFineness RatioRatio BodyBody 2 2 ( Iy,cylinder )local = [ W d / gc ] [( 1 / 16 ) + ( 1 / 12 ) ( l / d ) ]

n 100 2 2 ( Iy,cone )local = [ W d / gc ] [ ( 3 / 80 ) + ( 3 / 80 ) ( l / d ) ]

r nde e Cyli Con 10

Example for Ramjet Baseline at Launch ( xcg = 8.04 ft ) Assume missile can be approximated as a conical nose-cylinder 1 For the cone, d = 1.25 ft, l / d = 1.57, Wcone = 15.9 lb, xcg,cone = 1.308 ft of Inertia of

For the cylinder, l / d = 7.22, d = 1.698 ft, Wcylinder = 2214 lb, xcg,cylinder = 8.09 ft 2 Iy = ( Iy,cone )local + Wcone ( xcg,cone -xCG ) / gc + ( Iy,cylinder )local + Wcylinder ( xcg,cylinder - 2 xCG ) / gc 0.1 2 2 2 ( Iy,cone )local = [ 15.9 ( 1.25 ) / 32.2 ] [ 0.0375 + 0.0375 ( 1.57 ) ] = 0.10 slug-ft 2 2 2 ( Iy,cylinder )local = [ 2214 ( 1.698 ) / 32.2 ] [ 0.0625 + 0.0833 ( 7.22 ) ] = 872 slug-ft 2 Iy = 0.10 + 22.4 + 872 + 0.16 = 895 slug-ft

( Iy,local( W g / ( ) d2 ), Nondimensional Yaw Local Mome 0.01 0102030 l / d, Length / Diameter

2/24/2008 ELF 142 StructureStructure DesignDesign FactorFactor ofof SafetySafety IsIs GreaterGreater forfor HazardousHazardous SubsystemsSubsystems // FlightFlight ConditionsConditions

Pressure Bottle ( 2.50 / 1.50 ) Ground Handling Loads ( 1.50 / 1.15 ) 3.0 Captive Carriage and Separation Flight Loads ( 1.50 / 1.15 ) Motor Case ( MEOP ) ( 1.50 / 1.10 ) Free Flight Loads ( 1.25 / 1.10 ) 2.0 Δ Castings ( 1.25 / 1.25 ) FOS, Factor of Safety Δ Fittings ( 1.15 / 1.15 ) ( Ultimate / Yield ) Thermal Loads ( 1.00 / 1.00 ) 1.0

Note: 0 • MIL STDs include environmental ( HDBK-310, NATO STANAG 4370, 810F, 1670A ), strength and rigidity ( 8856 ), and captive carriage ( 8591 ). •The entire environment ( e.g., manufacturing, transportation, storage, ground handling, captive carriage, launch separation, post-launch maneuvering, terminal maneuvering ) must be examined for driving conditions in structure design. •FOS Δ for castings is expected to be reduced in future as casting technology matures. •Reduction in required factor of safety is expected as analysis accuracy improves will result in reduced missile weight / cost. 2/24/2008 ELF 143 StructureStructure ConceptsConcepts andand ManufacturingManufacturing ProcessesProcesses forfor LowLow PartsParts CountCount

Structure Manufacturing Process Alternatives Composites Metals Structure Vacuum Vacuum High Geometry Concept Assist Compression Filament Thermal Bag / Speed Strip Alternatives Alternatives RTM Mold Wind Pultrusion Form Autoclave Cast Machine Forming Laminate Lifting Body Monocoque Airframe Integrally Hoop – Stiffened Integrally – Longitudinal Stiffened Axisymmetric Monocoque Airframe Integrally Hoop Stiffened Integrally Longitudinal Stiffened Surface Solid

Sandwich

Note: Manufacturing process cost is a function of recurring cost ( unit material, unit labor ) and non-recurring cost ( tooling ). Note: Very Low Parts Count Low Parts Count Moderate Parts Count – High Parts Count 2/24/2008 ELF 144 LowLow PartsParts CountCount ManufacturingManufacturing ProcessesProcesses forfor ComplexComplex AirframesAirframes

Vacuum Assisted RTM

Resin Pump 3D Fiber Orientation

Filament Wind

Helical wind versus 2D Fiber Orientation ( 0-±45-90 deg ) radial wind Pultrusion …………………………………. Pour Cup Vent

Riser Metal Casting Mold Cavity Parting Line

2/24/2008 ELF 145 TacticalTactical MissileMissile AirframeAirframe MaterialMaterial AlternativesAlternatives

Buckling Max Tension Thermal Type Material Stability Short – Life Joining Cost Weight ( σTU / ρ ) Stress ( σBuckling / ρ ) Temp Metallic Aluminum 2219 – – Increasing Cost Steel PH 15-7Mo – – Titanium 6Al-4V –

Composite S994 Glass / Increasing Epoxy and S994 Cost Glass / Polyimide

Glass or – Graphite Reinforce Molding

Graphite / Epoxy – – and Graphite Polyimide

Note: Superior Above Average Average – Below Average

2/24/2008 ELF 146 StrengthStrength –– Elasticity Elasticity ofof AirframeAirframe MaterialMaterial AlternativesAlternatives

σt = P / A = E ε Kevlar Fiber Glass Fiber Note: w / o Matrix 400 w / o Matrix • High strength fibers are: Graphite Fiber – Very small diameter w / o Matrix – Unidirectional ( 400 – 800 Kpsi ) – High modulus of elasticity 300 – Very elastic – No yield before failure Very High Strength Stainless Steel σ , Tensile Stress, – Non forgiving failure t ( PH 15-7 Mo, CH 900 ) 3 10 psi High Strength Stainless Steel • Metals: 200 ( PH 15-7 Mo, TH 1050 ) – Ductile, – Yield before failure Titanium Alloy ( Ti-6Al-4V ) – Allow adjacent structure to absorb load 100 – Resist crack formation Aluminum Alloy ( 2219-T81 ) – Resist impact loads – More forgiving failure

E, Young’s modulus of elasticity, psi 0 P, Load, lb 0 1 2 3 4 5 ε, Strain, in / in A, Area, in2 -2 ε, Strain, 10 in / in Room temperature 2/24/2008 ELF 147 StructuralStructural EfficiencyEfficiency atat HighHigh TemperatureTemperature ofof ShortShort DurationDuration AirframeAirframe MaterialMaterial AlternativesAlternatives

Graphite / Polyimide ( ρ = 0.057 lb / in3 ), 0-±45-90 Laminate 12.0 Graphite / Epoxy ( ρ = 0.065 lb / in3 ) 0-±45-90 Laminate 10.0 3 Ti3Al ( ρ = 0.15 lb / in ) Ti-6Al-4V Annealed Titanium ( ρ = 0.160 lb / in3 ) 8.0 3

In. PH15-7 Mo Stainless Steel ( ρ = 0.277 lb / in ). Note:

5 Thin wall steel susceptible to buckling.

6.0 Graphite Density, 10

, Ultimate Tensile Strength / 4.0 Glass ρ /

TU Chopped Epoxy σ 2.0 Composites, 2219-T81 Random Orientation Aluminum ( ρ = 0.094 lb / in3 ) ( ρ = 0.101 lb / in3 ) 0 0 200 400 600 800 1,000 Short Duration Temperature, ° F

2/24/2008 ELF 148 HypersonicHypersonic MissilesMissiles withoutwithout ExternalExternal InsulationInsulation RequireRequire HighHigh TemperatureTemperature StructureStructure

2 ( Tmax )Titanium Aluminide ≈ 2,500 °F ) Tr = T0 ( 1 + 0.2 r M ) ( Tmax )Single Crystal Nickel Aluminides ≈ 3,000 °F 1 .9 = 0 .8 r 0 ( T ) ≈ 3,500 °F = max Ceramic Matrix Composite r = 2,000 r ( Tmax )Nickel Alloys ( e.g., Inconel, Rene, Hastelloy, Haynes ) F °

1,500 • Note: ( Tmax )Steel • γ = 1.4 • T = Recovery Temperature, R • ( Tmax )Ti Alloy r • T = Free stream temperature, R 1,000 • 0 • • T = Max temperature capability ( Tmax )Graphite Polyimide max • No external insulation assumed , Recovery Temperature, , Recovery Temperature, r • • r is recovery factor

T • 500 • ( Tmax )Al Alloy • h = 40k ft ( TFree Stream = 390 R ) ( Tmax )Graphite Epoxy • Stagnation r = 1 • Turbulent boundary layer r = 0.9 • Laminar boundary layer r = 0.8 • Short-duration flight ( less than 0 30 m ), but with thermal soak 0234561 M, Mach Number 2/24/2008 ELF 149 StructureStructure // InsulationInsulation TradesTrades forfor ShortShort DurationDuration FlightFlight

Example Structure / Insulation Concepts Mach Tmax kc ρα Increasing

Hot Metal Structure ( e.g., Al ) without Insulation 600 0.027 0.22 0.101 0.000722

Hot Metal Structure ( e.g., Al ) 600 0.027 0.22 0.101 0.000722 Internal Insulation ( e.g., Min-K ) 2000 0.0000051 0.24 0.012 0.00000106

Self-insulating Composite Structure ( e.g., Graphite Polyimide ) 1100 0.000109 0.27 0.057 0.00000410

Ext Insulation ( e.g., Micro-Quartz Paint ) 1200 0.0000131 0.28 0.012 0.00000226 Cold Metal Structure ( e.g., Al ) 600 0.027 0.22 0.101 0.000722 Internal Insulation ( e.g., Min-K ) 2000 0.0000051 0.24 0.012 0.00000106

Note: • Tactical missiles use passive thermal protection ( no active cooling ) • Small thickness allows more propellant / fuel for diameter constrained missiles ( e.g., VLS launcher ) • Weight and cost are application specific 2 • Tmax = max temp capability, ° F; k = thermal conductivity, BTU / s / ft / ° F / ft; c = specific heat or thermal capacity, BTU / lbm / ° F; ρ = density, lbm / in3; α = thermal diffusivity = k / ( ρ c ), ft2 / s

2/24/2008 ELF 150 ExternalExternal InsulationInsulation HasHas HighHigh PayoffPayoff forfor ShortShort DurationDuration FlightFlight

1,000 Example Airframe Temperature with No External Insulator – Steel Airframe Selected. 900 4.0 800 Mach 700 3.0 600 Mach 500 Number 400 2.0

Example Temperature ° F 300 Example Airframe Temperature with 0.012 in Insulator – Aluminum Airframe Acceptable for Short Duration. 200 1.0 Note: Short Range Air-to-Air Missile 100 Launch ~ 0.9 Mach at 10k ft Altitude Atmosphere ~ Hot Day ( 1% Risk ) Mil-HDBK-310 0 0 2 4 6 8 101214 Time After Launch ~ s

2/24/2008 ELF 151 PhPhenolicenolic C Compositesomposites AArere GGoodood IInsulatorsnsulators fforor HighHigh TemperatureTemperature StructureStructure andand PropulsionPropulsion

6,000 Graphites • Burn • ρ ~ 0.08 lb / in3 Medium Density Phenolic • Carbon / Carbon Composites • Char 5,000 3 Bulk Ceramics • ρ ~ 0.06 lb / in • Melt • Nylon Phenolic, Silica • ρ ~ 0.20 lb / in3 Phenolic, Glass 4,000 • Zirconium Ceramic, Phenolic, Carbon Hafnium Ceramic Phenolic, Graphite Tmax, Max Porous Ceramics Phenolic • Melt Temperature 3,000 • Resin Impregnated Low Density Capability, • ρ ~ 0.12 lb / in3 Composites • Carbon-Silicon • Char R Carbide • ρ ~ 0.03 lb / in3 2,000 • Micro-Quartz Plastics Paint, Glass- Cork-Epoxy, • Sublime Silicone Rubber • Depolymerizing 1,000 • ρ ~ 0.06 lb / in3 • Teflon 0 01234 Insulation Efficiency, Minutes To Reach 300° F at Back Wall Note: Assumed Weight Per Unit Area of Insulator / Ablator = 1 lb / ft2 2/24/2008 ELF 152 AA ““ThermallyThermally ThiThin”n” S Surfaceurface (( e.g.,e.g., MMetaletal AirframeAirframe )) HasHas UniformUniform InternalInternal TemperatureTemperature Example for Rocket Baseline Airframe: ( dT / dt )t = 0 = ( Tr -Tinitial ) h / ( c ρ z) x = 1.6 ft – h t / ( c ρ z ) Aluminum skin w/o external insulation T = Tr –( Tr –Tinitial ) e c = 0.215 BTU / lb / R, ρ = 0.10 lb / in3 = 172.8 lb / ft3, 1000 h = k NNU / x z = 0.16 in = 0.0133 ft, k = 0.027 BTU / s / ft2 / R / ft

Thermally thin ⇒ h ( z / k )surface < 0.1 Assume Mach 2 sustain flight, 20k ft altitude ( T0 = 447 R , k = 3.31 x 10-6 BTU / s / ft2 / R / ft ), Turbulent boundary layer, x = 1.6 ft 100 6 Rex = ρ0 M a0 x / μ0 = 12.56 x 10 0.8 NNU = 0.0271 Re = 12947 h = k N / x = 0.0268 BTU / s / ft2 / R 10 NU Test: h ( z / k )surface = 0.0132 < 0.1 ⇒ thermally thin 2 Rocket Baseline, Deg F / sec Calculate Tr = T0 [ 1 + 0.2 r M ] = 447 [ 1 + 0.2 ( 0.9 ) ( 2 )2 ] = 769 R

dT / dt, Initial Skin Temperature Rate for 1 At t = 0, Assume T = 460 R, or 0° F 0123456 initial ( dT / dt )t = 0 = ( 769 - 460 ) ( 0.0268 ) / [( 0.215 ) M, Mach Number (172.8 ) ( 0.01333 )] = 17°F / s h = sea level h = 20K ft h = 50K ft h = 80K ft At a sustain time t = 10 s, T = 769 - ( 769 – 460 ) e – 0.0268 ( 10 ) / [ 0.215 ( 172.8 ) ( 0.0133 )] = 589 R, or 129° F Note: No external insulation; thermally thin structure ( uniform internal temperature ); “Perfect” insulation behind airframe; 1-D heat transfer; Turbulent boundary layer; Radiation neglected; dT / dt = Temperature rate, R / s; Tr = Recovery ( max ) temperature, R; h = Convection heat transfer coefficient, BTU / s / ft2 / R; c = Specific heat, BTU / lb / R; ρ = Density, lb / ft3; z = 2 Thickness, ft; k = Conductivity, BTU / s / ft / R / ft; Re = Reynolds number; NNU = Nusselt number Reference: Jerger, J.J., Systems Preliminary Design Principles of Guided Missile Design, D. Van Nostrand Company, Inc., Princeton, New Jersey, 1960 2/24/2008 ELF 153 AA “Thermally“Thermally Thick”Thick” Surface Surface (( e.g.,e.g., RadomeRadome )) HasHas aa LargeLarge InternalInternal TemperatureTemperature GradientGradient 1/2 ( h z / k ) + h2 α t / k2 1/2 1/2 [ T ( z, t ) - Tinitial ] / [ Tr –Tinitial ] = erfc { z / [ 2 ( α t ) ]} – e erfc { z / [ 2 ( α t ) ] + h ( α t ) / k } h2 α t / k2 1/2 [ T ( 0, t ) - Tinitial ] / [ Tr –Tinitial ] = 1 - e erfc [ h ( α t ) / k ] Applicable for thermally thick surface: z / [ 2 ( α t )1/2 ] > 1 1 Example: Rocket Baseline Radome ] X = 1.6 ft z = 0.25 in = 0.0208 ft, k = 5.96 x 10-4 BTU / s / ft / R, initial 0 = α = 1.499 x 10-5 ft2 / s k .1 / 0 –( T ) T –( z =

r h k Mach 2, 20k ft alt ( T0 = 447 R ), Turbulent boundary layer, / z x = 19.2 in = 1.6 ft, t = 10 s, Tr = 769 R, Tinitial = 460 R h 0 1 1/2 ] / [( T ) 1 k ⇒ h = 0.0268 BTU / s / ft ⇒ ( h / k )( α t ) = 0.491 = /

0.5 k z 0 0 1/2 -5 1/2 initial / h 1 Test: z / [ 2 ( α t ) ] = 0.0208 / { 2 [ 1.499x10 ( 10 )] } = z = h 0.849 < 1 ⇒ not quite thermally thick k

z Inner wall ⇒ h z / k = 0.935 h [ T ( 0.0208, 10 ) - Tinitial ] / [ Tr –Tinitial ] = 0.0608 [ T ( z, t ) - ( T ) T ( 0.0208, 10 ) = 479 R ( Note: Tinner ≈ Tinitial )

0 Surface ⇒ h z / k = 0 0.1 1 10 100 [ T ( 0, 10 ) - T ] / [ T –T ] = 0.372 ( h / k )( α t )1/2 initial r initial T ( 0, 10 ) = 575 R

Note: T ( z,t ) ∼ ( T )initial; 1-D heat transfer; Radiation neglected; Turbulent boundary layer; Tr = Recovery temperature, R; h = Heat transfer coefficient, BTU / ft2 / s / R; k = Thermal conductivity of material, BTU / s / ft2 / R / ft; α = Diffusivity of material, 2 ft / s; zmax = Thickness of material, ft; erfc = Complementary error function Reference: Jerger, J.J., Systems Preliminary Design Principles of Guided Missile Design, D. Van Nostrand Company, Inc., Princeton, New Jersey, 1960 2/24/2008 ELF 154 InternalInternal InsulationInsulation TemperatureTemperature CanCan BeBe PredictedPredicted AssumingAssuming ConstantConstant FluxFlux ConductionConduction -z2 / ( 4 α t ) 1 / 2 1/2 [ T ( z, t ) – Tinitial ] / [ T ( 0, t ) – Tinitial ] = e –( π / α t ) ( z / 2 ) erfc { z / [ 2 ( α t ) ]} Applicable for thermally thick surface: z / [ 2 ( α t )1/2 ] > 1 Example for Rocket Baseline Airframe Insulation: 1 0.10 in Min-K Internal Insulation behind 0.16 in aluminum Skin Aluminum 0.16 in ] X = 1.6 ft 0.10 in initial z Min-K

Assume M = 2, 20k ft alt, x = 1.6 ft, Tinitial = 460 R, t = 10 s, 2 zMin-K = 0.10 in = 0.00833 ft, αMin-K = 0.00000106 ft / s, k = 5.96 x 10-4 BTU / s / ft, h = 0.0268 BTU / s / ft 0.5 Test: z / [ 2 ( α t )1/2 ] = 0.00833 / {2 [ 0.00000106 ( 10 )]1/2} = ] / [ T ( 0, t ) – T 1.279 > 1 ⇒ thermally thick

initial ( α t )1/2 / z = [ 0.00000106 ( 10 ) ]1/2 / 0.00833 = 0.3907

[ TMin-K ( 0.0217, 10 ) – 460 ] / [ TMin-K ( 0, 10 ) – 460 ] = 0.0359

Assume ( Tinner )aluminum = ( Touter )Min-K [ T ( z, t ) – T From prior example, ( Tinner )aluminum = 569 R at = 10 s Then, ( T ) = 569 R at t = 10 s 0 outer Min-K 0.1 1 10 100 Compute, ( Tinner )Min-K = 460 + ( 569 – 460 ) 0.0338 = 460 + 4 ( α t )1/2 / z = 464 R Note: 1-D conduction heat transfer, Radiation neglected, Constant heat flux input, T ( z,t ) = Inner temperature of insulation at time t, Tinitial = Initial temperature, T ( 0, t ) = Outer temperature of insulation at time t, α = Diffusivity of insulation material, 2 ft / s; zmax = Thickness of insulation material, ft; erfc = Complementary error function Reference: Carslaw, H. S. and Jaeger, J. C., Conduction of Heat in Solids, Clarendon Press, 1989 2/24/2008 ELF 155 AA SharpSharp NoseNose TipTip // LeadingLeading EdgeEdge HasHas HighHigh AerodynamicAerodynamic HeatingHeating h = N k / d r NUr r NoseTip Example for Rocket Baseline Nose Tip: 0.6 0.5 0.4 NNUr = 1.321 RedNoseTip Pr Assume M = 2, 20k ft alt, stagnation ( Tr = 805 R ) for a sharp nose tip ( e.g., 1% blunt ) 0.5

dNoseTip / dRef = 0.01 ⇒ dNoseTip = 0.01 ( 8 0.4 in ) = 0.08 in = 0.00557 ft 4 0.3 RedNoseTip = ρ0 V0 dNoseTip / μr = 3.39 x 10 N = 223 0.2 NUr 2 hr = 0.1745 BTU / ft / s / R 0.1 Outer surface temperature after 10 s heating

hr, Stagnation Heat Transfer Coeff for in sustain flight ( M = const, Tr = const ):

Rocket Baseline at h = 20k ft, BTU / ft2 / s / R 0 h2αt / k2 [ T ( 0, t ) - Tinitial ] / [ Tr –Tinitial ] = 1 – e 0123456erfc { h ( α t )1/2 / k } M, Mach Number [ T ( 0, 10 ) - 460 ] / [ 805 – 460 ] = 1 – e [( 0.1745 )2 ( 1.499 x 10-5 ) ( 10 ) / ( 5.96 x 10-4 )2 ] erfc { ( 0.1745 ) [ 1% Bluntness 2% Bluntness 1.499 x 10-5 ( 10 )]1/2 / ( 5.96 x 10-4 )]} = 0.845 5% Bluntness 10% Bluntness T ( 0, 10 ) = 460 + 345 ( 0.845 ) = 752 R

Note: 1-D conduction heat transfer; Laminar boundary layer; Stagnation heating; Radiation neglected; hr = Convection heat transfer coefficient for stagnation recovery, BTU / s / ft2 / R; N = Nusselt number for stagnation recovery; k = NUr r Air thermal conductivity at stagnation recovery ( total ) temperature, BTU / s / ft / R; dNoseTip = Nose tip diameter, ft; RedNoseTip = Reynolds number based on nose tip diameter, Pr = Prandtl number Reference: Allen, J. and Eggers, A. J., “A Study of the Motion and Aerodynamic Heating of Ballistic Missiles Entering the Earth’s Atmosphere at High Supersonic Speeds”, NACA Report 1381, April 1953. 2/24/2008 ELF 156 TacticalTactical MissileMissile RadiationRadiation HeatHeat LossLoss IsIs UsuallyUsually SmallSmall ComparedCompared toto ConvectiveConvective HeatHeat InputInput

-13 4 QRad = 4.76 x 10 ε T 100 2 QRad in BTU / ft / s, T in R Example: Ramjet Baseline Assume: 10 •Titanium skin with emissivity ε = 0.3 Radiation Heat •Long duration ( equilibrium ) Flux at heating at Mach 4 Equilibrium 1 •h = 80k ft, T0 = 398 R Temperature, •Turbulent boundary layer ( r = BTU / ft2 / s 2 0.9 ) ⇒ T = Tr = T0 ( 1 + 0.2 r M ) = 1513 R 0.1 Calculate: -13 4 QRad = 4.76 x 10 ( 0.3 ) ( 1513 ) = 0.748 BTU / ft2 / s 0.01 0123456 Cruise Mach Number

Emissivity = 0.1 Emissivity = 1

2/24/2008 ELF 157 DesignDesign CConcernsoncerns fforor LocalizedLocalized AerodynamicAerodynamic HeatingHeating andand ThermalThermal StressStress

Flare / Wedge Corner Flow Shock wave – boundary layer Body Joints interaction Hot missile shell Separated Flow Cold frames or bulkheads High heating at reattachment Causes premature buckling

Leading Edges IR Domes / RF Radomes Hot stagnation temperature on leading edge Large temp gradients due to low thermal conduction Small radius prevents use of external insulation Thermal stress at attachment Cold heat sink material as chord increases in thickness Low tensile strength leads to leading edge warp Dome fails in tension Shock wave interaction with adjacent body structure

Note: σTS = Thermal stress from restraint in compression or tension = α E ΔT

α = coefficient of thermal expansion, E = modulus of elasticity, ΔT = T2 –T1 = temperature difference. Example: Thermal Stress for Rocket Baseline Pyroceram Dome, α = 3 x 10-6, E = 13.3 x 106 psi

Assume M = 2, h = 20k ft alt, t = 10 s. Based on prior figure, ΔT = TOuterWall –TInnerWall = 102 R -6 6 Then σTS = 3 x 10 ( 13.3 x 10 ) ( 102 ) = 4,070 psi 2/24/2008 ELF 158 ExamplesExamples ofof AerodynamicAerodynamic HotHot SpotsSpots

Nose Tip

Leading Edge

Flare

2/24/2008 ELF 159 TacticalTactical MissileMissile BodyBody StructureStructure WeightWeight IsIs aboutabout 22%22% ofof thethe LaunchLaunch WeightWeight

WBS / WL ≈ 0.22 1000 Hellfire ( 0.22 ) Sidewinder ( 0.23 ) Sparrow ( 0.18 ) Phoenix ( 0.19 ) 100 Harpoon ( 0.29 ) Example for 500 lb missile SM 2 ( 0.20 )

WL = 500 lb SRAM ( 0.21 )

WBS = 0.22 ( 500 ) = 110 lb ASALM ( 0.13 )

WBS,Body Structure Weight, lb Weight, Structure WBS,Body SETE ( 0.267 ) 10 Tomahawk ( 0.24 ) 100 1000 10000 TALOS ( 0.28 ) WL, Launch Weight, lb

Note: WBS includes all load carrying body structure. If motor case, engine, or warhead case carry external loads then they are included in WBS. WBS does not include tail, wing, or other surface weight. 2/24/2008 ELF 160 BodyBody SStructuretructure ThicknessThickness IsIs BasedBased onon ConsideringConsidering ManyMany DesignDesign ConditionsConditions

Structure Design Conditions That May Drive Airframe Thickness Manufacturing Transportation Carriage Launch Fly-out Maneuvering Contributors to Required Thickness for Cylindrical Body Structure 0.4 Minimum Gage for Manufacturing: t = 0.7 d [( pext / E ) l / d ] . t ≈ 0.06 in if pext ≈ 10 psi Localized Buckling in Bending: t = 2.9 r σ / E Localized Buckling in Axial Compression: t = 4.0 r σ / E Thrust Force: t = T / ( 2 πσr ) Bending Moment: t = M / ( πσr2 ) Internal Pressure: t = p r / σ High Risk ( 1 ), Moderate Risk ( 2 ), and Low Risk ( 3 ) Estimates of Required Thickness

1. t = FOS x Max ( tMinGage , tBuckling,Bending , tBuckling,AxialCompression , tAxialLoad , tBending , tInternalPressure ) 2 2 2 2 2 2 1/2 2. t = FOS x ( t MinGage + t Buckling,Bending + t Buckling,AxialCompression + t AxialLoad + t Bending + t InternalPressure )

3. t = FOS x ( tMinGage + tBuckling,Bending + tBuckling,AxialCompression + tAxialLoad + tBending + tInternalPressure ) 2/24/2008 ELF 161 LocalizedLocalized BucklingBuckling MayMay BeBe AA CConcernoncern ffoorr ThinThin WallWall StructureStructure t r σBuckling,Bending / E ≈ 0.35 ( t / r ) Bending σ / E ≈ 0.25 ( t / r ) Buckling,AaxialCcompression Axial Compression Note: Thin wall cylinder with local buckling 0.1 σBuckling / E = Nondimensional buckling stress

σBucklingBending = Buckling stress in bending σ = Buckling stress in axial 0.01 BucklingAxialCompression compression E = Young’s modulus of elasticity t = Airframe thickness 0.001 r = Airframe radius Min thickness for fab and handling ≈ 0.06 in 0.0001 Example for Rocket Baseline in Bending: Nondimensional Buckling Stress 6 0.001 0.01 0.1 4130 steel motor case, E = 29.5 x 10 psi σ = 170,000 psi t / r, thickness / radius yield t = 0.074 in, r = 4 in t / r = 0.0185 Note: Actual buckling stress can vary +/- 50%, depending upon typical σ / E ≈ 0.35 ( 0.0185 ) = 0.006475 imperfections in geometry and the loading. Buckling,Bending σbuckling,Bending ≈ 191,000 psi σbuckling,Bending ~ σyield 2/24/2008 ELF 162 ProcessProcess forfor CaptiveCaptive andand FreeFree FlightFlight LoadsLoads CalculationCalculation Captive Flight

Free Flight Max Aircraft Maneuver Per MIL-A-8591

Maneuver Per Carriage Load Design Requirements

Weight load of bulkhead Weight load section of bulkhead Air Load section

Note: MIL-A-8591 Procedure A assumes max air Air Load loads combine with max g forces regardless of Obtained Air Load angle of attack. By Wind

Tunnel Example of αmax Calculated by MIL-A-8591 Using Procedure A for F-18 Aircraft Carriage: α = 1.5 n W / ( C q S ) max z,max max Lα Ref aircraft αmax = 1.5 ( 5 ) ( 49200 ) / [ 0.05 ( 1481 ) ( 400 )] = 12.5 deg

2/24/2008 ELF 163 MaximumMaximum BendingBending MomentMoment DependsDepends UponUpon LoadLoad DistributionDistribution Example for Rocket Baseline: c = 4, ejection load MB = N l / c l = 144 in ⇒ C = 8 for uniform loading N = 10,000 lb ( 20 g ) w = load per unit length

⇒ MB = 360,000 in-lb 0 l = length Total Coefficient C Length l Max Bending C = 7.8 for linear loading Load 100,000 8 Moment M 7.8 B w N 6 50,000 100 40,000 4 30,000 200 0l 300 20,000 400 500 C = 6 for linear loading to center 10,000 1 1,000 w 2,000 5,000 3,000 4,000 4,000 0l 3,000 5,000 C = 4 for load at center ( e.g., ejection load ) 2,000 10,000 N = Normal Force 20,000 1,000 30,000 40,000 l / 2 50,000 500 400 10 100,000 0 l 300 200,000 300,000 C = 1 for load at end ( e.g., control force ) 200 400,000 500,000 N = Normal Force 100 100 1,000,000 l 4 1 3 200 2,000,000 0 l 2 5 2/24/2008 ELF 164 BendingBending MomentMoment MayMay DriveDrive BodyBody StructureStructure WeightWeight

t t r A = 2 π r t I = I = π r3 t MB z Y

2 Note / Assumptions: t = MB ( FOS ) / [ π r σMax ] Thin cylinder Circular cross section Example for Rocket Baseline: Solid skin • Body has circular cross section Longitudinal strength • 2219-T81 aluminum skin ( σult = 65,000 psi ) Axial load stress and thermal • r = 4 in stress assumed small compared • Ejection load = 10,000 lb ( 20 g ) to bending moment stress 3 σ = MB r / IZ = MB r / (π r t ) • MB = 360,000 in ⋅ lb = M / (π r2 t ) • FOS = 1.5 B • t = 360,000 ( 1.5 ) / [ π ( 4 )2 ( 65,000 )] = 0.16 in

2/24/2008 ELF 165 TacticalTactical MissileMissile PropellantPropellant WeightWeight IsIs aboutabout 7272%% ofof RocketRocket MotorMotor WeightWeight

WP / WM ≈ 0.72 10000

b Hellfire ( 0.69 ) Sidewinder ( 0.61 ) 1000 Sparrow ( 0.64 ) Phoenix ( 0.83 ) ASALM ( 0.86 ) SM-2 ( 0.76 ) 100 Example for Rocket Baseline SRAM ( 0.71 ) W = 209 lb WP, Propellant Weight, l Weight, Propellant WP, M TALOS ( 0.66 ) WP = 0.72 ( 209 ) = 150 lb Increased propellant fraction if: 10 High volumetric loading Composite case 10 100 1000 10000 Low chamber pressure

WM, Total Motor Weight, lb Low flight loads

Short burn time Note: WM includes propellant, motor case, nozzle, and insulation. 2/24/2008 ELF 166 MotorMotor CaseCase WeightWeight IsIs UsuallyUsually DrivenDriven ByBy StressStress fromfrom InternalInternal PressurePressure

Assume motor case is axisymmetric, with a front ellipsoid dome and an aft cylinder body

Motor Case π/2 Cylinder σt t = - 0∫ p r sinθ dθ Hoop p p ( σ ) = p r / t Stress t Hoop Stress

Case Dome Nozzle b Motor Dome ( σt )Longitudinal Stress 2 1/2 Ellipsoid = [ 2 + ( a / b ) ] p ( a b ) / ( 6 t ) 2 a Longitudinal If a = b ( hemi dome of radius r ), Stress Case Cylinder then ( σt )Longitudinal Stress = p r / ( 2 t ) With metals – the material also reacts body bending In composite motor designs, extra ( longitudinal ) fibers must usually be added to accommodate body bending

2/24/2008 ELF 167 AA CompositeComposite MotorMotor CaseCase IsIs UsuallyUsually LighterLighter WeightWeight

Calculate Maximum Effective Operating Pressure ( Burst Pressure )

πk Δ T pburst = pBoost, Room Temp x e x ( Design Margin for Ignition Spikes, Welds, Other Design Uncertainty )

Assume Rocket Motor Baseline: diameter = 8 in., length = 55 in, ellipsoid dome a / b = 2, pBoost,RoomTemp = 1769 psi, πk = ( Δp / ΔT ) / pc = 0.14% / °F Assume Hot day T = 160° F ⇒ eπk ΔT = e0.0014 ( 160 - 70 ) = 1.134. Uncertainty factor is 1.134, 1σ 3 Assume a 3σ uncertainty design margin is provided by, pburst ≈ 1769 x ( 1.134 ) = 2,582 psi Assume Ultimate Factor of Safety FOS = 1.5

Rocket Baseline Steel Case ( σt )ult = 190,000 psi

tHoop = ( FOS ) x pburst x r / σt = 1.5 x 2582 x 4.0 / 190,000 = 0.082 in 1/2 2 1/2 2 tDome = ( FOS ) x pburst x ( a b ) x [ 2 + ( a / b ) ] / ( 6 σt ) = 1.5 x 2582 x [ 4 x 2 ] x [ 2 + ( 2 ) ] / [ 6 x 190,000 ] = 0.058 in

Weight = WCylinder + WDome = ρπd tHoop l+ ρ ( 2 π a b ) tDome = 30.8 + 0.8 = 31.6 lb for steel case

Try Graphite Fiber at σt = 450,000 psi Ultimate, Assume 60% Fiber / 40% Epoxy Composite

tHoop = 1.5 x 2582 x 4.0 / [ 450,000 ( 0.60 )] = 0.057 in radial fibers for internal pressure load

tDome = 0.041 in, for internal pressure load Weight = 11.1 lb for composite case ( w/o insulation, attachment, aft dome, and body bending fiber ) Must also add about 0.015 in of either longitudinal fibers or helical wind to counteract body bending load 2/24/2008 ELF 168 AA LowLow AspectAspect RatioRatio DeltaDelta WingWing AllowsAllows LighterLighter WeightWeight StructureStructure 1/2 1/2 1/2 WSurface σmax / [ ρ S Nmax ] = [ A ( 1 + 2 λ )] Note: W = ρ S t Surface is 2 panels ( Cruciform wing has 4 panels ) 3 Surface mac 1/2 WSurface = Surface weight sized by bending moment troot = [ FOS Nmax A ( 1 + 2 λ ) / σmax,] ρ = Density Assumption: Uniform loading σmax = Maximum allowable ( ultimate ) stress

tmac = Thickness of mean aero chord cmac 2 troot = Thickness of root chord croot

), Non-dimensional Weight ), Non-dimensional Weight Nmax = Maximum load

1/2 A = Aspect ratio max λ = Taper ratio S N ρ 1 Example for Rocket Baseline Wing ( 2219-T81 / ( Aluminum ): A = 2.82, λ = 0.175, c = 19.4 in, σ = 1/2 r max σ = 65k psi max ult σ Assume M = 2, h = 20k ft, α + δ = 22 deg

Surface From prior example, Nmax = 7525 lb W 0 Calculate troot = [ 1.5 ( 7525 ) ( 2.82 ) [ 1 + 2 ( 0.175 ) / 012365000 ]1/2 = 0.813 in A, Aspect Ratio troot / croot = 0.813 / 19.4 = 0.0419 = tmac / cmac t = 0.0419 ( 13.3 ) = 0.557 in Taper Ratio = 0 Taper ratio = 0.5 Taper Ratio = 1 mac 1/2 1/2 1/2 Wwing σmax / [ ρ S Nmax ] = [ A ( 1 + 2 λ )] .= 1.95

Wwing = 20.6 lb for 1 wing ( 2 panels ) 2/24/2008 ELF 169 DDomeome MMaterialaterial IIss DDrivenriven bbyy tthehe TTypeype ooff SSeekereeker andand FlightFlight EnvironmentEnvironment

Seeker Density Dielectric MWIR / Transverse Thermal Erosion, Max Short- Dome ( g / cm3 ) Constant LWIR Strength Expansion Knoop ( kg Duration Material Bandpass ( 103 psi ) ( 10-6 / ο F ) / mm2 ) Temp ( ο F )

RF-IR Seeker Zinc Sulfide 4.05 8.4 18 4 350 700 ( ZnS ) Zinc Selenide 5.16 9.0 8 4 150 600 ( ZnSe ) Sapphire / 3.68 8.5 - 28 3 1650 1800 Spinel Quartz / Fused 2.20 3.7 - 8 0.3 600 2000 Silica ( SiO2 ) Silicon Nitride 3.18 6.1 - 90 2 2200 2700 ( Si3N4 ) Diamond ( C ) 3.52 5.6 - 400 1 8800 3500 RF Seeker Pyroceram 2.55 5.8 - 25 3 700 2200 Polyimide 1.54 3.2 - 17 40 70 400 IR Seeker Mag. Fluoride 3.18 5.5 7 6 420 1000 ( MgF2 ) Alon 3.67 9.3 - 44 3 1900 1800 ( Al23O27N5 ) Germanium 5.33 - 16.2 15 4 780 200 ( Ge )

Superior Above Average Average Below Average - Poor 2/24/2008 ELF 170 RadomeRadome Weight Weight MayMay BeBe DrivenDriven byby OptimumOptimum ThicknessThickness RequiredRequired forfor EfficientEfficient TransmissionTransmission

WOptTrans = ρ Swet tOptTrans Note: 1 2 1/2 W = Weight at Optimum Transmission tOptTrans = 0.5 n λ0 / ( ε -sin θi ) OptTrans ρ = Density 90 deg θi S = Surface wetted area δ wet θ t = Optimum thickness for 100% transmission d OptTrans n = Integer ( 1, 2, … ) l λ0 = Wavelength in air ε = Dielectric constant

θi = Radar signal incidence angle = 90 deg - δ - θ θ = Surface local angle ), Non-dimensional Optimum Thickness ), Non-dimensional

0 δ = Seeker look angle λ Example for Rocket Baseline Pyroceram Radome: / ( N 3 opt

t 0.1 ε = 5.8, ρ = 0.092 lb / in , λ0 = 1.1 in, n = 1, tangent ogive, l = 19.2 in, d = 8 in, S = 326 in2 110ε, Dielectric Constant wet δ = 0 deg ⇒ ( θ ) ≈ 90 – 0 - 11.8 = 78.2 deg Incidence Angle = 0 deg Incidence Angle = 40 deg I avg 1/2 Incidence Angle = 80 deg tOptYtans = 0.5 ( 1 ) ( 1.1 ) / ( 5.8 – 0.96 ) = 0.25 in

WOptTrans = 0.092 ( 326 ) ( 0.25 ) = 7.5 lb

2/24/2008 ELF 171 MissileMissile ElectricalElectrical PowerPower SupplySupply AlternativesAlternatives

W = WE E + WP P Measure of Merit Power Supply Generator Lithium Battery Thermal Battery Storage Life Cost

WE, Weight / 0.0007 0.0012 0.0125 Energy ( kg / kW-s )

WP, Weight / Power 1.4 1.5 0.3 ( kg / kW ) Voltage Stability Superior Above Average Average Below Average

Example for Thermal battery: If E = 900 kW–s, P = 3 kW ⇒ W = WEE + WPP = 0.0125 ( 900 ) + 0.3 ( 3 ) = 12.2 kg Note: Generator provides highest energy with light weight for long time of flight ( e.g., cruise missile ). Lithium battery provides nearly constant voltage suitable for electronics. Relatively high energy with light weight. Thermal battery provides highest power with light weight ( may be required for actuators ).

2/24/2008 ELF 172 ElectromechanicalElectromechanical ActuatorsActuators AreAre LightLight WeightWeight andand ReliableReliable

W = WT TS Measure of Merit EM Cold Gas Pneumatic Hydraulic

WT, Weight / Stall Torque ( lb / 0.0025 0.0050 0.0034 in-lb ) Rate ( deg / s ) Up to 800 Up to 600 Up to 1000 Bandwidth ( Hz ) Up to 40 Up to 20 Up to 60 Reliability Cost

Superior Above Average Average Below Average Note: Schematic of Cold Gas Pneumatic Actuation •Actuation system weight based on four actuators. •Cold gas pneumatic actuation weight includes actuators, gas bottle, valves, regulator, and supply lines. •Hydraulic actuation weight includes actuators, gas generator or gas bottle, hydraulic reservoir, valves, and supply lines. •Stall torque ≈ 1.5 maximum hinge moment of single panel. Example weight for rocket baseline hydraulic actuation at Mach 2, 20k ft alt, α = 9 deg, with max control deflection of wing ( δ

= 13 deg ) ⇒ Hinge moment of one panel = 11,500 in-lb. TS = 1.5 ( 11500 ) = 17,250 in-lb ⇒ W = WTTS = 0.0034 ( 17250 ) = 59 lb 2/24/2008 ELF 173 ExamplesExamples ooff ElectromechanicalElectromechanical ActuatorActuator PackagingPackaging

Canard ( Stinger ) ……………

Tail ( AMRAAM ) …………………………………………………………………

Jet Vane / Tail ( Javelin ) ……

Movable Nozzle ( THAAD ) ……………………………………………………………

2/24/2008 ELF 174 SummarySummary ofof WeightWeight

Conceptual Design Weight Prediction Methods and Weight Considerations Missile system weight, cg, moment of inertia Factors of safety Aerodynamic heating Structure Dome Propulsion Insulation Power supply Actuator Manufacturing Processes for Low Parts Count, Low Cost Precision castings Vacuum assisted RTM Pultrusion / Extrusion Filament winding 2/24/2008 ELF 175 SummarySummary ofof WeightWeight (( contcont ))

Design Considerations Airframe materials Insulation materials Seeker dome materials Thermal stress Aerodynamic heating Technologies MEMS Composites Titanium alloys High density insulation High energy and power density power supply High torque density actuators Discussion / Questions? Classroom Exercise ( Appendix A )

2/24/2008 ELF 176 WeightWeight ProblemsProblems

1. Propulsion system and structure weight are driven by f_____ o_ s_____ requirements. 2. For a ballistic range greater than about 200 nautical miles, a t__ s____ missile is lighter weight. 3. Tactical missile weight is proportional to v_____. 4. Subsystem d______for tactical missiles is about 0.05 lb / in3 5. Modeling weight, balance, and moment-of-inertia is based on a build-up of s______. 6. Missile structure factor of safety for free flight is usually about 1.25 for ultimate loads and about 1.10 for y____ loads. 7. Manufacturing processes that can allow low parts count include vacuum assisted resin transfer molding of composites and c______of metals. 8. Low cost airframe materials are usually based on aluminum and steel while light weight airframe materials are usually based c______materials. 9. Graphite fiber has high strength and high m______o_ e______.

2/24/2008 ELF 177 WeightWeight ProblemsProblems (( contcont ))

10. The recovery factors of stagnation, turbulent boundary layer, and laminar boundary layer are 1.0, 0.9, and ___ respectively. 11. The most popular types of insulation for temperatures greater than 4,000 R are charring insulators based on p______composites. 12. Tactical missiles experience transient heating, and with increasing time the temperature approaches the r______temperature. 13. The inner wall temperature is nearly the same as the surface temperature for a t______t___ structure. 14. A thermally thick surface is a good i______. 15. A low conductivity structure is susceptible to thermal s_____. 16. The minimum gauge thickness is often set by the m______process. 17. A very thin wall structure is susceptible to localized b______. 18. Ejection loads and flight control loads often result in large b______moment. 19. An approach to increase the tactical missile propellant / motor weight fraction over the typical value of 72% would be c______motor case. 2/24/2008 ELF 178 WeightWeight ProblemsProblems (( contcont ))

20. The required rocket motor case thickness is often driven by the combustion chamber p______. 21. A low aspect ratio delta wing has reduced w_____. 22. For low speed missiles, a popular infrared dome material is z___ s______. 23. A thermal battery provides high p____. 24. The most popular type of actuator for tactical missiles is an e______actuator.

2/24/2008 ELF 179 OutlineOutline

Define Mission Requirements Alt Mission Establish Baseline Alt Baseline Aerodynamics

Propulsion

Weight Resize / Alt Config / Subsystems / Tech

Trajectory

Meet No Performance?

Yes No Measures of Merit and Constraints

Yes

2/24/2008 ELF 181 Flight Envelope Should Have Large Max Range, Small Min Range, and Large Off Boresight

Off Boresight Flyout Envelope / Range •Max •Min

Forward Flyout Envelope / Range Examples of Max / Min Range Limitations: •Max Fire Control System Range and Off Boresight •Min Seeker Range, Gimbal Angle, and Tracking Rate Maneuver Capability Time of Flight Closing Velocity

2/24/2008 ELF 182 ConceptualConceptual DesignDesign ModelingModeling VersusVersus PreliminaryPreliminary DesignDesign ModelingModeling Conceptual Design Modeling

CDO 1 DOF [ Axial force ( CDO ), thrust, weight ] CN

2 DOF [ Normal force ( CN ), axial force, thrust, weight ] CA C 3 DOF point mass [ 3 aero forces ( normal, axial, side ), N C thrust, weight ] A CY C N C 3 DOF pitching [ 2 aero forces ( normal, axial ), 1 aero m

moment ( pitching ), thrust, weight ] CA C N C C 4 DOF [ 2 aero forces ( normal, axial ), 2 aero moments m l ( pitching, rolling ), thrust, weight ] CA

CN Preliminary Design Modeling Cm Cl C A C 6 DOF [ 3 aero forces ( normal, axial, side ), 3 aero Cn Y moments ( pitching, rolling, yawing ), thrust, weight ] 2/24/2008 ELF 183 1-DOF1-DOF CoastCoast EquationEquation MayMay HaveHave GoodGood AccuracyAccuracy NearNear ZeroZero AngleAngle ofof AttackAttack

2.0

1.5 • • ( V )2-DOF / ( V )1-DOF, Predicted Deceleration 1.0 Comparison for Rocket Baseline 0.5

0 0246810

αTrim, Trim Angle of Attack, Deg Note: . – ( V. )2-DOF = Two-degrees-of-freedom deceleration – ( V )1-DOF = One-degree-of-freedom deceleration – Rocket baseline during coast – Mach 2, h = 20,000 ft

– αTrim ≈ 0.3 deg for 1-g flyout 2/24/2008 ELF 184 33-DOF-DOF SimplifiedSimplified EquationsEquations ofof MotionMotion ShowShow DriversDrivers forfor ConfigurationConfiguration SizingSizing

+ Normal Force + Thrust α << 1 rad V + Moment θ γ

W δ + Axial Force Configuration Sizing Implication .. .. Ι θ ≈Ι α ≈ q S d C α + q S d C δ High Control Effectiveness ⇒ C > y y Ref mα Ref mδ mδ C , I small ( W small ), q large . mα y ( W / g ) V γ ≈ q S C α + q S C δ -W cosγ Large / Fast Heading Change ⇒ C c Ref Nα Ref Nδ N large, W small, q large . ( W / g ) V ≈ T - C S q - C α2 S q - W sin γ High Speed / Long Range ⇒ Total c A Ref Nα Ref Impulse large, CA small, q small

Note: Based on aerodynamic control 2/24/2008 ELF 185 ForFor LongLong RangeRange Cruise,Cruise, MaximizeMaximize VV IIspsp,, LL // D,D, andand WeightWeight FractionFraction ofof FuelFuel // PropellantPropellant

R = ( V Isp ) ( L / D ) ln [ WBC / ( WBC -WP )] , Breguet Range Equation 1.00E+08 Wing ojet with t rb onic Tu ame l Subs ric Airfr Typica symmet 1.00E+07 with Axi Ramjet Typical rame etric Airf Axisymm cket with ypical Ro 1.00E+06 T Example: Ramjet Baseline at Mach 3 / 60k ft alt

R, Cruise Range, f Range, Cruise R, R = 2901 ( 1040 ) ( 3.15 ) ln [ 1739 / ( 1739 - 476 )] = ( 9,503,676 ) ln [ 1 / ( 1 - 0.2737 )] = 3,039,469 ft = 500 nm 1.00E+05 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 WP / WBC, Propellant or Fuel Weight / Weight at Begin of Cruise

( V ISP )( L / D ) = 2,000,000 ft ( V ISP )( L / D ) = 10,000,000 ft ( V ISP )( L / D ) = 25,000,000 ft

Note: R = cruise range, V = cruise velocity, ISP = specific impulse, L = lift, D = drag, WBC = weight at begin of cruise, WP = weight of propellant or fuel 2/24/2008 ELF 186 EfficientEfficient SteadySteady FlightFlight IsIs EnhancedEnhanced byby HighHigh LL // DD andand LightLight WeightWeight Steady Level Flight Steady Climb Steady Descent ( Glide ) D T – D – T T = D L L L γC L = W γD DT T D D V∞ γC V T W C W W V γ ∞ T = W / ( L / D ) VD D SIN γc = ( T – D ) / W = Vc / V∞ V = ( T – D ) V / W Note: c ∞ SIN γD = ( D – T ) / W = VD / V∞ R = Δh / tan γ = Δh ( L / D ) • Small Angle of Attack C C VD = ( D – T ) V∞/ W • Equilibrium Flight RD = Δh / tan γD = Δh ( L / D ) • VC = Velocity of Climb • VD = Velocity of Descent • γC = Flight Path Angle During Climb • γD = Flight Path Angle During Descent • V∞ = Total Velocity • Δh = Incremental Altitude Reference: Chin, S.S., “Missile Configuration Design,” • RC = Horizontal Range in Steady Climb McGraw Hill Book Company, New York, 1961 • RD = Horizontal Range in Steady Dive ( Glide ) 2/24/2008 ELF 187 FlightFlight TrajectoryTrajectory LoftingLofting // ShapingShaping ProvidesProvides ExtendedExtended RangeRange Apogee or Cruise

Climb Altitude Glide

Rapid Pitch Up

Line-Of-Sight Trajectory

RMAX R Range MAX

Lofted Trajectory Design Guidelines for Horizontal Launch: – High thrust-to-weight ≈ 10 for safe separation – Rapid pitch up minimizes time / propellant to reach efficient altitude – Climb at α≈0 deg with thrust-to-weight T / W ≈ 2 and q ≈ 700 psf to minimize drag / propellant

– Apogee at q ≈ 700 psf, followed by either ( L / D )MAX cruise or ( L / D )MAX glide 2/24/2008 ELF 188 SSmallmall TurnTurn RadiusRadius UsingUsing AeroAero CControlontrol RequiresRequires HighHigh AngleAngle ofof AttackAttack andand LowLow AltitudeAltitude FlightFlight . RT = V / γ ≈ 2 W / ( gc CN SRef ρ ) 1000000 Assumption: Horizontal Turn Note for Example Figure: W = Weight = 2,000 lb a / b = 1 ( circular cross section ), No wings 2 CN = sin 2 α cos ( α / 2 ) + 2 ( l / d ) sin α 100000 l / d = Length / Diameter = 10 2 SRef = 2 ft C = 0.2 DO ( L / D )Max = 2.5 q ≈ 700 psf ( L / D )Max α = 15 deg 10000 ( L / D )Max T = 740 lb ( L / D )Max Example: Δα = 10 deg RT, Example Instantaneous Turn Radius, ft Radius, Turn Instantaneous Example RT,

1000 CN = 0.94 0 5 10 15 20 h = 40k ft ( ρ = 0.000585 slug / ft3 )

Delta Alpha, Deg RT = 2 ( 2,000 ) / [( 32.2 ) ( 0.94 ) ( 2 ) ( 0.000585 )] = 112,000 ft h = sea level h = 20k ft h = 40k ft Note: Require ( RT )Missile ≤ ( RT )Target, for h = 60k ft h = 80k ft small miss distance

2/24/2008 ELF 189 HighHigh TurnTurn RateRate UsingUsing AeroAero CControlontrol RequiresRequires HighHigh AngleAngle ofof AttackAttack andand HighHigh VelocityVelocity . γ = gc CN ρ V SRef / ( 2 W ), rad / s Assumption: Horizontal Turn 20 Example for Lifting Body at Altitude h = 20,000 ft: Assume: n = • W = Weight = 2,000 lb 1 0 0 • a / b = 1 ( circular cross section ) 15 g • No wings • Negligible tail lift • Neutral static stability 2 10 CN = sin 2 α cos ( α / 2 ) + 2 ( l / d ) sin α 2 • SRef = 2 ft • l / d = Length / Diameter = 10 • α = 15 deg 5 • V = 2000 ft / s Then:

• N = Normal Force = CN q SRef

Example Gamma Dot, Turn Rate, deg / s / deg Rate, Turn Dot, Gamma Example 2 CN = sin [ 2 ( 15 )] cos ( 15 / 2 ) + 2 ( 10 ) sin ( 15 ) = 0 0.50 + 1.34 = 1.835 0 1000 2000 3000 q = Dynamic Pressure = 0.5 ρ V2 = 0.5 ( 0.001267 ) ( 2 Velocity, ft / s 2000 ) = 2534 psf N = 1.835 ( 2534 ) ( 2 ) = 9,300 lb N / W = 9300 / 2000 = 4.65 g Alpha = 15 deg Alpha = 30 deg . γ = 32.2 ( 1.835 ) ( 0..001267 ) ( 2000 ) ( 2 ) / [ 2 ( 2000 )] Alpha = 90 deg = 0.0749 rad / s = 4.29 deg / s

2/24/2008 ELF 190 ForFor LongLong RangeRange Coast,Coast, MaximizeMaximize InitialInitial VelocityVelocity andand AltitudeAltitude andand MinimizeMinimize DragDrag CoefficientCoefficient V / V = { 1 – [( g sin γ ) / V ] t } / { 1 + {[ g ρ S ( C ) V ] / ( 2 W )} t } i c i c AVG Ref D0 AVG i {[ g ρ S ( C ) ] / ( 2 W )} R = ln { 1 – [ g 2 ρ S ( C ) / ( 2 W )] [ sin γ ] t2 c AVG Ref D0 AVG c AVG Ref D0 AVG + {[ g ρ S ( C ) V ] / ( 2 W )} t } 1 c AVG Ref D0 AVG i V / Vi @ γ = 0 deg Note: Based on 1 DOF coast 0.8 dV / dt = - g C S q / W – g sin γ c D0 Ref c Assumptions: 0.6 • γ = constant 0.4 • α≈0 deg {[ g ρ S (C ) ] / ( 2 W )} R • D > W sin γ 0.2 c AVG Ref D0 AVG @ γ = 0 deg V = velocity during coast

0 Vi = initial velocity ( begin coast ) 00.511.52R = coast range [( g ρ S C V ) / ( 2W )] t, Non-dimensional Coast Time c Ref D0 i Vx = V cos γ, Vy = V sin γ

Example for Rocket Baseline: Rx = R cos γ, Ry = R sin γ •W = W = 367 lb, S = 0.349 ft2, V = 2,151 ft / s, γ = 0 deg, ( C ) = 0.9, h = 20,000 ft ( ρ = 0.00127 slug / ft3 ), t = 10 s BO Ref i D0 AVG •[( g ρ S ( C ) V ) / ( 2 W )] t = {[ 32.2 ( 0.00127 ) ( 0.349 ) ( 0.9 ) ( 2151 )] / [ 2 ( 367 ) ]} 10 = 0.376 c Ref D0 AVG i •V / V = 0.727 ⇒ V = 0.727 x 2151 = 1564 ft / s, {[( g ρ S ( C ) )] / ( 2 W )} R = 0.319 ⇒ R = 18,300 ft or 3.0 nm i c Ref D 0 AVG coast 2/24/2008 ELF 191 ForFor BallisticBallistic Range,Range, MaximizeMaximize InitialInitial Velocity,Velocity, OptimizeOptimize LaunchLaunch Angle,Angle, andand MinimizeMinimize DragDrag V / V = cos γ / { 1 + {[ g ρ S ( C ) V ] / ( 2 W )} t } x i i c AVG Ref D0 AVG i 1.2 ( V + g t ) / V = sin γ / { 1 + {[ g ρ S ( C ) V ] / ( 2 W )} t } y c i i c AVG Ref D0 AVG i 1 {[ g ρ S (C ) ] / ( 2 W cos γ )} R c AVG Ref D0 AVG i x 0.8 = ln { 1 + [ g ( ρ ) S ( C ) V ] / ( 2 W )} t } c AVG Ref D0 AVG i {[ g ρ S (C ) ] / ( 2 W sin γ )} ( h – h + g t2 / 2 ) 0.6 c AVG Ref D0 AVG i i c = ln { 1 + {[ g ρ S ( C ) V ] / ( 2 W ) t } c AVG Ref D0 AVG i 0.4 Assumptions: Thrust = 0, α = 0 deg, D > W sin γ, flat earth 0.2 Nomenclature: V = velocity during ballistic flight, Vi = initial velocity, Rx = horizontal range, h = altitude, hi = initial altitude, 0 Vx = horizontal velocity, Vy = vertical velocity 00.511.52 {[ g ρ S ( C ) V ] / ( 2 W )} t, Non-dimensional Time c AVG Ref D0 AVG i Example for Rocket Baseline:

•W = 367 lb, S = 0.349 ft2, V = V = 2,151 ft / s, γ = 0 deg, ( C ) = 0.9, h = 20,000 ft, ρ = 0.00182 slug / ft3, t = 35 s Ref i BO i D0 AVG i AVG •[ g ρ S ( C ) V / ( 2 W )] t = { 32.2 ( 0.00182 ) ( 0.349 ) ( 0.9 ) ( 2151 ) / [ 2 ( 367 ) ]} 35 = 1.821 c Ref D0 AVG i •V / V = 0.354 ⇒ V = 762 ft / s, ( V + 32.2 t ) / V = 0.354 ⇒ V = - 1127 ft / s, {[ g ρ S ( C )] / ( 2 W cos γ )} R = 1.037 ⇒ x i x y i y c Ref D 0 i x R = 42,900 ft or 7.06 nm, {[ g ρ S ( C ) ] / ( 2 W sin γ )} ( h – h + 16.1 t2 ) = 1.037 ⇒ h = 0 ft x c AVG Ref D 0 AVG i i 2/24/2008 ELF 192 HiHighgh PPropellantropellant WWeight,eight, HiHighgh ThThrust,rust, anandd LLowow DragDrag ProvideProvide HighHigh BurnoutBurnout VelocityVelocity

ΔV / ( gc ISP ) = - [ 1 – ( DAVG / T ) – ( WAVG sin γ / T )] ln ( 1 - Wp / Wi )

0.7 Example for Rocket Baseline: 0.6 Assume γ = 0 deg Assume M = 0.8, h = 20k ft 0.5 i Wi = WL = 500 lb

0.4 For boost, WP = 84.8 lb W / W = 0.1696 0.3 P L I = 250 s 0.2 SP T = 5750 lb

Incremental Velocity Incremental B 0.1 Assume D = DAVG = 635 lb

Delta VDelta / ( g ISP ), Nondimensional 0 DAVG / T = 0.110 0 0.10.20.30.40.5ΔV / [( 32.2 ) ( 250 )] = - ( 1 - 0.110 ) ln ( 1 - 0.1696 ) = 0.1654 Wp / Wi, Propellant Fraction ΔV = ( 0.1654 ) ( 32.2 ) ( 250 ) = 1331 ft / s DAVG / T = 0 DAVG / T = 0.5 DAVG / T = 1.0

Note: 1 DOF Equation of Motion with α≈0 deg, γ = constant, Wi = initial weight, WAVG = average weight, WP = propellant weight, ISP = specific impulse, T = thrust, Mi = initial Mach number, h = altitude, DAVG = average drag, ΔV = incremental velocity, gc = gravitation constant, Vx = V cos γ, Vy = V sin γ, Rx = R cos γ, Ry = R sin γ

Note: R = ( Vi + ΔV / 2 ) tB, where R = boost range, Vi = initial velocity, tB = boost time 2/24/2008 ELF 193 HighHigh MissileMissile VelocityVelocity andand LeadLead AreAre RequiredRequired toto InterceptIntercept HighHigh SpeedSpeed CrossingCrossing TargetsTargets

VM sin L = VT sin A, Proportional Guidance Trajectory 4

VM VT LA

3 Note: Proportional Guidance

VM = Missile Velocity VT = Target Velocity A = Target Aspect VM / VT 2 L = Missile Lead Angle ≈Seeker Gimbal A = 90° Example: A = 45° 1 L = 30 deg A = 45 deg VM / VT = sin ( 45° ) / sin ( 30° ) = 1.42 0 01020304050 L, Lead Angle, Deg

2/24/2008 ELF 194 MissileMissile ConceptConcept SynthesisSynthesis RequiresRequires EvaluationEvaluation ofof AlternativesAlternatives andand IterationIteration

Define Mission Requirements Alt Mission Establish Baseline Alt Baseline Aerodynamics

Propulsion

Weight Resize / Alt Config / Subsystems / Tech

Trajectory

Meet No Performance?

Yes No Measures of Merit and Constraints

Yes

2/24/2008 ELF 195 SummarySummary ofof FlightFlight PerformancePerformance

Flight Performance Activity in Missile Design Compute range, velocity, time-to-target, off boresight Compare with requirements Discussed in This Chapter Equations of motion Flight performance drivers Propulsion alternatives range comparison Steady level flight required thrust Steady climb and steady dive range prediction Cruise prediction Boost prediction Coast prediction Ballistic flight prediction Turn radius and turn rate prediction Target lead for proportional homing guidance 2/24/2008 ELF 196 SummarySummary ofof FlightFlight PerformancePerformance (( contcont ))

Flight Performance Strongly Impacted by Aerodynamics Propulsion Weight Discussion / Questions? Classroom Exercise ( Appendix A )

2/24/2008 ELF 197 FlightFlight PerformancePerformance ProblemsProblems

1. Flight trajectory calculation requires input from aero, propulsion, and w_____. 2. Missile flight envelope can be characterized by the maximum effective range, minimum effective range, and o__ b______. 3. Limitations to the missile effective range include the fire control system, seeker, time of flight, closing velocity, and m______capability. 4. 1 DOF simulation requires modeling only the thrust, weight, and a____ f____. 5. A 3 DOF simulation that models 3 aero forces is called p____ m___ simulation. 6. A simulation that includes 3 aero forces ( normal, axial, side ), 3 aero moments ( pitch, roll, yaw ), thrust, and weight is called a _ DOF simulation. .. 7. The pitch angular acceleration θ is approximately equal to the second time derivative of the a____ o_ a_____. 8. Cruise range is a function of velocity, specific impulse, L / D, and f___ fraction. 9. If thrust is equal to drag and lift is equal to weight, the missile is in s_____ l____ flight. 10. Turn rate is a function of normal force, weight, and v______.

2/24/2008 ELF 198 FlightFlight PerformancePerformance ProblemsProblems (( contcont ))

11. Coast range is a function of initial velocity, weight, drag, and the t___ of flight.

12. Incremental velocity due to boost is a function of ISP, drag, and p______weight fraction. 13. To intercept a high speed crossing target requires a high speed missile with a high g_____ angle seeker. 14. An analytical model of a rocket in co-altitude, non-maneuvering flight can be developed by patching together the flight phases of boost and c____. 15. An analytical model of a rocket in a short range, off-boresight intercept can be developed by patching the flight phases of boost and t___. 16. An analytical model of a guided bomb in non-maneuvering flight can be developed from the flight phase of a steady d___. 17. An analytical model of an unguided weapon can be developed from the b______flight phase. 18. An analytical model of a ramjet in co-altitude, non-maneuvering flight can be developed by patching the flight phases of boost and c_____.

2/24/2008 ELF 199 OutlineOutline

Define Mission Requirements Alt Mission Establish Baseline Alt Baseline Aerodynamics

Propulsion

Weight Resize / Alt Config / Subsystems / Tech

Trajectory

Meet No Performance?

Yes No Measures of Merit and Constraints

Yes

2/24/2008 ELF 201 MMeasureseasures ooff MMeriterit anandd LLaunchaunch PlPlatformatform IntegrationIntegration ShouldShould BeBe HarmonizedHarmonized

Launch Platform Integration / Robustness Firepower

Cost Lethality

Balanced Design

Reliability Miss Distance

Other Carriage and Survivability Launch Considerations Observables

2/24/2008 ELF 202 TacticalTactical MissilesMissiles MustMust BeBe RobustRobust

Robustness

Launch Platform Integration / Robustness Tactical Missiles Must Have Robust Capability to Firepower

Cost Lethality

Reliability Miss Distance

Other Carriage and Handle Survivability Launch Considerations Observables Adverse Weather Clutter Local Climate Flight Environment Variation Uncertainty Countermeasures EMI / EMP This Section Provides Examples of Requirements for Robustness

2/24/2008 ELF 203 AdverseAdverse WeatherWeather andand CloudCloud CoverCover AreAre PervasivePervasive

NOAA satellite image 1.0 Annual Average of earth cloud cover Fraction of North Atlantic Cloud Cover North Pole 0.8 Cloud Cover Region Over Ocean Rising Air Rising Air South Pole Descending Region Air 0.6 Cloud Descending Cover Air Over Land 0.4 Argentina, Southern Deserts ( Sahara, Africa and Australia Gobi, Mojave ) Note: Annual Average Cloud Cover 0.2 Global Average = 61% Global Average Over Land = 52% Global Average Over Ocean = 65% 0.0 85°N 65°N 45°N 25°N 5°N 0° 5°S 25°S 45°S 65°S 85°S Latitude Zone

Reference: Schneider, Stephen H. Encyclopedia of Climate and Weather. Oxford University Press, 1996.

2/24/2008 ELF 204 RadarRadar SeekersSeekers AreAre RobustRobust inin AdverseAdverse WeatherWeather

1000 O2, H2O Note: EO attenuation through cloud at 0.1 g / m3 and 100 100 m visibility H O H2O 2 EO attenuation through CO2 O2 rain at 4 mm / h Humidity at 7.5 g / m3 10 H O Millimeter wave and 2 microwave attenuation H2O, CO2 O2 through cloud at 0.1 CO2 3 1 gm / m or rain at 4 mm / h H2O 20° C H O EO sensors are ineffective 2 1 ATM through cloud cover ATTENUATION (dB / km) 0.1 O3 Radar sensors have good to superior performance

X Ku K Ka Q V W Very Long Long Mid Short through cloud cover and rain 0.01 RADAR MILLIMETER SUBMILLIMETER INFRARED VISIBLE 10 GHz 100 1 THz 10 100 1000 3 cm 3 mm 0.3 mm 30 µm 3.0 µm 0.3 µm Increasing Frequency Increasing Wavelength

Source: Klein, L.A., Millimeter-Wave and Infrared Multisensor Design and Signal Processing, Artech House, Boston, 1997

2/24/2008 ELF 205 RadarRadar SeekersSeekers AreAre DesirableDesirable forfor RobustRobust OperationOperation withinwithin thethe TroposphereTroposphere CloudCloud CoverCover

40 Cumulonimbus ( 2 – 36k ft ) Cirrus ( 16 – 32k ft )

h, Altitude, 20 103 ft Altostratus ( 8 – 18k ft ) Altocumulus ( 9 – 19k ft )

10 Cumulus ( 2 – 9k ft ) Stratus ( 1 – 7k ft ) Fog 0 Note: •IR seeker may be able to operate “Under the Weather” at elevations less than 2,000 ft using GPS / INS midcourse guidance •IR attenuation through cloud cover greater than 100 dB per km. Cloud droplet size ( 0.1 to 50 μm ) causes resonance. •mmW has ~ 2 dB / km attenuation through rain. Typical rain drop size ( ∼ 4 mm ) is comparable to mmW wavelength. 2/24/2008 ELF 206 Precision Strike Missile Target Sensors Are Complemented by GPS / INS / Data Link Sensors

Sensor Adverse ATR / ATA Range Moving Volume Hypersonic Diameter Weight and Maturity Weather in Clutter Target Search Dome Required Cost Impact Time Compat. • SAR - - • Active - - Imaging mmW • Passive -- - Imaging mmW • Active - - Imaging IR (LADAR) • Active Non- - image IR (LADAR) • Active Non- - image mmW • Passive - Imaging IR - • Acoustic - - - • GPS / INS / - Data Link

Note: Superior Good Below Average- Poor

2/24/2008 ELF 207 ImagingImaging SSensorsensors EnhanceEnhance TargetTarget AcquisitionAcquisition // DiscriminationDiscrimination Imaging LADAR Imaging Infrared SAR

Passive Imaging mmW Video of Imaging Infrared Video of SAR Physics

2/24/2008 ELF 208 ExampleExample ofof MidMid WaveWave –– Long Long WaveWave IRIR SeekerSeeker ComparisonComparison

Assume Exo-atmospheric Intercept with 2 Target diameter DT = 2 ft ( AT = 2919 cm ), temperature TT = 300 K, emissivity ε = 0.5 2 Diameter of seeker aperture do = 5 in ( Ao = 0.01267 m )

Diameter of pixel detector dp = 40 μm

Spot resolution if diffraction limited = dspot = dp = 40 μm

Temperature of pixel detector Td = 77 K 2 Focal plane array size 256x256 FPA ( Ad = 1.049 cm )

Pixel detector bandwidth Δfp = 50 Hz ( tinteg = 0.00318 s )

Required signal-to-nose ratio for detection ( S / N )D = 5 First Calculate MWIR Seeker Detection Range 1/2 1/2 -1 1/2 RD = { ( IT )Δλ ηa Ao { D* / [( Δfp ) ( Ad ) ]} ( S / N )D } , m -1 Radiant intensity of target within seeker bandwidth ( IT )Δλ = ε Lλ ( λ2 - λ1 ) AT, W sr 4 4 5 [ 1.44 x 10 / ( λ TT )] -2 -2 -1 Spectral radiance of target Lλ = 3.74 x 10 / { λ { e – 1 }}, W cm sr μm

Assume λ = 4 μm, λ2 = 5 μm, λ1 = 3 μm, then -2 -2 -1 -1 Lλ = 0.000224 W cm sr μm , ( IT )Δλ = 0.643 W sr 11 1/2 -1 Assume Hg0.67Cd0.33Te detector at λ = 4 μm and 77 K ⇒ D* = 8 x 10 cm Hz W 11 1/2 1/2 -1 1/2 RD = { ( 0.643 ) ( 1 ) ( 0.01267 ) {( 8 x 10 ) / [( 50 ) ( 1.049 ) ]} ( 5 ) } = 13,480 m

2/24/2008 ELF 209 ExampleExample ofof MidMid WaveWave –– Long Long WaveWave IRIR SeekerSeeker ComparisonComparison (( contcont ))

Next, Calculate LWIR Seeker Detection Range 1/2 1/2 -1 1/2 RD = { ( IT )Δλ ηa Ao { D* / [( Δfp ) ( Ad ) ]} ( S / N )D } , m -1 ( IT )Δλ = ε Lλ ( λ2 - λ1 ) AT, W sr 4 4 5 [ 1.44 x 10 / ( λ TT )] -2 -2 -1 Lλ = 3.74 x 10 / { λ { e – 1 }}, W cm sr μm Assume λ = 10 μm, λ2 = 13 μm, λ1 = 7 μm, then -2 -2 -1 -1 Lλ = 0.00310 W cm sr μm , ( IT )Δλ = 26.7 W sr 10 1/2 1/2 -1 Assume Hg0.80Cd0.20Te detector at λ = 10 μm and 77 K ⇒ D* = 5 x 10 cm Hz W 10 1/2 1/2 -1 1/2 RD = { ( 26.7 ) ( 1 ) ( 0.01267 ) {( 5 x 10 ) / [( 50 ) ( 1.049 ) ]} ( 5 ) } = 21,600 m MWIR Seeker Versus LWIR Seeker Selection Depends Upon Target Temperature ( λ ) = 2898 / T , Wein’s Displacement Law, T in K ( L ) T T 15 λ max

L W Subsonic Airframe I 10 R Mach 4 Airframe MW Jet Engine IR 5 Rocket Plume

Radiance, Microns Flare

Wavelength for Max Spectral 0 Example: TT = 300 K 0 500 1000 1500 2000 ( λ ) = 2898 / T ( Lλ )max T TT, Target Temperature, K = 2898 / 300 = 10.0 μm 2/24/2008 ELF 210 GPSGPS // INSINS PProvidesrovides RRobustobust SSeekereeker LLock-onock-on iinn AdverseAdverse WeatherWeather andand ClutterClutter • Target Image 480 Pixels

640 Pixels ( 300 m ) 175 m

Seeker Lock-on @ 850 m to go ( 1 pixel = 0.47 m ) Seeker Lock-on @ 500 m to go ( 1 pixel = 0.27 m ) 3 m GPS / INS error ⇒ n = 0.15 g, σ < 0.1 m 3 m GPS / INS error ⇒ n = 0.44 g, σ < 0.1 m Mreq Mreq

88 m 44 m Seeker Lock-on @ 250 m to go ( 1 pixel = 0.14 m ) Seeker Lock-on @ 125 m to go ( 1 pixel = 0.07 m ) 3 m GPS / INS error ⇒ n = 1.76 g, σ = 0.9 m 3 m GPS / INS error ⇒ n = 7.04 g, σ = 2.2 m Mreq Mreq Note: = Target Aim Point and Seeker Tracking Gate, GPS / INS Accuracy = 3 m, Seeker 640 x 480 Image, Seeker FOV = 20 deg, Proportional Guidance Navigation Ratio = 4, Velocity = 300 m / s, G&C Time Constant = 0.2 s. 2/24/2008 ELF 211 DataData LinkLink UpdateUpdate atat SSeekereeker Lock-onLock-on ReducesReduces MovingMoving TargetTarget ErrorError

2 2 1/2 TESeekerLock-on = [ TLE + ( VT tLatency ) ] 1000 m

VT = 1 m / s VT = 10 m / s 100 VT = 100 m / s VT = 1000 m / s Example: TLE = 10 m

tSeekerLock-on = 100 s Target Error at Seeker Lock-on, Lock-on, Seeker at Error Target tUdate = 90 s 10 VT = 10 m / s 0.1 1 10 100 1000 tLatency = tSeeker-tUdate = 100 – 90 = 10 s 2 2 1/2 TESeekerLock-on = [ TLE + ( VT tLatency ) ] Target Latency at Seeker Lock-on, s = { 102 + [ 10 ( 10 )]2 ]1/2 = 100.5 m

Note: tSeekerLock-on = Seeker Lock-on time, tUdate = Data Link Update Time, VT = Target Velocity, TLE = Target Location Error at Update = 10 m 2/24/2008 ELF 212 OptimumOptimum CruiseCruise IsIs aa FunctionFunction ofof MachMach Number,Number, Altitude,Altitude, andand PlanformPlanform Geometry Geometry

120 Scramjet 100 q = 200 psf

t Ramjet q = 500 psf 80 q = 1,000 psf 60 q = 2,000 psf q = 5,000 psf

h, Altitude, kf Altitude, h, 40 Subsonic Turbojet with Low Aspect Ratio Wing q = 10,000 psf 20 q = 20,000 psf Wingless Subsonic Turbojet Note: q = 1 / 2 ( ρ V2 ) 0 01234567 M, Mach number

Note: • U.S. 1976 Standard Atmosphere

• For Efficient Cruise, ( L / D )Max for Cruising Lifting Body Typically Occurs for 500 < q < 1,000 psf • ( L / D )Max for Cruise Missile with Low Aspect Ratio Wing Typically Occurs for 200 < q < 500 psf 2/24/2008 • q ≈ 200 psf lower limit for aero control ELF 213 MissileMissile GuidanceGuidance andand ControlControl MustMust BeBe RobustRobust forfor ChangingChanging EventsEvents andand FlightFlight EnvironmentEnvironment

Example High Performance Missile Has • Low-to-High Dynamic Pressure • Negative-to-Positive Static Margin • Thrust / Weight / cg Transients • High Temperature • High Thermal Load Level Out • High Vibration Engine Start Transient Cruise • High Acoustics Pitch-Over at Booster Shutdown High Alpha Transient at High Mach

Pitch-Up at High Alpha Engine Shutdown Dive Climb Transient Terminal at High Booster Ignition Dynamic Pressure Air Launch at Low Pitch-Over at High Alpha Precision Impact Mach ( high α ) / at α≈0 Deg Deploy Compressed Vertical Launch in Cross Wind ( high α ) Carriage Surfaces / Deploy Compressed Carriage Surfaces

2/24/2008 ELF 214 DesignDesign RobustnessRobustness RequiresRequires CConsiderationonsideration ooff FlightFlight AltitudeAltitude Troposphere ( h < 36,089 ft ) Stratosphere ( h > 36089 ft ) -6 T / TSL = 1 – 6.875 x 10 h, h in ft T = constant = 390 R 5.2561 - ( h – 36089 ) / 20807 p / pSL = ( T / TSL ) p / pSL = 0.2234 e 4.2561 - ( h – 36089 ) / 20807 ρ / ρSL = ( T / TSL ) ρ / ρSL = 0.2971 e 1 0 20406080100 Troposphere Stratosphere

Temperature Ratio Pressure Ratio 0.1 Density Ratio Speed of Sound Ratio

U.S. Standard Atmosphere, 1976 Characteristic at Altitude / Characteristic at Sea Level Characteristic – TSL = 519 R 2 – pSL = 2116 lb / ft 0.01 3 – ρSL = 0.00238 slug / ft h, Geometric Altitude, kft – cSL = 1116 ft / s

Note: TSL = Temperature at sea level, pSL = pressure at sea level, ρSL = density at sea level, cSL = speed of sound at sea level, h = altitude in ft. 2/24/2008 ELF 215 DesignDesign RobustnessRobustness RequiresRequires CConsiderationonsideration ooff ColdCold andand HotHot AtmospheresAtmospheres

Ratio: Cold-to-Standard 1.5 Atmosphere Ratio: Hot-to-Standard Atmosphere ( + 30 % ) Ratio: Polar-to-Standard 1 Atmosphere ( - 23% ) Ratio: Tropic-to-Standard Atmosphere 0.5

0 Variation from Standard Atmosphere Temp Density Speed of Sound

Note: • Based on properties at sea level •U. S. 1976 Standard Atmosphere: Temperature = 519 R, Density = 0.002377 slug / ft3, Speed of sound = 1116 ft / s 2/24/2008 ELF 216 DesignDesign RobustnessRobustness IsIs RequiredRequired toto HandleHandle UncertaintyUncertainty

Narrow Uncertainty ( e.g., 1 SDD Flight Performance )

Broad Uncertainty ( e.g., Conceptual Design Flight Performance ) Skewed Uncertainty ( e.g., Cost, Weight, Miss 0.5 Distance ) Bimodal Uncertainty ( e.g., Multi-mode Seeker Target Location ) Uniform Bias Uncertainty Example Normalized PDF ( e.g., Seeker Aim Point Bias ) 0 -20 -10 0 10 20 Typical % Error from Forecast Value

Note for normal distribution: PDF = { 1 / [ σ ( 2 π )1/2 ]} e {[( x - μ ) / σ ]2 / 2 }

2/24/2008 ELF 217 CCounteounterr--CountermeasuresCountermeasures bbyy MiMissilessile EEnhancenhance DesignDesign RobustnessRobustness

Examples of CM ( Threat ) Examples of CCM ( Missile ) EOCM Imaging Seeker directed laser Multi-spectral / Multi- flare mode Seeker smoke Temporal Processing RFCM Hardened GPS / INS active radar standoff acquisition jammer Integrated GPS / INS chaff directional antenna Decoy pseudolite / differential GPS Low Observables ATR / ATA Speed Speed Altitude Altitude Maneuverability Maneuverability Lethal Defense Low Observables Saturation 2/24/2008 ELF 218 ExamplesExamples ofof Countermeasure-ResistantCountermeasure-Resistant SeekersSeekers

IIR ( I2R AGM-130 ) ………………………………………………

Two Color IIR ( Python 5 )

Acoustic - IIR ( BAT ) …………………………………………..

IIR – LADAR ( LOCAAS ) ………………………………………

ARH – mmW ( AARGM )

ARH - IIR ( Armiger ) ……………………………………………. 2/24/2008 ELF 219 A Target Set Varies in Size and Hardness

Lethality Example of Precision Strike Target Set Launch Platform Integration / Robustness Firepower

Air Defense ( SAMs, Cost Lethality

AAA ) Reliability Miss Distance Other Carriage and Survivability Launch Considerations Observables

Armor Artillery TBM / TELs C3II Naval Counter Air Aircraft Transportation Choke Oil Points ( Bridges, Refineries Railroad Yards, Truck Parks )

Examples of Targets where Size and Hardness Drive Warhead Design / Technology •Small Size, Hard Target: Tank ⇒ Small Shaped Charge, EFP, or KE Warhead •Deeply Buried Hard Target: Bunker ⇒ KE / Blast Frag Warhead •Large Size Target: Building ⇒ Large Blast Frag Warhead Video Example of Precision Strike Targets 2/24/2008 ELF 220 76%76% ofof BaghdadBaghdad TargetsTargets StruckStruck FirstFirst NightNight ofof DesertDesert StormStorm WereWere CC33 TimeTime CriticalCritical TargetsTargets Targets: 1. Directorate of Military Intelligence; 2, 5, 8, 13, 34. Telephone switching stations; 3. Ministry of 1 Defense national computer complex; 4. Electrical transfer station; 6. Ministry of Defense headquarters; 7. Ashudad 2 4 highway bridge; 9. Railroad yard; 10. Muthena airfield ( military 3 section ); 11. Air Force headquarters; 12. Iraqi Intelligence Service; 14. Secret Police complex; 15. Army storage depot; 16. Republican Guard headquarters; 17. New presidential 6 5 7 palace; 18. Electrical power station; 19. SRBM assembly 23 25 factory ( Scud ); 20. Baath Party headquarters; 21. 8 24 31 Government conference center; 22. Ministry of Industry and 10 9 26 32 11 27 33 Military Production; 23. Ministry of Propaganda; 24. TV 21 22 transmitter; 25, 31. Communications relay stations; 26. 12 34 29 35 Jumhuriya highway bridge; 27. Government Control Center 13 14 15 16 30 South; 28. Karada highway bridge ( 14th July Bridge ); 29. 17 28 20 37 Presidential palace command center; 30. Presidential palace command bunker; 32. Secret Police headquarters; 36 33. Iraqi Intelligence Service regional headquarters; 35. National Air Defense Operations Center; 36. Ad Dawrah oil 19 refinery; 37. Electrical power plant 18 Source: AIR FORCE Magazine, 1 April 1998 2/24/2008 ELF 221 TypeType ofof TargetTarget DrivesDrives PrecisionPrecision StrikeStrike MissileMissile Size,Size, Speed,Speed, Cost,Cost, Seeker,Seeker, andand WarheadWarhead Anti-Fixed Surface Target Missiles ( large size, wings, subsonic, blast frag warhead )

AGM-154 Storm Shadow / Scalp KEPD-350 BGM-109 AGM-142 Anti-Radar Site Missiles ( ARH seeker, high speed or duration, blast frag warhead )

AGM-88 AS-11 / Kh-58 ARMAT Armiger ALARM Anti-Ship Missiles ( large size, KE / blast frag warhead, and high speed or low altitude )

MM40 AS-34 Kormoran AS-17 / Kh-31 BrahMos SS-N-22 / 3M80 Anti-Armor Missiles ( small size, hit-to-kill, low cost, shape charge, EFP, or KE warhead )

Hellfire LOCAAS MGM140 AGM-65 LOSAT Anti-Buried Target Missiles ( large size, high fineness, KE / blast frag warhead )

CALCM GBU-28 GBU-31 Storm Shadow MGM-140 2/24/2008 ELF Permission of Missile Index. 222 ExamplesExamples ooff LightLight WeightWeight AirAir LaunchedLaunched Multi-Multi- PurposePurpose PrecisionPrecision StrikeStrike WeaponsWeapons Weapon Fixed Moving Time Buried Adverse Firepower(6) Surface Targets(2) Critical Targets(4) Weather(5) Targets(1) Targets(3)

Example New Missile

AGM-65 –

Small Diameter Bomb – –

AGM-88 – – –

Hellfire / Brimstone / Longbow –

LOCAAS –

(1) – Multi-mode warhead desired. GPS / INS provides precision ( 3 m ) accuracy. Note: (2) - Seeker or high bandwidth data link required for terminal homing. Superior (3) - High speed with duration required ⇒ High payoff of high speed / loiter and powered submunition. (4) - KE penetration warhead required ⇒ High impact speed, low drag, high density, long length. Good (5) - GPS / INS, SAR seeker, imaging mmW seeker, and data link have high payoff. Average – (6) - Light weight required. Light weight also provides low cost Poor 2/24/2008 ELF 223 BlastBlast IsIs EffectiveEffective atat SmallSmall MissMiss DistanceDistance

1/3 1/3 2 1/3 3 1/3 4 Δ p / p0 = 37.95 / ( z p0 ) + 154.9 / ( z p0 ) + 203.4 / ( z p0 ) + 403.9 / ( z p0 ) 1000 e z = r / c1/3

Note: 1/2 Based on bare sphere of pentolite ( Ec = 8,500 ft / s ) Δp = overpressure at distance r from explosion 100 p0 = undisturbed atmospheric pressure, psi z = scaling parameter = r / c1/3 r = distance from center of explosion, ft c = explosive weight, lb

10 Example for Rocket Baseline Warhead: c = 38.8 lb

h = 20k feet, p0 = 6.8 psi r = 10 ft

Delta p / p0, Overpressure Ratio to Undisturbed Pressur z = 10 / ( 38.8 )1/3 = 2.95 1 1/3 0246810z p0 = 5.58

z ( p0 )1/3 Δp / p0 = 13.36 Δp = 90 psi Reference: US Army Ordnance Pamphlet ORDP-2—290-Warheads, 1980 2/24/2008 ELF 224 GuidanceGuidance AccuracyAccuracy EnhancesEnhances LethalityLethality

Rocket Baseline Warhead Against Typical Aircraft Target

PK > 0.5 if σ < 5 ft ( Δ p > 330 psi, fragments impact energy > 130k ft-lb / ft2 )

PK > 0.1 if σ < 25 ft ( Δp > 24 psi, fragments impact energy > 5k ft- lb / ft2 )

Note: Rocket Baseline 77.7 lb warhead C / M = 1, spherical blast, h = 20k ft.

Video of AIM-9X Flight Test Missile Impact on Target ( No Warhead ) 2/24/2008 ELF 225 WarheadWarhead BlastBlast andand FragmentsFragments AreAre EffectiveEffective atat SmallSmall MissMiss DistanceDistance

2.4 m witness plate

Hellfire 24 lb shaped charge warhead Roland 9 kg explosively formed warhead fragments are from natural fragmenting case multi-projectiles are from preformed case

Video of Guided MLRS 180 lb blast fragmentation warhead 2/24/2008 ELF 226 MaximumMaximum TotalTotal FragmentFragment KineticKinetic EnergyEnergy RequiresRequires HighHigh Charge-to-MetalCharge-to-Metal RatioRatio 2 KE = ( 1 / 2 ) Mm Vf = Ec Mc / ( 1 + 0.5 Mc / Mm )

0.4 Note: KE Based on Gurney Equation High Cylindrical Warhead w KE Lo KE = Total Kinetic Energy 0.3 Mm = Total Mass Metal Fragments Vf = Fragment Velocity Ec = Energy Per Unit Mass Charge Mc = Mass of Charge 0.2 Mwh = Mass of Warhead = Mm + Mc

Example: Rocket Baseline Warhead 0.1 Mc = 1.207 slug

Mm = 1.207 slug

Mc / Mm = 1 ( KE / Mwh ) / Ec, Non-dimensional Kinetic Energy 0 Ec Mc = 52,300,000 ( 1.207 ) = 63,100,000 ft-lb 0 0.5 1 1.5 2 2.5 3 KE = 63100000 / [1 + 0.5 ( 1 )] Mc / Mm, Charge-to-Metal Ratio = 42,100,000 ft-lb

Reference: Carleone, Joseph (Editor), Tactical Missile Warheads (Progress in Astronautics and Aeronautics, Vol 155), AIAA, 1993. 2/24/2008 ELF 227 MultipleMultiple ImpactsImpacts AreAre EffectiveEffective AgainstAgainst ThreatThreat VulnerableVulnerable AreaArea SubsystemsSubsystems

nhits PK = 1 - ( 1 - Av / Atp ) 1 Note: • A = Target vulnerable area 0.9 v • Atp = Target presented area 0.8 0.7 0.6 Av / Atp = 0.1 0.5 Av / Atp = 0.5 0.4 Av / Atp = 0.9 0.3 Example: Pk, Probability of Kil of Probability Pk, 0.2 If Av / Ap = 0.1, nhits = 22 gives PK = 0.9

0.1 If Av / Ap = 0.9, nhits = 1 gives PK = 0.9 0 0 5 10 15 20 25 30 nhits, Number of Impacts on Target

2/24/2008 ELF 228 SmallSmall MissMiss DistanceDistance ImprovesImproves NumberNumber ofof WarheadWarhead FragmentFragment HitsHits 2 nhits = nfragments [ AP / ( 4 πσ )] 100 Wwh = 5 lb Wwh = 50 lb 80 Wwh = 500 lb

60 Example for Rocket Baseline:

WWH = 77.7 lb 40 Mc / Mm = 1, Wm = 38.8 lb = 17,615 g Average fragment weight = 3.2 g 20 nfragments = 17615 / 3.2 = 5505 Number of Fragment Hits 2 AP = Target presented area = 20 ft 0 σ = Miss distance = 25 ft

0 20406080100 2 nhits = 5505 { 20 / [( 4 π ) ( 25 ) ]} = 14 Sigma, Miss Distance, ft Kinetic energy per square foot. = KE / ( 4 πσ2 ) = 42100000 / [ 4 π ( 25 )2 ] = 5,360 ft-lb / ft2 Note: • Spherical blast with uniformly distributed fragments 2 • nhits = nfragments [ AP / ( 4 πσ )] • Warhead charge / metal weight = 1 • Average fragment weight = 50 grains ( 3.2 g ) 2 • AP = Target presented area = 20 ft 2/24/2008 ELF 229 HighHigh FragmentFragment VelocityVelocity RequiresRequires HighHigh Charge-to-Charge-to- MetalMetal RatioRatio

1/2 1/2 Vf = ( 2 Ec ) [ ( Mc / Mm ) / ( 1 + 0.5 Mc / Mm )] 10000 HMX Explosive TNT Explosive 8000

Note: Based on the Gurney equation for a 6000 cylindrical warhead Example: 1/2 HMX Explosive ( 2 EC ) = 10,230 ft / s Baseline Rocket Warhead 1/2 4000 TNT Explosive ( 2 EC ) = 7,600 ft / s HMX Explosive Vf = Fragment initial velocity, ft / s 2 2 Ec = Energy per unit mass of charge, ft / s MC / Mm = 1 Mc = Mass of charge Vf, Fragment Velocity, / s ft 2000 Vf = 8,353 ft / s Mm = Total mass of all metal fragments Mwh = Mass of warhead = Mm + Mc 0 0123 Mc / Mm, Charge-to-Metal Ratio

2/24/2008 ELF 230 SmallSmall MissMiss DistanceDistance ImprovesImproves FragmentFragment PenetrationPenetration

150 Grains ( 9.7 g )

.375 Fragment ( in )

50 Grains ( 3.2 g ) .25 Steel Perforation by

.125 1020 30 40 50 60 70 80 90 100 110 120 Miss Distance ( ft ) Note: Typical air-to-air missile warhead • Fragments initial velocity 5,000 ft / s • Sea level • Average fragment weight 3.2 g • Fewer than 0.3% of the fragments weigh more than 9.7 g for nominal 3.2 g preformed warhead fragments • Small miss distance gives less reduction in fragment velocity, enhancing penetration 2/24/2008 ELF 231 HHypersonicypersonic HitHit-to-Kill-to-Kill EEnhancesnhances EEnergynergy onon TTargetarget forfor MissilesMissiles withwith SmallSmall WarheadsWarheads

2 ET / EC = [( 1 / 2 ) ( WMissile / gc ) V + EC ( WC / gc )] / [ EC ( WC / gc )]

9 Example for Rocket Baseline: Weight of 8 missile / W = 367 lb 7 Missile Weight of WC = 38.8 lb charge = 20 6 W / W = 9.46 Missile C Weight of 5 V = 2,000 ft / s missile / 4 ( 1 / 2 ) ( W / g ) V2 = 22.8 x 106 ft-lb ) Weight of Missile c charge = 10 6 EC ( WC / gc ) = 63.1 x 10 ft-lb Charge Energy Charge 3 E / E = 1.36 Weight of 2 T C missile / 1 Weight of charge = 5 0 ET Total / EC, Energy on Target / Warhead Weight of 0 1000 2000 3000 4000 5000 6000 missile / Missile Closing Velocity, ft / s Weight of charge = 2

1/2 Note: Warhead explosive charge energy based on HMX, ( 2 EC ) = 10,230 ft / s. 1 kg weight at Mach 3 closing velocity has kinetic energy of 391,000 J ⇒ equivalent chemical energy of 0.4 lb TNT. 2/24/2008 ELF 232 KineticKinetic EnergyEnergy WarheadWarhead Density,Density, Length,Length, andand VelocityVelocity ProvideProvide EnhancedEnhanced PenetrationPenetration

1/2 2/3 2 1/3 Note: P / d = [( l / d ) – 1 ] ( ρP / ρT ) + 3.67 ( ρP / ρT ) [( ρT V ) / σT ] V > 1,000 ft / s l / d > 2 60 Non-deforming ( high strength, sharp nose ) penetrator l = Penetrator length 50 d = Penetrator diameter V = Impact velocity

40 ρP= Penetrator density ρT = Target density σ = Target ultimate stress 30 T Example for 250 lb Steel Penetrator

Steel on Concrete Steel 20 l / d = 10 l = 48 in ( 4 ft ) d = 4.8 in ( 0.4 ft ) 10 Concrete target 3 3

P / d, Target Penetration / Penetrator Diameter for Diameter / Penetrator Penetration Target / d, P ρP = 0.283 lb / in ( 15.19 slug / ft ) 3 3 0 ρT = 0.075 lb / in ( 4.02 slug / ft ) 0 1000 2000 3000 4000 V = 4,000 ft / s

V, Velocity, ft / s σT = 5,000 psi ( 720,000 psf ) P / d = [ 10 – 1 }( 15.19 / 4.02 )1/2 + 3.67 ( 15.19 l / d = 2 l / d = 5 l / d = 10 / 4.02 )2/3 [ 4.02 ( 4000 )2 / 720000 ]1/3 = 57.3 P = ( 57.3 ) ( 0.4 ) = 22.9 ft Source: Christman, D.R., et al, “Analysis of High-Velocity Projectile Penetration,” Journal of Applied Physics, Vol 37, 1966 2/24/2008 ELF 233 ExamplesExamples ofof Kinetic-KillKinetic-Kill MissilesMissiles

Standard Missile 3 ( NTW ) PAC-3 THAAD

LOSAT LOSAT Video 2/24/2008 ELF 234 CEPCEP ApproximatelyApproximately EqualEqual toto 11σσ MissMiss DistanceDistance

Miss Distance

Launch Platform Integration / Robustness Firepower

Cost Lethality

Reliability Miss Distance Missile Circular Error Probable ( 50% Survivability Observables Extreme Missile of shots within circle ) Trajectory Missile 1σ Miss Distance ( 68% of shots within circle for a normal distribution of error )

Median Target Trajectory

Presented Target Area

Extreme Missile Trajectory For a normal distribution of error: Probability < 1σ miss distance = 0.68 Probability < 2σ miss distance = 0.95 Probability < 3σ miss distance = 0.997 Hypothetical Plane Through Target

Source: Heaston, R.J. and Smoots, C.W., “Introduction to Precision Guided Munitions,” GACIAC HB-83-01, May 1983.

2/24/2008 ELF 235 AA CollisionCollision InterceptIntercept HasHas ConstantConstant BearingBearing forfor aa ConstantConstant Velocity,Velocity, Non-maneuveringNon-maneuvering TargetTarget

Example of Miss Example of Collision Intercept ( Line-of-Sight Angle Diverging ) ( Line-of-Sight Angle Constant ) . . ( Line-of-Sight Angle Rate L ≠ 0 ) ( Line-of-Sight Angle Rate L = 0 )

Overshoot Miss

t2 t ( L 1 OS ) t1 1 > ( L OS ) 0 ( LOS )1 = ( LOS )0 t0 L t0 L Seeker Line-of-Sight A Seeker Line-of-Sight A

Missile Target Missile Target

Note: L = Missile Lead A = Target Aspect

2/24/2008 ELF 236 AA MManeuveringaneuvering TTargetarget anandd IInitialnitial HHeadingeading EErrorrror CauseCause MissMiss Target

A Collision Missile L Point γ M0 +Z

2 Maneuvering : τ d Z + dZ + N’ Z = –N’ cos A 1 a t2 2 T Target dt dt to –t to –t cos L 2 Initial Heading d2Z dZ Z : τ + + N’ = –VM γM 2 0 Error dt dt to –t

Note: to - t = 0 at intercept, causing discontinuity in above equations. N’ = Effective navigation ratio = N [ VM / ( VM -VT cos A )] N = Navigation ratio = ( dγ / dt ) / ( dL / dt ) Reference: Jerger, J.J., Systems Preliminary Design τ = Missile time constant, V = Velocity of missile, γ = Initial flight Principles of Guided Missile Design, D. Van Nostrand M M0 path angle error of missile, to = Total time of flight, aT = Acceleration Company, Inc., Princeton, New Jersey, 1960 of target, VT = Velocity of target 2/24/2008 ELF 237 MissileMissile TimeTime ConstantConstant CausesCauses MissMiss DistanceDistance

τ is a measure of missile ability to respond to target condition changes Input Time τ equals elapsed time from input of target t return until missile has i completed 63% or ( 1 – e-1 ) of corrective maneuver ( t = τ ) τ also called “rise time” 63% Contributions to time constant τ

Control effectiveness ( τδ ) Output ti Time . Control dynamics ( e.g., actuator rate ) ( τδ ) τ Dome error slope ( τDome ) Acceleration Achieved - t / τ Guidance and control filters ( τFilter ) = 1 – e Other G&C dynamics ( gyro dynamics, Acceleration Commanded accelerometer, processor latency, etc ) Seeker errors ( resolution, latency, blind range, Example for Rocket Baseline: tracking, noise, glint, amplitude ) M = 2, h = 20k ft, coast

Approach to estimate τ . τ = τδ + τδ + τDome τ = τ + τ . + τ δ δ Dome = 0.096 + 0.070 + 0.043 = 0.209 s

2/24/2008 ELF 238 TimeTime CConstantonstant ττδδ fforor CControlontrol EEffectivenessffectiveness IsIs DrivenDriven byby StaticStatic MarginMargin

Assumptions for τδ Control surface deflection limited Near neutral stability

Equation of motion is αMax, δMax αMax .. α = [ ρ V2 S d C / ( 2 I ) ] δ mδ y Max

Integrate to solve for αMax α = [ ρ V2 S d C / ( 8 I ) ] δ τ 2 τδ / 2 τδ Max mδ y Max δ

τδ is given by – δMax τ = [ 8 I ( α / δ ) / ( ρ V2 S d C )]1/2 δ y Max Max Ref mδ Contributors to small τδ Example for Rocket Baseline: Low fineness ( small Iy / ( SRef d )) 2 2 High dynamic pressure ( low altitude / high W = 367 lb, d = 0.667 ft, SRef = 0.349 ft , Iy = 94.0 slug-ft , speed ) M = 2, h = 20k ft ( ρ = 0.001267 slug / ft3 ),

Large C α = 9.4 deg, δ = 12.6 deg, Cm = 51.6 per rad, mδ Max Max δ 2 τδ = { 8 ( 94.0 ) ( 9.4 / 12.6 ) / [ 0.001267 ( 2074 ) ( 0.349 ) ( 0.667 ) ( 51.6 ) ]}1/2 = 0.096 s

2/24/2008 ELF 239 .. TimeTime ConstantConstant ττδδ forfor FlightFlight ControlControl SystemSystem IsIs DrivenDriven byby ActuatorActuator RateRate DynamicsDynamics

. α Max, δ Max α Max α Max Assumptions for τδ . . . Control surface rate limited ( δ = δ Max ) δ Near neutral stability 1 . . . τδ τδ Equation of motion for δ = +/- δ Max ... . 2 α = [ ρ V S d Cmδ / ( 2 Iy ) ] δ Max Equation of motion for “perfect” response . δ = ∞, δ = δMax .. 2 α = [ ρ V S d Cmδ / ( 2 Iy ) ] δMax . τδ is difference between actual response - δ Max Example for Rocket Baseline . to αMax and “perfect” ( τδ ) response • δ Max = 360 deg / s, δMax = 12.6 deg . Then Note: • τδ = 2 ( 12.6 / 360 ) = 0. 070 s . . Response for control rate limit τδ = 2 δMax / δ Max Response for no control rate limit

2/24/2008 ELF 240 TimeTime ConstantConstant ττDomeDome forfor RadomeRadome Is Is DrivenDriven byby DomeDome ErrorError SlopeSlope

| R | = 0.05 ( lN / d – 0.5 ) [ 1 + 15 ( Δ f / f ) ] / ( d / λ ) . τDome = N’ ( VC / VM ) | R | ( α / γ ) . α / γ = α ( W / g ) V / { q S [ C + C / ( α / δ )]} c M Ref Nα Nδ Substituting gives τ = N’ W V | R | / { g q S [ C + C / ( α / δ )]} Dome C c Ref Nα Nδ Example for Rocket Baseline at M = 2, h = 20k ft, q = 2725 psf 0.03 Tangent Ogive Assume V = 1,000 ft / s, giving V = 3,074 ft / s T C Δ f / f = 0.05 Dome Assume N’ = 4, f = 10 GHz or λ = 1.18 in, Δ f / f = 0.02 0.02 Δ f / f = 0.02 Configuration data are lN / d = 2.4, d = 8 in, SRef = 0.349 Δ f / f = 0 2 ft , W = 367 lb, CN = 40 per rad, CN = 15.5 per rad, α / δ = 0.75 α δ Faceted or Deg / Deg , Radome Error Slope, 0.01 Window Compute | R | = 0.05 ( 2.4 – 0.5 ) [ 1 + 15 ( 0.02 )] / ( 8 /

1.18 ) = 0.0182 deg / deg = 10 Dome λ / τDome = 4 ( 367 ) ( 3074 ) ( 0.0182 ) / [ 32.2 ( 2725 ) ( 0.349 ) ( 40 + 15.5 / 0.75 )] = 0.043 s @ d 0 Multi-lens

|R| 0123 Dome lN / d, Nose Fineness

2/24/2008 ELF 241 HighHigh InitialInitial AccelerationAcceleration IsIs RequiredRequired toto EliminateEliminate aa HeadingHeading ErrorError

N’ – 2 aM t0 / ( VM γM ) = N’ ( 1 – t / t0 ) 6 Note: Proportional Guidance τ = 0 Example: Exoatmospheric Head-on Intercept, N’ = 4 t0 = Total Time to Correct Heading Error Midcourse lateral error at t = 0 ( seeker lock-on ) = 200 m, 1 σ 6 aM = Acceleration of Missile VM = Velocity of Missile Rlock-on = 20000 m ⇒γM = 200 / 20000 = 0.0100 rad γ = Initial Heading Error of 4 M V = 5000 m / s, V = 5000 ⇒ t = R / ( V + V ) = Missile M T 0 lock-on M T aM t0 / ( VM γM ), 4 20000 / ( 5000 + 5000 ) = 2.00 s N’ = Effective Navigation Ratio Non-dimensional aM t0 / ( VM γM ) = 4 2 Acceleration 3 aM = 4 ( 5000 ) ( 0.0100 ) / 2.00 ) = 100 m / s

2.5 nM = 100 / 9.81 = 10.2 g 2 N’ = 2

0 0 0.2 0.4 0.6 0.8 1.0 t / t0, Non-dimensional Time 2/24/2008 ELF 242 MissileMissile MinimumMinimum RangeRange MayMay BeBe DrivenDriven ByBy 44 toto 88 TimeTime ConstantsConstants toto CorrectCorrect InitialInitial HeadingHeading ErrorError

-( t0 / τ ) N’ – 1 j σHE = VM γM t0 e j = 1∑ {( N’ - 2 )! [ - ( t0 / τ )] / [( j – 1 )! ( N’–j –1 )! j! ]} -( t0 / τ ) 2 0.3 If N’ = 3, σHE = VM γM t0 e [ ( t0 / τ ) - ( t0 / τ ) / 2 ] -( t0 / τ ) 2 3 If N’ = 4, σHE = VM γM t0 e [( t0 / τ ) - ( t0 / τ ) + ( t0 / τ ) / 6 ] -( t0/ τ ) 2 3 4 If N’ = 5, σHE = VM γM t0 e [( t0 / τ ) – ( 3 / 2 ) ( t0 / τ ) + ( t0 / τ ) / 2 – ( t0 / τ ) / 24 ] -( t0 / τ ) 2 3 4 5 If N’ = 6, σHE = VM γM t0 e [( t0 / τ ) - 2 ( t0 / τ ) + ( t0 / τ ) -( t0 / τ ) / 6 + ( t0 / τ ) / 120 ] N’ = 3 Note: Proportional Guidance ( σ ) shown in figure is the envelope of adjoint solution 0.2 HE Max ( σHE )Max = Max miss distance ( 1 σ ) from heading error, ft N’ = 4 VM = Velocity of missile, ft / s γM = Initial heading error, rad | ( σ ) / ( V γ t ) | t0 = Total time to correct heading error, s HE Max M M o τ = Missile time constant, s N’ = 6 N’ = Effective navigation ratio 0.1 Example: Ground Target, N’ = 4, τ = 0.2, GPS / INS error = 3 m, Rlock-on = 125 m, γM = 3 / 125 = 0.024 rad, VM = 300 m / s, t0 = 125 / 300 = 0.42 s

t0 / τ = 0.42 / 0.2 = 2.1, (σHE )Max / ( VM γM to ) = 0.12

( σHE )Max = 0.12 ( 300 ) ( 0.024 ) ( 0.42 ) = 2.2 m 0 024 6810 References: tO / τ •Donatelli, G.A., et al, “Methodology for Predicting Miss Distance for Air Launched Missiles,” AIAA-82-0364, January 1982 •Bennett, R.R., et al, “Analytical Determination of Miss Distances for Linear Homing Navigation,” Hughes Memo 260, March 1952 2/24/2008 ELF 243 RequiredRequired ManeuverabilityManeuverability IsIs aboutabout 3x3x thethe TargetTarget ManeuverabilityManeuverability forfor anan IdealIdeal (( ττ == 00 )) MissileMissile

N’ – 2 nM / nT = [ N’ / ( N’ – 2 )] [ 1 – ( 1 – t / t0 ) ] Where t = Elapsed Time

t0 = Time to Target N’ = 2 ∞ N’ = Effective Navigation Ratio ↑ 6 Assumptions: τ = 0 N’ = 2.5 VM > VT Example: τ = 0, N’ = 3, t / t = 1 n 0 M , 4 ⇒ nM / nT = 3 nT 3 Missile-to-Target 4 2 Acceleration 6 Ratio

0 0 0.2 0.4 0.6 0.8 1.0

t / t0, Non-Dimensional Time

2/24/2008 ELF 244 TargetTarget ManeuversManeuvers RequireRequire 66 toto 1010 TimeTime ConstantsConstants toto SettleSettle OutOut MissMiss DistanceDistance

2 -( t0 / τ ) N’ – 1 j σMAN = gc nT τ e j = 2∑ {( N’ - 3 )! [ - ( t0 / τ )] / [( j – 2 )! 0.3 ( N’ – j – 1 )! j! ]} N’ = 3 2 -( t0 / τ ) 2 If N’ = 3, σMAN = gc nT τ e [ ( t0 / τ ) / 2 ] 2 -( t0 / τ ) 2 3 If N’ = 4, σMAN = gc nT τ e [ ( t0 / τ ) / 2 - ( t0 / τ ) / 6 ] 2 -( t0 / τ ) 2 3 If N’ = 5, σMAN = gc nT τ e [ ( t0 / τ ) / 2 - ( t0 / τ ) / 3 + ( t0 / τ )4 / 24 ] 2 -( t0 / τ ) 2 3 If N’ = 6, σMAN = gc nT τ e [ ( t0 / τ ) / 2 - ( t0 / τ ) / 2 + ( t0 / 4 5 0.2 τ ) / 8 - ( t0 / τ ) / 120 ] Note: Proportional Guidance ( σ ) ( σMAN )Max is the envelope of adjoint solution MAN Max ( σ ) = Max miss ( 1 σ ) from target accel, ft g n τ2 N’ = 4 MAN Max c T nT = Target acceleration, g gc = Gravitation constant, 32.2 τ = Missile time constant, s 0.1 N’ = Effective navigation ratio τ = Time of flight, s N’ = 6 0

0 References: 02 4 6 8 10 tO / τ •Donatelli, G.A., et al, “Methodology for Predicting Miss Distance for Air Launched Missiles,” AIAA-82-0364, January 1982 •Bennett, R.R., et al, “Analytical Determination of Miss Distances for Linear Homing Navigation,” Hughes Memo 260, March 1952 2/24/2008 ELF 245 AnAn AeroAero ControlControl MissileMissile HasHas ReducedReduced MissMiss DistanceDistance atat LowLow AltitudeAltitude // HighHigh DynamicDynamic PressurePressure

2 Note: Proportional guidance ( σMan )Max = 0.13 gc nT τ @ N’ = 4, t0 / τ = 2 Target maneuver initiated for max miss ( t0 / τ = 2 ) ( σMan )Max in figure = Envelope of adjoint miss

100 distance τ = Missile time constant, s N’ = Effective navigation ratio = 4

nT = Target acceleration, g gc = Gravitation constant = 32.2 10 h = SL h = 20k ft h = 40k ft

Target, ft h = 60k ft h = 80k ft 1 Example for Rocket Baseline at Mach 2, coasting Assume:

• nT = 5g, VT = 1,000 ft / s, head-on intercept Rocket Baseline Maximum Due Miss to Maneuvering 0.1 •h = 20k ft ⇒τ= 0.209 s 2 0246810( σMan )Max = 0.13 ( 32.2 )( 5 )( 0.209 ) = 0.9 ft Target Maneuverability, g •h = 80k ft ⇒τ= 1.17 s 2 ( σMan )Max = 0.13 ( 32.2 )( 5 )( 1.17 ) = 28.7 ft

2/24/2008 ELF 246 GlintGlint MissMiss DistanceDistance DrivenDriven byby SeekerSeeker Resolution,Resolution, MissileMissile TimeTime Constant,Constant, andand NavigationNavigation RatioRatio 1/2 Note: σGlint = KN’ ( W / τ ) Proportional guidance

N’ / 4 0.8 KN’ = 0.5 ( 2 KN’= 4) Adjoint miss distance σGlint = Miss distance due to glint noise, ft KN’= 4= 1.206 W = Glint noise spectral density, ft2 / Hz W = ( b ) 2 / ( 3 π2 B ) τ = Missile time constant, s 0.6 T Res N’ = Effective navigation ratio

( bT )Res = Target span resolution at seeker blind range, ft B = Noise bandwidth, Hz ( 1 < B < 5 Hz ) 0.4 Example: Rocket Baseline at Mach 2, h = 20k ft altitude ⇒τ= 0.209 s Assume: 0.2 •N’ = 4 from Glint @ 2 Hz Bandwidth Hz 2 from Glint @ •B = 2 Hz

•( bT )Res = bt = 40 ft ( radar seeker beam Sigma / ( bT )Res, Nondimensional Miss Distance Miss Nondimensional ( / bT )Res, Sigma 0 width resolution of target wing span ) 00.20.40.60.81Calculate: Tau, Missile Time Constant, s W = ( 40 )2 / [ 3 π2 ( 2 )] = 27.0 ft2 / Hz 1/2 σ / ( b ) = K ’ ( W / τ ) / ( b ) N' = 3 N' = 4 N' = 6 Glint T Res N t Res = 1.206 ( 27.0 / 0.209 )1/2 / 40 = 0.343

Reference: σGlint = 0.343 ( 40 ) = 13.7 ft Bennett, R.R., et al, “Analytical Determination of Miss Distances for Linear Homing Navigation,” Hughes Memo 260, March 1952 2/24/2008 ELF 247 MinimizingMinimizing MissMiss DistanceDistance withwith GlintGlint RequiresRequires OptimumOptimum TimeTime ConstantConstant andand NavigationNavigation RatioRatio

2 2 1/2 σ = [( σMAN )Max + ( σGlint ) ] 50 Note: Proportional guidance Adjoint miss distance ( σ ) = Max miss distance from 40 MAN Max target maneuver, ft

σGlint = Miss distance from glint noise, ft 30 τ = Missile time constant, s N’ = Effective navigation ratio

Example for Rocket Baseline at Mach 2, 20 h = 20k ft altitude ⇒τ= 0.209 s Assume: 10 N’ = 4 Rocket Baseline Miss Distance, ft Distance, Miss Baseline Rocket •B = 2 Hz

0 •( bT )Res = 40 ft

0 0.2 0.4 0.6 0.8 1 •nT = 5g, VT = 1,000 ft / s, Head-on Tau, Missile Time Constant, s From prior figures: ( σ ) = 0.9 ft, σ = 13.7 ft N' = 3 N' = 4 N' = 6 MAN Max Glint Calculate: σ = [( σ ) 2 + ( σ )2 ]1/2 = 13.7 ft Reference: MAN Max Glint Bennett, R.R., et al, “Analytical Determination of Miss Distances for Linear Homing Navigation,” Hughes Memo 260, March 1952 2/24/2008 ELF 248 MissileMissile CarriageCarriage RCSRCS andand LaunchLaunch PlumePlume AreAre ConsiderationsConsiderations inin LaunchLaunch PlatformPlatform ObservablesObservables

Launch Platform Integration / Robustness Firepower

Cost Lethality

Reliability Miss Distance

Carriage and Survivability Observables Missile Carriage Alternatives Launch Observables Internal Carriage: Lowest Carriage RCS Conformal Carriage: Low Carriage RCS Conventional External Pylon or External Rail Carriage: High Carriage RCS Plume Alternatives

Min Smoke: Lowest Launch Observables ( H2O Contrail ) Reduced Smoke: Reduced Launch Observables ( e.g., HCl Contrail from AP Oxidizer )

High Smoke: High Launch Observables ( e.g., Al2O3 Smoke from Al Fuel )

2/24/2008 ELF 249 ExamplesExamples ofof WeaponWeapon BayBay InternalInternal CarriageCarriage andand Load-outLoad-out Center Weapon Bay Best for Ejection Launchers

F-22 Bay Loadout: 3 AIM-120C, 1 GBU-32 F-117 Bay Loadout: 1 GBU-27, 1 GBU-10 B-1 Bay Loadout: 8 AGM-69 Video Side Weapon Bay Best for Rail Launchers

AMRAAM Loading in F-22 Bay F-22 Side Bay: 1 AIM-9 Each Side Bay RAH-66 Side Bay: 1 AGM-114, 2 FIM- 92, 4 Hydra 70 Each Side Bay 2/24/2008 ELF 250 MinimumMinimum SmokeSmoke PropellantPropellant HasHas LowLow ObservablesObservables

High Smoke Example: AIM-7 Reduced Smoke Example: AIM-120 Minimum Smoke Example: Javelin

Particles ( e.g., metal fuel ) at all Contrail ( HCl from AP oxidizer ) at T < -10° F Contrail (H2O ) at T < -35º F atmosphere temperature. atmospheric temperature. atmospheric temperature.

High Smoke Motor

Reduced Smoke Motor

Minimum Smoke Motor

2/24/2008 ELF 251 HighHigh AltitudeAltitude FlightFlight andand LowLow RCSRCS EnhanceEnhance SurvivabilitySurvivability Launch Platform Integration / Robustness Firepower

Cost Lethality

Reliability Miss Distance 3 4 2 Other Survivability Survivability Observables Pt = ( 4 π ) Pr R / ( Gt Gr σλ ) Considerations

r 10000000

1000000

100000

Example for Pt = 50,000 W: 10000 Not detected if: 1000 h > 25k ft for σ = 0.001 m2 h > 77k ft for σ = 0.1 m2 Required for Detection, W Pt, Radar Transmitted Powe 100 020406080100 h, Geometric Altitude, kft

RCS = 0.1 m2 RCS = 0.01 m2 RCS = 0.001 m2

Note:

Range Slant Angle = 20 deg, Gt = Transmitter Gain = 40 dB, Gr = Receiver Gain = 40 dB, λ = Wavelength = 0.03 -14 m, Pr = Receiver Sensitivity = 10 W, σ = radar cross section ( RCS ) Based on Radar Range Equation with ( S / N )Detect = 1 and Unobstructed Line-of-Sight 2/24/2008 ELF 252 MissionMission PlanningPlanning andand HighHigh SpeedSpeed EnhanceEnhance SurvivabilitySurvivability Flyby -1 texp = 2 ( Rmax / V ) cos [ sin ( yoffset / Rmax )] – treact 2

ax treact V R m SAM

Site texp V yoffset 1 Exposure Time Example:

yoffset = 7 nm, Rmax = 10 nm = 60750 ft, 0 yoffset / Rmax = 0.7, treact = 15 s texp ( V / Rmax ), Non-dimensional Threat Threat Non-dimensional ), Rmax / V ( texp 0 0.2 0.4 0.6 0.8 1 If V = 1000 ft / s, treact ( V / Rmax ) = 0.247 yoffset / Rmax, Non-dimensional Offset Distance from -1 •texp ( V / Rmax ) = 2 cos [ sin ( 7 / 10 )] – Threat 15 ( 1000 / 60746 ) = 1.428 – 0.247 = 1.181

treact ( V / Rmax ) = 0 treact ( V / Rmax ) = 1.0 •texp = 1.181 ( 60746 / 1000 ) = 71.7 s If V = 4000 ft / s, t ( V / R ) = 0.988 Note: Based on assumption of constant altitude, constant heading flyby of react max

threat SAM site with an unobstructed line-of-sight. texp = exposure time to •texp ( V / Rmax ) = 0.440 SAM threat, Rmax = max detection range by SAM threat, V = flyby velocity, •texp = 0.440 ( 60746 / 4000 ) = 6.7 s yoffset = flyby offset, treact = SAM site reaction time from detection to launch 2/24/2008 ELF 253 LowLow AltitudeAltitude FlightFlight andand TerrainTerrain OObstaclesbstacles ProvideProvide MaskingMasking fromfrom ThreatThreat

2 hmask = ( hmask )obstacle + ( hmask )earth = hobstacle ( Rlos / Robstacle ) + ( Rlos / 7113 ) 2000 hmask = altitude that allows obstacle and earth curvature to mask exposure to surface threat LOS, ft

hobstacle = height of obstacle above terrain, ft 1500 Rlos = line-of-sight range to surface threat, ft

Robstacle = range from surface threat to obstacle, ft 1000 Height of low hill or tall tree ≈ 100 ft Height of moderate hill ≈ 200 ft 500 Height of high hill ≈ 500 ft

Exposure to Surface Threat, ft Threat, to Surface Exposure Height of low mountain ≈ 1000 ft hmask, Altitude that Altitude Masks Line-of-Sight hmask, 0 Example: 0 10203040 hobstacle = 200 ft Rlos, Line-of-Sight Range to Surface Threat, nm Robstaacle = 5.0 nm = 30395 ft

Rlos ( hobstacle / Robstacle ) = 100 ft Rlos = 10.0 nm = 60790 ft

Rlos ( hobstacle / Robstacle ) = 200 ft Rlos ( hobstacle / Robstaacle ) = 60790 ( 200 / Rlos ( hobstacle / Robstacle ) = 500 ft 30395 ) = 400 ft Rlos ( hobstacle / Robstacle ) = 1000 ft hmask = 200 ( 60790 / 30395 ) + ( 60790 / 7113 )2 = 400 + 73 = 473 ft above terrain 2/24/2008 ELF 254 InsensitiveInsensitive MunitionsMunitions ImproveImprove LaunchLaunch PlatformPlatform SurvivabilitySurvivability Critical Subsystems Rocket motor or fuel tank Warhead Severity Concerns Ranking of Power Output - Type 1. Detonation ( ~ 0.000002 s rise time ) 2. Partial detonation ( ~ 0.0001 s rise time ) 3. Explosion ( ~ 0.001 s rise time ) 4. Deflagration or propulsion rise time ( ~ 0.1 s rise time ) 5. Burning ( > 1 s ) Design and test considerations ( MIL STD 2105C ) Fragment / bullet impact or blast Sympathetic detonation Fast / slow cook-off fire Drop Temperature Vibration Carrier landing ( 18 ft / s sink rate ) 2/24/2008 ELF 255 HighHigh SystemSystem ReliabilityReliability IsIs ProvidedProvided byby HighHigh SubsystemSubsystem ReliabilityReliability andand LowLow PartsParts CountCount

Launch Platform Integration / Robustness Firepower Rsystem ≈ 0.94 = RArm X RLaunch X RStruct X RAuto X Cost Lethality

Reliability Miss Distance

Typical System Reliability RAct X RSeeker X RIn Guid X RPS X RProp X RFuze X RW/H Survivability Observables Reliability Arm ( 0.995 – 0.999 ) Launch ( 0.990 – 0.995 ) Structure ( 0.997 – 0.999 ) Autopilot ( 0.993 – 0.995 ) Typical Event / Actuators ( 0.990 – 0.995 ) Subsystem Seeker ( 0.985 – 0.990 ) Inertial Guidance ( 0.995 – 0.999 ) Power Supply ( 0.995 – 0.999 ) Propulsion ( 0.995 – 0.999 ) Fuze ( 0.987 – 0.995 ) Warhead ( 0.995 – 0.999 )

0.90 0.92 0.94 0.96 0.98 1.00 Typical Reliability 2/24/2008 ELF 256 SSensors,ensors, ElElectronicsectronics anandd PPropulsionropulsion DDriverive MissileMissile ProductionProduction CostCost

Launch Platform Integration / Robustness Firepower Cost Cost Lethality

Reliability Miss Distance

Dome Seeker Guidance and Propulsion Wings – Survivability Observables Control •Rocket •Airbreather Stabilizers –

Structure Power – Warhead – Aerothermal – Data Flight •Rocket – Supply and Fuzing Insulation Link Control •Airbreather

Very High High Moderate – Relatively Low ( > 25% Production Cost ) ( > 10% ) ( > 5% ) ( < 5% )

Note: System assembly and test ~ 10% production cost Propulsion and structure parts count / cost of airbreathing missiles are higher than that of rockets

2/24/2008 ELF 257 SensorsSensors andand ElectronicsElectronics OccupyOccupy aa LargeLarge PortionPortion ofof aa HighHigh PerformancePerformance // HighHigh CostCost Missile.Missile.

Example: Derby / R-Darter Missile

Source: http://www.israeli-weapons.com/weapons/missile_systems/air_missiles/derby/Derby.html

2/24/2008 ELF 258 CostCost ConsiderationsConsiderations

Life Cycle

System Development and Demonstration ( SDD )

Production

Logistics

Culture / processes

Relative Emphasis of Cost, Performance, Reliability, Organization Structure

Relaxed Mil STDs

IPPD

Profit

Competition 2/24/2008 ELF 259 SDDSDD CostCost IsIs DrivenDriven byby ScheduleSchedule DurationDuration andand RiskRisk

1.90 CSDD = $20,000,000 tSDD , ( tSDD in years ) 10000

1000 Example: 5 year ( medium risk ) SDD program C = $20,000,000 t 1.90 100 SDD SDD Low Moderate High = ( 20,000,000 ) ( 5 )1.90 Risk Risk Risk = $426,000,000 SDD CSDD, SDD Cost in Millions SDD SDD 10 0 2 4 6 8 10 12 14 tSDD, SDD Schedule Duration in Years

AGM-142 TOW 2 SLAM-ER MLRS LB Hellfire JASSM Hellfire II SLAM JDAM AGM-130 Harpoon ATACMS Tomahawk ESSM AIM-120A JSOW HARM Javelin BAT PAC-3 Patriot Note: SDD required schedule duration depends upon risk. Should not ignore risk in shorter schedule. -- Source of data: Nicholas, T. and Rossi, R., “U.S. Missile Data Book, 1999,” Data Search Associates, 1999 – SDD cost based on 1999 US$ 2/24/2008 ELF 260 LightLight WeightWeight MissilesMissiles HaveHave LowLow UnitUnit ProductionProduction CostCost

0.758 C1000th ≈ $6,100 WL , ( WL in lb ) 10000000

Javelin 1000000 Longbow Hellfire AMRAAM MLRS 100000 HARM JSOW Tomahawk

, Cost of Missile Number 1000, U.S.$ , Cost of Missile Number Example:

1000th 10000 2,000 unit buy of 100 lb missile: C 0.758 0.758 10 100 1000 10000 C1000th ≈ $6,100 WL = 6100 ( 100 ) = WL , Launch Weight, lb $200,000 Cost of 2,000 missiles = 2000 ( $200000 ) = $400,000,000 Note: -- Source of data: Nicholas, T. and Rossi, R., “U.S. Missile Data Book, 1999,” Data Search Associates, 1999 – Unit production cost based on 1999 US$ 2/24/2008 ELF 261 LLearningearning CCurveurve anandd LLargearge PProductionroduction RReduceeduce UnitUnit ProductionProduction CostCost

log2x Cx = C1st L , C2x = L Cx , where C in U.S. 99$ 1 L = 1.0

Javelin ( L = 0.764, C1st = $3.15M, Y1 = 1994 ) L = 0.9 Longbow HF ( L = 0.761, C1st = $4.31M, Y1 = 1996 ) AMRAAM ( L = 0.738, C1st = 0.1 $30.5M, Y1 = 1987 ) Example: MLRS ( L = 0.811, C1st = $0.139M, For a learning Y1 = 1980 ) curve coefficient L = 0.8 HARM ( L = 0.786, C1st = $9.73M, of L = 80%, cost of Y1 = 1981 ) unit #1000 is 11% JSOW ( L = 0.812, C1st = $2.98M, the cost of the first Y1 = 1997 ) unit L = 0.7 Cx / C1st, Cost of Cost / C1st, x of Unit Cost / Cx First Unit 0.01 Tomahawk ( L = 0.817, C1st = $13.0M, Y1 = 1980 ) 1 10 100 1000 10000 100000 1E+06 Labor intensive learning curve: L < 0.8 x, Number of Units Produced Machine intensive learning curve: L > 0.8 ) Contributors to the learning curve include: • More efficient labor Source of data: Nicholas, T. and Rossi, R., “U.S. Missile Data Book, • Reduced scrap 1999,” Data Search Associates, 1999 • Improved processes 2/24/2008 ELF 262 LowLow PartsParts CountCount ReducesReduces MissileMissile UnitUnit ProductionProduction CostCost

1000000

100000

10000

1000

100

Parts Count, Hours, or Cost ( US$ ) ( Cost or Hours, Count, Parts 10 Parts Fasteners Circuit Cards Connectors Assembly / Unit Test Hours Production Cost ( US$ )

Current Tomahawk Tactical Tomahawk

Note: Tactical Tomahawk has superior flexibility ( e.g., shorter mission planning, in-flight retargeting, BDI / BDA, modular payload ) at lower parts count / cost and higher reliability. Enabling technologies for low parts count include: casting, pultrusion / extrusion, centralized electronics, and COTS. 2/24/2008 ELF 263 TacticalTactical MissileMissile CultureCulture IsIs DrivenDriven byby RateRate ProductionProduction ofof SensorsSensors andand ElectronicsElectronics Copperhead Seeker and Electronics Production Patriot Control Section Production

Video of Hellfire Seeker and Electronics Production

2/24/2008 ELF 264 LogisticsLogistics CostCost ConsiderationsConsiderations

Peacetime Logistics Activity Wartime Logistics Activity

•Contractor Post-production Engineering •Training Manuals / Tech Data Package •Simulation and Software Maintenance •Deployment Alternatives •Configuration Management •Airlift •Engineering Support •Sealift •System Analysis •Combat Logistics •Launch Platform Integration •Launch Platform Integration •Requirements Documents •Mission Planning •Coordinate Suppliers •Field Tests •Storage Alternatives •Reliability Data •Wooden Round ( Protected ) •Maintainability Data •Open Round ( Humidity, Temp, Corrosion, Shock ) •Effectiveness Data •Reliability Maintenance •Safety Data •Surveillance •Testing •Maintenance Alternatives •First level ( depot ) •Two level ( depot, field ) •Disposal

2/24/2008 ELF 265 LogisticsLogistics CostCost LowerLower forfor SimpleSimple MissileMissile SystemsSystems

Simple: Stinger More Sophisticated: Hawk and SLAMRAAM Complex: PAC-3

Very Complex: THAAD Video of Logistics Alternatives

2/24/2008 ELF 266 LogisticsLogistics IsIs SimplerSimpler forfor LightLight WeightWeight MissilesMissiles

Support personnel for installation with 50 lb lift limit per person Support personnel for installation with 100 lb lift limit per person Machine lift for installation

2 for Installation

0 Support Personnel required Support Personnel 10 100 1000 10000 Video of Simple Logistics for a Missile Weight, lb Light weight Missile

Predator ( 21 lb ) Sidewinder ( 190 lb ) Sparrow ( 500 lb ) Laser Guided Bomb ( 2,500 lb )

2/24/2008 ELF 267 SSmallmall MEMSMEMS SSensorsensors CCanan PProviderovide HHealthealth Monitoring,Monitoring, ReducingReducing CostCost andand WeightWeight

Micro-machined Electro-Mechanical Systems ( MEMS ) Small size / low cost semiconductor manufacturing process 2,000 to 5,000 sensors on a 5 in silicon wafer Wireless ( RF ) Data Collection and Health Monitoring Distributed Sensors Over Missile Stress / strain Vibration Acoustics Temperature Pressure Reduced Logistics Cost and Improved Reliability Health monitoring Reduced Weight and Production Cost More Efficient Design 2/24/2008 ELF 268 MissileMissile CarriageCarriage Size,Size, Shape,Shape, andand WeightWeight AreAre DrivenDriven byby LaunchLaunch PlatformPlatform CompatibilityCompatibility Launch Platform Integration / Firepower US Launch Platform Launcher Carriage Span / Shape Length Weight

Launch Platform Integration / Robustness Firepower

Cost Lethality

Surface Ships Reliability Miss Distance VLS ~ 22” 263” 3400 lb Survivability Observables

~ 22”

Submarines CLS 263” 3400 lb 22”

Fighters / Rail / ~500 lb to Bombers / Ejection ~24” x 24” ~168” 3000 lb UCAVs

Ground Launch 158” 3700 lb Pods ~ 28” Vehicles ” ~ 28

Helos Rail ∼13” x 13” 70” 120 lb

2/24/2008 ELF 269 LightLight WeightWeight MissilesMissiles EnhanceEnhance FirepowerFirepower

F-18 C / E 5,000 lb

4,000 lb Weight E, carry 1

Max Strike Weapon 3,000 lb Inboard Asymmetric C, carry 1 E, carry 1 Bring-Back Load Limit 2,000 lb E, carry 2 C, carry 1 Outboard Asymmetric C, carry 2 E, carry 2 Bring-Back Load Limit E, carry 3 1,000 lb C, carry 3 C, carry 2 Clean Clean + CL Tank + CL Tank + 2 Inbd Tanks + 2 Inbd Tanks + CL Tk + 2 AIM-9 Tk + 2 + CL + CL Tk + 2 AIM-9 Tk + 2 + CL + CL Tk + 2 AGM-88 Tk + 2 + CL + CL Tk + 2 AGM-88 Tk + 2 + CL + 2 Inbd Tk + 2 AIM-9 + 2 Inbd Tk + 2 AIM-9 Configuration for Day Operation Configuration for Night Operation with Bring-Back Load with Bring-Back Load

2/24/2008 ELF 270 LaunchLaunch EnvelopeEnvelope LimitationsLimitations inin MissileMissile // LaunchLaunch PlatformPlatform PhysicalPhysical IntegrationIntegration

Off Boresight Seeker field of regard ⇒ potential obscuring from launch platform Minimum Range Launcher rail clearance and aeroelasticity ⇒ miss at min range Helo rotor downwash ⇒ miss at min range Safety Launcher retention ⇒ potential inadvertent release, potential hang-fire Launch platform local flow field α, β⇒potential unsafe separation Launch platform maneuvering ⇒ potential unsafe separation Handling qualities with stores ⇒ potential unsafe handling qualities Launch platform bay / canister acoustics ⇒ missile factor of safety Launch platform bay / canister vibration ⇒ missile factor of safety

2/24/2008 ELF 271 SStoretore SSeparationeparation WindWind TunnelTunnel TestsTests AreAre RequiredRequired forfor MissileMissile // AircraftAircraft CompatibilityCompatibility

F-18 Store Compatibility Test in AEDC 16T AV-8 Store Compatibility Test in AEDC 4T

Types of Wind Tunnel Testing for Store Compatibility - Flow field mapping with probe - Flow field mapping with store - Captive trajectory simulation - Drop testing

Example Stores with Flow Field Interaction: Kh-41 + AA-10

2/24/2008 ELF 272 ExamplesExamples ofof RailRail LaunchedLaunched andand EjectionEjection LaunchedLaunched MissilesMissiles

Example Rail Launcher: Hellfire / Brimstone Example Ejection Launcher: AGM-86 ALCM

Video of Hellfire / Brimstone Carriage / Launch Video of AGM-86 Carriage / Launch 2/24/2008 ELF 273 ExamplesExamples ofof SafeSafe StoreStore SeparationSeparation

Laser Guided Bombs Drop from F-117

AMRAAM Rail Launch from F-16 Video of Rapid Drop ( 16 Bombs ) from B-2 2/24/2008 ELF 274 ExamplesExamples ofof StoreStore CompatibilityCompatibility ProblemsProblems

Unsafe Separation Hang-Fire Store Aeroelastic Instability

2/24/2008 ELF 275 MIL-STD-8591MIL-STD-8591 AircraftAircraft StoreStore SuspensionSuspension andand EjectionEjection LauncherLauncher RequirementsRequirements

Store Weight / Parameter 30 Inch Suspension 14 Inch Suspension

♦ Weight Up to 100 lb Not Applicable Yes • Lug height ( in ) 0.75 • Min ejector area ( in x in ) 4.0 x 26.0

♦ Weight 101 to 1,450 lb Yes Yes • Lug height ( in ) 1.35 1.00 • Min lug well ( in ) 0.515 0.515 • Min ejector area ( in x in ) 4. 0 x 36.0 4.0 x 26.0

♦ Weight Over 1,451 lb Yes Not Applicable • Lug height ( in ) 1.35 • Min lug well ( in ) 1.080 • Min ejector area ( in x in ) 4.0 x 36.0

Ejection Stroke

2/24/2008 ELF 276 MIL-STD-8591MIL-STD-8591 AircraftAircraft StoreStore RailRail LauncherLauncher ExamplesExamples

Rail Launcher Forward Hanger Aft Hanger LAU-7 Sidewinder Launcher 2.260 2.260

LAU 117 Maverick Launcher 1.14 7.23

Note: Dimensions in inches. • LAU 7 rail launched store weight and diameter limits are ≤ 300 lb, ≤ 7 in •LAU 117 rail launched store weight and diameter limits are ≤ 600 lb, ≤ 10 in 2/24/2008 ELF 277 CompressedCompressed CarriageCarriage MissilesMissiles ProvideProvide HigherHigher FirepowerFirepower

Baseline AIM-120B AMRAAM

Compressed Carriage AIM-120C AMRAAM ( Reduced Span Wing / Tail )

Baseline AMRAAM: Loadout of 2 AMRAAM per F-22 Semi- Bay Compressed Carriage 17.5 in 17.5 in AMRAAM: Loadout of 3 AMRAAM per F-22 Semi-Bay

12.5 in 12.5 in 12.5 in Video of Longshot Kit on CBU-97 Note: Alternative approaches to compressed carriage include surfaces with small span, folded surfaces, wrap around surfaces, and planar surfaces that extend ( e.g., switch blade, Diamond Back, Longshot ). 2/24/2008 ELF 278 EExamplexample ooff AiAircraftrcraft CCarriagearriage anandd FiFirere CControlontrol InterfacesInterfaces

Fire Control / Folding Flight Control Avionics Electrical Suspension Access Cover Folding Wing Umbilical Safety Pin Wing Deploy Lug Suspension Connector Safety Pin Lug

Example: ADM-141 TALD ( Tactical Air-Launched Decoy ) Carriage and Fire Control Interfaces

2/24/2008 ELF 279 ExampleExample ofof ShipShip WeaponWeapon CarriageCarriage andand Launcher,Launcher, Mk41Mk41 VLSVLS Cell Cell Before After Canister Cell Hatch Firing Firing Exhaust Hatch Ship Deck Missile Cover

Plenum 8 Modules / Magazine Module Gas Management

Tomahawk Launch 8 Canister Cells / Module Standard Missile Launch 2/24/2008 ELF 280 RRobustnessobustness IIss RRequiredequired fforor CCarriage,arriage, ShiShipping,pping, andand StorageStorage EnvironmentEnvironment Environmental Parameter Typical Requirement Video: Ground / Sea Environment

Surface Temperature -60° F* to 160° F Surface Humidity 5% to 100% Rain Rate 120 mm / h** Surface Wind 100 km / h steady*** 150 km / h gusts**** Salt fog 3 g / mm2 deposited per year Vibration 10 g rms at 1,000 Hz: MIL STD 810, 648, 1670A Shock Drop height 0.5 m, half sine wave 100 g / 10 ms: MIL STD 810, 1670A Acoustic 160 dB

Note: MIL-HDBK-310 and earlier MIL-STD-210B suggest 1% world-wide climatic extreme typical requirement. * Lowest recorded temperature = -90° F. 20% probability temperature lower than -60° F during worst month of worst location. ** Highest recorded rain rate = 436 mm / h. 0.5% probability greater than 120 mm / h during worst month of worst location. *** Highest recorded steady wind = 342 km / h. 1% probability greater than 100 km / h during worst month of worst location. **** Highest recorded gust = 378 km / h. 1% probability greater than 150 km / h during worst month of worst location. 2/24/2008 ELF 281 SSummaryummary ooff MeasuresMeasures ooff MeritMerit andand LaunchLaunch PlatformPlatform IntegrationIntegration Measures of Merit Robustness Warhead lethality Miss distance Carriage and launch observables Other survivability considerations Reliability Cost Launch Platform Integration Firepower, weight, fitment Store separation Launch platform handling qualities, aeroelasticity Hang-fire Vibration Standard launchers Carriage and storage environment Discussion / Questions? Classroom Exercise ( Appendix A ) 2/24/2008 ELF 282 MeasuresMeasures ofof MeritMerit andand LaunchLaunch PlatformPlatform IntegrationIntegration ProblemsProblems

1. IR signal attenuation is greater than 100 dB per km through a c____. 2. GPS / INS enhances seeker lock-on in adverse weather and ground c______. 3. A data link can enhance missile seeker lock-on against a m_____ target. 4. An example of a missile counter-counter measure to flares is an i______i_____ seeker. 5. Compared to a mid-wave IR seeker, a long wave IR seeker receives more energy from a c___ target. 6. High fineness kinetic energy penetrators are required to defeat b_____ targets. 7. For the same lethality with a blast fragmentation warhead, a small decrease in miss distance allows a large decrease in the required weight of the w______. 8. For a blast / frag warhead, a charge-to-metal ratio of about one is required to achieve a high total fragment k______e_____. 9. A blast fragmentation warhead tradeoff is the number of fragments versus the individual fragment w_____.

2/24/2008 ELF 283 MeasuresMeasures ofof MeritMerit andand LaunchLaunch PlatformPlatform IntegrationIntegration ProblemsProblems (( contcont ))

10. Kinetic energy penetration is a function of the penetrator diameter, length, density, and v______. 11. In proportional homing guidance, the objective is to make the line-of-sight angle rate equal to z___. 12. Aeromechanics contributors to missile time constant are flight control effectiveness, flight control system dynamics, and dome e____ s____. 13. Miss distance due to heading error is a function of missile navigation ratio, velocity, time to correct the heading error, and the missile t___ c______. 14. A missile must have about t_____ times the maneuverability of the target. 15. Minimizing the miss distance due to radar glint requires a high resolution seeker, an optimum missile time constant and an optimum n______r____. 16. Weapons on low observable launch platforms use i______carriage. 17. Weapons on low observable launch platforms use m______smoke propellant. 18. For an insensitive munition, burning is preferable to detonation because it releases less p____.

2/24/2008 ELF 284 MeasuresMeasures ofof MeritMerit andand LaunchLaunch PlatformPlatform IntegrationIntegration ProblemsProblems (( contcont ))

19. Missile system reliability is enhanced by subsystem reliability and low p____ count. 20. High cost subsystems of missiles are sensors, electronics, and p______. 21. Missile SDD cost is driven by the program duration and r___. 22. Missile unit production cost is driven by the number of units produced, learning curve, and w_____. 23. First level maintenance is conducted at a d____. 24. A standard launch system for U.S. Navy ships is the V______L_____ S_____. 25. Most light weight missiles use rail launchers while most heavy weight missiles use e______launchers. 26. Higher firepower is provided by c______carriage. 27. The typical environmental requirement from MIL-HDBK-310 is the _% world- wide climatic extreme.

2/24/2008 ELF 285 OutlineOutline

Rocket Baseline Missile

Standoff range requirement

Wing sizing requirement

Multi-parameter harmonization

Lofted range comparison

Ramjet Baseline Missile

Range robustness

Propulsion and fuel alternatives

Velocity control

Computer Aided Conceptual Design Sizing Tools

Soda Straw Rocket Design, Build, and Fly

2/24/2008 ELF 287 AiAirr-to-Air-to-Air EngagementEngagement AnalysisAnalysis ProcessProcess andand AssumptionsAssumptions

F-pole range provides kill of head-on threat outside of threat weapon launch range Aircraft contrast for typical engagement C = 0.18 Typical visual detection range by target ( Required F-pole range )

RD = 3.3 nm Typical altitude and speed of launch aircraft, target aircraft, and missile h = 20k ft altitude

VL = Mach 0.8 = 820 ft / s

VT = Mach 0.8 = 820 ft / s

VM = 2 VT = 1,640 ft / s

2/24/2008 ELF 288 AssumedAssumed AiAirr-to-Air-to-Air EngagementEngagement ScenarioScenario forfor Head-onHead-on InterceptIntercept RL= VM tf + VT tf R = V t -V t t = 0 s (Launch Missile) F-Pole M f L f Red Aircraft ( 820 ft / s ) Blue Aircraft ( 820 ft / s ) Blue Missile ( 1640 ft / s )

RL= Launch Range = 10.0 nm

RF = Missile Flight Range = 6.7 nm

t = tf = 24.4 s ( Missile Impacts Target )

Blue Aircraft Red Aircraft ( 820 ft / s ) Destroyed

R F-pole = 3.3 nm

2/24/2008 ELF 289 TargetTarget CContrastontrast andand SSizeize DriveDrive VisualVisual DetectionDetection andand RecognitionRecognition RangeRange 1/2 2 RD = 1.15 [ Atp ( C – CT )] , RD in nm, Atp in ft 8 RR = 0.29 RD Visual Detection Range, m nm Visual Recognition 6 Range, nm

Note:

RD = Visual detection range for 4 probability of detection PD = 0.5 C = Contrast

Example: CT = Visual threshold contrast = 0.02 If C = 0.18 A = Target presented area = 50 ft2 2 tp RD = 3.3 nm RR = Visual recognition range RR = 1.0 nm θF = Pilot visual fovial angle = 0.8 deg Clear weather R, Visible for Range 50 ft2 Target, n 0 Pilot search glimpse time = 1 / 3 s 0.01 0.1 1 C, Contrast

C = 0.01 C = 0.02 C = 0.05 C = 0.1 C = 0.2 C = 0.5 C = 1.0 2/24/2008 ELF 290 HighHigh MissileMissile VelocityVelocity ImprovesImproves StandoffStandoff RangeRange

Note: Head-on intercept RF-Pole / RL = 1 – ( VT + VL ) / ( VM + VT )

RF-Pole = Standoff range at intercept R = Launch range 1 L VM = Missile average velocity e V = Target velocity 0.8 T VL = Launch velocity VL / VM = 0 0.6 VL / VM = 0.2 VL / VM = 0.5 0.4 VL / VM = 1.0

0.2 Example:

F-Pole / Range Rang Launch • VL = VT • V = 2 V 0 M T • Then VT / VM = VL / VM = 0.5 00.20.40.60.81• RF-Pole / RL = 0.33 • R = R = 3.3 nm Target Velocity / Missile Velocity F-Pole D • RL = 3.3 / 0.33 = 10.0 nm

2/24/2008 ELF 291 MissileMissile FlightFlight RangeRange RequirementRequirement IsIs GreatestGreatest forfor aa TailTail ChaseChase InterceptIntercept

( RF / RL )Head-on = ( VM / VT ) / [(VM / VT ) + 1 ]

3 ( RF / RL )TailChase = ( VM / VT ) / [(VM / VT ) - 1 ]

2.5

( RF / RL ) Head-on 1.5 ( RF / RL ) Tail Chase 1 Examples: •Head-on Intercept • V = 1,640 ft / s, V = 820 ft / s 0.5 M T • VM / VT = 1640 / 820 = 2 • RF / RL = 2 / ( 2 + 1 ) = 0.667

RF / RL, Missile Flight Range / Launch Range / Range Flight Missile RL, / RF • R = 10.0 nm 0 L • RF = 0.667 ( 10.0 ) = 6.67 nm 012345•Tail Intercept at same conditions • R / R = 2 / ( 2 – 1 ) = 2.0 VM / VT, Missile Velocity / Target Velocity F L • RF = 2.0 ( 10.0 ) = 20.0 nm

2/24/2008 ELF 292 DrawingDrawing ofof RocketRocket BaselineBaseline MissileMissile ConfigurationConfiguration

STA 60.8 STA 125.4 19.4 LEmac at 3.4 STA 131.6 18.5 LEmac at STA 67.0 Λ = 45° BL 8.0 BL 10.2 16.1 8.0 d 12.0

cgBO cgLaunch

Λ = 57° Rocket Motor 40.2 STA 0 19.2 46.1 62.6 84.5 138.6 143.9 Nose Forebody Payload Midbody Aftbody Tailcone Bay

Note: Dimensions in inches Source: Bithell, R.A. and Stoner, R.C., “Rapid Approach for Missile Synthesis, Vol. 1, Rocket Synthesis Handbook,” AFWAL-TR-81-3022, Vol. 1, March 1982.

2/24/2008 ELF 293 MassMass PropertiesProperties ofof RocketRocket BaselineBaseline MissileMissile

Component Weight, lb. C.G. STA, in. 1 Nose ( Radome ) 4.1 12.0 3 Forebody structure 12.4 30.5 Guidance 46.6 32.6 2 Payload Bay Structure 7.6 54.3 Warhead 77.7 54.3 4 Midbody Structure 10.2 73.5 Control Actuation System 61.0 75.5 5 Aftbody Structure 0.0 – Rocket Motor Case 47.3 107.5 Insulation ( EDPM – Silica ) 23.0 117.2 6 Tailcone Structure 6.5 141.2 Nozzle 5.8 141.2 Fixed Surfaces 26.2 137.8 Movable Surfaces 38.6 75.5 Burnout Total 367.0 76.2 Propellant 133.0 107.8 Launch Total 500.0 84.6

2/24/2008 ELF 294 RocketRocket BaselineBaseline MissileMissile DefinitionDefinition

Body Dome Material Pyroceram Airframe Material Aluminum 2219-T81 Length, in 143.9 Diameter, in 8.0 Airframe thickness, in 0.16 Fineness ratio 17.99 Volume, ft3 3.82 Wetted area, ft2 24.06 Nozzle exit area, ft2 0.078 Boattail fineness ratio 0.38 Nose fineness ratio 2.40 Nose bluntness 0.0 Boattail angle, deg 7.5 Movable surfaces ( forward ) Material Aluminum 2219-T81 Planform area, ft2 ( 2 panels exposed ) 2.55 Wetted area, ft2 ( 4 panels ) 10.20 Aspect ratio ( 2 panels exposed ) 2.82 Taper ratio 0.175 Root chord, in 19.4 Tip chord, in 3.4 Span, in ( 2 panels exposed ) 32.2 Leading edge sweep, deg 45.0

2/24/2008 ELF 295 RocketRocket BaselineBaseline MissileMissile DefinitionDefinition (( contcont ))

Movable surfaces ( continued ) Mean aerodynamic chord, in 13.3 Thickness ratio 0.044 Section type Modified double wedge Section leading edge total angle, deg 10.01 xmac, in 67.0 ymac, in ( from root chord ) 6.2 Actuator rate limit, deg / s 360.0 Fixed surfaces ( aft ) Material Aluminum 2219-T81 Modulus of elasticity, 106 psi 10.5 Planform area, ft2 ( 2 panels exposed ) 1.54 Wetted area, ft2 ( 4 panels ) 6.17 Aspect ratio ( 2 panels exposed ) 2.59 Taper ratio 0.0 Root chord, in 18.5 Tip chord, in 0.0 Span, in ( 2 panels exposed ) 24.0 Leading edge sweep, deg 57.0 Mean aerodynamic chord, in 12.3 Thickness ratio 0.027 Section type Modified double wedge Section leading edge total angle, deg 6.17 xmac, in 131.6 ymac, in ( from root chord ) 4.0 2/24/2008 ELF 296 RocketRocket BaselineBaseline MissileMissile DefinitionDefinition (( contcont ))

References values Reference area, ft2 0.349 Reference length, ft 0.667 Pitch / Yaw Moment of inertia at launch, slug-ft2 117.0 Pitch / Yaw Moment of inertia at burnout, slug-ft2 94.0 Rocket Motor Performance ( altitude = 20k ft, temp = 70° F ) Burning time, sec ( boost / sustain ) 3.69 / 10.86 Maximum pressure, psi 2042 Average pressure, psi ( boost / sustain ) 1769 / 301 Average thrust, lbf ( boost / sustain ) 5750 / 1018 Total impulse, lbf-s ( boost / sustain ) 21217 / 11055 Specific impulse, lbf-s / lbm ( boost / sustain ) 250 / 230.4 Propellant Weight, lbm ( boost / sustain ) 84.8 / 48.2 Flame temperature @ 1,000 psi, °F 5282 / 5228 Propellant density, lbm / in3 0.065 Characteristic velocity, ft / s 5200 Burn rate @ 1000 psi, in / s 0.5 Burn rate pressure exponent 0.3 2/24/2008 ELF 297 RocketRocket BaselineBaseline MissileMissile DefinitionDefinition (( contcont ))

Propellant ( continued ) Burn rate sensitivity with temperature, % / °F0.10 Pressure sensitivity with temperature, % / °F0.14 Rocket Motor Case Yield / ultimate strength, psi 170,000 / 190,000 Material 4130 Steel Modulus of elasticity, psi 29.5 x 106 psi Length, in 59.4 Outside diameter, in 8.00 Thickness, in (minimum) 0.074 Burst pressure, psi 3140 Volumetric efficiency 0.76 Grain configuration Three slots + web Dome ellipse ratio 2.0 Nozzle Housing material 4130 Steel Exit geometry Contoured ( equiv. 15° ) Throat area, in2 1.81 Expansion ratio 6.2 Length, in 4.9 Exit diameter, in 3.78

2/24/2008 ELF 298 RRocketocket BBaselineaseline MiMissilessile HHasas BBoost-Sustainoost-Sustain ThrustThrust -- Time Time HistoryHistory 8

6 Boost Total Impulse = ∫Tdt = 5750 ( 3.69 ) = 21217 lb-s

Thrust – 1,000 lb

2 Sustain Total Impulse = ∫Tdt = 1018 ( 10.86 ) = 11055 lb-s

0 0481216 Time – seconds Note: Altitude = 20k ft, Temperature = 70° F Total impulse drives velocity change 2/24/2008 ELF 299 RocketRocket BaselineBaseline MissileMissile AerodynamicAerodynamic CharacteristicsCharacteristics 2 SRef = 0.349 ft , lRef = d = 0.667 ft, CG at STA 75.7, δ = 0 deg 0 m -4.0 0.6 4.60 -8.0 M = 1.2 and 1.5

3.95 2.35 -12.0 2.0

Pitching Moment – C -16.0 20 M 1.5

N 16 2.0 2.35 1.2 2.87 12 0.6 3.95 4.60 8

Normal Force ~ C 4 0 048121620 24 α, Angle of Attack – Deg 2/24/2008 ELF 300 RocketRocket BaselineBaseline MissileMissile AerodynamicAerodynamic CharacteristicsCharacteristics (( contcont )) 0.3 .006 2 K2 0.2 .004 K

~ Per Deg 1 2 = 0 deg, Per Deg 0.1 .002 2 α , K C = C + K δ + K αδ

1 A Aα = 0 1 2 at K δ N 0

C 0

1.2 1.2 Power Off

= 0 deg 0.8 0.8 α = 0 deg, Per Deg at α

A Power On C

0.4 at 0.4 δ m C 0 0 012345 012345 M, Mach Number M, Mach Number

2/24/2008 ELF 301 HighHigh AltitudeAltitude LaunchLaunch EnhancesEnhances RocketRocket BaselineBaseline RangeRange

Burnout Vmax = 2524 ft / s 40

Termination Mach = 1.5 30 Boost / Coast ft

3 Sustain Vmax = 2147 ft / s 20

Altitude ~ 10 ML = 0.7 C = 0.65 10 DAVG Constant Altitude Flight Vmax = 1916 ft / s 0 0 5 10 15 20 25 Range ~ nm 2/24/2008 ELF 302 LowLow AltitudeAltitude LaunchLaunch andand HighHigh AlphaAlpha ManeuversManeuvers EnhanceEnhance RocketRocket BaselineBaseline TurnTurn PerformancePerformance

4 10 Alt. α 3

1 10k ft 15° Cross Range 1,000 ft. 2 10k ft 10° 5 1 Termination at M = 1.0 3 40k ft 15° 2 Marks at 2 s intervals 4 40k ft 10° 0 -10 -5 0 5 10 Down Range 1,000 ft. Note: Off boresight envelope that is shown does not include the rocket baseline seeker field-of-regard limit ( 30 deg ). 2/24/2008 ELF 303 ParedoParedo ShowsShows RangeRange ofof RocketRocket BaselineBaseline DrivenDriven byby IISPSP,, PropellantPropellant Weight,Weight, Drag,Drag, andand StaticStatic MarginMargin

1.5

Note: Rocket baseline: 1 hL = 20k ft, ML = 0.7, MEC = 1.5

R@ ML = 0.7, hL = 20k ft = 9.5 nm Nondimensional 0.5 Example: 10% increase in propellant Range weight ⇒ 8.8% increase in flight range Sensitivity to Parameter 0 Isp Prop. CD0 Drag- Static Thrust Inert Weight Due-to- Margin Weight -0.5 Lift

-1 Parameter

2/24/2008 ELF 304 BoostBoost -- Sustain Sustain TrajectoryTrajectory AssumptionsAssumptions

Assumptions 1 degree of freedom Constant altitude Simplified equation for axial acceleration based on thrust, drag, and weight

nX = ( T – D ) / W Missile weight varies with burn rate and time

W = WL –WP t / tB Drag is approximated by D = C q S DO

2/24/2008 ELF 305 ExampleExample ofof RocketRocket BaselineBaseline AxialAxial AccelerationAcceleration

nX = ( T - D ) / W 15 Note: t = 24.4 s Boost f ML = 0.8 hL = 20,000 ft g 10 TB = 5750 lb tB = 3.69 s TS = 1018 lb tS = 10.86 s D = 99 lb at Mach 0.8 5 D = 1020 lb at Mach 2.1 WL = 500 lb WP = 133 lb Sustain

nx, Axial Acceleration, Acceleration, Axial nx, 0 0 5 10 15 20 25 Coast

-5 t, Time, s

2/24/2008 ELF 306 ExampleExample ooff RocketRocket BaselineBaseline MissileMissile VelocityVelocity vsvs TimeTime

ΔV / ( gc ISP ) = -( 1 -DAVG / T ) ln ( 1 - Wp / Wi ), During Boost-Sustain V / V = 1 / { 1 + t / { 2 W / [ g ρ S ( C ) V ]}}, During Coast BO BO c AVG Ref D0 AVG BO

3000 Sustain

Boost Coast 2000

1000 V, Velocity, ft / s Note:

ML = 0.8

hL = 20k feet 0 0 5 10 15 20 25

t, Time, s

2/24/2008 ELF 307 RRangeange anandd TiTime-to-Targetme-to-Target ooff RRocketocket BBaselineaseline MissileMissile MeetMeet RequirementsRequirements

10 R = Δ Rboost + Δ Rsustain + Δ Rcoast

m Coast 6

(RF)Req = 6.7 nm @ t =24.4 s 4 Sustain R, Flight Range, n 2 Note:

ML = 0.8 Boost hL = 20k ft 0 0 5 10 15 20 25 t, Time, s

2/24/2008 ELF 308 SizingSizing ExamplesExamples

Rocket Baseline Missile

Standoff range requirement

Wing sizing requirement

Multi-parameter harmonization

Lofted range comparison

Ramjet Baseline Missile

Range robustness

Propulsion and fuel alternatives

Velocity control

Computer Aided Conceptual Design Sizing Tools

Soda Straw Rocket Design, Build, and Fly

2/24/2008 ELF 309 ExampleExample ooff WingWing SSizingizing toto SSatisfyatisfy RequiredRequired ManeuverManeuver AccelerationAcceleration

Size Wing for the Assumptions

( nZ )Required = 30 g to counter 9 g maneuvering target ) ( nZ ) = Δ ( nZ )Wing + Δ ( nZ )Body + Δ ( nZ )Tail

Rocket Baseline @ Mach 2 20,000 ft altitude 367 lb weight ( burnout )

From Prior Example, Compute

αWing = α’Max = ( α + δ )Max = 22 deg for rocket baseline Video of Intercept of Maneuvering Target α = 0.75δ, αBody = αTail = 9.4 deg

Δ ( nZ )Body = q SRef ( CN )Body / W = 2725 ( 0.349 ) ( 1.28 ) / 367 = 3.3 g ( from body )

Δ ( nZ )Tail = q STail [( CN )Tail ( SRef /STail )] / W = 2725 ( 1.54 ) ( 0.425 ) / 367 = 4.9 g ( from tail )

Δ ( nZ )Wing = ( nZ )Required - Δ ( nZ )Body - Δ ( nZ )Tail = 30 – 3.3 – 4.9 = 21.8 g

2 ( SW )Required = Δ ( nZ )Wing W / { q [( CN )Wing (SRef /SWing )]} = 21.8 ( 367 ) / {( 2725 ) ( 1.08 )} = 2.72 ft

2 Note: ( SW )RocketBaseline = 2.55 ft 2/24/2008 ELF 310 WingWing SizingSizing toto SatisfySatisfy RequiredRequired TurnTurn RateRate

Assume . ( γ )Required > 18 deg / s to counter 18 deg / s maneuvering aircraft

Rocket Baseline @ Mach 2 20,000 ft altitude 367 lb weight ( burnout )

γi = 0 deg

Compute . γ = gc n / V = [ q SRef CNα α + q SRef CNδ δ - W cos ( γ ) ] / [( W / gc ) V ] α / δ = 0.75 α’= α + δ = 22 deg ⇒δ= 12.6 deg, α = 9.4 deg γ. = [ 2725 ( 0.349 )( 0.60 )( 9.4 ) +2725 ( 0.349 )( 0.19 )( 12.6 ) – 367 ( 1 )] / ( 367 / 32.2 )( 2074 ) = 0.31 rad / s or 18 deg / s

Note: ( SW )RocketBaseline ⇒ 18 deg / s Turn Rate

2/24/2008 ELF 311 WingWing SizingSizing toto SatisfySatisfy RequiredRequired TurnTurn RadiusRadius

Assume Maneuvering Aircraft Target with . γ = 18 deg / s = 0.314 rad / s V = 1000 ft / s . ( RT )Target = V / γ = 1000 / 0.314 = 3183 ft

Assume Rocket Baseline @ Mach 2 20,000 ft altitude 367 lb weight ( burnout ) Compute . γ = 18 deg / s ( prior figure ) . ( RT )RocketBaselinet = V / γ = 2074 / 0.314 = 6602 ft

Note: ( RT )RocketBaselinet > ( RT )Target ⇒ Rocket Baseline Can Be Counter- measured by Target in a Tight Turn Counter-Countermeasure Alternatives Larger Wing Higher Angle of Attack Longer Burn Motor with TVC

2/24/2008 ELF 312 SizingSizing ExamplesExamples

Rocket Baseline Missile

Standoff range requirement

Wing sizing requirement

Multi-parameter harmonization

Lofted range comparison

Ramjet Baseline Missile

Range robustness

Propulsion and fuel alternatives

Velocity control

Computer Aided Conceptual Design Sizing Tools

Soda Straw Rocket Design, Build, and Fly

2/24/2008 ELF 313 CombinedCombined WeightWeight // MissMiss DistanceDistance Drivers:Drivers: NozzleNozzle ExpansionExpansion andand MotorMotor VolumetricVolumetric EfficiencyEfficiency

Sensitivity Parameter Baseline W* σ* Variation Fixed surface number of panels 4 3 +0.054 +0.100 Movable surface number of panels 4 2 +0.071 +0.106 Design static margin at launch 0.40 0.30 +0.095 +0.167 Wing movable surface sweep ( deg ) 45.0 49.5 -0.205 +0.015 Tail fixed surface sweep ( deg ) 57.0 60.0 +0.027 +0.039 Wing movable surface thickness ratio 0.044 0.034 +0.041 +0.005 Nose fineness ratio 2.4 2.6 -0.016 -0.745 Rocket chamber sustain pressure ( psi ) 301 330 -0.076 -0.045 Boattail fineness ratio ( length / diameter ) 0.38 0.342 +0.096 +0.140 Nozzle expansion ratio 6.2 6.82 -0.114 -0.181 Motor volumetric efficiency 0.76 0.84 -0.136 -0.453 Propellant density ( lb / in3 ) 0.065 0.084 -0.062 +0.012 Boost thrust ( lb ) 5,750 6,325 +0.014 -0.018 Sustain thrust ( lb ) 1,018 1,119 +0.088 +0.246 Characteristic velocity ( ft / s ) 5,200 5,720 -0.063 -0.077 Wing location ( percent total length ) 47.5 42.75 +0.181 -0.036 Baseline: Weight = 500 lb, Miss distance = 62.3 ft Note: Strong impact with synergy Strong impact W* = weight sensitivity for parameter variation = ΔW / W Moderate impact with synergy σ* = miss distance sensitivity for parameter variation = Δσ/ σ Moderate impact 2/24/2008 ELF 314 AA HarmonizedHarmonized MissileMissile CanCan HaveHave SmallerSmaller MissMiss DistanceDistance andand LighterLighter WeightWeight Missile Configured for Minimum: Parameter Baseline Value Weight Miss Distance Harmonized Judicious changes Boost thrust ( lb ) 5,750 3,382 3,382 3,382 Wing location ( percent missile length to 1/4 mac ) 47.5 47 44 46 Wing taper ratio 0.18 0.2 0.2 0.2 Nose fineness ratio 2.4 3.2 2.55 2.6 Nose blunting ratio 0.0 0.05 0.05 0.05 Nozzle expansion ratio 6.2 15 15 15 Sustain chamber pressure ( psi ) 301 1,000 1,000 1,000 Boattail fineness ratio 0.38 0.21 0.21 0.21 Tail leading edge sweep ( deg ) 57 50 50 50 Technology limited changes No. wing panels 4 2 2 2 No. tail panels 4 3 3 3 Wing thickness ratio 0.044 0.030 0.030 0.030 Wing leading edge sweep ( deg ) 45 55 55 55 Static margin at launch ( diam ) 0.4 0.0 0.0 0.0 Propellant density ( lb / in3 ) 0.065 0.084 0.084 0.084 Motor volumetric efficiency 0.76 0.84 0.84 0.84 Measures of Merit Total weight ( lb ) 500 385.9 395.0 390.1 Miss distance ( ft ) 62.3 63.1 16.2 16.6 Time to target ( s ) 21.6 23.8 23.6 23.8 Length ( in ) 144 112.7 114.7 114.9 Mach No. at burnout 2.20 2.08 2.09 2.07 Weight of propellant ( lb ) 133 78.3 85.4 85.9 Wing area ( in2 ) 368.6 175.5 150.7 173.8 Tail area ( in2 ) 221.8 109.1 134.5 112.0

2/24/2008 *Note: Value of driving parameter ELF 315 BaselineBaseline MissileMissile vsvs HarmonizedHarmonized MissileMissile

144”

45° 57° 4 wings / 4 tails Nose 2.4 Weight ( lb ); 500 Propellant Density 0.065 Surfaces; { 2 wings / 3 tails Fineness; 2.6 ( lb / in3 ); 0.084 390

55° 50° 115”

2/24/2008 ELF 316 SizingSizing ExamplesExamples

Rocket Baseline Missile

Standoff range requirement

Wing sizing requirement

Multi-parameter harmonization

Lofted range comparison

Ramjet Baseline Missile

Range robustness

Propulsion and fuel alternatives

Velocity control

Computer Aided Conceptual Design Sizing Tools

Soda Straw Rocket Design, Build, and Fly

2/24/2008 ELF 317 LoftedLofted GlideGlide TrajectoryTrajectory ProvidesProvides ExtendedExtended RangeRange

Using Rocket Baseline, Compare Lofted Launch-Coast-Glide Trajectory Lofted Launch-Ballistic Trajectory Constant Altitude Trajectory Assume for Lofted Launch-Coast-Glide Trajectory:

γi = 45 deg γ = 45 deg during boost and sustain γ = 45 deg coast

Switch to ( L / D )max glide at optimum altitude

( L / D )maxg glide trajectory after apogee

hi = hf = 0 ft Velocity, Horizontal Range, and Altitude During Initial Boost @ γ = 45 deg

ΔV = - gc ISP [ 1 – ( DAVG / T ) - ( WAVG sin γ ) / T ] ln ( 1 - Wp / Wi ) = -32.2 ( 250 ) [ 1 - ( 419 / 5750 ) – 458 ( 0.707 ) / 5750 ] ln ( 1 - 84.8 / 500 ) = 1,303 ft / s

ΔR = ( Vi + ΔV / 2 ) tB = ( 0 + 1303 / 2 ) 3.69 = 2,404 ft

ΔRx = ΔR cos γi = 2404 ( 0.707 ) = 1,700 ft

ΔRy = ΔR sin γi = 2404 ( 0.707 ) = 1,700 ft

h = hi + ΔRy = 0 + 1700 = 1,700 ft 2/24/2008 ELF 318 LoftedLofted GlideGlide TrajectoryTrajectory ProvidesProvides ExtendedExtended RangeRange (( contcont )) Velocity, Horizontal Range, and Altitude During Sustain @ γ = 45 deg

ΔV = - gc ISP [ 1 – ( DAVG / T ) – ( WAVG sin γ ) / T ] ln ( 1 - Wp / Wi ) = -32.2 ( 230.4 ) [ 1 – ( 650 / 1018 ) – 391 ( 0.707 ) / 1018 ] ln ( 1 - 48.2 / 415.2 ) = 81 ft / sec

VBO = 1303 + 81 = 1,384 ft / s

ΔR = ( Vi + ΔV / 2 ) tB = ( 1303 + 81 / 2 ) 10.86 = 14,590 ft

ΔRx = ΔR cos γi = 14590 ( 0.707 ) = 10,315 ft

ΔRy = ΔR sin γi = 14,590 ( 0.707 ) = 10,315 ft

h = hi + ΔRy = 1700 + 10315 = 12,015 ft

Velocity, Horizontal Range, and Altitude During Coast @ γ = 45 deg to h@( L / D )max V = V { 1 – [( g sin γ ) / V ] t } / { 1 + {[ g ρ S ( C ) V ] / ( 2 W )} t } = 1384 { 1 – coast i c i c AVG Ref D0 AVG i [( 32.2 ( 0.707 )) / 1384 ] 21 } / { 1 + {[ 32.2 ( 0.001338 ) ( 0.349 ) ( 0.7 ) ( 1384 )] / ( 2 ( 367 ))} 21 } = 674 ft / s R = { 2 W / [ g ρ S ( C ) )]} ln { 1 – [ g 2 ρ S ( C ) / ( 2 W )] [ sin γ ] t2 + coast c AVG Ref D0 AVG c AVG Ref D0 AVG {[ g ρ S ( C ) V ] / ( 2 W )} t } = { 2 ( 367 ) / [ 32.2 ( 0.001338 ) ( 0.349 ) ( 0.7 )] ln c AVG Ref D0 AVG i { 1 – [ (32.2)2 ( 0.001338 ) ( 0.349 ) ( 0.7 ) / (( 2 ( 367 ))] [ 0.707 ] ( 21 )2 + {[ 32.2 ( 0.001338 ) ( 0.349 ) ( 0.7 ) ( 1384 )] / ( 2 ( 367 ))} 21 } = 17148 ft

( Rx )coast = ( Ry )coast = Rcoast sinγ = 17148 ( 0.707 ) = 12124 ft

2/24/2008 ELF 319 LoftedLofted GlideGlide TrajectoryTrajectory ProvidesProvides ExtendedExtended RangeRange (( contcont ))

Flight Conditions At End-of-Coast Are: t = 35 s V = 674 ft / s h = 24,189 ft q = 251 psf M = 0.66

( L / D )max = 5.22 α( L / D )max = 5.5 deg Initiate α = α( L / D )max = 5.5 deg at h = 24,189 ft Incremental Horizontal Range During ( L / D )max Glide Is

ΔRx = ( L / D ) Δh = 5.22 ( 24189 ) = 126,267 ft Total Horizontal Range for Elevated Launch-Coast-Glide Trajectory Is

Rx = ΣΔRx = ΔRx,Boost + ΔRx,Sustain + ΔRx,Coast + ΔRx,Glide = 1700 + 10315 + 12124 + 126267 = 150406 ft = 24.8 nm

2/24/2008 ELF 320 LLoftedofted GlidGlidee TTrajectoryrajectory PProvidesrovides EExtendedxtended RangeRange (( contcont ))

Note: Rocket Baseline 30 z End of boost End of sustain

Ø ÈLofted ballistic apogee, t = 35 s, V = 667 ft / s, h = 21,590 ft g e d È G ÊLofted coast apogee, t = 35 s, V = 674 ft / s, h = 24,189 ft li 5 de 4 @ 20 = B ( ®Lofted ballistic impact, t = 68 s, γ = - 71 deg, V = 1368 ft / s c L γ i a / t l D l s i ) @ i s m l a ²Lofted glide impact, t = 298 s, γ = - 10.8 deg, V = 459 ft / s t l t x i s a c a B o Ä Co-altitude flight impact, t = 115 s, V = 500 ft / s C

h, Altitude, k ft n 10 i a t s u

z Co-altitude 0 z ® Ä ² 0 102030 R, Range, nm

2/24/2008 ELF 321 SizingSizing ExamplesExamples

Rocket Baseline Missile

Standoff range requirement

Wing sizing requirement

Multi-parameter harmonization

Lofted range comparison

Ramjet Baseline Missile

Range robustness

Propulsion and fuel alternatives

Velocity control

Computer Aided Conceptual Design Sizing Tools

Soda Straw Rocket Design, Build, and Fly

2/24/2008 ELF 322 RamjetRamjet BaselineBaseline IsIs aa ChinChin InletInlet IntegralIntegral RocketRocket RamjetRamjet (( IRRIRR ))

Sta 150.3 11.6 37°

11.5

16.5

Boost Nozzle 20.375 dia

Ramjet Fuel Guidance Warhead Boost Propellant Booster, and Chin Ramjet Engine Inlet Transport Air Duct Sta 0. 23.5 43.5 76.5 126.0 Forebody Payload Bay Mid-body Aft-body Tail Cone Nose 159.0 171.0

Note: Dimensions are in inches

Source: Bithell, R.A. and Stoner, R.C. “Rapid Approach for Missile Synthesis”, Vol. II, Air-breathing Synthesis Handbook, AFWAL TR 81-3022, Vol. II, March 1982. 2/24/2008 ELF 323 MassMass PropertiesProperties ofof RamjetRamjet BaselineBaseline MissileMissile Component Weight, lb CG Sta, in Nose 15.9 15.7 Forebody Structure 42.4 33.5 Guidance 129.0 33.5 Payload Bay Structure 64.5 60.0 Warhead 510.0 60.0 Midbody Structure 95.2 101.2 Inlet 103.0 80.0 Electrical 30.0 112.0 Hydraulic System for Control Actuation 20.0 121.0 Fuel Distribution 5.0 121.0 Aftbody Structure 44.5 142.5 Engine 33.5 142.5 Tailcone Structure 31.6 165.0 Ramjet Nozzle 31.0 165.0 Flight Control Actuators 37.0 164.0 Fins ( 4 ) 70.0 157.2 End of Cruise 1,262.6 81.8 Ramjet Fuel ( 11900 in3 ) 476.0 87.0 Start of Cruise 1,738.6 83.2 Boost Nozzle ( Ejected ) 31.0 164.0 Frangible Port 11.5 126.0 End of Boost 1,781.1 84.9 Boost Propellant 449.0 142.5 2/24/2008 Booster Ignition 2,230.1ELF 96.5 324 RamjetRamjet BaselineBaseline MissileMissile DefinitionDefinition

Inlet Type Mixed compression Material Titanium Conical forebody half angle, deg 17.7 Ramp wedge angle, deg 8.36 Cowl angle, deg 8.24 Internal contraction ratio 12.2 Percent Capture area, ft2 0.79 Throat area, ft2 0.29 Body Dome Material Silicon nitride Airframe Material Titanium Combustor Material Insulated Inconel Length, in 171.0 Diameter, in 20.375 Fineness ratio 8.39 Volume, ft3 28.33 Wetted area, ft2 68.81 Base area, ft2 ( cruise ) 0.58 Boattail fineness ratio N/A Nose half angle, deg 17.7 Nose length, in 23.5

2/24/2008 ELF 325 RamjetRamjet BaselineBaseline MissileMissile DefinitionDefinition (( contcont ))

Tail ( Exposed ) Material Titanium Planform area ( 2 panels ), ft2 2.24 Wetted area ( 4 panels ), ft2 8.96 Aspect ratio ( 2 panels exposed ) 1.64 Taper ratio 0.70 Root chord, in 16.5 Span, in. ( 2 panels exposed ) 23.0 Leading edge sweep, deg 37.0 Mean aerodynamic chord, in 14.2 Thickness ratio 0.04 Section type Modified double wedge Section leading edge total angle, deg 9.1

xmac, in 150.3 ymac, in ( from root chord ) 5.4 Reference values Reference area, ft2 2.264 Reference length, ft 1.698

2/24/2008 ELF 326 EngineEngine NomenclatureNomenclature andand FlowpathFlowpath GeometryGeometry forfor RamjetRamjet BaselineBaseline ( C ) = ( C ) x ( 1 - A / S ) D0 Nose Corrected D0 Nose Uncorrected c REF 20.375 in Ac = Inlet capture area SRef = Reference area

2 Ac = 114 in

120°

Ramjet Engine Station Identification

SRef

0 1 2 3 4 5 6 Subscripts 2 2 0 Free stream flow into inlet ( Example, Ramjet Baseline at Mach 4, α = 0 deg ⇒ A0 = 104 in . Note: AC = 114 in ) 2 1 Inlet throat ( Ramjet Baseline A1 = AIT = 41.9 in ) 2 2 Diffuser exit ( Ramjet Baseline A2 = 77.3 in ) 2 3 Flame holder plane ( Ramjet Baseline A3 = 287.1 in ) 2 4 Combustor exit ( Ramjet Baseline A4 = 287.1 in ) 2 5 Nozzle throat ( Ramjet Baseline A5 = 103.1 in ) 2 6 Nozzle exit ( Ramjet Baseline A6 = 233.6 in ) 2 Ref Reference Area ( Ramjet Baseline Body Cross-sectional Area, SRef = 326 in ) 2/24/2008 ELF 327 AerodynamicAerodynamic CharacteristicsCharacteristics ofof RamjetRamjet BaselineBaseline

2 SRef = 2.264 ft lRef = dRef = 1.698 ft Xcg @ Sta 82.5 in δ = 0 deg .40 4.0 A

N Mach Mach 1.2 .30 1.2 3.0 1.5 2.0 1.5 2.0 3.0 .20 2.0 4.0 3.0 4.0 .10 1.0 Axial Force Coefficient, C Axial Force Coefficient,

0 Normal Force Coefficient, C 0 0 4 8 12 16 0 4 8 12 16 α, Angle of Attack ~ deg α, Angle of Attack ~ deg

Source: Reference 27, based on year 1974 computer program from Reference 32.

2/24/2008 ELF 328 AerodynamicAerodynamic CharacteristicsCharacteristics ofof RamjetRamjet BaselineBaseline (( contcont ))

+ .4 2 SRef = 2.264 ft lRef = dRef = 1.698 ft Xcg @ Sta 82.5 in

m 0 δ = 0 deg

-.4

Mach -.8 4.0

3.0

-1.2

Pitching Moment Coefficient, C 2.0

1.5 -1.6 1.2 04 81216 α, Angle of Attack ~ deg

Source: Reference 27, based on year 1974 computer program from Reference 32.

2/24/2008 ELF 329 AerodynamicAerodynamic CharacteristicsCharacteristics ofof RamjetRamjet BaselineBaseline (( contcont ))

2 SRef = 2.264 ft lRef = dRef = 1.698 ft Xcg @ Sta 82.5 in δ= 0 deg -.4 α = 0 deg. .4 ~ per deg δ

m -.2 .3 C 0 D

0 C .2

.10 .1

.05 0 ~ per deg 01234 δ N

C M, Mach Number

0 Source: Reference 27, based on year 1974 computer program from 012 34Reference 32. M, Mach Number

2/24/2008 ELF 330 ThrustThrust ModelingModeling ofof RamjetRamjet BaselineBaseline

100000 b 10000 h = Sea Level h = 20k ft h = 40k ft h = 60k ft 1000 Example: M = 3.5, h = 60k ft, ϕ = 1 ⇒ Max Thrust = 1,750 lb h = 80k ft Tmax, Thrust, Max l Note: Standard atmosphere

T = Tmax ϕ 100 φ = 1 if stochiometric ( f / a = 0.0667 ) 01234α = 0 deg M, Mach Number

Figure based on Reference 27 prediction 2/24/2008 ELF 331 SpecificSpecific ImpulseImpulse ModelingModeling ofof RamjetRamjet BaselineBaseline

1,500

• • • Example: M = 3.5 ⇒ I = 1,120 s 1,000 SP • • • • •

• 500 Note: • , Specific Impulse, s , Specific Standard atmosphere SP I ϕ≤1

ISP based on Reference 27 computer prediction.

0 0 12 34 M, Mach Number

2/24/2008 ELF 332 RocketRocket BoosterBooster AccelerationAcceleration // PerformancePerformance ofof RamjetRamjet BaselineBaseline

( ISP )Booster = 250 s

10 Boost Thrust ~ 1000 lb 0 0 1.0 2.0 3.0 4.0 5.0 6.0 Time ~ s Standard atmosphere 3.0 2.0 ML = 0.80 Constant altitude flyout

1.0 2.5

Boost Range ~ nm 0

0204060 Burnout Mach Number 2.0 020406080 h, Altitude 1,000 ft h, Altitude 1,000 ft

2/24/2008 ELF 333 RamjetRamjet BaselineBaseline HasHas BestBest PerformancePerformance atat HighHigh AltitudeAltitude

500

400

60,000 ft

300

Range ~ nm 200 40,000 ft

100 20,000 ft

h = SL 0 01 2 34

Note: ML = 0.8, Constant Altitude Fly-out M, Mach Number

Example, Mach 3 / 60k ft flyout ⇒ 445 nm. Breguet Range Prediction is R = V ISP ( L / D ) ln [ WBC / ( WBC -Wf )] = 2901 ( 1040 ) ( 3.15 ) ln ( 1739 / ( 1739 - 476 )) = 3,039,469 ft or 500 nm. Predicted range is 10% greater than baseline missile data. 2/24/2008 ELF 334 FFromrom PParedoaredo SSensitivity,ensitivity, RRamjetamjet BBaselineaseline RRangeange Driven by I , Fuel Weight, Thrust, and C Driven by ISPSP, Fuel Weight, Thrust, and CDD00

1.5 Example: At Mach 3.0 / 60k ft altitude cruise, 10% increase in fuel weight 1 ⇒ 9.6% increase in flight range

0.5

0 to Parameter ISP Fuel Thrust CD0, Zero- CLA, Lift- Inert -0.5 Weight Lift Drag Curve- Weight Coefficient Slope Coefficient Nondimensional Range Sensitivity Sensitivity Range Nondimensional -1 Parameter

Sea Level Flyout at Mach 2.3 20k ft Flyout at Mach 2.5 40k ft Flyout at Mach 2.8 60k ft Flyout at Mach 3.0

2/24/2008 ELF 335 RamjetRamjet BaselineBaseline FlightFlight RangeRange UncertaintyUncertainty IsIs +/-+/- 7%, 7%, 11 σσ

Parameter Baseline Value at Mach 3.0 / 60k ft Uncertainty in Parameter ΔR / R from Uncertainty

1. Specific Impulse 1040 s +/- 5%, 1σ +/- 5%, 1σ

2. Ramjet Fuel Weight 476 lb +/- 1%, 1σ +/- 0.9%, 1σ

3. Cruise Thrust ( φ = 0.39 ) 458 lb +/- 5%, 1σ +/- 2%, 1σ

4. Zero-Lift Drag Coefficient 0.17 +/- 5%, 1σ +/- 4%, 1σ

5. Lift Curve Slope Coefficient 0.13 / deg +/- 3%, 1σ +/- 1%, 1σ

6. inert Weight 1205 lb +/- 2%, 1σ +/- 0.8%, 1σ

Level of Maturity Based on Flight Demo of Prototype, Subsystem Tests, and Integration Wind tunnel tests Direct connect, freejet, and booster firing propulsion tests Structure test Mock-up Hardware-in-loop simulation Flight Test Total Flight Range Uncertainty at Mach 3.0 / 60k ft Flyout 2 2 2 2 2 2 1/2 ΔR / R = [ (ΔR / R )1 + (ΔR / R )2 + (ΔR / R )3 + (ΔR / R )4 + (ΔR / R )5 + (ΔR / R )6 ] = +/- 6.9%, 1σ R = 445 nm +/- 31 nm, 1σ 2/24/2008 ELF 336 SizingSizing ExamplesExamples

Rocket Baseline Missile

Standoff range requirement

Wing sizing requirement

Multi-parameter harmonization

Lofted range comparison

Ramjet Baseline Missile

Range robustness

Propulsion and fuel alternatives

Velocity control

Computer Aided Conceptual Design Sizing Tools

Soda Straw Rocket Design, Build, and Fly

2/24/2008 ELF 337 SSlurrylurry FuelFuel andand EEfficientfficient PackagingPackaging ProvideProvide ExtendedExtended RangeRange RamjetRamjet

Propulsion / Configuration Fuel Type / Volumetric Fuel Volume (in3) / ISP (s) / Cruise Performance (BTU / in3) / Fuel Weight (lb) Range at Mach 3.5, Density (lb / in3) 60k ft (nm)

Liquid Fuel Ramjet RJ-5 / 581 / 0.040 11900 / 476 1120 / 390

Ducted Rocket ( Low Smoke ) Solid Hydrocarbon / 1132 / 7922 / 594 677 / 294 0.075

Ducted Rocket ( High Boron / 2040 / 0.082 7922 / 649 769 / 366 Performance )

Solid Fuel Ramjet Boron / 2040 / 0.082 7056 / 579 1170 / 496

Slurry Fuel Ramjet 40% JP-10, 60% boron 11900 / 595 1835 / 770 carbide / 1191 / 0.050

Note: Flow Path Available Fuel Rcruise = V ISP ( L / D ) ln [ WBC / ( WBC -Wf )] 2/24/2008 ELF 338 SizingSizing ExamplesExamples

Rocket Baseline Missile

Standoff range requirement

Wing sizing requirement

Multi-parameter harmonization

Lofted range comparison

Ramjet Baseline Missile

Range robustness

Propulsion and fuel alternatives

Velocity control

Computer Aided Conceptual Design Sizing Tools

Soda Straw Rocket, Design, Build, and Fly

2/24/2008 ELF 339 ExampleExample ofof RamjetRamjet VelocityVelocity ControlControl ThroughThrough FuelFuel ControlControl

Ramjet Baseline Equivalence Ratio Ramjet Baseline Fuel Flow Rate, lb / s

10 Example for Ramjet Baseline: T Mi = 4, h = sea level, T0 = 519R T + W - D = 0 W = W = 1263 lb W BO 1 2 D = CD q SRef = 3353 CD MI = 3353 ( 0.14 ) ( 4 )2 =0 7511 lb 0

Trequired = D - W = 7511 - 1263 = 6248 lb D . wf = T / ISP = 6248 / 1000 = 6.25 lb / s φ = T / T = 6248 / 25000 = 0.25 0.1 required φ = 1 Note: Excess air provides cooling of 01234 combustor Mi, Impact Mach Number at Sea Level

Note: Ramjet baseline, vertical impact at sea level, steady state velocity at impact, T = thrust, W = weight, D = drag, W = burnout weight, C = zero-lift drag coefficient, M = impact Mach number, T = required thrust for steady BO . D0 i required state flight, wf = fuel flow rate, ISP = specific impulse, φ = equivalence ratio ( φ = 1 stochiometric ) 2/24/2008 ELF 340 SizingSizing ExamplesExamples

Rocket Baseline Missile

Standoff range requirement

Wing sizing requirement

Multi-parameter harmonization

Lofted range comparison

Ramjet Baseline Missile

Range robustness

Propulsion and fuel alternatives

Surface impact velocity

Computer Aided Conceptual Design Sizing Tools

Soda Straw Rocket Design, Build, and Fly

2/24/2008 ELF 341 ComputerComputer SizingSizing CodeCode ShouldShould HaveHave FastFast TurnaroundTurnaround andand BeBe EasyEasy toto UseUse

Objective of Conceptual Design Search Broad Solution Space Iterate to Design Convergence Characteristics of Good Conceptual Design Sizing Code Fast Turnaround Time Easy to Use Directly Connect Predictions of Aeromechanics and Physical Parameters to Trajectory Code Simple, Physics Based Methods Includes Most Important, Driving Parameters Provides Insight into Relationships of Design Parameters Stable Computation Imbedded Baseline Missile Data Human Designer Makes the Creative Decisions

2/24/2008 ELF 342 ExampleExample ofof DODOSS-Based-Based ConceptualConceptual SizingSizing ComputerComputer CodeCode –– ADAM ADAM

Conceptual Sizing Computer Program Advanced Design of Aerodynamic Missiles ( ADAM ) PC compatible Written in DOS Aerodynamic Module Based on NACA 1307 Calculates Static and dynamic stability derivatives Control effectiveness and trim conditions 3, 4, 5, and 6-DOF Simulation Modules Proportional guidance Input provided automatically by aerodynamic module Configurations Benchmarked with Wind Tunnel Data Greater than 50 Input Parameters Available Defaults to benchmark configuration ( s )

2/24/2008 ELF 343 EExamplexample ooff SSpreadsheetpreadsheet BBasedased CConceptualonceptual SizingSizing ComputerComputer CodeCode -- TMD TMD SpreadsheetSpreadsheet

Conceptual Sizing Computer Code Tactical Missile Design ( TMD ) Spreadsheet PC compatible Windows Excel spreadsheet Based on Tactical Missile Design Short Course and Textbook Aerodynamics Propulsion Weight Flight trajectory Measures of merit

2/24/2008 ELF 344 ExampleExample ooff SSpreadsheetpreadsheet BasedBased CConceptualonceptual SizingSizing ComputerComputer Code,Code, TMDTMD SpreadsheetSpreadsheet

Define Mission Requirements [ Flight Performance ( RMax, RMin, VAVG ) , MOM, Constraints ] Alt Mission Establish Baseline ( Rocket , Ramjet ) Alt Baseline

Aerodynamics Input ( d, l, lN, A, c, t, xcg ) Aerodynamics Output [ CD , CN, xac, Cm , L / D, ST ] 0 δ Resize / Alt Config / Subsystems / Tech Propulsion Input ( pc, ε, c*, Ab, At, A0, Hf, ϕ, T4, Inlet Type ) Propulsion Output [ I , T , p / p , w., T , T , ΔV ] sp cruise t2 t0 boost sustain Boost

Weight Input ( WL, WP, ρ, σmax ) Weight Output [ WL, WP, h, dT / dt, T, t, σbuckling, MB, σ, Wsubsystems, xcg, Iy ]

Trajectory Input ( hi, Vi, Type ( cruise, boost, coast, ballistic, turn, glide ) Trajectory Output ( R, h, V, and γ versus time )

Meet No [ R , R , V ] Performance? Max Min AVG

Yes No [ pBlast, PK, nHit, V , P , Measures of Merit and Constraints fragments KE KEWarhead, τTotal, Yes σHE, σMAN,Rdetect,

2/24/2008 ELF CSDD, C1000th, Cunit x ] 345 ExampleExample ofof TMDTMD SpreadsheetSpreadsheet SizingSizing CodeCode Verification:Verification: Air-to-AirAir-to-Air RangeRange RequirementRequirement

Example Launch Conditions

hL = 20k ft ML = 0.8 Example Requirement

RF = 6.7 nm with tf < 24.4 s Solutions for Rocket Baseline

ADAM: RF = 6.7 nm at tf = 18 s TMD Spreadsheet: RF = 6.7 nm at tf = 19 s 3 DOF using wind tunnel aero data: RF = 6.7 nm at tf = 21 s Differences in Flight Time to 6.7 nm Mostly Due to Zero-Lift Drag Coefficient. For Example: ADAM prediction at Mach 2.0: ( C ) = 0.53 D0 coast TMD Spreadsheet prediction at Mach 2.0: ( C ) = 0.57 D0 coast Wind tunnel aero data at Mach 2.0: ( C ) = 1.05 D0 coast Wind Tunnel Data / Baseline Missile Data Correction Required to Reduce Uncertainty in C D0

2/24/2008 ELF 346 SizingSizing ExamplesExamples

Rocket Baseline Missile

Standoff range requirement

Wing sizing requirement

Multi-parameter harmonization

Lofted range comparison

Ramjet Baseline Missile

Range robustness

Propulsion and fuel alternatives

Surface impact velocity

Computer Aided Conceptual Design Sizing Tools

Soda Straw Rocket Design, Build, and Fly

2/24/2008 ELF 347 ExampleExample ofof Design,Design, Build,Build, andand FlyFly CustomerCustomer RequirementsRequirements

Objective – Design, Build, and Fly Soda Straw Rocket with: Flight Range Greater Than 90 ft Weight Less Than 2 g Furnished Property Launch System Distance Measuring Wheel Weight Scale Micrometer Scale Engineer’s Scale Scissors Furnished Material 1 “Giant” Soda Straw: 0.28 in Diameter by 7.75 in Length, Weight = 0.6 g 1 Strip Tabbing: ½ in by 6 in, Weight = 1.4 g 1 Ear Plug: 0.33 – 0.45 in Diameter by 0.90 in Length, Weight = 0.6 g 1 “Super Jumbo” Soda Straw: 0.25 in Diameter by 7.75 in Length

2/24/2008 ELF 348 ExampleExample ooff Design,Design, Build,Build, andand FlyFly CCustomerustomer RequirementsRequirements (( contcont ))

Furnished Property Launch System with Specified Launch Conditions Launch Tube Diameter: 0.25 in Launch Tube Length ( e.g., 6 in ) Launch Pressure ( e.g., 30 psi ) Launch Elevation Angle ( e.g., 40 deg ) Predict Flight Trajectory Range and Compare with Test

2/24/2008 ELF 349 SodaSoda StrawStraw RocketRocket LauncherLauncher andand TargetingTargeting

9. Rocket on Launcher 8. Launch Tube 7. Inclinometer 6b. Manual Valve Launcher ( 0.1 s average response ) 6a. Solenoid Valve Launcher ( 0.025 s average response ) 5. Launch Switch 4. Pressure Gauge 3. Air Hose

2. Pressure Tank

1. Pump 11. Rockets with Various Length, Tail Geometry, Nose Geometry, and Other Surfaces 10. Laser Pointer Targeting Device 2/24/2008 ELF 350 ItIt IsIs EasyEasy toto MakeMake aa SodaSoda StrawStraw RocketRocket

1. Cut Large Diameter “Giant” Soda Straw to Desired Length

2. Twist and Squeeze Ear Plug to Fit Inside Soda Straw

3. Slide Ear Plug Inside Soda Straw

4. Cut Adhesive Tabs to Desired Height and Width of Surfaces

5. Apply Adhesive Tabs to Soda Straw

6. Wrap Front of Ear Plug and Straw with Tape 7. Slide Giant Soda Straw Rocket Over Smaller Diameter “Super Jumbo” Soda Straw Launch Tube

2/24/2008 ELF 351 SodaSoda StrawStraw RocketRocket BaselineBaseline ConfigurationConfiguration

Ear Plug Soda Straw Strip Tabbing

0.25 in 0.28 in

0.5 in

lc = 6.0 in

l = 7.0 in

2/24/2008 ELF 352 SodaSoda StrawStraw RocketRocket BaselineBaseline WeightWeight andand BalanceBalance

Component Weight, g cg Station, in Nose ( Plug ) 0.6 0.5 Body ( Soda Straw ) 0.5 3.5 Fins( Four ) 0.5 6.75 Total 1.6 3.39

2/24/2008 ELF 353 SodaSoda StrawStraw RocketRocket BaselineBaseline DefinitionDefinition

Body Material Type HDPE Plastic Material density, lb / in3 0.043 Material strength, psi 4,600 Thickness, in 0.004 Length, in 7.0 Diameter, in 0.28 Fineness ratio 25.0 Nose fineness ratio 0.5 Fins Material Plastic Planform area, in2 ( 2 panels exposed ) 0.25 Wetted area, in2 ( 4 panels ) 1.00 Aspect ratio ( 2 panels exposed ) 1.00 Taper ratio 1.0 Chord, in 0.5 Span ( exposed ), in 0.5 Span ( total including body ), in 0.78 Leading edge sweep, deg 0

xmac, in 6.625

2/24/2008 ELF 354 SodaSoda StrawStraw RocketRocket BaselineBaseline DefinitionDefinition (( contcont ))

Nose Material Type Foam Material density, lb / in3 0.012 Average diameter 0.39 in Length 0.90 in Reference Values Reference area, in2 0.0616 Reference length, in 0.28 Thrust Performance Inside cavity length, in 6.0 Typical Pressure, psi 30 Maximum thrust @ 30 psi pressure, lb 1.47 Time constant, s ( standard temperature ) 0.025

2/24/2008 ELF 355 SodaSoda StrawStraw RocketRocket BaselineBaseline StaticStatic MarginMargin

( xAC )B d xCG xAC ( xAC )T l

For body-tail geometry, static margin given by

( xAC –xCG ) / d = - {( CN α )B {[ xCG –( xAC )B ] / d } + ( CNα )T {[ xCG –( xAC )T ] / d }( ST / SRef )} / [( CNα )B + ( CNα )T ST / SRef ] For baseline soda straw configuration 2 2 xCG = 3.39 in, d = 0.28 in, ( CNα )B = 2 per rad, ST = 0.25 in , SRef = 0.0616 in ( xAC )B = [( xAC )B / lN ] lN = 0.63 ( 0.14 ) = 0.09 in ( CNα )T = π AT / 2 = π ( 1 ) / 2 = 1.57 ( xAC )T = 6.5 + 0.25 ( cmac )T = 6.63 Substituting

( xAC -xCG ) / d = - { 2 ( 3.39 – 0.09 ) / 0.28 + [ 1.57 ( 3.39 – 6.63 ) / 0.28 ] [( 0.25 ) / 0.0616 ]} / [ 2 + 1.57 ( 0.25 ) / 0.0616 ] = 6.00 ( statically stable )

xAC = 6.00 ( 0.28 ) + 3.39 = 5.07 in from nose

2/24/2008 ELF 356 SodaSoda StrawStraw RocketRocket HasHas HighHigh AccelerationAcceleration BoostBoost PerformancePerformance – t / τ T = ( p – p0 ) A = pgauge ( 1 – e ) A Thrust ( T ) from Pressurized Tube of Area A a ≈ 32.2 T / W, V = ∫ a dt, s = ∫ V dt T = ( p – p ) A = p ( 1 – e – t / τ ) A 100 0 gauge A = ( π / 4 ) ( 0.25 )2 = 0.0491 in2, τ = Valve Rise Time Example:

80 Assume pgauge = 30 psi, lt = 6 in, τ = 0.025 s ( Average for Solenoid Valve ), s = lc = 6 in Thrust Equation Is: – t / 0.025 – 40.00 t 60 T = 30 ( 1 - e ) ( 0.0491 ) = 1.4726 ( 1 - e ) Note: Actual Boost Thrust Lower ( Pressure Loss, Boundary Layer, Launch Tube Leakage, Launch Note: Time Tics Tube Friction ) 40

V, fps Velocity, Every 0.01 s Equations for Acceleration ( a ), Velocity ( V ), and Distance ( s ) During Boost Are: a ≈ 32.2 T / W = 32.2 ( 1.4726 ) ( 1 - e –40.00 t ) / 0.00352 20 = 13471.1 ( 1 - e – 40.00 t ) V = ∫ a dt = 13471.1 t + 336.78 e – 40.00 t –336.78 s = ∫ V dt = 6735.57 t2 – 8.419 e – 40.00 t – 336.78 t + 0 8.419 0246810End of Boost Conditions Are:

s, Distance Traveled During Launch, Inches s = lc = 6 in = 0.500 ft ⇒ t = 0.0188 s a = 7123 ft / s2 = 221 g pgauge = 15 psi pgauge = 30 psi V = 75.2 ft / s pgauge = 60 psi q = ½ ρ V2 = ½ ( 0.002378 ) ( 75.2 )2 = 6.72 psf M = V / c = 75.2 / 1116 = 0.0674 2/24/2008 ELF 357 MostMost ooff thethe SSodaoda SStrawtraw RocketRocket DragDrag CCoefficientoefficient IsIs fromfrom BodyBody SkinSkin FrictionFriction

CD0 = ( CD0 )Body,Friction + ( CD0 )Base,Coast + ( CD0 )Tail,Friction 0.2 0.2 = 0.053 ( l / d ) [ M / ( q l )] + 0.12 + nT { 0.0133 [ M / ( q cmac )] } ( 2 ST / SRef ) 1.5

2 Example: V = 75.2 fps, ST = 0.00174 ft , SRef = 2 0.000428 ft ⇒ ST / SRef = 4.07 Compute: 1 C = 0.053 ( 25.0 ){ 0.0674 / [( 6.72 ) ( 0. 583 )]}0.2 + D0 0.12 + 2 { 0.0133 { 0.0674 / [( 6.72 ) ( 0.0417 )]}0.2 }[ 2 ( 4.07 )] = 0.58 + 0.12 + 0.16 = 0.86 Note: • Above Drag Coefficient Not Exact 0.5 • Based on Assumption of Turbulent Boundary Layer • Soda Straw Rocket Small Size and Low Velocity ⇒ CD0, Zero-Lift Drag Coefficient Laminar Boundary Layer ⇒ Large Boundary Layer Thickness on Aft Body at Tails Compute Drag Force: 0 Dmax = CD qmax SRef = 0.86 ( 6.72 ) ( 0.000428 ) = 02468100.00247 lb ST / SRef, Tail Planform Area / Reference Area Compare Drag Force to Weight: Dmax / W = 0.00247 / 0.00352 = 0.70 V = 40 fps V = 80 fps Note: Drag Force Smaller Than Weight

2/24/2008 ELF 358 SodaSoda StrawStraw RocketRocket BaselineBaseline HasHas aa BallisticBallistic FlightFlight RangeRange GreaterGreater ThanThan 9090 FeetFeet R = { 2 W cos γ / [ g ρ S C ]} ln { 1 + t / { 2 x i c Ref D0 Example, Assume l = 6 in, p = 30 psi, γ W / [ g ρ S C V ]}} t gauge i c Ref D0 i = 30 deg, τ = 0.025 sec, Soda Straw Baseline, t = timpact = 1.8 s h = { 2 W sin γi / [ gc ρ SRef CD ]} ln { 1 + t / { 2 W / [ g ρ S C V ]}} +0 h -g t2 / 2 c Ref D0 i i c Horizontal Range At Impact = Rx = { 2 ( 40 0.00352 ) cos γi / [ 32.2 ( 0.002378 ) ( h Note: Time Tics 0.000428 ) ( 0.86 )]} ln { 1 + t / { 2 ( every 0.5 s 0.00352 ) / [ 32.2 ( 0.002378 ) ( 30 0.000428 ) ( 0.86 ) ( 75.2 )]}}

= 249.8 cos γi ln ( 1 + 0.301 t ) 20 = 249.8 ( 0.866 ) ln [ 1 + 0.301 ( 1.8 )] = 93.7 ft Height, ft Height,

Height At Impact = h = { 2 ( 0.00352 ) 10 sin γi / [ 32.2 ( 0.002378 ) ( 0.000428 ) ( 0.86 )} ln { 1 + t / { 2 ( 0.00352 ) / [ 32.2

h - hi, Initialh - above Height Launc ( 0.002378 ) ( 0.000428 ) ( 0.86 ) ( 75.2 0 2 )]}} + hi – 32.2 t / 2 020406080100 = 249.8 sin γi ln ( 1 + 0.301 t ) + hi – Rx, Horizontal Range, ft 32.2 t2 / 2 = 249.8 ( 0.5 ) ln [ 1 + 0.301 ( 2 1.8 )] + hi – 32.2 ( 1.2 ) / 2 Gamma = 10 Deg Gamma = 30 Deg Gamma = 50 Deg = hi + 1.9 ft 2/24/2008 ELF 359 SSodaoda SStrawtraw RocketRocket RangeRange DrivenDriven byby InsideInside ChamberChamber LengthLength andand LaunchLaunch AngleAngle

Note: Decreased chamber length ⇒ 0.8 shorter duration thrust ( decreased total impulse ) ⇒ decreased end-of- Example: 10% decrease in boost velocity inside chamber length ⇒ 7.7% decrease in range at t = Soda Straw Rocket Baseline: 0.6 1.8 s. Note: Result is nonlinear because inside chamber length = launcher W = Weight = 0.00423 lb length. Increase in lc also 0.4 leads to decrease in range. lc = inside chamber length = 6 in Nondimensional Range τ = Time constant to open solenoid Sensitivity to valve = 0.025 s Parameter 0.2 pgauge = gauge pressure = 30 psi

γi = Initial / launch angle angle = 30 deg

lt = 7 in 0 V = Launch velocity = 75.2 fps lc Gamma pgauge W tau CD0 CD0 = Zero-lift drag coefficient = 0.86

timpact = Time from launch to impact = -0.2 1.8 s

Rx = Horizontal range = 94 ft 2/24/2008 ELF 360 SSodaoda StStrawraw RRocketocket BBaselineaseline FliFlightght RRangeange UncertaintyUncertainty IsIs +/-+/- 2.4%, 2.4%, 11 σσ

Parameter Baseline Value Uncertainty in ΔR / R Due to Parameter Uncertainty 1. Inside Chamber Length 6 in +/- 2%, 1 σ +/- 1.5%, 1σ 2. Launch Angle 30 deg +/- 3%, 1σ +/- 1.7%, 1σ 3. Gauge Pressure 30 psi +/- 3%, 1σ +/- 0.5%, 1σ 4. Weight 1.6 g +/- 6%, 1σ +/- 0.4%, 1σ 5. Solenoid Time Constant 0.025 s +/- 20%, 1σ +/- 0.2%, 1σ 6. Zero-Lift Drag Coefficient 0.86 +/- 20%, 1σ +/- 0.2%, 1σ

Estimate of Level of Maturity / Uncertainty of Soda Straw Rocket Baseline Parameters Based on Wind tunnel test Thrust static test Weight measurement Prediction methods Total Flight Range Uncertainty for 30 psi launch at 30 deg 2 2 2 2 2 2 1/2 ΔR / R = [ (ΔR / R )1 + (ΔR / R )2 + (ΔR / R )3 + (ΔR / R )4 + (ΔR / R )5 + (ΔR / R )6 ] = +/- 2.4%, 1σ R = 94 ft +/- 2.3 ft, 1σ

2/24/2008 ELF 361 HouseHouse ofof QualityQuality TranslatesTranslates CustomerCustomer RequirementsRequirements intointo EngineeringEngineering EmphasisEmphasis

Chamber Length Tail Planform Area

Flight Range 7 8 2 Weight 3 6 4 74 = ( 7x8 + 3x6 ) 26 = ( 7x2 + 3x4 )

1 2 Note: Based on House of Quality, inside chamber length most important design parameter.

Note on Design Characteristics Sensitivity 1 - Customer Requirements Matrix: ( Room 5 ): 2 – Customer Importance Rating ( Total = 10 ) ++ Strong Synergy 3 – Design Characteristics + Synergy 4 – Design Characteristics Importance Rating ( Total = 10 ) 0 Near Neutral Synergy 5 – Design Characteristics Sensitivity Matrix - Anti-Synergy 6 – Design Characteristics Weighted Importance - - Strong Anti-Synergy 7 – Design Characteristics Relative Importance

2/24/2008 ELF 362 DDOEOE ExploresExplores thethe BroadBroad PossiblePossible DesignDesign SSpacepace withwith aa ReasonablyReasonably SmallSmall SetSet ofof AlternativesAlternatives

Design Space for Design of Experiments ( DOE )

Engineering lc, Inside Chamber ST, Tail Planform Area, Characteristics Range Length, in in2 Lower Value 4 0.125 Upper Value 6 0.25

Full Factorial DOE Based on Upper / Lower Values of k = 2 Parameters: Number of Combinations = 2k = 22 = 4

Concept Sketch lc, Inside Chamber ST, Tail Planform Area, Length, in in2 “Big Kahuna” 6 0.25 “Shorty” 4 0.25 “Stiletto” 6 0.125 “Petite” 4 0.125

Note: DOE concepts should emphasize customer driving requirements and the driving engineering characteristics.

2/24/2008 ELF 363 EngineeringEngineering ExperienceExperience SShouldhould GGuideuide thethe DDOEOE SetSet ofof AlternativesAlternatives andand thethe PreferredPreferred DesignDesign

As an Example, for the Soda Straw Rocket, from Experience We Know That Soda Straw Rocket Must Fit on Launcher Maximum Boost Velocity Occurs When Chamber Length = Launch Tube Length Three or Four Tails Best for Stability Tails That Are Too Small May Result in an Unstable Flight Tails That Are Too Large Add Weight and Cause Trajectory Dispersal Canards Require Larger Tails for Stability, Add Weight, and Cause Trajectory Dispersal Wings Add Weight, Add Drag, and Cause Trajectory Dispersal

2/24/2008 ELF 364 EngineeringEngineering ExperienceExperience SShouldhould GGuideuide thethe DDOEOE SetSet ofof AlternativesAlternatives andand PreferredPreferred DesignDesign (( contcont ))

As an Example, Soda Straw Rocket Geometry Should Be Comparable to an Operational Rocket with Near-Neutral Static Stability ( e.g., Hydra70 )

Concept Sketch l / d, b / d, c / d, Total Length / Total Tail Span / Tail Chord / Diameter Diameter Diameter “Big Kahuna” 25 2.79 2 “Shorty” 17.9 2.79 2 “Stiletto” 25 1.89 2 “Petite” 17.9 1.89 2 Hydra 70 15.1 2.66 1

Note: For a subsonic rocket with the center-of-gravity in the center of the rocket, slender body theory and slender surface theory give total tail span and chord for neutral stability of bNeutralStability ≈ 2 d and cNeutralStability > ≈ d respectively.

2/24/2008 ELF 365 OptimumOptimum DesignDesign ShouldShould HaveHave BalancedBalanced EngineeringEngineering CharacteristicsCharacteristics

As an Example, for the Soda Straw Rocket Design We Should Reflect Customer Emphasis of Requirements for Range Weight Provide Balanced Emphasis of Most Important Engineering Characteristics Chamber Length Tail Size / Span

2/24/2008 ELF 366 SummarySummary ofof SizingSizing ExamplesExamples

Rocket Powered Missile ( Sparrow Derived Baseline ) Standoff range requirement Wing area sizing requirements for maneuverability, turn rate, and turn radius Multi-parameter harmonization Ballistic versus lofted glide flight range Ramjet Powered Missile ( ASALM Derived Baseline ) Robustness in range uncertainty Propulsion and fuel alternatives Surface target impact velocity Computer Aided Sizing Tools for Conceptual Design ADAM Analytical prediction of aerodynamics Numerical solution of equations of motion

2/24/2008 ELF 367 SummarySummary ofof SizingSizing ExamplesExamples (( contcont ))

Computer Aided Sizing Tools for Conceptual Design ( cont ) TMD analytical sizing spreadsheet ( based on this text ) Analytical prediction of aero, propulsion, and weight Closed form analytical solution of simplified equations of motion Soda Straw Rocket Design, Build, and Fly Static margin Drag Performance Sensitivity study House of Quality Design of Experiment ( DOE ) Discussion / Questions? Classroom Exercise ( Appendix A )

2/24/2008 ELF 368 SizingSizing ExamplesExamples ProblemsProblems

1. Required flight range is shorter for a head-on intercept and it is longer for a t___ c____ intercept. 2. The rocket baseline center-of-gravity moves f______with motor burn. 3. The rocket baseline is an a______airframe. 4. The rocket baseline thrust profile is b____ s______. 5. The rocket baseline motor case and nozzle are made of s____.

6. The rocket baseline flight range is driven by ISP, propellant weight fraction, drag, and s_____ m_____. 7. Contributors to the maneuverability of the rocket baseline are its body, tail, and w___. 8. Although the rocket baseline has sufficient g’s and turn rate to intercept a maneuvering aircraft, it needs a smaller turn r_____. 9. Compared to a co-altitude trajectory, the rocket baseline has extended range with a l_____ glide trajectory. 10. The ramjet baseline has a c___ inlet. 11. The Mach 4 ramjet baseline has a t______airframe. 2/24/2008 ELF 369 SizingSizing ExamplesExamples ProblemsProblems (( contcont ))

12. Although the ramjet baseline combustor is a nickel-based super alloy, it requires insulation, due high temperature. The super alloy is i______.

13. The flight range of the ramjet baseline is driven by ISP, weight, thrust, zero-lift coefficient, and the weight fraction of f___. 14. Extended range for the ramjet baseline would be provided by more efficient packaging of subsystems and the use of s_____ fuels. 15. A conceptual design sizing code should be based on the simplicity, speed, and robustness of p______based methods. 16. The House of Quality room for design characteristics weighted importance indicates which engineering design characteristics are most important in meeting the c______r______. 17. Paredo sensitivity identifies the design parameters that are most i______. 18. DOE concepts should emphasize the customer driving requirements and the driving e______characteristics 19. If the total tail span ( including body diameter ) is twice the body diameter, the missile is approximately n______s_____. 2/24/2008 ELF 370 OutlineOutline

Technology Roadmap Establishes Time-phased Interrelationships for Technology development and validation tasks Technology options Technology goals Technology transition ( ATD, ACTD, DemVal, PDRR, SDD ) Technology Roadmap Identifies Key, enabling, high payoff technologies Technology drivers Key decision points Critical paths Facility requirements Resource needs

2/24/2008 ELF 372 RelationshipRelationship ofof DesignDesign MaturityMaturity toto thethe USUS Research,Research, Technology,Technology, andand AcquisitionAcquisition ProcessProcess

Research Technology Acquisition

6.1 6.2 6.3 6.4 6.5

System Basic Exploratory Advanced Demonstration System Development Production Research Development Development & Validation and Upgrades Demonstration

~ $0.1B~ $0.3B ~ $0.9B ~ $0.5B ~ $1.0B ~ $6.1B ~ $1.2B

Maturity Level Conceptual Design Preliminary Design Detail Design Production Design Drawings ( type ) < 10 ( subsystems ) < 100 ( components ) > 100 ( parts ) > 1000 ( parts )

First Technology Technology Prototype Full Scale 1-3 Block Limited Block Development Demonstration Demonstration Development Upgrades ~ 2 Years ~ 5 ~ 10 Years ~ 8 Years ~ 4 Years ~ 5 Years ~ 5-15 Years Years Production Note: Total US DoD Research and Technology for Tactical Missiles ≈ $1.8 Billion per year Total US DoD Acquisition ( SDD + Production + Upgrades ) for Tactical Missiles ≈ $8.3 Billion per year Tactical Missiles ≈ 11% of U.S. DoD RT&A budget US Industry IR&D typically similar to US DoD 6.2 and 6.3A 2/24/2008 ELF 373 TechnologyTechnology ReadinessReadiness LevelLevel (( TRLTRL )) IndicatesIndicates thethe MaturityMaturity ofof TechnologyTechnology

TRL 1- 3 TRL 4 TRL 5 TRL 6 TRL 7 Category 6.1 Category 6.2A Category 6.2B Category 6.3 Category 6.4

Basic Exploratory Exploratory development development research Advanced tech Prototype of a of a demo of a component, demonstration subsystem subsystem conceptual design studies, and prediction methods

Initial assessment ⇒ component test ⇒ subsystem test ⇒ integrated subsystems ⇒ integrated missile

2/24/2008 ELF 374 CConceptualonceptual DesignDesign HasHas BroadBroad AlternativesAlternatives WhileWhile DetailDetail DesignDesign HasHas HighHigh DefinitionDefinition

1000

100 Number of Concepts Number of Drawings 10 or Number of Design Drawings Design of Number or 1 Typical Number of Alternative Concepts 0 5 10 15 Time ( Years )

Conceptual Prelim. Detail Production Design Design Design Design 2/24/2008 ELF 375 USUS TacticalTactical MissileMissile Follow-OnFollow-On ProgramsPrograms OccurOccur aboutabout EveryEvery 2424 YearsYears

Short Range ATA, AIM-9, 1949 - Raytheon AIM-9X ( maneuverability ), 1996 - Hughes

Medium Range ATA, AIM-7,1951 - Raytheon AIM-120 ( autonomous, speed, Hypersonic Missile, > 2007 range, weight ), 1981 - Hughes

Anti-radar ATS, AGM-45, 1961 - TI AGM-88 ( speed, range ), 1983 - TI Hypersonic Missile > 2007

Long Range STA, MIM-104, 1966 - Raytheon PAC-3 (accuracy), 1992 - Lockheed Martin

Man-portable STS, M-47, 1970 - McDonnell Douglas Javelin ( gunner survivability, lethality, weight ), 1989 - TI

Long Range STS, BGM-109, 1972 - General Dynamics Hypersonic Missile > 2007

Long Range ATS, AGM-86, 1973 - Boeing AGM-129 ( RCS ), 1983 - General Dynamics

Medium Range ATS, AGM-130, 1983 - Rockwell JASSM ( cost, range, observables ), 1999 - LM 1950 1965 1970 1975 1980 1985 1990 1995 > 2000 Year Entering SDD 2/24/2008 ELF 376 MiMissilessile DDesignesign VValidationalidation // TTechnologyechnology DevelopmentDevelopment IsIs anan IntegratedIntegrated ProcessProcess •Rocket Static Propulsion •Turbojet Static IM Tests •Ramjet Tests Propulsion Model -Direct Connect -Freejet Airframe Structure Test Wind Tunnel Aero Model Tests Hardware Flight Test Progression Guidance In-Loop ( Captive Carry,Jettison, Simulation and Control Model Digital Simulation Separation, Unpowered Guided Flights, Powered Tower Guided Flights, Live Seeker Warhead Flights ) Lab Tests Tests Actuators / Initiators

Sensors Lab Tests Environment Autopilot / Electronics Tests Power •Vibration •Temperature Supply

Warhead Ballistic Tests Witness / Arena Tests IM Tests Sled Tests

2/24/2008 ELF 377 EExamplesxamples ooff MiMissilessile DDevelopmentevelopment TTestsests anandd FacilitiesFacilities

Airframe Wind Tunnel Test ………………………………………………………

Propulsion Static Firing with TVC ……..

Propulsion Direct Connect Test …………………………………….

Propulsion Freejet Test …………

2/24/2008 ELF 378 EExamplesxamples ooff MiMissilessile DDevelopmentevelopment TTestsests anandd FacilitiesFacilities (( contcont ))

Warhead Arena Test ……………………………………………………….

Warhead Sled Test ………………………

Insensitive Munition Test ……………………………………………..

Structure Test …………………………………………..

2/24/2008 ELF 379 EExamplesxamples ooff MiMissilessile DDevelopmentevelopment TTestsests anandd FacilitiesFacilities (( contcont ))

Seeker Test ……………………………………………………….

Hardware-In-Loop ………

Environmental Test ……………………………………………..

Submunition Dispenser Sled Test ……………………

2/24/2008 ELF 380 ExamplesExamples ofof MissileMissile DevelopmentDevelopment TestsTests andand FacilitiesFacilities (( contcont ))

RCS Test ……………………………………………………………….

Store / Avionics Test

Flight Test ……………………………………………………………………….

Video of Facilities and Tests

2/24/2008 ELF 381 MissileMissile FlightFlight TestTest ShouldShould CoverCover ExtremesExtremes ofof FlightFlight EnvelopeEnvelope Example: Ramjet Baseline Propulsion Test Validation ( PTV )

High L / D Cruise Flight 7 Flight 3 e sur es Pr ic m na Dy w High Aero Heating Lo Flight 7

e Flight 1 ur ss re P ic Flight 7 Flight 7 am yn D Booster Transition: Thrust - Drag Flight 3 gh Hi Flight 7 Flight 3

Note: Seven Flights from Oct 1979 to May 1980. Flight 1 failure of fuel control. As a result of the high thrust, the flight Mach number exceeded the design Mach number. 2/24/2008 ELF 382 ExampleExample ofof AeroAero TechnologyTechnology DevelopmentDevelopment

Conceptual Design ( 5 to 50 input parameters ) Prediction Preliminary Design ( 50 to 200 input parameters ) Prediction Missile DATCOM. Contact: AFRL. Attributes include: Low cost MISL3. Contact: NEAR. Attributes include: Modeling vortex shedding SUPL. Contact: NEAR. Attributes include: Paneling complex geometry AP02. Contact: NSWC. Attributes include: Periodic updates CFD. Contact: Georgia Tech. Attributes include: Model runs on Parallel Processing PCs Preliminary Design Optimization Response Surface Model: Contact: Georgia Tech. Attributes include 10x more rapid computation Probabilistic Analysis: Contact: Georgia Tech. Attributes include an evaluation of design robustness

2/24/2008 ELF 383 ExampleExample ofof AeroAero TechnologyTechnology DevelopmentDevelopment (( contcont ))

Wind Tunnel Test Verification Body buildup force and moment Control effectiveness and hinge moment Store carriage and separation Flow field ( may be required ) Pressure distribution ( may be required ) Plume, heat transfer, and dynamic stability ( usually not required ) Inlet ( if applicable ) 3 to 6-DOF Digital Simulation Hardware-in-loop Simulation Detail Design ( over 200 input parameters ) Flight Test Validation 2/24/2008 ELF 384 ExampleExample ofof MissileMissile TechnologyTechnology State-oState-off-the-Art-the-Art Advancement:Advancement: Air-to-AirAir-to-Air MissileMissile ManeuverabilityManeuverability

AIM-7A 60 AM-9B g R530 50 AA-8 Controls Augmented with Propulsion AIM-54 40 Devices ( TVC, R550 Reaction Jet ) Skyflash 30 Python 3 AA-10 20 Aspide Super 530D AA-11 10 AIM-120 Operational Angle of Attack, De Python 4 0 AA-12 1950 1960 1970 1980 1990 2000 2010 MICA AIM-132 Year IOC AIM-9X

2/24/2008 ELF 385 ExampleExample ofof MissileMissile TechnologyTechnology State-oState-off-the-Art-the-Art Advancement:Advancement: RamjetRamjet PropulsionPropulsion

6 Scramjet 5 Ramjet 4 3 2 1

Mcruise, Cruise Mach Number 0 1950 1960 1970 1980 1990 2000 2010 Year Flight Demonstration

Cobra X-7 Vandal/Talos St-450 SE 4400 RARE Bloodhound BOMARC Typhon STATEX D-21 CROW SA-6 Sea Dart LASRM ALVRJ 3M80 ASALM AS-17 / Kh-31 ASMP ANS Kh-41 SLAT BrahMos Meteor HyFly SED

2/24/2008 ELF 386 EnablingEnabling TechnologiesTechnologies forfor TacticalTactical MissilesMissiles

Dome G & C Electronics Insulation Data Link Flight Control Faceted / Window GPS / INS COTS Hypersonic BDI / BDA EM and Multi-mode In-flight Optimize High Density In-flight Retarget Piezoelectric Multi-spectral α, β Feedback Central Moving Target TVC / Reaction Jet Multi-lens ATR Power Phased Array Dedicated Roll MEMS

Seeker Airframe Propulsion Multi-mode Lifting Body Hypersonic Turbine-Based Multi-spectral Neutral Static Margin Liquid / Solid Fuel Ramjet SAR Lattice Fins Variable Flow Ducted Rocket Strapdown Split Canard Scramjet Uncooled Imaging Low ΔxAC Wing / Low Hinge Moment Control Combined Cycle Propulsion High Gimbal Free-to-Roll Tails High Temperature Turbine Compressed Carriage High Temperature Combustor Warhead Low Drag Inlet High Density Fuel / Propellant High Energy Density Mixed Compression Inlet High Throttle Fuel Control Multi-mode Single Cast Structure Endothermic Fuel High Density Penetrator VARTM, Pultrusion, Extrusion, Filament Wind Composite Case Boosted Penetrator High Temperature Composites Pintle / Pulsed / Gel Motor Smart Dispenser Titanium Alloy High Burn Rate Exponent Propellant Powered Submunition MEMS Data Collection Low Observable Low Observable Shaping and Materials 2/24/2008 ELF 387 SummarySummary ofof DevelopmentDevelopment ProcessProcess

Development Process Technology roadmap Development activities Time frame Level of Design Maturity Related to Stage of Development Missile Follow-on Programs Subsystems Development Activities Subsystems Integration and Missile System Development Flight Test Activities Missile Development Tests and Facilities State-of-the-Art Advancement in Tactical Missiles New Technologies for Tactical Missiles Discussion / Questions? Classroom Exercise ( Appendix A )

2/24/2008 ELF 388 DevelopmentDevelopment ProcessProcess ProblemsProblems

1. A technology roadmap establishes the high payoff technologies g____. 2. The levels of design maturity from the most mature to least mature are production, detail, preliminary, and c______design. 3. Technology transitions occur from basic research to exploratory development, to advanced development, to d______and v______. 4. Approximately 11% of the U.S. RT&A budget is allocated to t______m______. 5. In the U.S., a tactical missile has a follow-on program about every __ years. 6. Compared to the AIM-9L, the AIM-9X has enhanced m______. 7. Compared to the AIM-7, the AIM-120 has autonomous guidance, lighter weight, higher speed, and longer r____. 8. Compared to the PAC-2, the PAC-3 has h__ t_ k___ accuracy. 9. Guidance & control is verified in the h______in l___ simulation. 10. Airbreathing propulsion ground tests include direct connect tests and f______tests. 11. Aerodynamic force and moment data are acquired in w___ t_____ tests. 2/24/2008 ELF 389 OutlineOutline

• Mission / Scenario Update Definition Initial Revised

• Weapon Concept Alternate Concepts ⇒ Select Preferred Design ⇒Eval / Refine Design Synthesis

• Technology Initial Tech Initial Revised Assessment and Tech Trades Roadmap Roadmap Dev Roadmap Note: Typical design cycle for conceptual design is usually 3 to 9 months

2/24/2008 ELF 391 ExploitExploit DiverseDiverse SkillsSkills forfor aa BalancedBalanced DesignDesign

Customer ( requirements pull ) ⇒ mission / MIR weighting

Operations analysts ⇒ system-of-systems analysis

System integration engineers ⇒ launch platform integration

Missile design engineers ⇒ missile concept synthesis

Technical specialists ( technology push ) ⇒ technology assessment / roadmap

2/24/2008 ELF 392 UtilizeUtilize CreativeCreative SkillsSkills

Use Creative Skills to Consider Broad Range of Alternatives Ask Why? of Requirements / Constraints Project into Future ( e.g., 5 – 15 years ) State-of-the-art ( SOTA ) Threat Scenario / Tactics / Doctrine Concepts Technology Impact Forecast Recognize and Distill the Most Important, Key Drivers Develop Missile Concept that is Synergistic within a System-of-Systems Develop Synergistic / Balanced Combination of High Leverage Subsystems / Technologies

2/24/2008 ELF 393 IdentifyIdentify andand QuantifyQuantify thethe HighHigh PayoffPayoff MeasuresMeasures ofof MeritMerit

Time to Max / Min Robustness Range Target

Reliability Lethality Miss Distance

Observables Survivability Weight

2/24/2008 ELF 394 StartStart withwith aa GoodGood BaselineBaseline

I would have used the wheel as a baseline.

2/24/2008 ELF 395 ConductConduct Balanced,Balanced, UnbiasedUnbiased TradeoffsTradeoffs

Propulsion

Aerodynamics

Structures Production

Seeker

Guidance and Control Warhead – Fuze

2/24/2008 ELF 396 EvaluateEvaluate ManyMany AlternativesAlternatives

AA- 8 / R-60 Python 4 Magic 550 U-Darter

Python 5 Derby / R-Darter AIM-9L Aspide

AA-10 / R-27 Skyflash AIM-7 R-37

AA-12 / R-77 AIM-9x Super 530D AIM-132

AA-11 / R-73 AIM-54 AIM-120 Mica

IRIS-T Meteor A-Darter Taildog

Note: Although all of the above are supersonic air-to-air missiles, they have different configuration geometry

2/24/2008 ELF 397 SearchSearch aa BroadBroad DesignDesign SolutionSolution SpaceSpace (( GlobalGlobal OptimizationOptimization vsvs LocalLocal OptimizationOptimization ))

Local Optimum ( e.g., Lowest Cost Only in Local Solution Space )

Global Optimum ( e.g., Lowest Cost in Global Solution Space ) within Constraints

2/24/2008 ELF 398 EvaluateEvaluate andand RefineRefine asas OftenOften asas PossiblePossible

2/24/2008 ELF 399 ProvideProvide BalancedBalanced EmphasisEmphasis ofof AnalyticalAnalytical vsvs ExperimentalExperimental

Albert Einstein: "The only real Thomas Edison: "Genius is 1% valuable thing is intuition." inspiration and 99% perspiration."

2/24/2008 ELF 400 UseUse Design,Design, Build,Build, andand FlyFly Process,Process, fforor FeedbackFeedback ThatThat LeadsLeads toto BroaderBroader KnowledgeKnowledge

Design Wisdom Where is the wisdom we have lost in knowledge? Where is the knowledge we have lost in information?--T. S. Prediction Satisfies e No g Eliot ( The Rock )

Customer e l Understanding Knowledge comes by taking things Requirements? w apart: analysis. But wisdom comes by o

n putting things together.--John A.

K Morrison f

o Knowledge Build r We are drowning in information but e starved for knowledge.--John Naisbitt d

d ( Megatrends: Ten New Directions No a

L Transforming Our Lives ) Is it Producible? Information b We learn wisdom from failure much m

i l more than from success. We often C discover what will do, by finding out Fly ( Test ) Failure / what will not do; and probably he who Success never made a mistake never made a discovery.--Samuel Smiles ( Self Help ) Test Results Satisfy No Customer Requirements Data and Consistent with Prediction? Yes

2/24/2008 ELF 401 EvaluateEvaluate TechnologyTechnology RiskRisk

2/24/2008 ELF 402 KeepKeep TrackTrack ofof AssumptionsAssumptions andand DevelopDevelop Real-Real- TimeTime DocumentationDocumentation

It’s finally finished ! . . .

2/24/2008 ELF 403 DevelopDevelop GoodGood DocumentationDocumentation

Technolo gy Roadmap Unit p roduction cost and dev elopment cost W eight and balance

Three-view drawing of preferred concept( s ) Traceability of system driving MIRs Sensitivity of system / subsystem parameters Mission flight profiles of preferred concept( s ) Aero and propulsion characteristics Justification of cept(s) recommended con ernative Sketches of alt concepts eighting MIRs W

2/24/2008 ELF 404 UtilizeUtilize GroupGroup SkillsSkills

Conceptual Design – 2% Preliminary Design – 8%

Other Than Design – Detail / 60% Production (Test, Analysis, Design – Configuration 30% Management, Software, Program Management, Integration, Requirements, etc.)

Source: Nicolai, L.M., “Designing a Better Engineer,” AIAA Aerospace America, April 1992

2/24/2008 ELF 405 BalanceBalance thethe TradeoffTradeoff ofof ImportanceImportance vsvs PriorityPriority

Production Programs / Detail Design SDD Programs / Advanced Programs / Preliminary Design Conceptual Design

2/24/2008 ELF 406 EvaluateEvaluate AlternativesAlternatives andand IterateIterate thethe ConfigurationConfiguration DesignDesign

Define Mission Requirements Alt Mission Establish Baseline Alt Baseline Aerodynamics

Propulsion

Weight Resize / Alt Config / Subsystems / Tech

Trajectory

Meet No Performance?

Yes No Measures of Merit and Constraints

Yes

2/24/2008 ELF 407 CConfigurationonfiguration SiSizingzing CConceptualonceptual DDesignesign Guidelines:Guidelines: AeromechanicsAeromechanics

Configuration Sizing Parameter Aeromechanics Design Guideline Body fineness ratio 5 < l / d < 25

Nose fineness ratio lN / d ≈ 2 if M > 1 Boattail or flare angle < 10 deg Efficient cruise dynamic pressure q < 1,000 psf

Missile homing velocity VM / VT > 1.5 Ramjet combustion temperature > 4,000° F Oblique shocks prior to inlet normal > 2 oblique shocks / compressions if M > shock to satisfy MIL-E-5008B 3.0, > 3 shocks / compressions if M > 3.5

Inlet flow capture Shock on cowl lip at Mmax cruise Ramjet Minimum cruise Mach number M > 1.2 x MInletStart , M > 1.2 MMaxThrust = Drag Subsystems packaging Maximize available volume for fuel / propellant

2/24/2008 ELF 408 ConfigurationConfiguration SizingSizing ConceptualConceptual DesignDesign Guidelines:Guidelines: GuidanceGuidance && ControlControl

Configuration Sizing Parameter G&C Design Guideline

Body bending frequency ωBB > 2 ωACT Trim control power α / δ > 1 Neutral stability tail-body If low aspect ratio, b / d ≈ 2, c / d > ≈ 1 Stability & control cross coupling < 30% Airframe time constant τ < 0.2 s

Missile maneuverability nM / nT > 3 Proportional guidance ratio 3 < N’ < 5

Target span resolution by seeker < btarget . . Missile heading rate γ M > γ T Missile turn radius R < R TM TT

2/24/2008 ELF 409 WrapWrap UpUp (( PartPart 11 ofof 22 ))

Missile design is a creative and iterative process that includes System considerations Missile concepts and sizing Flight trajectory evaluation Cost / performance drivers may be “locked in” during conceptual design Missile design is an opportunity for a diverse group to work together for a better product Military customer ⇒ mission / scenario definition Operations analysts ⇒ system-of-systems modeling System integration engineers ⇒ launch platform integration Missile design engineers ⇒ missile concept synthesis Technical specialists ⇒ technology assessment / technology roadmap

2/24/2008 ELF 410 WrapWrap UpUp (( PartPart 22 ))

The missile conceptual design philosophy requires Iteration, iteration, iteration Evaluation of a broad range of alternatives Traceable flow-down allocation of requirements Starting with a good baseline Paredo sensitivity analysis to determine the most important, driving parameters Synergistic compromise / balanced subsystems and technologies that are high leverage Awareness of technology SOTA / technology assessment Technology impact forecast Robust design Creative design decisions made by the designer ( not the computer ) Fast, simple, robust, physics-based prediction methods

2/24/2008 ELF 411 OutlineOutline

2/24/2008 ELF 412 ReferencesReferences

1. “Missile.index,” http://missile.index.ne.jp/en/ 2. AIAA Aerospace Design Engineers Guide, American Institute of Aeronautics and Astronautics, 1993 3. Bonney, E.A., et al, Aerodynamics, Propulsion, Structures, and Design Practice, “Principles of Guided Missile Design”, D. Van Nostrand Company, Inc., 1956 4. Jerger, J.J., Systems Preliminary Design Principles of Guided Missile Design, “Principles of Guided Missile Design”, D. Van Nostrand Company, Inc., 1960 5. Chin, S.S., Missile Configuration Design, McGraw-Hill Book Company, 1961 6. Mason, L.A., Devan, L., and Moore, F.G., “Aerodynamic Design Manual for Tactical Weapons,” NSWCTR 81-156, 1981 7. Pitts, W.C., Nielsen, J.N., and Kaattari, G.E., “Lift and Center of Pressure of Wing-Body-Tail Combinations at Subsonic, Transonic, and Supersonic Speeds,” NACA Report 1307, 1957 8. Jorgensen, L.H., “Prediction of Static Aerodynamic Characteristics for Space-Shuttle-Like, and Other Bodies at Angles of Attack From 0° to 180°,” NASA TND 6996, January 1973 9. Hoak, D.E., et al., “USAF Stability and Control DATCOM,” AFWAL TR-83-3048, Global Engineering, 1978 10. “Nielsen Engineering & Research (NEAR) Aerodynamic Software Products,” http://www.nearinc.com/near/software.htm 11. Ashley, H., Engineering Analysis of Flight Vehicles, Dover Publications, Inc., 1974 12. Anderson, John D. Jr., “Modern Compressible Flow,” Second Edition, McGraw Hill, 1990 13. Kinroth, G.D. and Anderson, W.R., “Ramjet Design Handbook,” CPIA Pub. 319 and AFWAL TR 80-2003, June 1980 14. “Technical Aerodynamics Manual,” North American Rockwell Corporation, DTIC AD 723823, June 1970 15. Oswatitsch, K.L., “Pressure Recovery for Missiles with Reaction Propulsion at High Supersonic Speeds”, NACA TM - 1140, 1947 16. Carslaw, H.S. and Jaeger, J. C., Conduction of Heat in Solids, Clarendon Press, 1988

2/24/2008 ELF 413 ReferencesReferences (( contcont ))

17. Allen, J. and Eggers, A.J., “A Study of the Motion and Aerodynamic Heating of Ballistic Missiles Entering the Earth’s Atmosphere at High Supersonic Speeds”, NACA Report 1381, April 1953. 18. Schneider, S.H., Encyclopedia of Climate and Weather, Oxford University Press, 1996 19. Klein, L.A., Millimeter-Wave and Infrared Multisensor Design and Signal Processing, Artech House, Boston, 1997 20. US Army Ordnance Pamphlet ORDP-20-290-Warheads, 1980 21. Carleone, J. (Editor), Tactical Missile Warheads, “AIAA Vol. 155 Progress in Astronautics and Aeronautics,” American Institute of Aeronautics and Astronautics, 1993 22. Christman, D.R. and Gehring, J.W., “Analysis of High-Velocity Projectile Penetration Mechanics,” Journal of Applied Physics, Vol. 37, 1966 23. Heaston, R.J. and Smoots, C.W., “Precision Guided Munitions,” GACIAC Report HB-83-01, May 1983 24. Donatelli, G.A. and Fleeman, E.L., “Methodology for Predicting Miss Distance for Air Launched Missiles,” AIAA-82- 0364, January 1982 25. Bennett, R.R. and Mathews, W.E., “Analytical Determination of Miss Distances for Linear Homing Navigation Systems,” Hughes Tech Memo 260, 31 March 1952 26. Nicholas, T. and Rossi, R., “US Missile Data Book, 1996,” Data Search Associates, 1996 27. Bithell, R.A. and Stoner, R.C., “Rapid Approach for Missile Synthesis,” AFWAL TR 81-3022, March 1982 28. Fleeman, E.L. and Donatelli, G.A., “Conceptual Design Procedure Applied to a Typical Air-Launched Missile,” AIAA 81- 1688, August 1981 29. Hindes, J.W., “Advanced Design of Aerodynamic Missiles ( ADAM ),” October 1993 30. Frits, A.P., et al, “A Conceptual Sizing Tool for Tactical Missiles, “ AIAA Missile Sciences Conference, November 2002 31. Bruns, K.D., Moore, M.E., Stoy, S.L., Vukelich, S.R., and Blake, W.B., “Missile DATCOM,” AFWAL-TR-91-3039, April 1991

2/24/2008 ELF 414 ReferencesReferences (( contcont ))

32. Moore, F.G., et al, “The 2002 Version of the Aeroprediction Code”, Naval Surface Warfare Warfare Center, March 2002 33. Nicolai, L.M., “Designing a Better Engineer,” AIAA Aerospace America, April 1992

2/24/2008 ELF 415 BibliographyBibliography ofof OtherOther ReportsReports andand WebWeb SitesSites

System Design Fleeman, E.L., “Tactical Missile Design,” American Institute of Aeronautics and Astronautics, 2006 “DoD Index of Specifications and Standards,” http://stinet.dtic.mil/str/dodiss.html “Periscope,” http://www.periscope1.com/ Defense Technical Information Center, http://www.dtic.mil/ NATO Research & Technology Organisation, http://www.rta.nato.int/ “Missile System Flight Mechanics,” AGARD CP270, May 1979 Hogan, J.C., et al., “Missile Automated Design ( MAD ) Computer Program,” AFRPL TR 80-21, March 1980 Rapp, G.H., “Performance Improvements With Sidewinder Missile Airframe,” AIAA Paper 79-0091, January 1979 Nicolai, L.M., Fundamentals of Aircraft Design, METS, Inc., 1984 Lindsey, G.H. and Redman, D.R., “Tactical Missile Design,” Naval Postgraduate School, 1986 Lee, R.G., et al, Guided Weapons, Third Edition, Brassey’s, 1998 Giragosian, P.A., “Rapid Synthesis for Evaluating Missile Maneuverability Parameters,” 10th AIAA Applied Aerodynamics Conference, June 1992 Fleeman, E.L. “Aeromechanics Technologies for Tactical and Strategic Guided Missiles,” AGARD Paper presented at FMP Meeting in London, England, May 1979 Raymer, D.P., Aircraft Design, A Conceptual Approach, American Institute of Aeronautics and Astronautics, 1989 Ball, R.E., The Fundamentals of Aircraft Combat Survivability Analysis and Design, American Institute of Aeronautics and Astronautics, 1985 “National Defense Preparedness Association Conference Presentations,” http://www.dtic.mil/ndia

2/24/2008 ELF 416 BibliographyBibliography ofof OtherOther ReportsReports andand WebWeb SitesSites (( contcont ))

System Design ( continued ) Eichblatt, E.J., Test and Evaluation of the Tactical Missile, American Institute of Aeronautics and Astronautics, 1989 “Aircraft Stores Interface Manual (ASIM),” http://akss.dau.mil/software/1.jsp “Advanced Sidewinder Missile AIM-9X Cost Analysis Requirements Description (CARD),” http://deskbook.dau.mil/jsp/default.jsp Wertz, J.R and Larson W.J., Space Mission Analysis and Design, Microprism Press and Kluwer Academic Publishers, 1999 “Directory of U.S. Military Rockets and Missiles”, http://www.designation-systems.net/ Fleeman, E.L., et al, “Technologies for Future Precision Strike Missile Systems,” NATO RTO EN-018, July 2001 “The Ordnance Shop”, http://www.ordnance.org/portal/ “Conversion Factors by Sandelius Instruments”, http://www.sandelius.com/reference/conversions.htm “Defense Acquisition Guidebook”, http://akss.dau.mil/dag/

Aerodynamics “A Digital Library for NACA,” http://naca.larc.nasa.gov/ Briggs, M.M., Systematic Tactical Missile Design, Tactical Missile Aerodynamics: General Topics, “AIAA Vol. 141 Progress in Astronautics and Aeronautics,” American Institute of Aeronautics, 1992 Briggs, M.M., et al., “Aeromechanics Survey and Evaluation, Vol. 1-3,” NSWC/DL TR-3772, October 1977 “Missile Aerodynamics,” NATO AGARD LS-98, February 1979 “Missile Aerodynamics,” NATO AGARD CP-336, February 1983 “Missile Aerodynamics,” NATO AGARD CP-493, April 1990 “Missile Aerodynamics,” NATO RTO-MP-5, November 1998 Nielsen, J.N., Missile Aerodynamics, McGraw-Hill Book Company, 1960

2/24/2008 ELF 417 BibliographyBibliography ofof OtherOther ReportsReports andand WebWeb SitesSites (( contcont ))

Aerodynamics ( continued ) Mendenhall, M.R. et al, “Proceedings of NEAR Conference on Missile Aerodynamics,” NEAR, 1989 Nielsen, J.N., “Missile Aerodynamics – Past, Present, Future,” AIAA Paper 79-1818, 1979 Dillenius, M.F.E., et al, “Engineering-, Intermediate-, and High-Level Aerodynamic Prediction Methods and Applications,” Journal of Spacecraft and Rockets, Vol. 36, No. 5, September-October, 1999 Nielsen, J.N., and Pitts, W.C., “Wing-Body Interference at Supersonic Speeds with an Application to Combinations with Rectangular Wings,” NACA Tech. Note 2677, 1952 Spreiter, J.R., “The Aerodynamic Forces on Slender Plane-and Cruciform-Wing and Body Combinations”, NACA Report 962, 1950 Simon, J.M., et al, “Missile DATCOM: High Angle of Attack Capabilities, AIAA-99-4258 Burns, K.A., et al, “Viscous Effects on Complex Configurations,” WL-TR-95-3060, 1995 Lesieutre, D., et al, “Recent Applications and Improvements to the Engineering-Level Aerodynamic Prediction Software MISL3,’’ AIAA-2002-0274 Moore, F.G., Approximate Methods for Weapon Aerodynamics, American Institute of Aeronautics and Astronautics, 2000 “1976 Standard Atmosphere Calculator”, http://www.digitaldutch.com/atmoscalc/ “Compressible Aerodynamics Calculator”, http://www.aoe.vt.edu/~devenpor/aoe3114/calc.html Ashley, H. and Landahl, M., Aerodynamics of Wings and Bodies, Dover Publications, 1965 John, James E.A., Gas Dynamics, Second Edition, Prentice Hall, 1984 Zucker, Robert D., Fundamentals of Gas Dynamics, Matrix Publishers, 1977

Propulsion Chemical Information Propulsion Agency, http://www.cpia.jhu.edu/ St. Peter, J., The History of Aircraft Gas Turbine Engine Development in the United States: A Tradition of Excellence, ASME International Gas Turbine Institute, 1999 2/24/2008 ELF 418 BibliographyBibliography ofof OtherOther ReportsReports andand WebWeb SitesSites (( contcont ))

Propulsion ( continued ) Mahoney, J.J., Inlets for Supersonic Missiles, American Institute of Aeronautics and Astronautics, 1990 Sutton, G.P., Rocket Propulsion Elements, John Wiley & Sons, 1986 “Tri-Service Rocket Motor Trade-off Study, Missile Designer’s Rocket Motor handbook,” CPIA 322, May 1980 Humble, R.W., Henry, G.N., and Larson, W.J., Space Propulsion Analysis and Design, McGraw-Hill, 1995 Jenson, G.E. and Netzer, D.W., Tactical Missile Propulsion, American Institute of Aeronautics and Astronautics, 1996 Durham, F.P., Aircraft Jet Powerplants, Prentice-Hall, 1961 Bathie, W.W., Fundamentals of Gas Turbines, John Wiley and Sons, 1996 Hill, P.G. and Peterson, C.R., Mechanics and Thermodynamics of Propulsion, Addison-Weshley Publishing Company, 1970 Mattingly, J.D., et al, Aircraft Engine Design, American Institute of Aeronautics and Astronautics, 1987

Materials and Heat Transfer Budinski, K.G. and Budinski, M.K., Engineering Materials Properties and Selection, Prentice Hall, 1999 “Matweb’s Material Properties Index Page,” http://www.matweb.com “NASA Ames Research Center Thermal Protection Systems Expert (TPSX) and Material Properties Database”, http://tpsx.arc.nasa.gov/tpsxhome.shtml Harris, D.C., Materials for Infrared Windows and Domes, SPIE Optical Engineering Press, 1999 Kalpakjian, S., Manufacturing Processes for Engineering Materials, Addison Wesley, 1997 MIL-HDBK-5J, “Metallic Materials and Elements for Aerospace Vehicle Structures”, Jan 2003 “Metallic Material Properties Development and Standardization ( MMPDS )”, http://www.mmpds.org

2/24/2008 ELF 419 BibliographyBibliography ofof OtherOther ReportsReports andand WebWeb SitesSites (( contcont ))

Materials and Heat Transfer ( continued ) Mallick, P.K., Fiber-Reinforced Composites: Materials, Manufacturing, and Design, Second Edition, Maecel Dekker, 1993 Chapman, A.J., Heat Transfer, Third Edition, Macmillan Publishing Company, 1974 Incropera, F.P. and DeWitt, D.P., Fundamentals of Heat and Mass Transfer, Fourth Edition, John Wiley and Sons, 1996

Guidance, Navigation, Control, and Sensors Zarchan, P., Tactical and Strategic Missile Guidance, “AIAA Vol. 124 Progress in Astronautics and Aeronautics,” American Institute of Aeronautics and Astronautics, 1990 “Proceedings of AGARD G&C Conference on Guidance & Control of Tactical Missiles,” AGARD LS-52, May 1972 Garnell, P., Guided Weapon Control Systems, Pergamon Press, 1980 Locke, A. S., Guidance, “Principles of Guided Missile Design”, D. Van Nostrand, 1955 Blakelock, J. H., Automatic Control of Aircraft and Missiles, John Wiley & Sons, 1965 Lawrence, A.L., Modern Inertial Technology, Springer, 1998 Siouris, G.M., Aerospace Avionics Systems, Academic Press, 1993 Stimson, G.W., Introduction to Airborne Radar, SciTech Publishing, 1998 Lecomme, P., Hardange, J.P., Marchais, J.C., and Normant, E., Air and Spaceborne Radar Systems, SciTech Publishing and William Andrew Publishing, 2001 Wehner, D.R., High-Resolution Radar, Artech House, Norwood, MA, 1995 Donati, S., Photodetectors, Prentice-Hall, 2000 Jha, A.R., Infrared Technology, John Wiley and Sons, 2000 Schlessinger, M., Infrared Technology Fundamentals, Marcel Decker, 1995

2/24/2008 ELF 420 Follow-upFollow-up CommunicationCommunication

I would appreciate receiving your comments and corrections on this text, as well as any data, examples, or references that you may offer.

Thank you, Gene Fleeman Tactical Missile Design E-mail: [email protected] Web Site: http://genefleeman.home.mindspring.com

2/24/2008 ELF 421 OutlineOutline