Final Proposal: Advanced Tactical Missile II (ATM) IPT 2006 Team H

Final Proposal: Advanced Tactical Missile II (ATM)

IPT 2006 Team H

Submitted By:

May 2, 2006

Submitted To: Dr. Robert A. Frederick, Jr. Associate Professor Technology Hall N231 Department of Mechanical and Aerospace Engineering University of Alabama in Huntsville Huntsville, AL 35899 [email protected] Class Web Page: http://www.eb.uah.edu/ipt/

Contributors

Project Office Jerry Dickson System Engineering Marie Vogan Aerodynamics Stephen Strand Propulsion Stephen Strand Weight/ Structures Ricardo Naranjo Trajectory Jason Williams, Mutasem Shannag Avionics Jason Martin

Review Team C. Stephen Cornelius, Chairman AMRDEC Christina Davis, Customer AMRDEC Kader Frendi UAH Joe Hudock GDATP Richard Kretzschmar AMRDEC George Sanders AMRDEC Dean Slocum GDATP James Snider UAH

Department of Mechanical and Aerospace Engineering The University of Alabama in Huntsville May 2, 2006

Executive Summary [J. Dickson]

The Viper Company of America is proud to submit the Puff Adder Advanced Tactical Missile II concept in response to the U.S. Army's Concept Description Document dated 2 February 2006. The Puff Adder concept completely fulfills the Army's requirement to upgrade the existing 2.75 tactical missile at an affordable cost. The Puff Adder's technical design approach employs a combination of mature proven technologies (propulsion, warhead, structural materials) coupled with the most innovative technologies in guidance and control (controllable diverter thrusters and radar). Particular emphasis has been placed on using commercial off the shelf technology where appropriate. The Puff Adder has no outside movable aerodynamic control surfaces, which is a unique advantage over other conventional missile systems. Aerodynamic control is provided by 4 rings of thrusters, each containing twelve thrusters that are software controllable. The use of diverter thruster technology increases overall missile reliability, reduces system cost and eases assembly and integration operations. Another unique technological advancement found in the Puff Adder is the simplistic W-band frequency modulated continuous wave radar. The radar is used for ground track, roll rate determination and warhead deployment. The propulsion system uses a double base, minimum smoke propellant which is cartridge loaded. The existing M261 warhead has been maintained.

The Puff Adder's performance is extraordinary since we meet the threshold range of 8000 meters (26,246 ft) at below the threshold weight 15.39 < 15.63 Kg (33.85 < 34.38 lbs). The Puff Adder payload of 38 rockets (two pods) reduces the payload weight allowance by 9.12 kg (20.064 lbs). At the average cost of $1 million dollars per pound weight reduction cost for a helicopter development program such as the Comanche, the Army can immediately realize a cost avoidance of $20.064 million dollars with the Puff Adder. The Puff Adder Advanced Tactical Missile II meets the Army's critical threshold production cost of less than $15k per round at $11,450. The Puff Adder's length is 181.43 cm (71.43 in) which is below the objective length of 182.1 cm (71.7 in)

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ATM Compliance List [J. Dickson] The following list details the location of all specification compliances for the ATM. The list shows the location in the CDD provided by the Army of every specification and the number of the page where that specification is dealt with in this proposal. CDD Proposal Specification Location Location Operational between 61.0 m (200 ft) below MSL and 6,096.0 m 2.2.1.1.1 1.3.3, 2.7.3 (20,000 ft) above MSL Range of 1 km (0.62 mi) to 8 km (4.97 mi) when fired from 2.2.1.2.1 2.7.3 Helicopter Range of 1 km (0.62 mi) to 4 km (2.5 mi) when fired from Ground 2.2.1.2.1 2.7.3 Maximum Platform Error of 19 milliradians 2.2.1.2.2 2.6.4.2 Operational under Maximum Crosswind of 7.7 m/s (15 knots) 2.2.1.2.3 2.6.6 Minimum Smoke Signature 2.2.1.2.5 2.4.4 Motor Cannot Produce Damaging Ejecta 2.2.1.2.6 2.4.4 Capable of being loaded in military issued clothing 2.2.2.1 1.3.3 Compatible with the M261 Launcher 2.2.2.2 2.5.4,2.8 Compatible with the M261 Launcher Interfaces 2.2.2.2.1 2.8 Minimal Longitudinal Force Greater than 13.5 times the Maximum 2.2.2.2.2 2.2,2.4.4 System Weight Modified Fusing System for M261 MPSM Warhead 2.2.2.3 2.6.4 Submunition Deployment to occur at ± 10 m of Wall in Space 2.2.2.3.1 2.6.4 Safe and Arm device 2.2.2.3.2 2.6.4 Maximum lateral acceleration of 79 g 2.2.2.3.3 2.4.4 Submunition Deployment Velocity 603 m/s (1978 fps) 2.2.2.3.4 2.7 Maximum System Weight of 297 kg (654.6 lbs), Objective Weight 2.2.3 2.5.1,G.2 of 267.9 kg (590.0 lbs) Maximum System Length of 202.4 cm (79.7 in), Objective Length 2.2.3.1 2.5.1,G.1 of 182.1 cm (71.7 in) Maximum Outer Diameter of 70 mm (2.794 in) 2.2.3.2 2.5.1,G.1 Minimum Service Life of 10 years, Objective of 25 years 2.2.4.1 3.5 Maximum Unit Production Cost of $15,000/unit on 10,000 units w/ 2.2.4.2 3.1 Objective Cost of $10,000/unit Storage Temperature Range from -53.8oC (-65oF) to 73.9oC (165oF) 2.2.5.1 2.4.4,2.6.3 Operational Temperature Range from –31.7oC (-25oF) to 65.5oC 2.2.5.1 2.2,2.4.4,2.6.3 (150oF) Operational During or After Constant 100% Humidity 2.2.5.2 2.4.4,2.6.3 Minimum Hazard Classification of 1.1 with Objective of 1.3 2.2.6.1 2.4.4 Satisfying IM Compliance Requirements 2.2.6.2 2.4.4 Flight Fail Safe 2.2.6.3 2.7.3, I Minimum Ballistic Trajectory of 3.5 km (2.17 mi) 2.7.3, I Objective Ballistic Trajectory of 5 km(3.11 mi) 2.7.3, I All Components of System shall be Unclassified 2.2.7 complies Documentation 2.2.8 included

ATM II Project Ground Rules and Assumptions [M. Vogan]

All teams in the project adopted a set of common ground rules and assumptions to focus their efforts. This focused their efforts to fit the resources of time and tools available for the project. Each team could also make Team-specific ground rules and assumptions for their study. This page shows the Global and Team Specific ground rules and assumptions.

Global Ground Rules and Assumptions [R. Frederick] 1. Ground Rules a. The GPS location of the launch platform and the target are available in electronic form outside of the launcher 10 seconds before launch. 2. Assumptions a. The control system has precise position coordinates available to at one second intervals during flight. b. Cross winds are constant throughout predicted flight.

Team Specific Ground Rules and Assumptions [M. Vogan]

3. Ground Rules a. The position and target data can be transmitted through the launcher to the missile b. This data allows the missile to know both where it is located, and where its target is located prior to launch. c. The operational requirement of launch at 20,000 ft above MSL as quoted in the CDD refers not to an altitude of 20,000 ft. above the ground, but rather to the capability for the missile to launch and fly in the atmosphere found at 20,000 ft above MSL. d. All technologies shall be unclassified. 4. Assumptions a. The warhead used is of a constant design with no significant modifications, as it was taken from the baseline missile.

Table of Contents

1.0 ATM-Advanced Tactical Missile...... 14 1.1 The Need [J. Dickson]...... 14 1.2 The Requirements [J. Dickson] ...... 14 1.3 The Solution [J. Dickson, M. Vogan] ...... 15 1.4 The Performance [J. Dickson, M. Vogan] ...... 17 1.5 The Implementation [J. Dickson, M. Vogan] ...... 18 2.0 Technical Description of Methods Used ...... 19 2.1 Project Office [J. Dickson] ...... 19 2.2 Systems Engineering [M. Vogan] ...... 20 2.3 Aerodynamics [S. Strand] ...... 25 2.4 Propulsion [S. Strand] ...... 31 2.5 Structures [R. Naranjo]...... 36 2.6 Avionics [J. Martin]...... 38 2.7 Trajectory [J. Williams, M. Shannag, S. Strand, J. Martin] ...... 50 2.9 Trade Studies and Interactions of Subsystems [S. Strand]...... 56 3.0 Implementation Issues...... 56 3.1 Production Cost [M. Vogan]...... 56 3.2 Manufacturability [R. Naranjo] ...... 57 3.3 Test Schedule [M. Vogan] ...... 59 3.5 Discussion of Application and Feasibility [M. Vogan] ...... 60 4.0 Company Capabilities [J. Dickson]...... 61 4.1 Viper Company of America Overview [J. Dickson] ...... 61 4.2 Personnel Description [M. Vogan] ...... 61 5.0 Summary and Conclusions [M. Vogan]...... 62 6.0 Recommendations [J. Dickson] ...... 63 Appendix A - Concept Description Document [J. Dickson]...... 64 Appendix B - Electronic File Index [J. Martin]...... 79 Appendix C - Project Office [J. Dickson] ...... 81 Appendix D – Systems Engineering [M. Vogan]...... 83 Appendix E – Aerodynamics [S. Strand]...... 86 Appendix F - Propulsion [S. Strand]...... 92

Appendix G - Weight and Structures [R. Naranjo]...... 100 Appendix H - Avionics [J. Martin, J. Dickson] ...... 129 Appendix I – Trajectory [J. Williams, M. Shannag, S. Strand, J. Martin]...... 136 Appendix J - Platform Integration Radar [J. Dickson, M. Vogan]...... 146 Appendix K – Implementation Issues [M. Vogan]...... 148 Appendix L – Responses to Review Team Questions [S. Strand, J. Martin] ...... 150

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List of Figures

Figure 1. Puff Adder Concept [J. Williams]...... 15 Figure 2. Puff Adder Three-View Drawing [J. Williams]...... 16 Figure 3. Operations Scenario [M. Vogan]...... 17 Figure 4. Pseudomorphic Power Mimic1 ...... 19 Figure 5. Viper Team Design Process Flowchart [M. Vogan] ...... 21 Figure 6. Cross-Sectional Drawing of the Missile [M. Vogan] ...... 22 Figure 7. PRODAS Aeroodynamics Model Screen Shot [S. Strand] ...... 27 Figure 8. Pitch Damping vs. Mach Number for Level Flight [S. Strand]...... 27 Figure 9. Roll Rate vs. Time (PRODAS Output) [S. Strand] ...... 28 Figure 10. Drag vs. Mach Number [S. Strand] ...... 29 Figure 11. Unguided Y-Axis Movement due to Spin [S. Strand] ...... 29 Figure 12. CLα vs. Mach Number [S. Strand]...... 30 Figure 13. Angle of Attack vs. Time [S. Strand] ...... 30 Figure 14. Propellant Grain Cross-Section [S. Strand]...... 33 Figure 15. Puff Adder Thrust Profile [S. Strand]...... 35 Figure 16. General Layout of the Puff Adder ...... 36 Figure 17. Overview of Avionics Functionality [J. Martin]...... 39 Figure 18. Squib Ring Geometry (One of Four) ...... 42 Figure 19. Puff Adder Radar Ring [J. Dickson] ...... 46 Figure 20. Transmitter Waveform ...... 47 Figure 21. Puff Adder FMCW Transmitter...... 47 Figure 22. Millimeter Wave Receiver ...... 48 Figure 23. PRODAS Flowchart [J. Williams] ...... 51 Figure 24. 2-D PRODAS Mass Model [J. Williams]...... 51 Figure 25. Sectioned PRODAS Model [J. Williams] ...... 52 Figure 26. 3-D IDEAS Model [J. Williams]...... 52 Figure 27. Downrange Helicopter Mission (500m); All Conditions...... 54 Figure 28. Downrange Helicopter Mission (8,000m); All Conditions...... 54 Figure 29. Downrange Ground Mission (500m); All Conditions ...... 55 Figure 30. Downrange Ground Mission (4,000m); All Conditions ...... 55 Figure 31. Overall Technology Development Schedule [M. Vogan] ...... 60 Figure 32. Viper Company of America...... 81 Figure 33. Phase 2 Baseline System Decomposition ...... 83 Figure 34. Trajectory Organization Chart...... 136 Figure 35: Puff Adder 2-D Sectioned Model [J. Williams] ...... 137 Figure 36: 2-D Nozzle & Fin Assembly [J. Williams]...... 137 Figure 37. 2-D M2045 Assembly...... 138 Figure 38: 2-D DACS Assembly [J. Williams] ...... 138 Figure 39. M261 MPSM Warhead Assembly...... 139 Figure 40. 3-D IDEAS Model...... 140 Figure 41. 3-D IDEAS Nozzle Model...... 141 Figure 42. 3-D IDEAS Nozzle Wireframe...... 141 Figure 43. Project Development Flow Chart...... 149

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List of Tables

Table 1: Final Concept Evaluation [J. Dickson, M. Vogan] ...... 18 Table 2. Summary of Technical Parameters Calculations [M. Vogan] ...... 23 Table 3. Vehicle Weight Statement [R. Naranjo]...... 24 Table 4. Reference Mission Trajectory Data, Required [M. Shannag, S. Strand] ...... 24 Table 5. Roll Rate vs. Mach Number [S. Strand] ...... 28 Table 6. Summary of Aerodynamic Data and Calculations ...... 31 Table 7. Propellant Analysis Input Data [S. Strand]...... 34 Table 8. Summary of Propulsion Data and Calculations [S. Strand] ...... 35 Table 9. Thermal Battery Requirements...... 44 Table 10. Requirement Evaluation Matrix...... 82 Table 11: BOOST Matrix for Viper Team Alternative Missiles ...... 84 Table 12. Primary Missile Characteristics ...... 85 Table 13. Avionics Subcomponent Pricing List ...... 148

Common Terms and Acronyms List [M. Vogan]

AIAA American Institute of Aeronautics and Astronautics ADCs Analog-to-Digital Converters ASICs Application-Specific Integrated Circuits ATM Advanced Tactical Missile BOOST Matrix Barbie Outfit Slider Thingie cm Centimeters CG Center of Gravity DATCOM Data Communication DIT Divert Impulse Thruster FPGAs Field-Programmable Gate Arrays FM-CW Frequency-Modulated Carrier-Wave GPS Global Positioning System HC Hazard Classification HFSS High-Frequency Simulation of Structures IDEAS CAD modeling program HE High Explosive IF Intermediate Frequency IM Insensitive Munitions IMU Inertial Measurement Unit INS Inertial Navigation System IPT Integrated Product Team KCAS Knots Calibrated Air Speed ft Feet fps Feet Per Second g Acceleration of Gravity in inches DOF Degree of Freedom CG Center of gravity CDD Concept Description Document lb Pounds m Meters M Mach m/s Meters Per Second MAE Mechanical and Aerospace Engineering mi Miles MIL-STD Military Standard mils Milliradians max Maximum min Minimum MPSM Multi-Purpose Submunition MSL Mean Sea Level N Newtons NA Not Applicable Ns Newton-seconds

Pa Pascals PADs Programmable Analog Devices psi Pounds per Square Inch R&D Research and Development UAH University of Alabama in Huntsville Web CT Web Course Tools

List of Symbols [M. Vogan]

a Burn Rate coefficient Abi Initial Propellant Burning Surface Area amax Max Acceleration At Initial Throat Area c Specific Heat c* Characteristic Velocity C1st Cost of First Unit Produced CD Coefficient of drag CG Center of Gravity CL Coefficient of Lift CLα Coefficient of lift with respect to Angle of Attack CLP Coefficient of lift with respect to Pressure CM Pitching Moment Coefficient CNtrim Trim Normal Force Cx Cost of Number “x” Unit Produced dprop Diameter of Propellant h Altitude Isp Specific Impulse It Total Impulse L Length L/D Lift over Drag Lc Learning Curve MB Bending moment mprop Propellant Mass N Normal Force n Burn Rate Exponent P Tensile Load Pc Chamber Pressure Pmax Maximum Pressure Q Dynamic Pressure r Radius of the Casing R Range rb Burn Rate ρprop Density of Propellant rt Turn radius S Surface planform area sprop Propellant Temperature Sensitivity Sref Reference area T0 Initial Thrust Tmax Maximum Thrust Tref Reference Temperature V Velocity Vprop Propellant Volume W Launch Weight of Missile

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WL Missile Weight in Pounds, Minus Avionics Equipment z Thickness α Angle of Attack γi Initial Launch or Flight Path Angle θ Initial Pitch Angle θi Radar Signal Incidence Angle λ Line of Sight λo Radar Seeker Wavelength in Air

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IPT 2006: Feasibility of Advanced Tactical Missile (ATM) 1.0 ATM-Advanced Tactical Missile

1.1 The Need [J. Dickson]

The Army's current Advanced Tactical Missile is an unguided weapon delivery system which has limited consistent lethality effects. The missile has a ballistic trajectory with no guidance correction capability. This mandates the Army (AMCOM) to maintain a very large inventory of highly inaccurate missiles which requires a very expensive logistics footprint for support. With the Viper Company of America's Viper Puff Adder Advanced Tactical Missile II, the Army will have a more lethal weapon delivery system at a substantially lower cost. The Viper Puff Adder Advanced Tactical Missile II – at an average cost per unit of $11,450 – meets the Army's critical threshold production cost of less than $15,000 per round, while meeting or exceeding all requirements. More importantly to the Army, the overall cost is substantially reduced as a result of our increased lethality which reduces the required logistics footprint - fewer missiles are required for an increase in lethality. In Army terms, cost per kill decreases.

1.2 The Requirements [J. Dickson]

The Army via AMCOM has set forth their requirements for an Advanced Tactical Missile system upgrade in the Concept Description Document. This document specifies the characteristic, performance, design, logistic, environmental and developmental requirements for the Advanced Tactical Missile upgrade.

The following requirements are defined as "must meet" requirements in order for the Viper Puff Adder missile to be successful: Range, weight, length, unit production cost, launcher interface capability and weapon deployment scenarios. The minimum desired range is 1000 meters (3280 ft) with an objective of 500 meters (1641 ft). The maximum desired range is 8000 meters (26,246 ft) with an objective of 10000 meters (32,808 ft). The maximum weight per missile is 15.63 Kg (34.45 lbs) with an objective weight of 14.1 Kg (31.02 lbs). The maximum length is 202.4 cm (79.7 in) with an objective length of 182.1 cm (71.7 in). The unit production cost maximum is $15K with an objective cost of $10 K per missile with a production quantity of 10,000 units. The missile must be compatible with the current M261 launcher interfaces. The missile must be capable of delivering the M261 warhead +/- 10 meters (32.8 ft) to the center of a wall in space. The center of the wall in space is defined as being 300 meters (984 ft) in front of the target and 150 meters (492 ft) above the target.

The requirements that makes this upgrade the most challenging are the unit cost production and delivery of the warhead. It is extremely difficult to develop any missile, even if all the components are off the shelf, for a believable and realistic production cost of $15K. An accurate delivery of the warhead requires some form of active guidance techniques, which therefore drives cost upward.

1.3 The Solution [J. Dickson, M. Vogan]

The Viper Puff Adder ATM, shown in Figure 1 and Figure 2 below, satisfies all of the CDD requirements – and in many cases exceeds them – while using readily-available, affordable technology, and innovative guidance and control features that dramatically improve its performance over the baseline missile. The Viper Puff Adder uses small reliable diverter impulse thrusters as a means of momentum-based control, as opposed to moving fins or canards. The elimination of small moving parts greatly reduces the risk of damage or malfunction of the missile during loading and flight, while keeping it accurate within the required 19 mils for all trajectories. The reduction of parts also increases reliability, reduces test and integration costs. The guidance system employs an off the shelf inertial measuring unit (IMU) and a W-band frequency modulated continuous wave radar. Both of these components complement the small diameter of our missile. The combination of these technologies provides extremely accurate warhead deployment at an affordable cost. The Viper Puff Adder uses a standard minimum-smoke propellant with a hazard classification of 1.3 for optimal safety of our troops. The Viper Puff Adder is 100% compatible with the current launcher and all platforms specified by the customer. Our Viper Puff Adder also meets the threshold range 8000 meters (26,246 ft) at below the threshold weight 15.63 > 15.39 Kg (34.38 > 33.85 lbs). The Viper Puff Adder payload of 38 rockets reduces the payload weight allowance by 9.12 kg (20.064 lbs). This fact allows, for example a helicopter development program, to reduce the weight allowance for the Viper Puff Adder system and thus allocate the reduced weight to another system or objective. At the average cost of $1 million dollars per pound weight reduction cost, the Army can immediately realize a cost avoidance of $20.064 million dollars with the Viper Puff Adder.

1.3.1 Concept Overview

Figure 1. Puff Adder Concept [J. Williams]

1.3.2 Dimensional Properties

Figure 2. Puff Adder Three-View Drawing [J. Williams]

1.3.3 Operations Scenario [M. Vogan, J. Dickson]

The scenarios researched and simulated during the design of the Viper Puff Adder utilize the existing 19-round M261 launcher, and can be mounted to either helicopter-based or vehicle- based platforms. Figure 3 shows the operational scenario of the missile firing from the helicopter mission and the M261 launcher. Because the mission AMCOM supports requires extensive use of both helicopters and various vehicle-based platforms, the Viper Puff Adder is an ideal addition to such platforms to support a wide range of missions. The missile is capable of flying to a maximum range of 9.4km from a vehicle-based platform, and to a maximum range of 9.0km from a helicopter-based platform; these ranges may even be longer under certain conditions.

As the missile exits the launcher, the diverter impulse thrusters fire to pitch the missile up a required amount for a given trajectory. The main propulsion motor burns on average for 2.8 seconds, after which it is guided to its target. In the event of a guidance failure, the missile is capable of flying ballistically to a safe distance of nearly 8 km (ground launch, 20 degrees), preventing harm to any friendly troops in the path of the missile. During flight, a W-band radar senses the ground to determine the missile’s altitude and roll rate. The missile altitude is used to provide a fusing signal to the missile computer. The Viper Puff Adder receives GPS information from the platform before launch that tells the computer where it is (Viper Puff Adder) and where the target is. A solution is then calculated. Since the Viper Puff Adder knows how long the mission should take, the missile's computer uses the altitude information to release the warhead at the appropriate altitude at the wall in space. The roll rate data is sent to the guidance system to compensate for errors in the IMU. The combination of this radar with the IMU gives this upgraded tactical missile much greater precision than its predecessors and all other competitors at significantly lower cost.

Figure 3. Operations Scenario [M. Vogan]

1.4 The Performance [J. Dickson, M. Vogan]

Table 1 below summarizes the Viper Puff Adder’s compliance with all required characteristics given in the CDD. The calculation of these parameters is discussed in greater detail in section 2.0 of this report. The biggest weakness with the baseline Hawkeye design was its lack of a thoroughly-designed guidance and control system; the Puff Adder’s combination of IMU and radar guidance, and it’s squib-based control system, have been thoroughly researched and fully integrated into the design of this missile, thus addressing this void in the baseline.

Table 1: Final Concept Evaluation [J. Dickson, M. Vogan]

NA | z SCORING Not Analyzed Does Not Meet Partially Meets Meets LEGEND -- 0 3 6

CDD PARAGRAPH Requirement Comment Haweye Concept 2.2.1.1.1 Firing Envelope Max Alt. 6096 m MSL 3 NA z Meets Min Alt. -61 m MSL 2.2.1.2.2 Platform Error Maximum of 19 mils. 3 | z Meets 2.2.1.2.3 Crosswind Maximum of 7.7 m/s 3 | z Meets 2.2.1.2.4 Range: Helicopter Min. Range 1 km ;Max. Range 8 km 4 z z * Exceeds 2.2.1.2.4 Range: Ground Min. Range 1 km;Max. Range 4 km 4 z z Exceeds 2.2.1.2.5 Smoke Signature Minimum Smoke 4 z z Meets 2.2.2.2.1 Launcher Interfaces Compatible with M261 Launcher 3 z z Meets 2.2.2.2.2 Longitudinal Force Min.of 13.5 times missile weight 4 z z Meets 2.2.2.3.1 Submunition Deploy. +/- 10 meters of the Wall in Space 3 NA z Meets 2.2.2.3.2 Acceleration Maximum of 79 g’s 4 z z Meets 2.2.2.3.3 Vel. at Sub Deploy. Maximum 603 m/s 4 z z Meets 2.2.3 Weight Max. weight 297 kg 4 z z Meets 2.2.3.1 Length Maximum of 202.4 cm 4 z z Exceeds (<) 2.2.3.2 Outer Diameter Maximum 70 mm 4 z z Meets 2.2.4.1 Service Life Minimum of 10 years 3 | z Meets 2.2.4.2 Unit Production Cost Maximum of 15K/unit; (10,000 5 z z Meets units) 2.2.5.1 Temperature Operation Condition;-31.7°- 65.5°C 4 | z Meets 2.2.5.2 Humidity Operate during/after 100% Humidity 3 NA z Meets 2.2.6.1 Hazards Classification 1.1 Threshold; 1.3 Objective 3 z z Exceeds 2.2.6.3 Flight Fail Safe Minimum Ballistic Traj. of 3.5 km 3 NA z Exceeds

TOTAL SCORE 282 432 Meets

* Feature denoted with “exceeds” indicates this value meets the objective, rather than the threshold.

1.5 The Implementation [J. Dickson, M. Vogan]

The Viper Puff Adder's design approach employs a combination of mature proven technologies (propulsion, warhead, structural materials) coupled with the most innovative technologies in guidance and control (controllable thrusters and radar). Particular emphasis has been placed on using commercial off the shelf (COTS) technology such as the IMU.

There are only two subsystems of the entire Viper Puff Adder missile that require minimum research and development (R&D) efforts - the diverter impulse thrusters and the radar. All other subsystems of the Viper Puff Adder are already developed and have proven mature manufacturing processes established by the Hydra-70 baseline.

The radar system is composed of the transmitter, receiver, antenna, and intermediate frequency (IF) amplifier. All of the microwave millimeter integrated circuits (mimic) and manufacturing technology already exists at certain foundries such as Northrop Grumman in Redondo Beach, CA (formerly TRW) and Lockheed Martin. The transmitter module was built on an automated assembly line at Northrop Grumman in 19991. The power chips have already been designed and previously built1. Figure 4 (below) shows a 0.1 µm pseudomorphic power mimic. The only R&D efforts required for the radar are to actually complete the design efforts of the receiver and antenna subsystems. With simulation tools such as the High Frequency Simulation of Structures (HFSS), the R&D efforts should be minimal in funds and time required. The receiver should contain no more than 3 mimics - two low noise amplifiers and one rat race image reject mixer for down conversion to the IF frequency.

Figure 4. Pseudomorphic Power Mimic1 The patch antenna will require the most R&D effort to design, simulate and build a high gain, low beamwidth patch antenna suitable for the Viper Puff Adder requirements. Additional, antenna analysis should include the effects, if any, that the missile radius might have on the directional fixed beam antenna pattern. The manufacturing costs for the patch antenna are low since they involve well understood batch wafer techniques. The overall R&D efforts for the receiver, patch antenna and IF amplifier are considered low risk ($2.5M over 9 months). The analyses were well beyond the scope of this effort. 2.0 Technical Description of Methods Used

2.1 Project Office [J. Dickson]

The Team Viper Project Office worked all semester in conjunction with the Systems Engineering group to coordinate all the other subsystems in the design process and making sure every discipline stayed within the design constraints defined in the CDD. The Project Office initiated and carried out the three-phase program of this effort. The three phases were

1. Dickson, J. and Turnage, J., “Results of the W-band Power Amplifier Module Production Readiness Review,” US Army AMCOM Special Report RD-SE-01-01, Huntsville, AL, August 2001.

composed of Phase 1: Baseline Concept Analysis and Definition; Phase 2: Alternative Concept Development; Phase 3: Concept Refinement.

Phase 1 mainly focused on getting to know the Baseline ATM design. During this phase, the project office worked diligently with the customer to define the new CDD requirements. Through this partnership, a release of the CDD was initiated in order for work on the program to begin. In addition, it was during this phase of the program that the Project Office was responsible with working with the Project Manager, Dr. Robert Frederick, to determine the appropriate definition processes for the various disciplines.

Moving on to Phase 2 of the program, Team Viper focused on developing three unique concepts that were based on the original ATM design. With the guidance and oversight from the Project Office, Team Viper chose the Puff Adder configuration as the design to take into refinement. A discussion of the down-select criteria and selection matrix used to make this choice is discussed further in Appendix C. Although all three initial designs being considered were valid, realistic designs that would be capable of meeting the customer’s requirements, the Puff Adder appeared to be the optimal combination of both low-cost and low-risk, since the missile has very few moving parts, has an overall lower weight, and is based on proven – though uncommon – technology. Throughout Phase 3 of the program, the Project Office continued to provide oversight and direction from the customer and Project Manager. This communication of information was critical in meeting deadlines and achieving deliverables. Throughout, Phase 3 the design of the Puff Adder evolved with a myriad of research and additional documents for concept refinement. Consequently, the Project Office worked to provide the various deliverables to the customer that includes this final report and the final briefing.

Overall, the design process was a good lesson in tradeoffs and constraints for the team. This process helped the team understand the challenges associated with last-minute design changes and the resulting teamwork is prevalent in the everyday world. Team Viper was able to produce an excellent result, as will become clear through the following technical sections.

2.2 Systems Engineering [M. Vogan]

The design process implemented by the Viper team during the IPT 2006 Advanced Tactical Missile II project followed a logical methodology, allowing the group to draw on strengths from all team members, resulting in a design with a strong technical foundation. Figure 5 below shows the logical flow of this design process. The process began in Phase 1 with perhaps the most critical step, defining the mission requirements, which is indicated in the first block in Figure 5. This required a thorough evaluation of the CDD and close interaction with the customer to resolve any issues with the mission or design requirements. The team collectively evaluated the project requirements and provided this input to the customer; the customer, in turn, outputted an amended version of the CDD to be used throughout the process.

Figure 5. Viper Team Design Process Flowchart [M. Vogan]

Following this, a baseline was established with which the team could determine its strengths and weaknesses, and determine several reasonable alternative designs as improvements over the baseline. The baseline was thoroughly evaluated and decomposed to assist the team in understanding its strengths and weaknesses, and compared to the amended CDD to determine compliance. The main weakness of the baseline design – its guidance and control systems – became the main design driver in this process. Three separate control systems were researched and considered for this project. A BOOST matrix format was used to select the features of these three alternatives; this matrix and the selection criteria used are discussed more thoroughly in Appendix D. Two alternative designs involved aerodynamic control using either fins or canards. The Puff Adder – the design that was selected – uses momentum control with a series of small squibs that fire to change the course of the missile. This design minimizes the amount of drag on the missile body, thus making the propulsion system more effective and allowing for a slightly shorter design than the threshold specified by the customer. Although this control system is less common than the others researched, it has been successfully implemented in currently-deployed missiles on varying scales, and all modeling and research indicates it is both highly-effective and low-risk due to its lack of intricate moving parts. By establishing necessary details of the control system, the other

disciplines – such as aerodynamics, propulsion, and structures – could be designed to further support the needs of the control system.

Phase 2 feedback from the review team helped the Viper team in more effectively communicating our design goals. Some specific areas of concern raised during Phase 2 include the feasibility and reasonable cost of the ground-sensing radar, and the technical maturity of the divert-impulse thrusters used for control. Detailed research has gone into selecting an appropriate radar system which is fully capable of handling the Puff Adder’s mission. Furthermore, the thrust-diverter technology has been used in currently-deployed systems, and the professional experience of several team members in designing this type of technology has given the team confidence in both its ability to work properly, and its reasonable cost.

Phase 3 involved modeling and simulation of the selected design to optimize the various subsystems and allow the missile the greatest amount of control while still meeting the CDD requirements for performance, such as range, velocity, and acceleration. This part of the process is denoted at the bottom of Figure 5, where a continuous design loop is established through the subsystem design blocks, the trajectory section, and the need to meet requirements. The final design described here meets all customer requirements set out in the CDD, and exceeds several by meeting the objective standards, rather than the thresholds.

Of all the design options considered, the Puff Adder missile best meets the customer’s needs, while still being low-risk and low-cost. A cross-sectional drawing of the Puff Adder is shown in Figure 6 below. The missile is 2.75 inches in diameter and 71.4 inches in length – below the objective value of 71.7 inches – and is controlled with four rings of twelve divert- impulse thrusters each, shown just behind the warhead section. It weighs 33.9 pounds, which is below the threshold value of 34.45 pounds. Aerodynamic stability is provided by the four flip-out fins deployed at the missile’s tail. The fins and fluting of the missile’s main nozzle gives it a spin rate capable of keeping the missile stable without interfering with the ground- sensing radar. The missile’s center of gravity is located to the rear of the avionic section, and the center of pressure is located at the forward end of the motor; because the center of pressure remains located behind the center of gravity throughout flight, the missile remains stable. The double-base propellant used has enough energy to meet the velocity needs of the missile, while still being low-smoke and producing no ejecta, per the CDD.

Figure 6. Cross-Sectional Drawing of the Missile [M. Vogan]

Meticulous tracking of all changes to the design throughout Phase 3 has been critical in the success of the design process. Because several disciplines – particularly aerodynamics and propulsion – worked through a number of iterations of modeling to optimize the characteristics of these missile subsystems, even small changes to the size of the missile’s features needed to be carefully recorded. All changes have served as inputs and been logged in revised trajectory models throughout the process, allowing the trajectory models to generate the most accurate, up-to-date outputs as possible. Because of continuous teamwork and communication among disciplines during Phase 3 that allowed all new data to be accurately logged in the most current models, and because these models were controlled by only one team member, no separate input / output document was needed during the process. The primary characteristics of this final design can be found below in Table 2, and the overall mass breakdown of the missile – which was important in determining the cost per unit of the Puff Adder design – is found in

Table 3.

Table 2. Summary of Technical Parameters Calculations [M. Vogan] Parameter Value Gross Mass, kg (lb) 15.4 (33.9) Propellant Mass, kg (lb) 4.1 (9.0) Missile Length, cm (in) 181.4 (71.4) Maximum Drag Coefficient .8 @ M=1.05 Propellant Isp, sec 191.5 Total Impulse, N-sec (lbf-sec) 7,107.2 (1,597.8) Case Thickness, cm (in) 0.2 (0.06) Max Pressure, Mpa (psi) 9.8 (1,420.4) Ideal Change in Velocity2, m/s (ft/s) 698.8 (2,292.6) Ideal Max Acceleration2, m/s2 (ft/s2) 171.3 (562.0) Burn Time (s) 2.9

2 Ideal Velocity Change is based on no drag, no gravity, and constant thrust and is ΔV = Ispg ln (Final Mass/Initial Mass) 2 Ideal Max accell = (Isp) (g0) (propellant-mass) / ((burn-time) (grossmass))

Table 3. Vehicle Weight Statement [R. Naranjo] Subsystem Value 2.1 Warhead Total, kg (lb) 6.169 (13.60) 2.2 Avionics Unit 2.2.1 Avionics Case 0.42 (0.92) 2.2.2 Avionics Control 0.75 (1.65) 2.2.3 Autopilot 0.09 (0.19) 2.2.4 Power 0.69 (1.54) Avionics Total, kg (lb) 1.95 (4.29) 2.3 Propulsion Unit 2.3.1 Case Assembly 2.32 (5.11) 2.3.1 Igniter/Electric 0.02 (0.03) 2.3.3 Propellant 4.41 (9.71) 2.3.4 Nozzle Assembly 0.47 (1.03) 2.3.5 Fins/Control 0.07 (0.15) Propulsion Unit Total, kg (lb) 7.27 (16.03) Missile Net Takeoff Weight kg (lb) 15.39 (33.93) Contingency kg (lb) 0.24 (0.53) Gross Takeoff Weight kg (lb) 15.63 (34.46)

Table 4 below shows the basic performance characteristics of the Puff Adder for both the ground and air missions, calculated in cold, nominal, and hot conditions. Because the performance of the missile changes significantly at the varying altitudes of the given missions and under extreme temperatures, it is very important to insure it continues to meet the requirements of the CDD under all these conditions. As Table 4 indicates, the Puff Adder design successfully satisfies the necessary requirements at all given operating conditions.

Table 4. Reference Mission Trajectory Data, Required [M. Shannag, S. Strand] Ambient Conditions Air Mission, Target 500m Cold Nominal Hot

Launch Angle, deg 20 20 20 Launcher Altitude, m 0 0 0 Temperature, C -45.6 21.1 65.5 Launcher Exit Velocity, m/s 31.74 35.94 39.22 Launcher Exit Force, N 4020.64 4960.84 5701.3 Maximum Acceleration, gs 48.01 59.85 66.56 Velocity at Dispense Point, m/s 471 502 493 Lateral Error At Dispense Point*, m 0.065 0.052 0.046 Altitude at Dispense Point*, m 151.5 148.5 149.5 Air Mission, Target 8000 m Cold Nominal Hot Launch Angle, deg 15 15 15 Launcher Altitude, m 100 100 100 Temperature, C -45.6 21.1 65.5 Launcher Exit Velocity 31.74 35.94 39.22 Launcher Exit Force 4020.64 4960.84 5701.3 Maximum Acceleration, gs 48.01 59.85 66.56 Velocity at Dispense Point 213 234 243 Lateral Error At Dispense Point*, m 6.7 2.4 2.6 Altitude at Dispense Point*, m 149 148 145 Ground Mission, Target 500m Cold Nominal Hot Launch Angle, deg 1.8 1.8 1.8 Launcher Altitude, m 0 0 0 Temperature, C -45.6 21.1 65.5 Launcher Exit Velocity 31.74 35.94 39.22 Launcher Exit Force 4020.64 4960.84 5701.3 Maximum Acceleration, gs 48.01 59.85 66.56 Velocity at Dispense Point 468 499 490 Lateral Error At Dispense Point*, m 0.062 0.051 0.045 Altitude at Dispense Point* 148.4 149.6 149.5 Ground Mission, Target 8000 m Cold Nominal Hot Launch Angle, deg 15 15 15 Launcher Altitude, m 0 0 0 Temperature, C -45.6 21.1 65.5 Launcher Exit Velocity 31.74 35.94 39.22 Launcher Exit Force 4020.64 4960.84 5701.3 Maximum Acceleration, gs 48.01 59.85 66.56 Velocity at Dispense Point 267 313 318 Lateral Error At Dispense Point*, m 0.76 0.62 0.57 Altitude at Dispense Point* 148.8 150.2 152.1 * Trajectories run “open loop” with commands inserted to control trajectories. Some distances would be slightly smaller or larger during “guided” runs.

2.3 Aerodynamics [S. Strand]

2.3.1 Overview

The aerodynamics analysis was conducted to determine the flight performance of the initial concept missile and to then change those characteristics to accommodate the needs of the other disciplines, if necessary. The primary characteristics analyzed and adjusted were roll rate and static margin. The roll rate of the missile is no more than 16 Hz at any time, and the static margin is no less than 0.6 calibers. Other characteristics that were quantified, but not necessarily adjusted, included drag, Magnus forces, and lift. The coefficient of drag on the Puff Adder was calculated to be no higher than 0.8, and the lift is negligible. The results of this analysis feeds directly into the active guidance system as input tables.

2.3.2. Methods & Assumptions

The three main methods used to calculate the aerodynamic forces and moments and rates on the missile were hand calculations, the missile DATCOM software tool, and the PRODAS software tool. Hand calculations – which are fully derived in Appendix E – were used only to verify that the results of the software tools were reasonable. The DATCOM tool has strengths in analyzing supersonic bodies and bodies at any reasonable angle of attack, and PRODAS was most useful in modeling the wrap around fins and calculating roll rates.

For the purposes of the Puff Adder aerodynamic analysis, a standard atmosphere was used and the flow was assumed to be inviscid, adiabatic, and isentropic, particularly for the hand calculations performed. Additionally, it was assumed that the flow does not separate for the hand calculations, and that the PRODAS and DATCOM tools used provided accurate results, particularly for the more complicated interactions.

2.3.3 DATCOM and PRODAS Analysis Tools

The DATCOM software tool easily computes the static margin, drag coefficients, and pitch- damping coefficient at various angles of attack and velocities, and can calculate the drag without the effects of the base. It can also calculate a number of other coefficients and derivatives that are needed by an active control system. Using this tool to optimize the fin size is done through trial and error. The input file includes the physical characteristics of the body and the requests tables that are the desired output. However, DATCOM cannot easily compute CLα, which must be done by the user in a spreadsheet. In general the output is difficult to manipulate, but the tool runs quickly and gives reasonable results.

Because PRODAS is a trajectory tool, unlike DATCOM, it can explicitly provide a number of coefficients and variables that DATCOM cannot. For example, PRODAS directly presents roll rate, and the magnitude of Magnus effects and yaw motion becomes more apparent. Like DATCOM, PRODAS is a tool that must be used iteratively to optimize a characteristic. In the case of roll, the fins are the physical feature that must be changed to increase or reduce roll rate. PRODAS can be manipulated more quickly than DATCOM, once the physical model is created. Despite this, PRODAS does provide a good visual tool

for viewing the data, and has very good tabular output of the results. DATCOM and PRODAS generate similar output for the values of CLp and CL, the comparison of which is detailed further in Appendix I.

2.3.4 Discussion of Aerodynamic Analysis

Overall, the Puff Adder is relatively simple aerodynamically: it has a tangent ogive nose with a blunt tip, a body with a given diameter and length, and one set of four wrap-around tail fins. The base is flat due to the required interface with the existing launcher. Using wrap around fins provides more space for the nozzle and allows for a more efficient propulsion system. The specific dimensions of the tail fins are constrained by the physical interface to the launcher and the diameter of the missile. Other constraints include the required use of the M261 warhead, which restricts the modification of the nose, a critical element in missile aerodynamics. Also, the tail must remain physically compatible with the existing launcher, which effectively prohibits creating a boat tail to reduce drag.

Initial analysis was performed using the fins and nozzle of the existing MK66 rocket motor. The software tools were used to get the model started and then verified against those of the Hydra-70 missile3. This provided a baseline for further fin changes. The compromise between roll rate and static margin resulted in a configuration with 4 wrap around fins with maximum chord for the space available and a span that provides the lowest roll rate without becoming unstable at high angles of attack. Each fin has 82.296 mm in chord, 20.72 mm in span, and leading and trailing edges beveled to 10 degrees.

2.3.5 Resulting Performance

The Puff Adder is a relatively stable missile. The Cp is behind CG for all expected flight conditions. Figure 7 shows the minimum static margin at level flight with propellant (motor on). The CG moves forward as the propellant burns, which increases the static margin. The missile has adequate control authority given that the missile is controlled by a side thruster. There is enough damping to keep the missile from tumbling when the control thrusters are fired. Cmq is always negative, Figure 8 shows the pitch damping for level flight.

Figure 7. PRODAS Aeroodynamics Model Screen Shot [S. Strand]

3 Dahlke; Batiuk. “Technical Report RD-SS-90-6: Hydra-70 MK66 Aerodynamics and Roll Analysis.” July 1990.

Figure 8. Pitch Damping vs. Mach Number for Level Flight [S. Strand] The roll rate versus Mach is shown below in Table 5. The Puff Adder does not actively control the roll rate; instead, the roll rate is a function of Mach. However, the system does not exceed 17Hz in designed flight conditions. This is an acceptable rate for the missile’s other subsystems to function properly, such as the ground-sensing radar.

Table 5. Roll Rate vs. Mach Number [S. Strand]

SS Spin Rate SS Spin Rate Mach Number (deg/m) (cyc/s)

0.01 10.13 0.1 0.4 10.18 3.85 0.6 10.21 5.79 0.7 10.24 6.78 0.75 10.26 7.27 0.8 10.27 7.77 0.85 10.3 8.28 0.88 10.32 8.53 0.9 10.33 8.79 0.93 10.34 9.04 0.95 10.35 9.3 0.98 10.39 9.57 1 10.42 9.85 1.02 10.43 10.1 1.05 10.43 10.35

1.1 10.44 10.85 1.2 10.45 11.86 1.35 10.49 13.38 1.5 10.52 14.91

Figure 9 shows the roll rates as a result of the time during a PRODAS simulation run. The spin rate on this plot is shown in radians; for reference, the maximum value of 100rad/sec is equal to 15.92 Hz.

Figure 9. Roll Rate vs. Time (PRODAS Output) [S. Strand] The drag of the Puff Adder is relatively low. The missile’s small diameter and short fins allow the Puff Adder to more efficiently use the available propulsion. Figure 10 shows the coefficient of drag versus the Mach number. These are slightly below the values for the Hydra-70, which is expected because of the smaller fins. Figure 11 shows the unguided movement on the y axis due to the spin of the missile. This distance is easily corrected by the guidance system, but must be accounted for in the guidance algorithms.

Drag vs Mach

0.9

0.8

0.7

0.6

0.5 Prodas CX0(off) DATCOM Cd(on) DATCOM Cd(off) 0.4

0.3

0.2

0.1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Mach

Figure 10. Drag vs. Mach Number [S. Strand]

Figure 11. Unguided Y-Axis Movement due to Spin [S. Strand]

As mentioned previously, the Puff Adder cannot maintain an angle of attack; however, for the brief periods in time that it is angled, the missile does experience some force. Figure 12 below shows the CLα as a function of Mach, where angle of attack is in radians. Figure 13 graphically shows the duration of angle of attack for this missile through both ballistic and guided trajectories, simulated in standard, hot, and cold conditions. As can be seen from this plot, the cold-temperature, guided trajectory reaches the highest angles of attack during flight.

CLa vs Mach

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Mach

Figure 12. CLα vs. Mach Number [S. Strand]

Figure 13. Angle of Attack vs. Time [S. Strand]

In conclusion, the aerodynamic analysis of the Puff Adder shows the missile is adequately stabilized while maintaining control margin, and does not roll faster than the internal components can withstand. Table 6 shows a summary of primary aerodynamic parameters that are demonstrated by the Puff Adder missile.

Table 6. Summary of Aerodynamic Data and Calculations Paramter [Revision 01] Value Cd @ M=1.2 0.7816 Cmq @ M=1.2 and burnout -1504.508, -1538.719 Cl @ M=1.2 0.017087 Clp @ M=1.2 -2.1103 Max roll rate due to aerodynamics 15.68Hz Minimum static margin -.689 calibers at M=1.5 and alpha = +5deg

2.4 Propulsion [S. Strand]

2.4.1 Overview

The purpose of the propulsion system is to provide the physical energy to move the missile from the launch point to the target. Generally, propulsion systems for missiles use chemical reactions to generate thrust, which propels the missile through the air. The propulsion system for the Puff Adder missile consists of a double base propellant with a center slot grain, wrapped by a case, with an igniter at the forward end, and a nozzle. The vast majority of the analysis of the propulsion system consisted of optimizing the grain shape and the nozzle size to achieve the desired thrust profile for the system. The propellant, igniter were not analyzed in great detail due to time constraints. The results of this analysis are: thrust profile tables, which are loaded as input to the PRODAS trajectory simulation; and pressure tables and

propellant and nozzle mass information which is provided to the weight and structures discipline for input into that analysis.

2.4.2 Methods & Assumptions

There are few publicly available tools for analyzing rocket motors. In the analyses conducted, hand calculations were performed to verify the output of the Grains2.xls4 spreadsheet, and the MissileFlight program and the simple spreadsheets used for 1-DOF analysis to verify performance. The following assumptions were made during the propulsion analysis of the Puff Adder:

• The missile uses a perfect rocket; • Throat erosion is constant as a function of time; • Estimation used for degradation of thrust coefficient when separation in nozzle occurs is reasonable; • Sliver end area calculation using a triangle approximates the actual area of the sliver; • Propellant properties are a reasonable approximation of the existing MK66 propellant; • There is no transient behavior of the gas in the combustion chamber; • Erosive burning, while likely to be present, does not significantly alter the thrust profile; • Burn rate acceleration due to the missile spin does not significantly alter the thrust profile.

2.4.3 Key Rocket Motor Characteristics

The ratio of burn area to throat area is one of the most important characteristics of solid rocket motor design. This single factor can be manipulated to create a large variety of thrust profiles and burn times. It directly affects chamber pressure and therefore propellant burn rate. The equations to calculate burn area are very geometric in nature. The simplest way to do this by hand is to compute the burn area for a given web thickness. Web thickness begins with the maximum thickness of propellant (in any direction) and ends at zero. If the grain is center perforated then the initial burn area is the perimeter of the perforation times the length of the grain, plus the surface area of any exposed ends. It is important to calculate the burn area at key points along the burn distance, generally these points occur when regions of the area no longer have propellant to burn. The burn area equation significantly changes at those distances.

A detailed analysis of propellant chemistry and geometry was done to “downselect” the most effective motor for the Puff Adder. For a detailed explanation of the analysis techniques used, please see Appendix F. In this section, these calculations are broken out mathematically in great detail. Among these analyses were calculations for the mass flow rate, chamber pressure, burn rate, expansion ratio, and other factors, which ultimately led to a calculation for the expected thrust profile of the motor under standard and extreme temperature ranges. This formed the input for thrust in the 6-DOF (PRODAS) and other simulations.

4 Grains2.xls Software, Version 1.0, 1999, Troy Prideaux, Victoria Australia.

Burn time is best calculated using very small time increments and stepping through the burn rate, chamber pressure, sequence until the web is consumed. At each incremental step, the burn rate is multiplied by the time step increment and the distance burned is determined; or, conversely, distance steps can be used to determine the time it takes to make that step. Smaller increments provide a more accurate result due to the variation of burn rate over time.

Grains2.xls is a spreadsheet that can quickly help determine an approximate thrust profile, and to some extent, estimate the chamber pressure. This tool was used to determine the basic grain shape that should best serve the needs of the design. The limitations of the tool prevent it from being the final solution. Grain2 calculates the optimum expansion ratio for each time step, there is no nozzle equation other than the input of the throat diameter. The other limitation is that the spreadsheet does not do any calculations in regard to the propellant. The input for the propellant is the optimal Isp, which may not be very accurate. As a result, Grains2 cannot evaluate hot/cold/ambient temperature variations.

The MissileFlight program began life as a component of a project for UAH MAE 559 in the fall of 2006. The application is written in C++ with contributions from Stephen Strand, Jason Martin and Chris Morton. The basic functionality of the code was verified against spreadsheet calculations during the course. For this analysis, the components of code that needed to change were the inclusion of the grain shape as an input and the burn area equations. Those equations are included in Appendix F. MissileFlight provides a simple analysis of a solid rocket motor design with a few simplifying assumptions, discussed previously. It can analyze five grain shapes and can extend that to a simplified boost-sustain grain. It considers throat erosion to some extent and initial grain temperature conditions. MissileFlight also uses as input the burn rate coefficient and exponent of the propellant used in the motor. MissileFlight, like Grains2, must be used iteratively: the user edits the input file, reruns the application, and checks the output. It provides reasonable second-order results.

2.4.4 Results and Discussion

Figure 14 shows the full-scale cross-section of propellant grain. The dotted line represents the nozzle throat location and size. The center slot measures 16 mm by 37 mm, and has a 2 mm radius on the corners to prevent cracking. The outer diameter of the grain is 65.85 mm, which allows for insulation around the entire grain and the case.

Figure 14. Propellant Grain Cross-Section [S. Strand]

The reason for the grain shape selection was to obtain a delay in the main time of thrust so that the control thrusters could orient the missile in the correct direction before the bulk of the thrust was used. As a precaution, the side thrusters are not active until the missile is 16 m from the launch point. With some grain shapes, the over half the burn time would be used in about that distance. The other consideration was a need to be symmetrical about the x-axis, as this is a spinning missile. The resulting burn profile is a progressive-regressive shape, and the burn time of the progressive portion extends to 1.1 seconds in standard conditions.

The propellant selected is a double-base propellant with some ammonium perchlorate and aluminum. This propellant has a hazard classification of 1.3. During the analysis of the motor, the propellant data shown in Table 7 was used.

Table 7. Propellant Analysis Input Data [S. Strand] Input Characteristic Value Propellant Density (kg/m3) 1646.95 Propellant Specific Heat Ratio 1.215 Burning Rate Coefficient 0.0000233 Propellant Temperature Sensitivity 0.0018 Pressure Exponent / Burn Rate 0.4 Sigma P Reference Temperature (oC) 21.1 Characteristic Velocity (m/s) 1512.74

These values are reasonable for the type and class of propellant that was chosen. The primary advantage of the double-base propellant with metal additives is the relative low cost

of manufacturing, as this material can be extruded. The other advantage is that it can meet the 1.3 hazard classification. It has several disadvantages, the nitro glycerin can bleed out during storage, but will meet the storage requirements of the CDD; the relatively low performance compared to other propellants; and the potential problem caused by the extrusion manufacturing process of a mesa shaped burn rate profile that can further reduce performance.

The nozzle was iteratively designed with a few constraints that restricted most options. The initial design is based on the MK66 nozzle, which uses a carbon insert to reduce throat erosion. The exit diameter is restricted to 53 mm by the need to remain physically compatible with the existing launcher. With that constraint, the throat diameter is the only parameter that can be altered. By iteratively running the MissileFlight software and altering the throat, an optimal value for total Isp at standard atmosphere was determined. A value of 0.2 mm per second was chosen as a reasonable erosion rate, so the optimal diameter of 24.8 mm includes the effects of throat erosion. The nozzle does have some grooves to accelerate the roll rate but the angle of those grooves is greatly reduced from the MK66 motor. By using the grooves, the missile achieves 10 Hz rate at 0.5 seconds sooner than without.

Thrust misalignment was not evaluated, but because this is a rolling missile, the impact can be considered inconsequential. The effects of erosive burning must be determined empirically, and could be considered in the nozzle design or grain design to control the effects and achieve essential the same profile. The same is true for the longitudinal acceleration of the motor, roll rates over 7 Hz induce a 10-g force on the grain and accelerate the burning, if that is accounted for in nozzle and grain design, the resulting profile could be approximately the same as the more basic analysis developed.

The thrust profile of the Puff Adder motor is presented below in Figure 15. Table 8 provides a summary of standard atmosphere characteristics. The temperatures used are: Cold, -45.6C; Std, 21.1C; and Hot, 65.6C. This covers the operational temperature range specified by the CDD.

Puff Adder Thrust Profiles

9000

8000

7000

) 6000 N (

5000 Thrust-Cold Thrust-Std Thrust Thrust 4000 Thrust-Hot

3000

2000

1000

0 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (s)

Figure 15. Puff Adder Thrust Profile [S. Strand]

Table 8. Summary of Propulsion Data and Calculations [S. Strand]

Parameter Value Total Impulse 7,107.2 sec (standard) Burn Time 2.9 sec (standard) Maximum Chamber Pressure 9,793,587.6 Pa (hot) Maximum Chamber Temperature 2,975.0 K (hot) Minimum Initial Thrust 4,020.6 N (cold)

Packaging and sealing of the unit can be assumed to be similar to the existing system, allowing for the assumption that the unit is indeed protected from humidity according to the requirements of the CDD.

2.5 Structures [R. Naranjo]

2.5.1 Structures Overview

The main components and dimensions of the Puff Adder are shown in Figure 16.

Figure 16. General Layout of the Puff Adder

All the components have a maximum diameter of 6.985 cm (2.75 in.) in order to be compatible with current 2.75-inch storage, transportation, and launch containers. The fins are curved and wrapped around the tail so that they fit inside that diameter. The total length of the missile is 181.45 cm (71.43 in.), i.e. below the CDD objective length, and its weight 15.39 kg (33.93 lb), which is 1.52 % less than the CDD maximum weight. The CG at takeoff and burn out of the Puff Adder are 84.3 cm (33.19 in.) and 68.72 cm (27.06 in.) respectively. Appendix G.2 contains the mass properties of the Puff Adder and its components.

2.5.2 Warhead Structures

As specified in the CDD, the warhead is supplied by the customer. It corresponds to the M261 MPSM Warhead (Appendix G.1, Figure G.2). The fuse is the only element that can be modified in this component, so that it shall be compatible with the missile fire signal.

The mechanical interface of the warhead is through a 2.40-6 Stub special ACME male thread, 6.35 cm (2.5 in.) long.

2.5.3 Avionics Section Structures

In the avionics section will be allocated the divert-impulse thrusters, the electronics elements, the radar, the IMU, and the thermal battery. Figure G1.3 in Appendix G.1 shows the detailed dimensions of this section. Its front has been designed with a female thread, which matches with the ACME thread of the warhead. In the adjacent section of approximate 15 cm (5.9 in.) long x 6.38 cm (2.51 in.) diameter, there is enough space for all the avionics elements, with the exception of the thermal battery. The void inside the male thread, at the rear end of the avionics case, will contain the thermal battery. This thread is the interface with the motor section and it has the same design as the ACME male thread of the warhead.

Aluminum and steel alloys were considered for the manufacturing of the avionics section. Composite materials were not considered due to the threaded construction of the interfaces. The selection of the material was mainly based on the tensile and yield strengths of the material, its density, its machinability, and its cost.

Aluminum 7075-T6 was selected for this application because it has a high tensile yield strength (503 MPa), which offers a good factor of security, and also a low density and a machinability of 70%. A comparative table of the alloys considered is shown in Appendix G.3.

Appendix G.8 details the stress analysis of this section. The analysis shows that for this material a 0.3 cm (0.12 in.) thickness for the thinner wall will support the applied loads.

2.5.4 Motor Section Structures

AISI 4340 steel was selected for the motor case considering that this component supports the greater loads of the missile. The stresses applied to the case could also be supported for a composite material, but for aerodynamics considerations steel was preferred to obtain a center of gravity farther away from the nose. The materials considered for this section were selected based again on the material’s tensile and yield strengths, its density, weldability, machinability, and cost. The figure G1.4 in Appendix G.1 shows the cross-section of the motor.

The matrix selection is shown in Appendix G.4, and the technical data of the AISI 4340 steel in Appendix G.6.

The motor has a frontal bulkhead with female thread ACME that matches with the avionics male thread. The base of the bulkhead is 0.5 cm (0.20 in.) thick which supports the pressure of the combustion chamber. The motor side of the bulkhead wall has a void to allocate an ATJ graphite insulator. The frontal bulkhead shall be welded to the case. The AISI 4340 steel can be welded with appropriate preheat and post heat procedures.

A detailed analysis of the thermal, static and dynamic loads was developed for the motor case (shown in Appendices G.9 and G.10), which is one of the critical components of the missile. The analysis shows that a minimum thickness of 0.15 cm (0.06 in.) of the steel case with a 0.25 cm (0.10 in.) insulator ATJ graphite liner is required for the wall case.

In the rear side of the motor section other welded bulkhead will be attached. This bulkhead is required to allocate a retention ring for the tail section. The bulkhead and the inside liner have the same diameter, so that the propellant cartridge could be loaded inside the motor by the rear side.

2.5.5 Nozzle/Tail Sections Structures

The interface of the motor and the tail/nozzle section is shown in Appendix G.1, Figure G1.5. The body of the nozzle is also designed using Aluminum 7075-T6, with carbon inserts allocated in part of the inner lateral wall and in the throat to insulate the metal from the high temperature exhaust gases. 2.4 cm (0.09 in.) of the frontal side of the nozzle fits inside the motor rear bulkhead, and it is locked with a retention ring laterally inserted to the interface. This section of the nozzle has also a groove to allocate an o-ring that seals the hot gases of the combustion chamber. The external side of the nozzle has two additional grooves for the retention mechanism of the launcher and for the ignition system of the missile. The cross- section of the nozzle is shown in Appendix G.1, Figure G.6.

Four curved aluminum fins, as required by the aerodynamic design, are wrapped around the tail. When the missile is launched the fins are deployed by springs that are compressed against the external wall of the nozzle.

2.6 Avionics [J. Martin]

2.6.1. Avionics Overview

Active control of the Puff Adder is achieved using divert impulse thrusters (DITs) arranged in four rings of twelve. These thrusters provide the necessary impulse to create the moments and translational forces needed to guide the missile to its target.

Initially, the missile is provided by the platform with a target location, and after launch it will use onboard sensor technologies to stay aware of its own position relative to the launch platform and the assigned target. To accomplish this, the missile uses a fusion of data from two main sources: a frequency-modulated carrier-wave (FM-CW) radar array and an inertial measurement unit (IMU). The radar system is designed to provide the missile with both its distance above and direction to the earth. As a result, it will also be able to calculate the precise roll rate. The IMU will provide the missile with all of the other data required to accurately accomplish its mission.

Figure 17. Overview of Avionics Functionality [J. Martin]

The “brain” of the system is a microprocessor system, which has the primary responsibility of fusing sensor data into a meaningful trajectory model, and adjusting that trajectory by firing the DITs at the appropriate times. When the trajectory model is satisfied that missile has reached its target, the processor will issue a fire command to the warhead for submunition deployment. Figure 17 approximates the primary avionics functions and data flow.

The avionics unit is powered by a thermal battery located in the aft of the avionics unit, adjacent to the flight motor. This battery is initiated just before launch of the missile and supplies power only to the components within the avionics case.

2.6.2 Avionics Assumptions

The design of the avionics subsystem of the Puff Adder included the following assumptions:

• The missile’s target is provided in the appropriate format to the missile prior to launch. This coordinate system can be relatively arbitrary; since the missile does not use GPS, it does not need to know it’s own exact position. It needs only a relative vector to the target.

• The warhead can be modified to allow command detonation from the avionics section, but this is outside the scope of this project and is assumed both feasible and of zero cost.

2.6.3. Avionics Design Methods

To design the avionics section, several steps were taken. First, the masses of all components were estimated for ballistic trajectory modeling. Upon completion of this step, the number of thrusters required and the requisite thrust profile of each thruster were considered. This was done by estimating the thrust and size of the thrusters that would be used, and placing them on the on the model. Ballistic trajectories were “modified” by the firing of thrusters and compared to one another.

The second step in avionics design was the IMU/radar navigation system. The first step was selection of a COTS IMU for use in this system. After the IMU was selected, the accuracy requirements of the roll-rate / elevation sensing radar could be compared with that of the IMU and the filtering scheme created. With these requirements identified, the radar system was designed and integrated accordingly.

Next, the processing unit of this system had to be developed. The processor(s) used had to be able to collect, filter, and merge data from the sensors, use that data to form a trajectory model, and issue corrective commands to the DITs as necessary. This was a big task, and once a suitable candidate was chosen, the right support and integration circuitry was identified (at a high level).

The final step was integration of the power supply. The power requirements of the IMU, thrusters, and processor(s) combined to determine the power supply needs of the system. Once these needs were identified, a thermal (or other) battery could be identified to power the system and fit within the remaining space allowed in the avionics unit.

At this time, all integration concerns could be addressed. Did the final weight or size match the estimate closely? How does the “real” weight or size affect the predictive models? Do the components within the IMU system require insulation, padding, or shielding that was previously unaddressed, or did the combination of the components of the system create unpredicted problems? The results of all of these studies are presented below.

All COTS components are “gun-hard” and specified to withstand the operating and storage temperature requirements and the altitude requirements of the CDD. All non-COTS parts, to include the radar and the thrusters (semi-COTS), shall be designed to that specification with minimal difficulty. The avionics unit will be hermetically sealed.

2.6.4 Avionics Results and Discussion [J. Martin]

2.6.4.1. Divert Impulse Thrusters

The first step in sizing thrusters was to determine the maximum amount of “impulse” available in the squib section. It is accepted in industry that for each cubic inch of thruster (including detonators, propellant, electronics, and case material), approximately 12lbf-sec of total impulse can be achieved as a theoretical “average” from propellant-based thrusters. Much larger impulses can be achieved from HE (high explosive, such as RDX) based energetics and hybrid varieties. The total amount of “impulse” that could be obtained therefore was largely determined by the volume and mass allowed by those respective budgets, as well as by the structural properties of the avionics casing.

This quickly ruled out HE, as this option would result in damage to the missile with each squib firing. Following the path of propellant-based thrusters, it was decided that possibly up to 5 rings of thrusters could be fit into the avionics housing, arranged in groups of 12, each with a theoretical impulse of approximately 828Ns. Allowing for 10% undershoot or overshoot in target squib impulse, 911Ns was used for structural checks and 740Ns was used for trajectory calculations. The squibs had to fire for less than one half the time it takes the missile to make one revolution. At 20Hz, this would be 0.025 seconds.

Consultation with industry professionals at Pacific Scientific5 provided us with a probable burn time of around 0.01 seconds -- less than half the “maximum” burn time. With volume and impulse determined, it was finally reasoned that 12 thrusters in each ring would be the appropriate amount, giving both the desired dimensional characteristics as well as trigonal and quadrature symmetry. Our final configuration was presented to experts in the field who provided confirmation that this design was realistic and feasible. These thrusters also can be expected to provide very predictable and repeatable burn profiles – a requirement for accurate control. Appendix H contains more information about the predicted accuracy and repeatability of these squibs.

The length and mass budgets allowed for up to 5 rings of thrusters, but careful analysis was done to determine the optimum number of rings, compared to the amount of additional flight motor that could be added instead. In the end, the results of this analysis indicated a proper number of 4 thruster rings. For more details of this analysis, please see Appendix I. See Figure 18 for a visualization of this configuration:

5 Personal Conversation regarding Divert Impulse Thrusters with Mr. Steve Nelson of Pacific Scientific EMC, Valencia, CA, 13 April 2006.

Figure 18. Squib Ring Geometry (One of Four)

Based on information from companies who manufacture these thrusters (Such as Pacific Scientific), they can be designed to fire with very little energy using miniature low energy exploding foil initiators (LEEFIs), adding a trivial requirement to the power supply. The firing capacitors can be charged within 10 ms and be ready to fire, giving the system time to charge and arm up to 35 thrusters before the system is even outside of the safe thruster firing window.

2.6.4.2 Inertial Measurement Unit

The IMU that was selected for use in the Puff Adder is the SiIMU02 from BAE Systems. This IMU was chosen because of its high accuracy at high roll rates. Looking at the specifications (Appendix H1), it clearly meets the minimum requirements for the ranges necessary to function on this missile. With that said, all IMUs, including this one, are subject to errors that are somewhat random. Many IMU errors can be measured and corrected, creating a reduction in error, but many others can not be helped even with compensation. Slight variations in temperature, vibration, and lifespan of the device can create unrecoverable error. This error is cumulative, which means that over the span of the missile flight, it can compound into great error in positioning at the end of the flight.

According to BAE Systems6, that this IMU is most accurate at high roll rates, near 3600 degrees/sec (10Hz), which is exactly the range that the Puff Adder flies within. At this rate,

6 Personal Conversation regarding the BAE Systems SiIMU02 Inertial Measurement Unit with Mr. Charlie Hopper, BAE Systems, Ft. Worth, TX, 5 April 2006.

BAE reports an approximate error of 0.03 degrees/sec (ambient temperature), which at a flight time of 40 seconds results in a maximum miss angle of 1.2 degrees. Uncompensated, this could result in a miss of almost 30m (az, el, or combined) for every 1000m of downrange missile travel. Alone, this is too much error, and must somehow be reduced.

2.6.4.3 IMU Error Correction and Filtering

To help correct for these errors in the IMU data, an additional source of situational data was desired to provide additional navigation data. One possible alternative is to use a GPS receiver. A GPS receiver could provide timely corrections that could assist in navigation by “resetting” the IMU to a known position at regualar intervals during flight. This initially appears to be the best solutions, but there are several reasons why this is a bad choice.

All GPS receivers that are constrained in size have a trade space of accuracy, signal quality (satellite reception), and speed. A GPS receiver that is designed to maximize all three attributes must be unacceptably large, meaning that one, two, or all three of these objectives must be compromised if designing in a small space. Furthermore, even the fastest and largest GPS receivers cannot acquire accurate position data much faster than 20 Hertz. At 300 m/s, this is 15 meters of uncertainty in measurement. Assuming that this rate is achievable at all within the constrained size of the missile, non-differential GPS receivers are limited in accuracy (typically) to +/-5 meters. Additionally, quickly acquiring satellites and keeping them acquired throughout a 20-30 second flight is another difficult proposition. Even for a non-rolling missile this would be tricky at best, but the rolling nature of this missile makes effective antenna design nearly impossible.

To obtain a GPS with the desired attributes of this flight, a non-COTS solution would have to be pursued, with no guarantee that an adequate GPS receiver is even feasible at all within given cost limits.

Another alternative, the one we ultimately chose, is an FM-CW radar system, mounted cylindrically around the avionics housing. The radar is capable of providing direct position and velocity measurements in the elevation direction, as well as providing the missile with a known directional vector to the surface of the earth and a roll rate calculation with respect to the missile body axis. This would serve a similar purpose as the GPS in correcting the “walk” of the IMU system. This data, when fused with the IMU data through adaptive multi-source Kalman filtering7, will provide data accurate enough for the guidance objectives outlines in the CDD.

It has the additional advantage of being much lighter and cheaper than GPS-based solutions, though it also carries the disadvantage of being a non-COTS alternative. Even so, historical data from other weapons systems using similar systems supports our assertion that the cost and effectiveness of a custom-manufactured radar system is superior to a GPS alternative. The technology is very mature; in the case of FM-CW radar, custom manufacturing will be required due to form factor restrictions, but the technology will require little or no research and development.

7 Ref. H8: B. Burchett and M. Costello, "Specialized Kalman Filtering for Guided Projectiles”

2.4.6.4 Microprocessor

A number of suitable processing units can be used to provide the “brain” of this missile system. Historically, microprocessor units have been used in conjunction with separate analog-to-digital converters (ADCs), filters, and other interface circuitry. In these cases, many processors made by Texas Instruments, Motorola, and others could be used along with discrete analog and logic components to provide this functionality.

A more modern and cost-saving approach is to place as much of these functions as possible on programmable devices (digital, analog, or mixed) such as ASICs, FPGAs, and PADs8. Not only does it reduce the cost and weight of the system based on pure component cost, but development is almost entirely soft. For example, Altera’s Stratix and Cyclone devices include an embedded Nios II processor and a DSP builder unit. This DSP and processor unit is capable of providing the hardware acceleration needed for radar data pre-processing, kalman filtering, and trajectory calculations. Though these functions can be done in a processor without dedicated hardware, adding hardware acceleration allows them to be done faster, decreasing time between calculations and increasing the fidelity of guidance and navigation measurements.

This approach is not only more powerful, but gives the advantage of upgradeability without costly hardware modifications. Developmental T&E can be done with currently fielded hardware, quickly, and with little prototyping cost. Upgrades can also be quickly integrated into existing models that have already come off of the assembly line. The end result is a reduction of total life cycle cost and faster time to the field.

2.6.4.5 Power and Initialization

The thermal battery was chosen to satisfy the final electrical requirements of the system, determined at the conclusion of the avionics design. A summary of those requirements is provided in Table 9 below: Table 9. Thermal Battery Requirements Subsystem Nominal Voltage Peak Current (mA) Avg. Power (W) Total Energy† (W- (VDC) s) DIT system* 12 300 (300@12V) 3.6 3.6 IMU 5 600(300@12V) 3 120 FM-CW radar 4 2500(900@12V) 10 400 Processor circuitry 3.3 1000(350@12V) 3.3 132

Totalұ 12 1850 22.2 655.6 *data assumes no two thrusters charged at once, and includes the electronics of the firing subsystem † Calculated by (duration of use) x (avg. power consumed) ұ Current @12V, power includes DC-DC conversion loss estimates

8 “Application Specific Integrated Circuits”, “Field Programmable Gate Arrays”, and “Programmable Analog Devices” – visit www.altera.com, www.lattice.com, or www.motorola.com for more information on these technologies and their applications.

Based on these requirements, and the size requirements of the Puff Adder platform, we decided upon a thermal battery. Companies like Eagle-Picher9 can build thermal batteries to the specifications of their target systems if provided with the right geometric volume, and typically produce a high peak power density of around 10 W/cm3. With approximately 83 cm3 of thermal battery area, minus a margin of 20%, that gives a peak power output of approximately 664 W. If the battery operates at a nominal voltage of 28 V (+/-4V) this yields a peak current of 24 A. Lithium-type thermal batteries can be designed to these specifications with life spans exceeding 60 seconds, which is beyond the limits of the most taxing mission requirements of this system. Based on the totals in the chart above, such a battery is an over-design, and could be optimized further to reduce weight if necessary. It merely represents what is possible in the space allowed. Many companies offer COTS batteries that fulfill these requirements. One such company is Eagle-Picher10, whose catalog contains many acceptable batteries, even some potential COTS candidates that would not even require custom packaging.

Some of the components have startup delays which must be addressed. The IMU has a startup delay of 350 ms, which means that the thermal battery needs to be fully initiated at least 350 ms before launch. The thermal battery will also have a delay before it is fully initiated, usually in the range of 200-300 ms. This will also need to be built into the startup time of the battery.

2.6.4.6 Fusing and Arming

It was assumed that the M261 warhead would need to be modified to allow for a new set of firing criteria for the Puff Adder; this modification was also assumed to be out of the design scope of this project, and assumed free. However, it would be remiss to neglect the mechanism by which the new controls would arm and detonate the modified warhead, which is covered briefly here. We will not remove the longitudinal force requirement from the fuse train; indeed we would like to keep the 13.5 g mechanical arming device in place. Instead of an analog timer for detonation, however, we would like to add a command detonate signal from the CPU of the avionics unit. This detonation signal comes when the Avionics unit is satisfied that the missile has traveled to within 10 meters (longitudinally) of the “wall in space” as defined by the CDD. To protect for premature squib firing, the squibs could be electronically “shorted” through the motor fuse, so that only after the main motor has been fired can the thrusters be fired as well.

To verify this requirement, we merely take the maximum speed of the Puff Adder at long ranges (likely to be the least accurate) and multiply by the sample period to obtain our “uncertainty.” This number happens to be approximately (250m/s)*(1/50kHz) = 0.005 meters. This is based on the radar sample rate, the “trusted” source of data between IMU samples. We also expect that our drift along the longitudinal axis should be well within 10

9 Web Site, http://www.eaglepicher.com/NR/rdonlyres/F3E95B16-6BB3-42D0-8AF4- 727DBA26C113/0/ThermalDesign.pdf, Information on Thermal Batteries, Assessed April 2006.

10 Web Site, www.eaglepicher.com, Information on Production of Thermal Batteries, Assessed April 2006.

meters @ 1.0m/s/sqrt(hr) (Appendix H1). It follows that since we can accurately target the center of the wall in space “basket” (shown later) that the requirement is therefore met.

2.6.5 Frequency Modulated Continuous Wave (FM-CW) Radar [J. Dickson]

2.6.5.1 Overview

The FM-CW radar has two primary functions. The radar will provide range information (height of the Puff Adder above the ground) and to determine the precise roll rate of the Puff Adder during flight. The range to ground is given by R = Tt (c) / 2. R is range, Tt is round trip time to ground and return, and c is the speed of light. The roll rate is determined by a sinusoidal output from the sampling circuitry. The sinusoidal waveform has a peak at ground detection.

A W-band millimeter wave radar was the natural selection because of the small diameter (2.75 inches) of the Puff Adder. All of the components of the radar (transmitter, receiver, antenna, and IF amplifier) are uniquely packaged and mounted on an assembly known as the radar ring. The ring configuration, shown in Figure 19, allows ease of assembly, bench testing and final integration into the Puff Adder avionics section. Another unique feature of this radar is the patch antenna, which is conformally mounted and recessed into the missile body.

Figure 19. Puff Adder Radar Ring11 [J. Dickson]

2.6.5.2 Radar Characteristics

Since no millimeter wave simulation tools where available, only hand calculations will be presented for the transmitter. The other subsystems (receiver and IF amplifier) are assumed to operate at the minimum required levels for fundamentally sound radar operation. At this time, the IF amplifier characteristics require future development but will be assumed to have the sampling capability of 50 KHz to fulfill the Nyquist sampling theory requirements for proper FFT analysis. The patch antenna was found in open literature12

11 Dickson, J., and Yang, D., “Development of a Low Cost, Highly Producible Sense and Destroy Armor (SADARM) Transceiver for Smart Munition Application,” US Army AMCOM Technical Report RD-SE-01- 01, Huntsville, AL, January 2001. 12 Ref. H9: Miniature Radar Altimeter Mk VI, Roke Manor Research, 10 April, 2006.

The FMCW radar has a very simple transmitter architecture. The triangular ramp waveform, shown in Figure 20, was selected with a center frequency of 94.0 GHz. The triangular waveform permits measuring Doppler frequency shift13. The triangular waveform has a bandwidth of 1 GHz and a sweep time of 66.7 µs. The 1 GHz frequency deviation provides a potential time resolution of 1 ns and a corresponding range resolution of .15 meters. The modulation frequency is 14.993 KHz. The transmitter, shown in Figure 21 Figure 3, has an output power of 250 mW.

Figure 20. Transmitter Waveform

Figure 21. Puff Adder FMCW Transmitter14

The maximum height, H, for which the radar must locate the ground is 2000 meters for a maximum air mission. At 2000 meters with an antenna beamwidth of 1 degree, the radar cross section is 3893 m2. This radar cross section yields a reflected return power of -125.6 dBm for deciduous trees. The slant range is 2030 meters. The minimum height for the radar is 50 meters. At 50 meters, the radar cross section is 2.44 m2. This radar cross section yields

13 Ref. H10: Principles and Applications of Millimeter-Wave Radar, edited by Nicholas C. Currie and Charles E. Brown, 1987. 14 Dickson, J. and Turnage, J., “Results of the W-band Power Amplifier Module Production Readiness Review,” US Army AMCOM Special Report RD-SE-01-01, Huntsville, AL, August 2001.

a reflected return power of -92.45 dBm for deciduous trees. The slant range is 50.8 meters. These figures represent the most severe conditions that the radar must endure.

The receiver must be capable of receiving and amplifying return signals from long ranges while also being capable of receiving short range signals without becoming saturated. A W- band receiver with a measured noise figure of 2.5 with a gain of 8dB and a bandwidth of 500 MHz is shown in Figure 22. This receiver was built in 1994 with Aluminum Gallium Arsenide chips. The minimum signal to noise ratio of the Viper Adder receiver should be greater than 3 dB. Actually the signal to noise ratio for this radar should be significantly greater than 3dB. With today's technology advancements in receiver front end technology (low noise amplifiers either in Aluminum Gallium Arsenide or Indium Phosphide), a receiver noise figure of 1db is readily achievable since the first low noise amplifier determines the receiver noise figure. The bandwidth of the receiver should be at least 1GHz with suitable dynamic range.

Figure 22. Millimeter Wave Receiver15 The radar will have two patch antennas - one for transmit and one for receive. The antennas will be recessed into the missile body so that the antenna surface will be flush with the missile's skin. The antennas will be mounted opposite on the missile body. This distance is much greater than 10 wavelengths which aides in isolation. The long cylindrical nature of the Viper Adder aides with the requirement for a high gain patch antenna network. The antenna characteristics were derived from a commercial 77 GHz altimeter developed by Roke Manor Research16. The patch antenna is 75 mm wide x 50 mm long x 3.2 mm thick with a beamwidth of +/- 35 degrees @ -3dB. No gain information was listed. The maximum gain (36.6 dBi) was determined by using the listed dimensions and assuming no losses. For the Viper Adder antenna calculations, 6 dBi was subtracted from the maximum gain for loss correction. Also the beamwidth was reduced to 1 degree for the reflected return power calculations. Batch manufacturing techniques should allow for a very low cost antenna.

2.6.6 Guidance [J. Martin]

Because this system uses a modified ballistic trajectory to reach its target, proportional navigation will most likely result in undershoot for long range targets and therefore is not the best choice for this missile. The Puff Adder will be guided instead with a “model predictive” controller17. This type of control works by quickly estimating the impact point, and

15 Courtesy of US Army Aviation & Missile Command, Manufacturing Science and Technology Division. 16 Miniature Radar Altimeter Mk VI, Roke Manor Research, 10 April, 2006. 17 Ref. H3: B. Burchett and M. Costello, “Model Predictive Lateral Pulse Jet Control of an Atmospheric Rocket.”

comparing this estimate to the known target location. As the estimated impact point diverges from the target location, thrusters are fired at the appropriate time, attempting to minimize the error. This differs slightly from a more traditional guidance approach, known as “trajectory tracking,” though they are indeed very similar.

Trajectory trackers typically calculate a 6-DOF trajectory prior to firing to develop a trajectory solution to the target. That trajectory is then followed using a trajectory tracking algorithm throughout flight. Because 6-DOF and higher-order models require much processing time, this model can not be updated during flight, and so for moving targets or for miscalculated trajectories, this method must be aided by some other algorithm (such as proportional navigation). It is also a difficult algorithm for squib-controlled weapons, since the squibs are discrete force injections. This prevents the algorithm from effectively utilizing derivative control and tends to cause large overshoot in corrections.

This is why, for the Puff Adder, it is recommended instead that a model predictive controller, based on projectile linear theory be used (as modified by Burchett and Costello for nontrivial pitch and yaw angles)18. This complete trajectory (and hit point) can be rapidly calculated during flight and the miss vector calculated. This can be combined with the estimated effect of firing a squib, and in real time a “miss window” can be established. From the controller’s point of view, a moving ellipsoid is projected on the target, centered around the estimated hit point of the missile. If the miss window shrinks or moves in such a way as to not include the target, a squib is fired in the appropriate direction to “re-center” the window. More on model predictive control and modified linear theory can be found in the appendix and in the reports by Costello, et al. and McCoy’s Modern Exterior Ballistics, chapters 9, 10 and 1119.

Data from the radar and IMU, after processing, is fed to the controller and the output is used to make a firing decision. When the system output indicates that a thruster firing is necessary, the output of the controller is simply a directional vector. This output must then be compared with a list of unfired thrusters and the appropriate thruster selected. The roll rate, p, is then used along with the time to impulse center (Δtsquib/2) and the angular coordinate of the available thruster to determine the appropriate firing time. Please see Appendix H for more detailed information.

According to Burchett and Costello3 this model predictive controller can sufficiently guide a system of this type to a target at a distance of 9000ft (2743m) to within a miss distance of 10 feet using less than 6 thrusters. Differences in the model used by those authors and our own, as well as our more demanding requirements on missile performance mean that our system will require more thrusters, but the principles remain the same. A brief summary of the mathematics and assumptions used for this controller is provided in the Burchett and Costello report3 on the same subject, along with in-depth simulation results. For a more complete review of this control strategy, please refer to this article.

18 Ref. H5: L.C. Hainz, M. Costello, “Modified Projectile Linear Theory for Rapid Trajectory Prediction” 19 Ref. H16: Modern Exterior Ballistics, McCoy

According to the CDD, the guidance and control system of the Puff Adder is required to be able to overcome 19 milliradians of platform error. A comparison of various trajectories developed from the firing of different numbers of squibs will show this to be possible for the elevation axis (Appendix H), but the azimuth direction warrants its own look, since many of the non-aerodynamic forces are different. We handle this case directly, by specifically targeting an object which is 19 milliradians “out of alignment” with range centerline (x axis). This is easily overcome by the Puff Adder, with the firing of only 6 squibs, including one “oversteer” correction. This implies that the Puff Adder could easily overcome even larger misalignment in mid-range shots by utilizing more squibs. The results of shot referenced above can be seen in Appendix H, as well as an overview of the total control authority of the Puff Adder.

Unfortunately, due to limitations in PRODAS and our respective controller model, it was not possible to model and test a 15 knot crosswind as specified by the CDD, but reviewing the control authority examination in Appendix H, we believe that a crosswind of this magnitude would pose no serious threat to the operation of the Puff Adder, except in the most extreme conditions. As this is currently untestable, it is one of the very first items that should be tested in the next phase of development, when the development of more advanced (native code) models allow for more specific analyses.

2.7 Trajectory [J. Williams, M. Shannag, S. Strand, J. Martin]

2.7.1 Methods and Assumptions [J. Williams]

The modeling and simulation of the Puff Adder was completed with the aid of a six-degree of freedom (6-DOF) trajectory software called PRODAS. Using this software, the Puff Adder’s performance could be easily evaluated with only a few user inputs. Modeling the projectile in PRODAS significantly cut down on the hand calculations required, considerably reducing the time from conception to flight analysis. The internal PRODAS calculations were assumed to be correct; as long as the PRODAS outputs were similar to the outputs expected, no extra calculations or checks were done. The basic flow of the PRODAS 6-DOF is contained below in Figure 23.

Figure 23. PRODAS Flowchart [J. Williams]

A comparison study for design refinement was completed for the Divert and Attitude Control System (DACS) that included all avionics components, the Puff Adder motor and propellant design, and the aft section that included the nozzle and fins. One physical dimension or characteristic would be altered per testing set to optimize the performance based on that piece or setting. Physical limits of each piece of the projectile were set such that the optimized design could still contain all the necessary components and fit inside the required launch envelope and meet the required stipulations set forth in the CDD. This mass model can be seen below in Figure 24.

Figure 24. 2-D PRODAS Mass Model [J. Williams]

In addition, the sectioned PRODAS version of the Puff Adder can be found below in Figure 25.

Figure 25. Sectioned PRODAS Model [J. Williams]

Moreover, additional analysis was done in the structural arena which can be found in that representative section of this report. This was done with the aid of the IDEAS software. An isometric view of the Puff Adder modeled in IDEAS can also be found below in Figure 26.

Figure 26. 3-D IDEAS Model [J. Williams]

2.7.2 Results and Discussion [J. Williams]

The Puff Adder meets both the short and long range objectives for the ground launched and helicopter launched scenarios in all of the required atmospheric conditions specified in the CDD. In addition, the Puff Adder reaches the stressing cases (long and short range) in 26.97 and 1.64 seconds, respectively. The ATM maintains stability throughout the entire flight, even in cold conditions. Total fail safe ranges for the missile for the stressing cases is a minimum range of 6108.5 meters and a maximum range of 8208 meters. The graphs of these ballistic trajectories are contained in Appendix I.

The target basket criteria in the CDD is met with the aid of our guidance and thrusters. Moreover, as the colder conditions are the stressing scenario for the ATM, the Puff Adder meets all requirements in all required climates. In fact, due to the mechanism by which the Puff Adder ascends, warmer atmospheric conditions also stressed the operation of the Puff

Adder – which the Puff adder also handles nicely. Appendix I contains the tables that approximate the flights of the Puff Adder and additional information that can be used to aid in the assessment of the ATM’s capabilities.

2.7.3 6-DOF Trajectory [M. Shannag, J. Martin]

The six-degree of freedom trajectory analysis in PRODAS predicts the performance characteristics of the ATM throughout its flight. In order to perform such analysis, other software was utilized to acquire the inputs need to run PRODAS, these tools were DATCOM, MISSILEFLIGHT, and GRAINS2. DATCOM is widely used by USAF, and its outputs include, but are not limited to: drag and lift coefficients, configuration geometry, attitude, and Mach numbers. The MISSILEFLIGHT tool shows the maximum range contours of the target area. GRAINS2 is used to analyze the grain and use its output in PRODAS. PRODAS was used to successfully calculate the trajectories specified in the CDD for the Puff Adder.

The Puff Adder trajectory model uses 48 DITs arranged in four banks of twelve to guide itself to its target. Because the Puff Adder generates very little lift, it is forced to expend many of its DITs to achieve the necessary angle to the horizon before the flight motor burn is complete. The sooner the DITs can fire, the more the impulse can be directed vertically, thus making it imperative for them to fire as early as possible during the burn. This limitation is further complicated by the fact that the missile must clear 50ft from the launch platform before the DITs fire. Lastly, the DITs cannot fire too closely to one another without destabilizing the missile, and sending it towards an angle of attack that is beyond what PRODAS can reasonably predict. It was decided that no more than 12 separate angles of attack would be used, due to increased error in measurement. This ultimately allowed up to 36 DITs to fire before the motor expired, leaving as few as 12 to guide the trajectory after burnout. In some cases, not all 36 DITs were used for the missile’s initial pitch-up, allowing more for guidance later in flight.

The Puff Adder has a unique advantage over canard or air-brake controlled varieties. Because it does not generate significant aerodynamic control forces, but rather uses small rocket motors for control, it actually becomes much more maneuverable in atmosphere of a lower density. It is easy to verify that this missile does indeed perform to the requirement of launchability at 20,000ft, which is done and presented in Appendix I. 200 feet below sea level is similarly examined, with less severe, but equally telling results.

Different scenarios were considered in the trajectory analysis, both guided and ballistic, ground launch and helicopter launch, all of which were run for three different temperature environments (cold, standard, and hot). Figure 27 and Figure 28 show the maximum and minimum horizontal range for all three temperature cases for a guided helicopter launched scenario, respectively, as functions of time and Figures 29 and 30 show the maximum and minimum required horizontal range for all three temperature cases for the ground launched scenario, respectively, as functions of time. As seen from these graphs, guidance has improved on the mission’s downrange. A more detailed analysis of the ATM’s trajectory is discussed in Appendix I.

Figure 27. Downrange Helicopter Mission (500m); All Conditions

Figure 28. Downrange Helicopter Mission (8,000m); All Conditions

Figure 29. Downrange Ground Mission (500m); All Conditions

Figure 30. Downrange Ground Mission (4,000m); All Conditions

2.8 Platform Integration [J. Dickson, M. Vogan]

The Puff Adder missile is fully compatible with the existing M261 launcher, as specified by the CDD. The diameter of the missile has been maintained at 70 mm (2.794 in), and the length was reduced to 181.43 cm (71.43 in) which is below the objective length of 182.1 cm (71.7 in). The Puff Adder's weight is 15.39 kg (33.93 lbs) which is .24 kg (.528 lbs) below the threshold weight specified in the CDD. With 38 Puff Adder missiles, the helicopter launcher platform weight is significantly reduced by 9.12 kg (20.064 lbs). The Puff Adder

employs four aerodynamic fins at the base of the rocket motor. The fins are wrapped around the missile body just as the Hydra-70 baseline. The Puff Adder is loaded and retained within the launcher using the same procedure and locking mechanism as the baseline. The launcher cannot distinguish between the two missiles. The Puff Adder's guidance scheme is 100% compatible with the current electrical connections of the launcher. The same interfaces (helicopter or ground-based platform) are used to provide initial GPS coordinates to the Puff Adder.

2.9 Trade Studies and Interactions of Subsystems [S. Strand]

The most extensive trade studies involved in the Puff Adder design process took place under the aerodynamic analysis. Because the missile must roll to remain stable, but cannot roll too quickly to avoid interference with the divert-impulse thrusters and ground-sensing radar, a number of iterations of fin sizing were required to achieve the proper roll rate and still maintain stability. The studies of the fin sizing were started using the wrap-around fin design of the Hydra-70, inputting this design into the DATCOM and PRODAS software tools to verify accuracy of the tools and inputs, and then iteratively modifying the fin sizing to generate output at acceptable levels.

As discussed previously, the Puff Adder employs a set of four, curved, wrap-around fins at the base of the missile that are deployed at launch. The sizing of these fins greatly impacts the performance of the missile. Fins with greater chord length create higher roll damping than fins with the same span but shorter chord. Fins with a larger span create higher roll moments than fins with the same chord but less length. Leading and trailing edges also affect roll moment, and larger fins move the center of pressure towards the rear of the missile, and conversely smaller fins move the Cp towards the nose. Additional fins create higher roll damping, add drag and move the Cp towards the rear of the missile.

The compromise between roll rate and static margin resulted in the four wrap-around fins having a maximum chord for the space available and a span that provides the lowest roll rate without becoming unstable at high angles of attack. Each fin has 82.296 mm in chord, 20.72 mm in span, and leading and trailing edges beveled to 10 degrees. 3.0 Implementation Issues

3.1 Production Cost [M. Vogan]

The production cost of the Puff Adder was calculated using a combination of weight-based equations from Fleeman’s Tactical Missile Design text20, and individual pricing on more expensive components contained within the avionics section. All components contained in the weight-based calculations are commercially-available raw components with relatively low manufacturing costs, or components of the warhead that have not changed from the original Hydra-70 design.

20 Fleeman, Eugene L. Tactical Missile Design. AIAA Educational Series. 2006.

The cost of the first unit was calculated using the weight of the motor section and the weight of the warhead. This data was combined into the following formula, which accounts for development costs such as design work, testing, and tooling for manufacturing:

0.758 C1st = $6,100WL

Where C1st is the cost of the first unit, and WL is the weight of the missile minus the avionics equipment. This calculation yielded a cost of approximately $84,940 for the first Puff Adder unit produced. In order to calculate the average cost of one unit assuming a total production of 10,000 units – per the CDD – the following equation was used:

log X Cx = C1stLc 2

where Cx is the cost of a given unit within the total of 10,000, and Lc is a learning curve factor. The learning curve factor was assumed to be 0.8 based on recommendations from Fleeman. This factor falls between that for the process of building a developmental missile (Lc > 0.8) and the factor for a high rate of production process (Lc < 0.8), since the production of the Puff Adder involves both types of processes. Cx was calculated for all 10,000 units to be produced using this formula, and then averaged over the entire number to obtain a cost for a single unit. Using this process, the weight-based cost of one unit came to $6,450.

The components of the avionics section and integration costs were priced separately based on bulk-purchasing estimates obtained from the manufacturers of the equipment. The total cost of all avionics equipment adds an additional $5,000 to the cost of each missile. Integration costs are expected to be minimal, since the missile is fully compatible with the launcher, there are no extra protrusions to accommodate, and the majority of components will be of common materials, and simple to manufacture. This hybrid approach yields a total average unit cost of $11,450, which is well below the threshold limit in the CDD of $15,000 per unit.

3.2 Manufacturability [R. Naranjo]

3.2.1 Avionics

The avionics section casing shall be manufactured from a solid round bar of 7075-T6 aluminum having an outer diameter ≥ 7.1 cm (2.80 in.), and a length ≥ 24.0 cm (9.45 in.). The basic shape of the component will be done in a CNC lathe.

3.2.2 Radar [J. Dickson]

The fundamental building blocks of the radar are the mimic chips. The transmitter chips will be processed on 4 inch wafers using a power doping process (0.1 µm Pseudomorphic High Electron Mobility Transistor, 2-mil thick Gallium Arsenide or Indium Phosphide substrates). The receiver chips will also be processed on 4 inch wafers using a low noise doping process. All probe transitions will be custom designed but will be built with standard thin-line or co- planar alumina processing techniques. The modules maybe built out of Kovar to match the thermal coefficient of expansion to either Gallium Arsenide or Indium Phosphide. However

since the time of flight of the Puff Adder is very small and the missile is not constantly power cycled, a less dense module housing material may be possible to use. It may be even possible to mount the chips and other circuitry directly to the radar ring. This is one area of further evaluation. All the modules will be built using automatic epoxy dispense and robotic pick and place assembly lines. The modules will be tested on automatic test equipment suited for high volume production. Since the architecture of the radar receiver and transmitter are simple relatively speaking, no rework will be conducted. The final acceptance testing will be go no-go. The patch antennas will be processed using highly automated batch manufacturing processes. All the mimic chips and antenna circuits will be wafer probed to ensure a very high module yield rate. We are very confident we can achieve our cost goal of $1250 per radar system using these techniques.

3.2.3 Motor

The frontal bulkhead of the motor shall be manufactured from a solid round bar of AISI 4340 steel having an outer diameter ≥ 7.1 cm (2.80 in.) and a length ≥ 6.5 cm (2.56 in.). This section will require a previous turning process before welding to the motor case.

The rear bulkhead of the motor shall be manufactured from a hollow round bar of AISI 4340 steel having an outer diameter ≥ 7.1 cm (2.80 in.), an inner diameter ≤ 5.6 cm (2.20 in.), and a length ≥ 1.6 cm (0.63 in.). This part will also require a previous turning process before being welded to the motor case.

The next step of the manufacturing process will be the welding of the two bulkheads to the motor case. The welding will require a pre heating and post heating processes. The final steps are the turning of both and the quenching of the whole piece.

3.2.4 Propellant

The Puff Adder will use a cartridge propellant type which will be loaded by the rear side of the missile before the assembly of the nozzle.

3.2.5 Nozzle/Tail

The nozzle body shall be manufactured from a hollow round bar of 7075-T6 aluminum having an outer diameter ≥ 7.1 cm (2.80 in.), an inner diameter ≤ 3.0 cm (1.18 in.), and a length ≥ 16.0 cm (6.30 in.). The graphite insert will be previously turned to fit inside the nozzle body. Once fitted, the assembly will be machined to its final dimensions.

3.2.6 Fins

Fins will be manufactured by mean of an extrusion process in order to obtain parts with a shape close to the required configuration. Then the parts will be processed in CNC milling machines to receive their final dimensions.

3.3 Test Schedule [M. Vogan]

Prior to the manufacturing of the Puff Adder, a number of additional developmental steps must take place. If this design is to be pursued, more detailed modeling and simulation over a larger range of trajectories and conditions would be ideal. The current design meets the requirements set out by the customer in this CDD, but further research into the needs this missile will fulfill may reveal additional operational requirements. This step should take no more than 2-4 additional months of work.

In addition to more thorough modeling, a more detailed set of blueprints and manufacturing drawings of both the missile and the necessary tooling to manufacture it must be generated to produce a prototype of the missile. These detailed drawings of both the missile and the tooling must then be programmed for use in CNC milling machines and other automated production tools. Establishment of the production process and production of a prototype, given that many needed facilities already exist, should take no more than 6-8 months.

The prototype must then be measured and evaluated in terms of masses and moments, and should be tested in a wind tunnel to verify aerodynamic characteristics that have only been simulated previously. The propellant cartridges produced for the Puff Adder should be randomly examined and X-rayed to determine any defects, and those defects corrected. Any design modifications should then be made to the models and drawings in accordance with the output of this testing. In addition, the manufacture of a prototype missile will reveal any flaws or bottlenecks in the production process that can be corrected prior to serial production. Evaluation of the physical prototype should be a fast process since the missile is so small with so few subsystems, and can likely be completed within 1 month of manufacturing. Adjusting the production process accordingly may take longer, up to 2-3 months.

Once a working prototype has been obtained, a flight test program of the missile is recommended to verify all performance characteristics, and to further refine the model if necessary. Ideally, the missile should be flown through a wide range of conditions and from multiple platforms to ensure it meets the requirements for all missions. A thorough flight test program – barring any scheduling conflicts at test ranges – could likely be completed within 6-8 months. This should include any small changes to the design as appropriate.

Lastly, as the missile enters serial production and begins its deployment to the military, a set of additional training and operational guidelines must be established, and personnel intending to use this weapon system must be trained and become well-versed in its technology, hazards, and design details that separate it from previous hardware they may have used. Such training can likely be completed within a one week for a group; schedules for this training will vary depending on the needs of the customer. This full schedule of testing, redesign, and production is shown in the timeline below in Error! Reference source not found..

Figure 31. Overall Technology Development Schedule [M. Vogan]

3.5 Discussion of Application and Feasibility [M. Vogan]

The Puff Adder missile has been designed to use as much commercially-available equipment and raw materials as possible for the ease of manufacturing and to keep the costs reasonable for this type of upgrade. As discussed in the manufacturing section, the main components of the missile – the motor and avionics casing, the nozzle, and the propellant – can all be manufactured with easily-obtained materials using facilities the government already owns. The warhead of the missile has not changed, preventing the need for any additional manufacturing of this component. Additionally, because approved facilities and processes already exist for the type of manufacturing required for the Puff Adder, it is expected that the environmental and social impact of developing this new missile will be minimal.

The aspect of the missile that could potentially present a feasibility challenge is the guidance and control system; however, the technology used on the Puff Adder has been thoroughly researched and successfully used on deployed missiles on varying scales, and so is believed to be technically mature enough to handle the ATM II mission.

Although the DITs and ground-sensing radar used in the Puff Adder are not available off-the- shelf, discussions with the manufacturers of this technology has proven that, on the scale of 10,000 to which the Puff Adder will be manufactured, these components can be obtained for a relatively low cost. Details on the pricing of individual avionics components is discussed further in Appendix K.

In addition to cost, the issue of service life has been addressed. The Puff Adder is expected to fully meet the required 10 year service and storage life span indicated by the CDD. The only factors that limit the span of the Puff Adder’s life are the life span of the propellant, which should be at least 15-20 years for the type selected, and the life span of the battery, which should be no less than 20 years. Because the missile has no moving parts, such as actuators that would be needed for moveable fins or canards, there are no external components to damage during storage and handling, or to decompose over time.

4.0 Company Capabilities [J. Dickson]

4.1 Viper Company of America Overview [J. Dickson]

Viper Company of America is comprised of a diverse group of energetic engineers and managers drawing on the skills of all its employees. Viper Company of America, known in the industry as Viper, works to meet the needs of its customers with innovative engineering solutions implemented with great professionalism and technical prowess. During Phases 1 and 2 of the IPT 2006 Advanced Tactical Missile II concept development, Viper developed a solid plan to draw on the strengths of all team members in the brainstorming and evaluation of design ideas that would meet or exceed all the requirements outlined in the Army's CDD. The multi-discipline Viper team worked cohesively to examine all available design possibilities for the ATM, while maintaining a realistic view of the Army requirements. Viper demonstrated a tremendous ability to take full advantage of all simulation and other design tools at our disposal during our development of the Puff Adder. Engineering programs such as PRODAS, DATCOM, and IDEAS were integral in the design process and allowed for in-depth trade studies of alternatives being considered. The technical expertise of all team members contributed to the successful use of these advanced tools to create the best design in the most efficient manner possible. As a result, the Puff Adder concept was down-selected with the lowest cost and most manageable level of risk.

Furthermore, Viper’s ability to effectively communicate our design ideas and answer critical questions from the customer has been evident in the technical packages delivered during both Phases 1 and 2 of the concept design process. We closely examined all recommendations provided by the review team, and objectively examined our design choices as a result and worked to include all suggestions made by the reviewers. Our team showed strong collective understanding of our design through our responses to the questions posed by the review team. Additionally, our presentation at the 2006 UAH IPT Open House allowed us to further communicate the details of the exciting new design features being incorporated into the Puff Adder with the local public and technical community. Our engineering expertise has been demonstrated by communicating directly with company representatives with questions about the IMU performance and mimic chip availability. In summary, the Viper team is comprised of many experts in a variety of fields. When this proposal is accepted, Viper Company of America will promptly move forward with the Puff Adder development.

4.2 Personnel Description [M. Vogan]

• Mr. Jerry Dickson – Viper Team Project Office Mr. Dickson’s 19 years of experience in program management and international project office support to missile, space, and aviation systems makes him ideal to lead the Viper Team. He has continuously demonstrated the unique ability to plan, organize, and bring to fruition a broad attack on complex problems. His participation has been sought on special task forces and committees as the principal spokesman, and he has authored over 40 publications and technical reports and three U.S. patents.

• Ms. Marie Vogan – Viper Team System Engineer Ms. Vogan’s background in multiple areas of technical and engineering supervision and testing of complex missile systems will enable the Viper team to successfully implement the Puff Adder Project. Her attention to detail and ability to coordinate production efforts will keep this project on track in terms of both scheduling and finance.

• Mr. Stephen Strand – Viper Team Lead Aerodynamics and Propulsion Engineer Mr. Strand’s education and experience will enable him to be a valuable asset to the propulsion and aerodynamics analysis of the Puff Adder Project. His abilities with writing c++ helped the team develop a functional propulsion model that accounted for several assumptions in the grains2 spreadsheet. Mr. Strand, with the help of team members, was responsible for Aerodynamics and Propulsion.

• Mr. Ricardo Naranjo – Viper Team Lead Structural Engineer Mr. Naranjo, a mechanical engineer with 12 years experience in structural design and manufacturing & testing of turbo machinery equipment has given the Viper Team a definite advantage in the design and analysis of the weights and structures of the Puff Adder missile. He has worked for several years in multidisciplinary technical teams to develop industrial machinery, and this experience has benefited the Viper Team tremendously.

• Mr. Jason Martin – Viper Team Lead Avionics Engineer Mr. Martin’s three years of experience in test and evaluation of tactical missile systems, including the Hydra-70, and his experience as an electrical engineer with background in electronics design has aided the team greatly in the design of the Puff Adder’s control system. His extensive work in embedded hardware and software development for missile data acquisition systems (DASs) is directly applicable to the challenges of the ATM II project.

• Mr. Jason Williams – Trajectory Lead Mr. Williams’ knowledge has allowed him to lead a successful integration effort in the modeling and simulation arena for the Viper Team. His previous experiences in program and technical management in the United States Army Research and development field for the U.S. Army Space and Missile Defense Command have added an extreme benefit to the design of the ATM. His past experiences and excellent work ethic have made him a key asset to the Viper team.

• Mr. Mutasem Shannag – Viper Team Trajectory Simulation Expert Mr. Shannag is the backup for the Trajectory Simulation team, with 1 year experience in missile systems trajectory and simulation tests. His knowledge is a valuable asset to the Viper Team. 5.0 Summary and Conclusions [M. Vogan]

Given all the data shown above, it is clear that the Puff Adder design meets the needs of the customer while using advanced, innovative technology that, although uncommon, has been

proven and is technically mature enough to handle the challenges associated with an Advanced Tactical Missile. The main driver – the control system – has been shown to be capable of successfully controlling the missile under a wide range of given conditions with no moving parts, thereby resulting in a lower risk of missile malfunction, and an extension in the missile’s service life. The propellant chosen meets all the customer’s needs for minimum smoke, and no ejecta, while also meeting the objective desire of being a hazard classification of 1.3. Even with these characteristics, the propulsion system is capable of firing the missile to the objective ranges for both the air and ground missions without exceeding the maximum velocity for submunition deployment. The aerodynamic surfaces have been designed to be a minimal size, yet the correct dimensions to give the missile the roll it needs to remain stable. The materials chosen for the missile structures of each subsystem are strong enough to withstand the aerodynamic forces and extreme heating that will occur during flight, yet are designed to be light enough to minimize the cost. Many of the components used are either available off-the-shelf or with little alteration needed, or can be manufactured in bulk for a very reasonable cost. This makes the manufacturing considerations of the missile relatively simple, with final assembly able to be performed in existing facilities. Overall, the Puff Adder successfully meets the requirements of the CDD at a reasonable cost, and would be an excellent choice for the Army’s next Advanced Tactical Missile. 6.0 Recommendations [J. Dickson]

At this stage of the design process, the Puff Adder baseline meets or exceeds all the Army's CDD requirements. However, if a pre-planned product improvement (P3I) effort were to be considered in the near term future, the radar packaging and the propellant could be improved. The unique radar packaging would center the modules on the inside radius of the Puff Adder radar ring instead of on the flat outside of the ring. This packaging concept would allow for lower antenna receive and transmit losses and reduce the total weight of the ring assembly. Changing the propellant from a standard double base to a double base propellant with a plateau burn rate curve could provide additional burn duration at a slightly lower thrust. This would allow more time for the directional control thrusters to maneuver the missile. This would allow a larger engagement window which would provide more range. The total P3I effort would require approximately $1M and 15 months to accomplish both efforts. The unit production cost requirement needs to be adjusted to reflect 2006 real fiscal dollars. The CDD threshold and objective cost requirements are unrealistic and do not take into account such categories as cost of money, overhead, profit and G&A. All of these items reflect costs that are associated with every contractor's proposal and are costs that are allowed under all contracts.

Appendix A - Concept Description Document [J. Dickson]

Appendix B - Electronic File Index [J. Martin]

The following files are included on this list: • Spec Sheets • Input and Output files from Simulation/Analysis Software • Electronic References • Source Code • Worksheets for calculations (MathCAD/EXCEL, etc) • CAD Drawings

Other files may also be included at the discretion of the authors.

Filename Description of Software Contents Required to Run or View the File MATHCAD\*.* MATHCAD files used MATHCAD in structural calculations PRODAS\Puff_rev12mod1std.pr3 Main Model -Standard PRODAS PRODAS\Puff_rev12mod1hot.pr3 Main Model -Hot PRODAS PRODAS\Puff_rev12mod1cold.pr3 Main Model -Cold PRODAS PRODAS\PuffAdderRev12AeroPrediction.txt PRODAS Aero Any Text Editor Analysis PRODAS\PuffAdderRev12SpinAndStability.txt PRODAS Stability Any Text Editor Analysis PRODAS\PuffAdderRev12MassProperties.txt PRODAS Mass Any Text Editor Properties Analysis DATCOM\puffrev12datcominput.dat DATCOM Aero DATCOM / Text Analysis input file Editor DATCOM\puffrev12output.dat DATCOM Aero DATCOM / Text Analysis output file Editor Grains2\Grains2.xls Propellant Burn MS EXCEL Predictor Grains2\PuffAdderPropellantGrains2Input.ppf Input file for Grains2 Grains2.xls Grains2\centerSlotGrain2Input.mt Input file for Grains2 Grains2.xls MissileFlight\*.* Propellant Burn Any good “c” Predictor Source Code compiler CAD\PuffAdder.mf1 CAD missile IDEAS Drawings CAD\PuffAdder.mf2 Cad Drawings IDEAS CAD\*.bmp Cad files (bmp format) Any Image Viewer Specs\SiIMU02.pdf Specs for IMU Acrobat Reader Ref\DahlkeCW_Hydra_70.pdf Hydra 70 Aero Acrobat Reader

Analysis Ref\tech-manufact-propellant.pdf Propellant Acrobat Reader Manufacturing Reference EXCEL\*.* Excel Worksheets for MS EXCEL miscellaneous calculations

Appendix C - Project Office [J. Dickson]

The Project Office holds responsibility to interact with the customer and make sure that the guidance is carried out accordingly. To do this the Viper Project Office met during Phase I with the customer to set the CDD requirements. Through these initial meetings the specifications and requirements for the design were discussed and specific changes were accepted by the signing of the CDD document. Through the communications between the Project Office and the other subgroups set in place, Viper was able to work to achieve the objective of delivering a practical design for application to the warfighter. In addition, for making sure that the customer requirements are met, the Project Office is to oversee and approve all design changes. To do this the Viper Project Office divided up the team into six areas: Systems Engineering, Aerodynamics, Propulsion, Weight & Structures, Trajectory, and Avionics. These subgroups were given a team lead who reported directly to the Project Office. Figure 32 shows the Viper Company of America team. In addition, the Viper team initiated a charter to have a written record of basic regulations for meeting and governance. The charter is as follows:

Viper Company of America Charter

1) To focus on work related problems and behaviors that are within the Team’s span of control and influence. 2) To avoid gossip and other talk detrimental to team unity. 3) The majority rules but the minority is heard and respected. 4) To listen to what individuals have to say and give everyone an equal opportunity to be able to voice ideas and concerns. 5) The main meeting for IPT Team H will be Tuesdays and Thursdays at the regular class time of 0935 and other agreed to time as necessary. 6) If a team member is to miss a meeting, inform someone else on the team beforehand.

Jerry Dickson Marie Vogan Jason Williams Stephen Strand Mutasem Shannag Ricardo Naranja Jason Martin Project Office Systems Engineering Trajectory Aerodynamics Trajectory Structures Avionics Figure 32. Viper Company of America

Selection of Phase 3 Design

The entire family of Adder missiles developed by Team Viper in Phase 2 met the basic customer performance requirements for the Advanced Tactical Missile. In order to choose one of these concepts for further refinement and design during Phase 3, the characteristics of each concept was compared to the requirements laid out in the CDD and graded on a weighted scale based on the importance and design impact of each requirement. The total

scores were then compared to determine which design would be selected. The scoring of the designs is summarized in the Requirement Evaluation Matrix, shown in Table 10. As the scoring in this matrix demonstrates, two concepts (Night Adder and Puff Adder) scored an identical score of 390. Therefore cost became the ultimate tie breaker. Using the cost formula and going strictly by weight estimates the Puff Adder was selected over the Night Adder. The Puff Adder had a projected cost ($10,870) just slightly over the objective ($10K) unit production cost and substantially under the threshold cost of $15K.

Table 10. Requirement Evaluation Matrix NA | z SCORING LEGEND Not Analyzed Does Not Meet Partially Meets Meets -- 0 3 6

Death Night Puff CDD PARAGRAPH Requirement Score Wt. Hawk-eye Adder Adder Adder

2.2.1.1.1 Firing Envelope Max Alt. 6096 m MSL 3 NA z z z Min Alt. -61 m MSL 2.2.1.2.2 Platform Error Maximum of 19 mils. 3 | z z z 2.2.1.2.3 Crosswind Maximum of 7.7 m/s 3 | z z z 2.2.1.2.4 Range: Helicopter Min. Range 1 km Mission Max. Range 8 km 4 z z z z 2.2.1.2.4 Range: Ground Min. Range 1 km 4 z z z z Mission Max. Range 4 km 2.2.1.2.5 Smoke Signature Minimum Smoke 4 z z z z 2.2.2.2.1 Launcher Interfaces Compatible with current M261 3 z z z z Launcher 2.2.2.2.2 Longitudinal Force Minimum of 13.5 times the weight 4 z z z z of missile 2.2.2.3.1 Submunition +/- 10 meters of the Wall in Space 3 NA NA NA NA Deployment 2.2.2.3.2 Acceleration Maximum of 79 g’s 4 z z z z 2.2.2.3.3 Velocity at Sub Maximum 603 m/s 4 z z z z Deployment 2.2.3 Weight Max. weight added to launcher is 4 z z z z 297 kg 2.2.3.1 Length Maximum of 202.4 cm 4 z z z z 2.2.3.2 Outer Diameter Maximum 70 mm 4 z z z z 2.2.4.1 Service Life Minimum of 10 years 3 | NA NA NA 2.2.4.2 Unit Production Cost Maximum of 15K/unit (10Kunits) 5 z z z z 2.2.5.1 Temperature Operation Conditions 4 | NA NA NA -31.7°C to 65.5°C 2.2.5.2 Humidity Operate during or after 100% 3 NA NA NA NA Humidity 2.2.6.1 Hazards Classification 1.1 Threshold z z z z 1.3 Objective 3 2.2.6.3 Flight Fail Safe Minimum Ballistic Trajectory of 3 NA z z z 3.5 km USER SUPPLIED Static Stability Missile must be statically stable 3 | z z z Risk/Reliability Lowest risk of design features 3 z | z z failing Total Score 300 369 390 390

Ultimate Tie breaker: Cost 11,449 11,493 10,870

Appendix D – Systems Engineering [M. Vogan]

Phase 2 of the Puff Adder design process involved decomposing the baseline missile into its subsystems, evaluating each system for technical merit and completeness of analysis. The decomposition of the system is shown in the block diagram in Figure 33, below.

ATM II System

1.0 Platform 2.0 ATM 3.0 Launcher

2.1 Warhead 2.2 Avionics Unit 2.3 Propulsion Unit

2.2.1 Avionics Case 2.3.1 Case

2.2.2 Avionics Control 2.3.2 Igniter/Electrical

2.2.3 Autopilot 2.3.3 Propellant

2.2.4 Power 2.3.4 Nozzle

2.3.5 Fins/Control

Figure 33. Phase 2 Baseline System Decomposition

Based on perceived weaknesses in the baseline missile design and the need to consider all design alternatives for the ATM II system upgrade, three alternate solutions were examined. To select the features of these three alternative designs, the team made extensive use of the BOOST matrix format, shown in Table 11 below. Using this format, the team was able to consider all reasonable options for each subsystem, and select combinations of features to come up with three unique designs.

Table 11: BOOST Matrix for Viper Team Alternative Missiles

The three alternate designs considered by the Viper Team – the Death Adder, the Night Adder, and the Puff Adder – all met more of the CDD criteria than the baseline Hawkeye design, and either fully met or exceeded nearly all the criteria. The choice to continue development on the Puff Adder, as opposed to the other two designs came down to a combination of cost and risk. The Puff Adder was, by far, the least expensive design because of its small size compared to the other two designs. Because some of the technology is less common, it was estimated that the Puff Adder was of medium risk, particularly when compared to the canard option. However, because of the lack of moving parts and fins, and the missile’s resulting ability to fit easily with the existing launcher, it was determined that this design is both most cost efficient, and would likely have the longest life span and simplest operating requirements, despite the moderate risk. Therefore, the Puff Adder was the missile chosen to explore further in Phase 3.

The design process during Phase 3 involved the further refinement of the Puff Adder design. Even from the time the design was selected from the above BOOST matrix, a number of design features were changed. An initial attempt to generate an input/output type document for control of the changing design features was determined unnecessary by the System Engineer. Because all of these data points feed directly into the PRODAS trajectory model of the missile, and because the output from PRODAS is the final step in the design process, it was determined the that trajectory modeling lead would maintain control of any changes to the overall missile model, and incorporate them into the latest revision. Any alterations that did not pass through that individual did not make it into the design and, consequently, no unintended changes were made to the working missile design. The removal of the I/O document served to simplify the design process by removing the middleman, and effectively resulted in tighter overall control of the working model.

The resulting Puff Adder design is a 2.75 in by 71.43 in missile with an overall mass of 33.93 lbs. The missile uses divert impulse thrusters for control, and a set of four pop-out fins at the base of the missile for aerodynamic and roll stability. The main features of the Puff Adder missile are detailed in Table 12 below.

Table 12. Primary Missile Characteristics Missile Characteristic Value Length (in) 71.43 Diameter (in) 2.75 Weight (lb) 33.93 Cost per Unit $11,450.35 Max Ground Range (m) 4,000 Min Ground Range (m) 500 Max Helicopter Range (m) 8,000 Min Helicopter Range (m) 1,000 Accuracy (mils) < 19 Timeline to Deployment (months) ~ 20-24

Appendix E – Aerodynamics [S. Strand]

Appendix E1: Derivation of Aerodynamic Calculations

Stability of the missile is determined by the static margin. The static margin is defined as the distance between the center of pressure due to aerodynamic forces and the center of gravity21, and determines the moment arm created by aerodynamic forces and the amount of side thrust needed to turn the missile body. If the static margin is too large, then the force required to turn could break the missile. If the static margin is too small, then the maneuvering forces could cause the missile to become unstable and tumble. The Puff Adder must have negative pitch damping throughout the flight envelope, as this counteracts pitch forces that, uncontrolled, would cause the missile to tumble. The center of pressure is found using the following equation11:

∂Cm hm − h =− . ∂Cl

Roll rate is defined as the revolutions per time unit made by the body during flight. In order to accommodate the needs of the control system on the Puff Adder, the roll rate needed to remain below 20 Hz, and the aerodynamic features of the missile were adjusted accordingly. Roll rate can be approximated using the following equation, which is further derived in Appendix E: C l p = l C u l p 0

Drag is the force that acts against the forward motion of the body. The drag is non- 22 dimensionalized into a coefficient, Cd, by dividing the drag force by the following term :

1 ρu2 S 2 ∞

A low drag allows for a more efficient flight. Drag is calculated by adding the forces on the body that interact with the free stream. Assuming the Puff Adder is at zero angle of attack, the sources of drag on the missile are the ogive nose and the four fins. An example of the equations used for compressible flow over a cone is as follows, where C is pε obtained from NACA Report 113523: 2 C γM 2 2 pc Ac 4Rc pc pε ∞ Cd = 2 Sc where Sc = = 2 and = +1 γM∞ p∞ Ab Db p∞ 2

21 “Foundations of Aerodynamics” Kuethe and Chow, John Wiley and Sons, 4th Ed, 1986 22 “Dynamics of Flight, Stability and Control”, Etkin, John Wiley and Sons, 2nd Edition, 1982 23 “Report 1135, Equations, Tables, and Charts for Compressible Flow”, National Advisory Committee for Aeronautics, 1953

Magnus force is defined as a force that is induced by the rotation of the body. This force acts at the center of pressure and in the direction of the cross product between the spin axis and the direction of the airflow that is perpendicular to that axis. The pertinent non- dimensionalized equation for yaw is24: 2m (2μD − C )β − C pˆ + (2μ − C )rˆ − C φ − C ζ = 0 where μ = yβ y p yr L0 yζ ρSc

A crosswind will cause a force to be applied either up or down, depending on the direction. This is similar to the way in which an angle of attack will cause a lateral direction change. The rolling motion (identified as C pˆ in the above equation) is y p inducing a sideways motion, and that is the largest contributor to uncontrolled direction change (other than gravity).

Lift in this missile is small and very brief in duration. This missile has no control surfaces and therefore cannot maintain an angle of attack. This missile has no lift at zero angle of attack without a crosswind. C is the largest contributor of lift in this missile but Lα the duration of positive angle of attack is very short.

Static Margin vs Mach

3.5

2.5

1.5

0.5

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Mach

24 “Dynamics of Flight, Stability and Control”, Etkin, John Wiley and Sons, 2nd Edition, 1982

Mach Number 0.03 Static Margin 2.37 Calibers

Mach Number 0.73 Static Margin 2.95 Calibers

Mach Number 1.06 Static Margin 3.28 Calibers

Mach Number 1.50 Static Margin 2.87 Calibers

Forces

Moments

Magnus

Appendix E.2 : Derivation of roll rate estimation

Beginning with the non-dimensional linear theory equations for rolling motion, the roll rate can be derived as follows:

−C β + (i D − C )pˆ − (i D + C )rˆ − (C D + C )ξ − C ζ = 0 lβ A l p E lr lξ lξ lζ

To greatly simplify the equation, one can assume that all except the dominant term can be neglected, that dominant term is the roll due to forces acting directly on p, which is the roll rate about the missile relative x-axis. This force is normally caused by canting fins on a missile. Leaving:

(i D − C )pˆ = 0 A l p

pb Non-dimensional rate of rotation: pˆ = , 2u0 d pb (i t* − C ) = 0 = 0, A l p dt 2u0 d Shorthand for derivative with respect to the time constant: D = t* , dt d pb (i t* − C ) = 0, A l p dt 2u0 l Aerodynamic time constant: t* = , u0 l d pb (i − C ) = 0, A l p u0 dt 2u0

pb l d pb i − C = 0, A l p 2u0 u0 dt 2u0 d Torque or moment equation: T = Iα ∴C = i p , assuming mass stays relatively l A dt constant.

b l pb C − C = 0, l l p 2u0 u0 2u0

l C = C p l l p u0

C l p = l , seconds per rotation. C u l p 0

Roll rate in Hz is therefore 1/p

Appendix F - Propulsion [S. Strand]

Appendix F.1: Propellant Analysis

Propellant calculations begin with the chemical composition of the material. From that composition, computer programs can determine the partial fraction of each species of molecule in the combustion reaction as well as the temperature of combustion. This can then be used to determine the average molar specific heats Cp and the specific heat ratio, γ . The burn rate coefficients, a, and exponents, n, are typically determined empirically 25 as is the sensitivity to initial grain temperature, σ p . There are a few software packages that can estimate these values based on chemical composition. Analysis of the Puff Adder did not include the development of a new propellant formula. Instead, tables of known double base propellants were examined and the propellant that was most similar to the existing MK66 performance was selected. The selection of that particular propellant is based on the assumption that an existing propellant would be the least expensive to produce, and with known performance characteristics, there is less developmental risk.

Mass Flow Rate

Throat area can be assumed to choke when M=1 at the throat. This provides the upper limit for the mass flow from the missile. And follows the following equation26: γ +1 ⎡ 2 ⎤ γ −1 ⎣⎢ (γ +1)⎦⎥ mÝ = At pcγ γRTc

Chamber Pressure

Chamber pressure is determined using characteristics of the propellant, the burn area and the area of the throat. A mass flow balance is achieved when16:

1 ⎛ ⎞ 1−n Ab pc = ⎜ aρc* ⎟ ⎝ At ⎠ with γRT c* = c , and is a known value based on the propellant composition16. γ +1 ⎛ ⎞ γ −1 γ ⎜ 2 ⎟ ⎝ γ +1⎠

Burn Rate

25 "Aerothermodynamics of Gas Turbine and Rocket Propulsion, Revised and Enlarged", Oates, AIAA Education Series, 1988 26 “Rocket Propulsion Elements”, Sutton and Biblarz, John Wiley and Sons, 7th Ed, 2001

27 n The burn rate of the propellant is also a result of the chamber pressure : r = apc Other effects on burn rate were not considered in this analysis, as discussed later.

Expansion Ratio

Expansion ratio is the area of the exit divided by the area of the throat. The expansion ratio determines the velocity of the exhaust. With the velocity at the throat constrained to M=1, for isentropic flow17: γ +1 ⎡⎛ ⎞ ⎤ 2(γ −1) Ae 1 2 ⎛ γ −1 2 ⎞ = ⎢⎜ ⎟⎜ 1 + Me ⎟⎥ At Me ⎣⎝ γ +1⎠⎝ 2 ⎠⎦

The exit Mach number is then solved numerically. The pressure is then calculated based on the mach number using this equation17: γ ⎛ γ −1 ⎞ γ −1 p = p ⎜1 + M 2⎟ e c⎝ 2 e ⎠ If the exit pressure is greater than the ambient pressure outside of the exit, then the nozzle p is considered to be underexpanded and thrust is adjusted by the pressure ratio e times p0 the exit area. When exit pressure is less than the external pressure, then the nozzle is p overexpanded, the adjustment for thrust is still applicable until e = .4, when separation p0 will start to occur in the nozzle. The separation pressure remains relatively constant at

ps = .4 p0 . The area ratio that has that creates that pressure is the effective area ratio of the nozzle, As. The flow remains axially symmetric; so at the distance from the throat that equates to As, an oblique shock is formed that increases the exit pressure to equal the external pressure. As the pressure continues to fall in the motor, the oblique shock becomes normal, again so that the exit pressure can equal the external pressure, and the flow after the strong normal shock is subsonic28. In analysis of the Puff Adder, As an appromimation to the more complicated method above, a simple calculation was used to determine the new effective exit area and resulting loss in thrust due to the internal shock waves. The exit area for optimal expansion was determined and assumed to be the new exit area. The resulting thrust coefficient was then reduced by 20% to account for the oblique shock waves. The normal shock wave was not considered, but this occurs very near the end of the burn and the thrust is very low, so this was neglected.

Thrust

The thrust coefficient is a result of the pressure ratios and is calculated as follows17:

27 “Rocket Propulsion Elements”, Sutton and Biblarz, John Wiley and Sons, 7th Ed, 2001 28 "Gas Dynamics, Volume 1" Zucrow and Hoffman, John Wiley and Sons, 1976

γ +1⎡ γ −1⎤ 2 ⎛ ⎞ γ −1 ⎛ ⎞ γ ⎛ ⎞ 2γ 2 ⎢ pe ⎥ pe − p0 Ae CF = ⎜ ⎟ 1−⎜ ⎟ + ⎜ ⎟ γ −1⎝ γ +1⎠ ⎢ ⎝ p ⎠ ⎥ p ⎝ A ⎠ ⎣⎢ c ⎦⎥ c t

Thrust is:

F = CF At pc

A thrust profile is developed by plotting the value for thrust at each time increment.

F.2. Full explanation of burn area for the center slot grain:

Beginning with these fundamental values, the burn area can be calculated by web burned:

A ′ = A − 2r0

B ′ = B − 2r0 ⎛ A ′ ⎞ 2 B ′ d = R2 −⎜ ⎟ − 1 ⎝ 2 ⎠ 2 ⎛ B ′ ⎞ 2 A ′ d = R2 −⎜ ⎟ − 2 ⎝ 2 ⎠ 2 h = A ′ 2 + B ′ 2 d3 = R − h

Burn perimeter S equals the sum of all perimeters.

S = 2SA + 2SB + 4SC + 4SsliverA + 4SsliverB

SA = A ′ when 0 ≤ wb < d1 − r0 ⎛ B ⎞ 2 B S = 2 R2 −⎜ + w ⎟ when d − r ≤ w < R − A ⎝ 2 b ⎠ 1 0 b 2

SB = B ′ when 0 ≤ wb < d2 − r0 ⎛ A ⎞ 2 A S = 2 R2 −⎜ + w ⎟ when d − r ≤ w < R − B ⎝ 2 b ⎠ 2 0 b 2 A S = 0 when w ≥ R − B b 2 π S = ()w + r when 0 ≤ w < d − r C b 0 2 b 3 0

SC = 0 when wb ≥ d3 − r0 using the power of a point (ref vvv) to find the x,y coordinates for the intersection between the circles.

A ′ R2 − h 2 B ′ B ′ R2 − h 2 A ′ xA = + yA = − 2 R + wb + r0 , 2 R + wb + r0

A ′ R2 − h 2 B ′ B ′ R2 − h 2 A ′ xB = − yB = + 2 R + wb + r0 , 2 R + wb + r0

Then the arc angles can be found to be

⎛ A ′ ⎞ ⎜ xA − ⎟ −1 2 θA = sin ⎜ ⎟ ⎜ wb + r0 ⎟ ⎝ ⎠

⎛ B ′ ⎞ ⎜ xB − ⎟ −1 2 θB = cos ⎜ ⎟ ⎜ wb + r0 ⎟ ⎝ ⎠

SsliverA = 0 when 0 ≤ w b < d3 − r0

S =+r θ sliverA ()0 A when d3 − r0 ≤ w b < d1 − r0

SsliverA = 0 when w b ≥ d1 − r0

SsliverB = 0 when 0 ≤ w b < d3 − r0

S = w + r θ sliverB ()b 0 B when d3 − r0 ≤ w b < d2 − r0

SsliverA = 0 when w b ≥ d2 − r0

The area of a burning end is determined in a similar manner. With one exception, where a simplified method was needed: by making an assumption that the surface area of the sliver is approximately that of the triangle created by the points of intersection of the circles and the edge of the point on the d1 or d2 line that the web has burned to, one can estimate the sliver area to have the equation:

⎡⎛ B ′ ⎞ A ′ ⎛ A ′ ⎞⎤ ⎛ A ′ ⎞ ⎛ A ′ ⎛ B ′ ⎞ ⎞ AsliverA = ⎢⎜ + d1⎟ −⎜ ()wb + r0 ⎟⎥ + ⎜ xA ()wb + r0 − yA ⎟ + ⎜ yA − ⎜ + d1⎟ xA ⎟ ⎣⎝ 2 ⎠ 2 ⎝ 2 ⎠⎦ ⎝ 2 ⎠ ⎝ 2 ⎝ 2 ⎠ ⎠ while w b < d1 − r0 and

⎡⎛ A ′ ⎞ B ′ ⎛ B ′ ⎞⎤ ⎛ B ′ ⎞ ⎛ B ′ ⎛ A ′ ⎞ ⎞ AsliverB = ⎢⎜ + d2 ⎟ −⎜ ()wb + r0 ⎟⎥ + ⎜ xB ()wb + r0 − yB ⎟ + ⎜ yB −⎜ + d2⎟ xB ⎟ ⎣⎝ 2 ⎠ 2 ⎝ 2 ⎠⎦ ⎝ 2 ⎠ ⎝ 2 ⎝ 2 ⎠ ⎠ while w b < d2 − r0

F.3. Excerpt from the method that calculates the burn area from MissileFlight.exe: case InputData::CENTERSLOT:

p1x = slotSideA / 2; p1y = slotSideB / 2;

// this is the A side

baseDistance1 = sqrt(pow(R_RM, 2) - pow(p1x, 2)) - p1y; totalBurnDistance1 = R_RM - p1y - R1_RM;

if (webBurned <= totalBurnDistance1) { if (webBurned <= baseDistance1 - R1_RM) { temp = p1y + baseDistance1; seg1 = pow(R_RM,2) * acos(temp / R_RM) - temp * sqrt(pow(R_RM, 2) - pow(temp, 2)); per1 = slotSideA; area1 = slotSideA * (baseDistance1 - webBurned - R1_RM) + seg1; sec1 = 0; } else { temp = p1y + R1_RM + webBurned; seg1 = pow(R_RM,2) * acos(temp / R_RM ) - temp * sqrt(pow(R_RM, 2) - pow(temp, 2)); sec1 = 2 * sqrt(pow(R_RM,2) - pow(temp, 2)); per1 = sec1; area1 = seg1; } } else { per1 = 0; area1 = 0; sec1 = 0; seg1 = 0; }

// the B side baseDistance2 = sqrt(pow(R_RM,2) - pow(p1y,2)) - p1x; totalBurnDistance2 = R_RM - p1x - R1_RM;

if (webBurned <= totalBurnDistance2) { if (webBurned <= baseDistance2 - R1_RM) { temp = p1x + baseDistance2; seg2 = pow(R_RM,2) * acos(temp / R_RM) - temp * sqrt(pow(R_RM,2) - pow(temp, 2)); per2 = slotSideB; area2 = slotSideB * (baseDistance2 - webBurned - R1_RM) + seg2; sec2 = 0; } else { temp = p1x + R1_RM + webBurned; seg2 = pow(R_RM,2) * acos(temp / R_RM) - temp * sqrt(pow(R_RM,2) - pow(temp, 2)); sec2 = 2 * sqrt(pow(R_RM,2) - pow(temp, 2)); per2 = sec2; area2 = seg2; } } else { per2 = 0; area2 = 0; sec2 = 0; seg2 = 0; }

// the circle if (baseDistance1 > baseDistance2) { totalBurnDistance3 = baseDistance1 - R1_RM; } else { totalBurnDistance3 = baseDistance2 - R1_RM; }

if (webBurned <= totalBurnDistance3) {

hypotenuse = sqrt(pow(p1x,2) + pow(p1y,2)); radius = webBurned + R1_RM; baseDistance3 = R_RM - hypotenuse;

if (webBurned <= baseDistance3 - R1_RM) { arc3 = M_PI / 2 * (radius); area3 = M_PI / 2 * (pow(baseDistance3,2) - pow(radius,2));

x1 = p1x; y1 = p1y + baseDistance1; x2 = p1x; y2 = baseDistance3; x3 = baseDistance3 * cos(p1x / hypotenuse); y3 = baseDistance3 * sin(p1x / hypotenuse);

arc1 = 0; sliver1 = fabs((x2*y1 - x1*y2) + (x3*y2-x2*y3) + (x1*y3 - x3*y1)) / 2;

x1 = p1x + baseDistance2; y1 = p1y; x2 = baseDistance3; y2 = p1y;

arc2 = 0; sliver2 = fabs((x2*y1 - x1*y2) + (x3*y2-x2*y3) + (x1*y3 - x3*y1)) / 2;

} else { arc3 = 0; area3 = 0;

// applies to the following slivers a = (pow(R_RM, 2) - pow(radius, 2) + pow(hypotenuse, 2)) / (2 * hypotenuse); p0x = 0; p0y = 0; p2x = p0x + a * (p1x - p0x) / hypotenuse; p2y = p0y + a * (p1y - p0y) / hypotenuse; h = sqrt(pow(R_RM, 2) + pow(a, 2));

// the A side sliver if (webBurned <= baseDistance1 - R1_RM) { p3x = p2x - h * (p1y - p0y); theta = asin((p3x-p1x)/radius);

arc1 = radius * theta;

p3y = p2y + h * (p1x - p0x);

x1 = p1x; y1 = p1y + baseDistance1; x2 = p1x; y2 = radius; x3 = p3x; y3 = p3y;

sliver1 = fabs((x2*y1 - x1*y2) + (x3*y2-x2*y3) + (x1*y3 - x3*y1)) / 2; } else { arc1 = 0; sliver1 = 0;

}

// the B side sliver if (webBurned <= baseDistance2 - R1_RM) { p3x = p2x + h * (p1y - p0y);

theta = acos((p3x-p1x)/radius); arc2 = radius * theta;

p3y = p2y - h * (p1x - p0x);

x1 = p1x + baseDistance2; y1 = p1y; x2 = radius; y2 = p1y; x3 = p3x; y3 = p3y;

sliver1 = fabs((x2*y1 - x1*y2) + (x3*y2-x2*y3) + (x1*y3 - x3*y1)) / 2; } else { arc2 = 0; sliver2 = 0; } } } else { arc1 = arc2 = arc3 = 0; area3 = sliver1 = sliver2 = 0; }

// put it all together perimeter = 2 * per1 + 2 * per2 + 4 * arc3 + 4 * 0 * arc1 + 4 * 0 * arc2; areaEnd = 2 * area1 + 2 * area2 + 4 * area3 + 4 * 0 * sliver1 + 4 * 0 * sliver2; burnArea = (L01_RM- numEndsBurning*webBurned)*perimeter+numEndsBurning*areaEnd;

mass = (areaEnd) * (L01_RM - numEndsBurning * webBurned) * RHO_P_RM; break;

100

Appendix G - Weight and Structures [R. Naranjo]

G.1: Drawings

The basic dimensions of the Puff Adder are shown in the figures on the following pages.

Figure G1.1.- General Layout drawing Figure G1.2.- Details of the Warhead Figure G1.3.- Avionic Section Figure G1.4.- Motor Section Figure G1.5.- Motor-Tail interface Figure G1.6.- Nozzle

101

Fig. G1.1.- Puff Adder Layout

102

Fig. G1.2.- Warhead with detailed dimensions of the ACME thread

103

Fig. G1.3.- Avionics Section

104

Fig. G1.4.- Motor Section

105

Fig. G1.5.- Motor-Tail Interface

106

Fig. G1.6.- Nozzle Section

107

G.2: Mass Properties

PUFF ADDER MASS PROPERTIES

At Take Off At Burnout Section Weight Cg Weight Cg (kg) (lb) (m) (in) (kg) (lb) (m) (in) Warhead 6.171 13.60 0.427 16.81 6.171 13.60 0.427 16.81

Avionics 1.949 4.30 0.723 28.44 1.709 3.77 0.723 28.44

Motor 6.726 14.82 1.193 46.95 2.320 5.11 1.123 44.19

Nozzle 0.547 1.21 1.668 65.65 0.547 1.21 1.668 65.65

Overall 15.393 33.93 0.843 33.19 10.747 23.69 0.687 27.06

Objective 14.10 31.08 Weight % in 9.17% excess Maximun 15.63 34.45 Weight Difference -1.52% (%)

G.3: Material Trade Studies, Avionics Case

The materials considered for the construction of the Avionics Case are indicated in the table below

T. Strength, Density Machinability Cost Commentary Yield MPa kg/m3 % $/kg (ksi) (lb/in3) AISI 301 Steel 205 7900 75 26.82 Not recommended (30) (0.285) for high density AISI 4340 Steel 938 7850 50 5.41 Not recommended (136) (0.283) for high density Aluminum 7075-T6 503 2810 70 22.8 Selected. Requires chec- (73) (0.101) king by stress analysis Aluminum 7178-T6 538 2830 70 N/A Not selected for low (78) (0.102) availability.

108

G.4: Material Trade Studies, Motor Case

The materials considered for the construction of the Motor Case are indicated in the table below

T. Strength, Density Machinability Cost Commentary Yield MPa kg/m3 % $/kg (ksi) (lb/in3) AISI 301 Steel 205 7900 75 26.82 Not recommended (30) (0.285) for its low Yield Strength AISI 4340 Steel 938 7850 60 5.41 Selected for its high Yield (136) (0.283) Strength. Required to resist the pressures loads at high temperatures Aluminum 7075-T6 503 2810 70 22.8 Not selected because did (73) (0.101) not passed the preliminary stress analysis. Aluminum 7178-T6 538 2830 70 N/A Not selected for low (78) (0.102) availability and for similar reason of the Al 7075-T6

G.5: Mechanical Properties of Aluminum 7075-T6

Material General Characteristics: Very high strength material used for highly stressed structural parts.

Mechanical Properties at 25 C

Physical Properties Metric English Comments Density 2810 kg/m3 0.102 lb/in3 Hardness, Rockell A 53.5 53.5 Ultimate Tensile Strength 572 MPa 83000 psi Tensile Yield Strength 503 MPa 73000 psi Elongation at Break 11 % 11 % Modulus of Elasticity 71.7 Mpa 10400 ksi Poisson’s Ratio 0.33 0.33 Shear Modulus 26.9 GPa 3900 ksi Shear Strength 331 MPa 48000 psi Machinability 70 % 70 % Specific Heat Capacity 0.96 J/g-C 0.229 BTU/lb-F Thermal Conductivity 130 W/m-K 900 Unit: BTU-in/hr-ft2-F Melting Point 477-635 C 890-1175 F

109

Strength at High Temperatures

Stress strain curves for aluminum 7075 in T6 condition at room and elevated temperatures.

110

G.6: Mechanical Properties of AISI 4340 Steel

Material General Characteristics: Low alloy steel with excellent hardenability. Quench and temper heat treatments develop excellent combinations of strength and toughness, making this alloy attractive for critical applications at low and high temperatures.

Mechanical Properties, Oil Quenched at 845 C, Tested at 25 C

Physical Properties Metric English Comments Density 7850 kg/m3 0.284 lb/in3 Hardness, Rockwell C 52 52 Typical Ultimate Tensile Strength 1005 MPa 146000 psi Tensile Yield Strength 938 MPa 136000 psi Elongation at Break 20 % 20 % Modulus of Elasticity 213 Mpa 30900 ksi Poisson’s Ratio 0.29 0.29 Shear Modulus 82 GPa 11900 ksi Machinability 60 % 60 % Specific Heat Capacity 0.475 J/g-C 0.114 BTU/lb-F Thermal Conductivity 44.5 W/m-K 309 Unit: BTU-in/hr-ft2-F Melting Point 1427 C 2600 F

Strength at High Temperatures

Stress strain curves for an AISI 4340 steel tube, 2-14 in. OD x 7/8 in. ID, at room and at elevated temperatures. For the project the oil quenched + 1050 F air cooled curve is used.

111

Fig. G6.1

112

G.7: Bending Moment Analysis

Free Body Diagram for Bending Moment Analysis29

CNaB := 3.25

Missile Dimensions: DPA := 0.06985⋅m Missile Diameter LPA := 1.82⋅m Missile Length

AERODYNAMIC LOADS Aerodynamic Data from Prodas Model: Worse Condition: Mach No. M:= 1.38 Angle of Attack α := 0.16⋅ deg

Drag Coefficient CX := 0.63 Normal Force Coef.

29 Web Site, http://exploration.grc.nasa.gov/education/rocket/presar.html, NASA Article, “Aerodynamic Forces,” April 2006.

113

Assumptions : Axial and Normal forces uniformly distributed over missile length Air at Standard Conditions N γ := 1.4 p := 101300⋅ T := 296.15⋅K o 2 o m Calorically perfect gas

Calculations : Cross sectional area

2 D ⎛ PA ⎞ − 3 2 A := π⋅⎜ ⎟ A = 3.83× 10 m PA ⎝ 2 ⎠ PA

Free stream dynamic pressure ⎛ γ ⎞ 2 5 q := ⎜ ⎟⋅p ⋅M q = 1.35× 10 Pa o ⎝ 2 ⎠ o o

Drag Force

Drag:= CX⋅qo⋅APA Drag= 326.01N

Lift Force

Lift:= CNaB⋅qo⋅APA Lift= 1681.79N

Normal Force

FN := Drag⋅ sin()α + Lift⋅ cos()α FN = 1682.69N

Axial Force

FA := Drag⋅ cos()α − Lift⋅ sin()α FA = 321.31N

Normal load, considered uniformly distributed over the missile length

FN kg w := w= 924.56 [ kg/s2=N/m ] L 2 PA s

114

Bending Moment

2 1 ⎛ LPA ⎞ M := − ⋅ w⋅⎜ ⎟ M = −382.81J [ J = N m ] max 2 ⎝ 2 ⎠ max

Bending Moment - Aerodynamic Forces 0

100

1 − ⋅w⋅()1.82− x ⋅x 200 2

300 Bending Moment (N-m)

400 0 0.5 1 1.5 x Distance from nose (m)

SQUIB LOADS

Squib Load and Arm from nose

Fs := 740⋅ N

Ls := 0.72⋅m

Maximum Bending Moment, punctual squib force: x = Ls

⎛ Ls ⎞ Mmaxs := −Fs⋅Ls⋅⎜ 1 − ⎟ Mmaxs = −322.02J ⎝ LPA ⎠

115

M = −649.21J TOTAL BENDING MOMENTS MT

Avionics Section For xAV := 0.86⋅m

⎛ xAV ⎞ Msquib AV := −Fs⋅Ls⋅⎜ 1 − ⎟ MsquibAV = −281.04J LPA ⎝ ⎠ 1 Maero := − ⋅ w⋅()1.82⋅ m − x ⋅x Maero = −381.66J AV 2 AV AV AV

Total Bending Moment

MAV := Msquib AV + MaeroAV MAV = −662.69J

Motor Section

For xMT := 0.91⋅m

⎛ xMT ⎞ Msquib MT := −Fs⋅Ls⋅⎜ 1 − ⎟ MsquibMT = −266.40J LPA ⎝ ⎠ 1 Maero := − ⋅ w⋅()1.82⋅ m − x ⋅x Maero = −382.81J MT 2 MT MT MT

Total Bending Moment

MMT := Msquib MT + MaeroMT

116

G.8: Stress Analysis of the Avionics Case

σupper = σBending - σThrust

MAX. BENDING MOMENT M

THRUS T

σlower = − σBending - σThrust

Avionics Dimensions:

Outer Diameter Do:= 0.06985⋅m

Minimum Thickness t 0.003m := ⋅ Inner Diameter Di:= Do− 2⋅t Di= 0.064m

Load Data:

Maximum Bending Moment, Avionics Section MmaxAV := 662.69⋅ N⋅m

Motor Thrust (worse condition, T amb= 65.5 C) FT := 7642⋅ N

117

Avionics Max. Bending Stress:

Section Modulus

4 4 ⎛ π ⎞ Do − Di − 5 3 S := ⎜ ⎟⋅ S = 1.0098× 10 m AV ⎝ 32 ⎠ Do AV

Maximum Bending Stress

MmaxAV 6 σB := σB = 65.63× 10 Pa SAV

Avionics Axial Stress, Thrust Cross section area

π 2 2 − 4 2 A := ⋅()Do − Di A = 6.3005× 10 m AV 4 AV

Axial Stress, Thrust

F T 6 σA := σA = 12.13× 10 Pa AAV

Total Avionics Stress, Upper Fiber 6 σAVtotal_upper := σB − σA σAVtotal_upper = 53.5× 10 Pa

Total Avionics Stress, Lower Fiber 6 σAVtotal_lower := −σσB − A σAVtotal_lower = −77.76× 10 Pa

CONCLUSION The values of the total axial stresses in the upper and lower fiber of the avionics section are 12.94% and 18.80%, respectively, of the allowable tension and compression yield strength of the 7075-T6 Aluminum (413.42 MPa at 65.5 C, Material Data Sheet). Consequently, the 3 mm thickness of the Avionics Section will support the operational loads of the missile with a high FOS.

118

Appendix G.9 [R.Naranjo]

Thermal Analysis of the Motor Case

Finite-Difference Method of Analysis The analysis was developed using the Interactive Heat Transfer software IHT version 2.0(G12). For building the finite-difference equations required to determine the temperature distribution within the case wall, we used the Finite-Difference Equations/One-Dimensional/ Transient option, and the tutorial suggested procedure that applied to our problem.

Model - Nodal Network The case wall is represented by ten nodes arranged as follows: Node 0 - at the outer surface of the wall, x = 0; Nodes 1-9, interior nodes; and, Node 10 - at the inner surface of the wall, x = L, subjected to convection with the hot gas at a maximum temperature of 65.5 C, (hot ambient temperature case).

Assumptions Outer Surface Node (0): We can consider the adiabatic (insulated) boundary, x = 0, as a plane of symmetry for the temperature distribution and treat Node 0 as an interior node.

rho*cp*der(T0,t) = fd_1d_int(T0,T1,T1,k,qdot,deltax)

Node 0: one-dimensional, transient conditions

Wall Interior Nodes:

Node 1: rho*cp*der(T1,t) = fd_1d_int(T1,T2,T0,k,qdot,deltax)

Node 2: rho*cp*der(T2,t) = fd_1d_int(T2,T3,T1,k,qdot,deltax)

Node 3: rho*cp*der(T3,t) = fd_1d_int(T3,T4,T2,k,qdot,deltax)

Node 4: rho*cp*der(T4,t) = fd_1d_int(T4,T5,T3,k,qdot,deltax)

Node 5: rho*cp*der(T5,t) = fd_1d_int(T5,T6,T4,k,qdot,deltax)

Node 6: rho*cp*der(T6,t) = fd_1d_int(T6,T7,T5,k,qdot,deltax)

Node 7: rho*cp*der(T7,t) = fd_1d_int(T7,T8,T6,k,qdot,deltax)

Node 8: rho*cp*der(T8,t) = fd_1d_int(T8,T9,T7,k,qdot,deltax)

Node 9: rho*cp*der(T9,t) = fd_1d_int(T9,T10,T8,k,qdot,deltax)

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Inner Surface Node (10): The inner surface of the case wall, x = L, experiences convection with the hot exhaust gases at a maximum of 2975 K (from propulsion tables, worse case, Tamb = 65.5 C).

Node 10: surface node, transient conditions

rho * cp * der(T10,t) = fd_1d_sur_e(T10,T9,k,qdot,deltax,Tinf,h,q''a10)

Surface node specifications: one-dimensional, transient conditions, with convection film coefficient 150 W/m2 K.

Assigned Variables Nodal network: Spatial increment, x-axis, m deltax = L/10 Wall thickness L = 0.015 m

Thermo physical properties, Insulator ATJ Carbon: Density rho = 1650 kg/m^3 Specific heat, cp = 707 J/kg.K Thermal conductivity k = 95 W/m.K

Thermal conditions: Volumetric heat generation qdot = 0 W/m^3 Exhaust gases temperature Tinf = 2975 K Convection coefficient h = 150 W/m^2.K

Solving of the Model Time parameters: Start 0.00 s End 4.00 s Step 0.10 s

Initial Conditions (all nodes): Ti 338.65 K (=65.5 C)

Temperature Distribution: The variation of the inner surface wall temperature versus time is plotted in Figure G9.1. The thermal model was developed from 0 to 4 seconds with purpose of extending the end of the curve, but the propulsion data shown that for the 65.5 C condition, the burnout will occur at 2.5 seconds. At that time the temperature of the case inner surface will be 383.9 K (110.75 C, 231.35 F). Is at this temperature that the tensile yield strength of the AISI 4340 steel should be determined and used in the stress analysis of the motor case.

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MOTOR CASE: INNER WALL TEMPERATURE vs. TIME 500

460

420

380 Temperature (K)

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300 0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 Time (s)

T0 Fig. G9.1.- Inner wall temperature vs. time of the motor case

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G.10: Stress Analysis of the Motor Case

Dimensions:

Outer Diameter Do:= 0.06985⋅m

Thickness t:= 0.0015⋅m

Inner Diameter Di:= Do− 2⋅t Di= 0.06685m

Material Properties at 383.9 K (AISI 4340 Steel OQ/AC): 6 Tensile Yield Strength σyield := 931100000P⋅ a σyield = 931.10× 10 Pa

σyield 6 Shear Yield Strength τ := τ = 465.55× 10 Pa yield 2 yield

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Load Data:

Maximum Bending Moment, Motor Section MmaxMT := 649.21⋅ N⋅m

Maximum Chamber Pressure pM := 9793587.60P⋅ a

Motor Max. Bending Stress:

Section Modulus

4 4 ⎛ π ⎞ Do − Di − 6 3 S := ⎜ ⎟⋅ S = 5.3881× 10 m MT ⎝ 32 ⎠ Do MT

Maximum Bending Stress

MmaxMT 6 σB := σB = 120.49× 10 Pa SMT

Motor Axial Stress, Chamber Pressure

Cross section area

π 2 2 − 4 2 A := ⋅()Do − Di A = 3.2209× 10 m MT 4 MT

Transversal Inner Area π 2 2 At := ⋅Di At = 0m MT 4 MT

Axial Force 4 Faxial:= pM⋅AtMT Faxial= 3.437× 10 N

Axial Stress, Thrust

Faxial 6 σA := σA = 106.72× 10 Pa AMT

Fleeman's equation (for reference)

pM⋅Di 6 σ := σ = 109.12× 10 Pa AFle 4t⋅ AFle

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Total Motor Axial Stress, Upper Fiber 6 σMTaxial_upper := σB − σA σMTaxial_upper = 13.77× 10 Pa

Total Motor Axial Stress, Lower Fiber 6 σMTaxial_lower:= −σσB − A σMTaxial_lower= −227.21× 10 Pa

Motor Circumferential Stress, Chamber Pressure

Unitary Longitudinal Inner Area 2 AcMT := 1m⋅ ⋅Di AcMT = 0.07 m

Unitary Circumferential Force 5 Fcirc:= pM⋅AcMT Fcirc= 6.547× 10 N

Unitary circumferential case area 2 Ac:= 2⋅ t⋅1⋅m Ac= 0.003m

Circumferential Stress, Thrust

Fcirc 6 σ := σ = 218.23× 10 Pa C Ac C

Fleeman's equation (for reference)

pM⋅Di 6 σ := σ = 218.23× 10 Pa CFle 2t⋅ CFle

Failure Analysis, Von Mises-Henky Theory

Criteria : Von Mises Stress (Sy) should be lower than Material Yield Strength / FOS

Upper Fiber.- Plane Stresses 6 σx_u := σMTaxial_upper σx_u = 13.77× 10 Pa

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8 σy_u := σC σy_u = 2.18× 10 Pa

τxy_u := 0.0

Von Mises Stress

2 2 6 Sy_u := σx_u −σσx_u⋅σy_u + y_u + 3⋅τxy_u Sy_u = 211.69× 10 Pa

σyield FOS_u := FOS_u= 4.4 Sy_u

Lower Fiber.- Plane Stresses 6 σx_l:= σMTaxial_lower σx_l = −227.21× 10 Pa

6 σy_l := σC σy_l = 218.23× 10 Pa

τxy_l := 0.0

Von Mises Stress

2 2 6 Sy_l := σx_l −σσx_l⋅σy_l + y_l + 3⋅τxy_l Sy_l = 385.79× 10 Pa

σyield FOS_l := S y_l

FOS_l= 2.41 CONCLUSIONS

The values of the Factor of Security for the upper and lower critical fibers of the motor case section are 4.40 and 2.41 respectively, consequently, the 1.5 mm thickness of the Motor Case wall is suited to support the operational loads of the missile.

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G.11: Avionics Case, Buckling Analysis

Avionics Case Dimensions:

Outer Diameter Do:= 0.06985⋅m

Wall Thickness t:= 0.003⋅m

Inner Diameter Di:= Do− 2⋅t Di= 0.06385m

Mean Radius ⎛ Di+ Do ⎞ r:= 0.5⋅⎜ ⎟ r= 0.033425m ⎝ 2 ⎠

Material Properties (Aluminum 7075-T6): 6 6 Tensile Yield Strength σyield := 503⋅ 10 ⋅Pa σyield = 503.00× 10 Pa

9 9 Modulus of Elasticity E:= 71.7⋅ 10 ⋅Pa E= 71.7× 10 Pa

Poisson's Ratio μ := 0.33

Load Data: 6 Maximun Bending Stress, Compresion σAVtotal_lower := 77.7610⋅ ⋅Pa

Critical Buckling Stress for Bending, Unpressurized Cylinder :

Radius to thickness ratio r Ratio := Ratio= 11.14 t

γ factor

1 r φ := ⋅ φ = 0.21 16 t

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γ factor φ γ := 1.0− 0.901⋅( 1− e ) γ = 1.21

Critical Stress (applies for r/t < 1500) ⎛ t ⎞ γ⋅E⋅⎜ ⎟ ⎝ r ⎠ 9 σcr := σcr = 4.76× 10 Pa 2 31⋅()− μ

Factor of Security

σcr FOS := FOS= 61.2 σAVtotal_lower

CONCLUSION

This high Factor of Security implies that the operational conditions are safe from the point of view of a failure of the Avionics Section for buckling.

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G.12: Motor Case, Buckling Analysis

Motor Case Dimensions:

Outer Diameter Do:= 0.06985⋅m Wall Thickness t:= 0.0015⋅m

Inner Diameter Di:= Do− 2⋅t Di= 0.06685m

Mean Radius ⎛ Di+ Do ⎞ r:= 0.5⋅⎜ ⎟ r= 0.034175m ⎝ 2 ⎠

Material Properties (AISI 4340 Steel at 383.9 K OQ/AC) 6 6 Tensile Yield Strength σyield := 938⋅ 10 ⋅Pa σyield = 938.00× 10 Pa

9 9 Modulus of Elasticity E:= 213⋅ 10 ⋅Pa E= 213× 10 Pa

Poisson's Ratio μ := 0.29

Load Data:

Maximum Bending Stress, Compression MmaxMT := 649.21⋅ N⋅m

Chamber Pressure pMT := 9793587.60P⋅ a

Critical Bending Moment for Buckling, Pressurized Cylinder :

Radius to thickness ratio r Ratio := Ratio= 22.78 t

Factor γ

1 r φ := ⋅ φ = 0.30 16 t

γ factor

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φ γ := 1.0− 0.731⋅( 1− e ) γ = 1.25

Increased Buckling-Stress Coefficient for internal pressure (Figure G12.1)

⎡p 2⎤ MT ⎛ r ⎞ − 2 − 2 Xval := ⎢ ⋅⎜ ⎟ ⎥ Xval = 2.39× 10 ===> Δγ := 2.6⋅ 10 ⎣ E ⎝ t ⎠ ⎦

Fig. G12.1.- Increase in Axial-Compressive Buckling Stress

Critical Bending Moment (applies for r/t < 1500)

2 ⎡ γ ⎤ π 3 Mcr := π⋅r⋅E⋅t ⋅⎢ + Δγ⎥ + ⋅pMT⋅r Mcr = 40880.2J ⎢ 2 ⎥ 2 ⎣ 31⋅()− μ ⎦

Factor of Security

Mcr FOS := FOS= 62.97 MmaxMT

CONCLUSION

This high Factor of Security implies that the operational conditions are safe from the point of view of a failure of the Motor Section for buckling.

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Appendix H - Avionics [J. Martin, J. Dickson]

Appendix H.1 – IMU (BAE SiIMU)

Figure 1. BAE SiIMU02 (typical)

Figure 2. SiIMU Specifications30

30 Source: BAE SiIMU sales brochure/datasheet (included electronically)

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Appendix H.2 - Radar [J. Dickson]

The characteristics for a FMCW radar to have a high range resolution capability are for the transmitter waveform to have a highly linear sweep which is highly repeatable. Since the Puff Adder's radar is only trying to determine height at any given time, we are only trying to find Mother Earth (the ground). This greatly simplifies the design. The radar will have 2 antennas - one for receive and one for transmit. The antennas will be on opposite sides of the missile to help with isolation. As the missile rotates, the transmitter will fire and the receiver will receive only when the transmitter is looking down at the ground. Therefore, the IF output to the guidance section will be a maximum when the ground (height is determined) and a minimum when the transmitter is looking elsewhere. The roll rate of the missile will be determined by how many times the transmitter looks at the ground per time period.

Waveform Determination - The following formula was used to determine the FMCW triangular ramp waveform: ΔF/Fb = TC/2R where ΔF = 1GHz = difference of highest transmitter frequency - lowest transmitter frequency Fb = difference in received frequency - transmitter frequency T = round trip time from target C = speed of light (3.8 x 108 m/s) or (984.24 x 106 ft/s)

For a linear FMCW waveform, the theoretical time resolution is equal to the inverse of the frequency deviation (ΔF)2. Therefore, a frequency of 1 x 109 cycles/sec provides a potential time resolution of 1ns. The corresponding range resolution is determined by R = TC/2 = .15 meters (.49 ft). The transmitter sweep time was set at 66.7 µs. This sweep time sets the modulation frequency at 14.993 KHz. Therefore, the sampling time of our IF circuits (to satisfy the Nyquist criteria) must be at least 30 KHz. The sampling time was picked to be 50 KHz.

A patch antenna, designed by Roke Manor Research of England1, was used to determine the reflected power from the ground at maximum and minimum anticipated altitudes. The Roke Manor Research antenna was 75 mm wide x 50 mm long x 3.2 mm thick (2.95 inches wide x 2.04 inches long x .126 inches thick) with a beamwidth of +/- 35° @ -3dB at 77 GHz. The 3 following formula was used to determine the maximum gain of the antenna: GdB = 10 log 2 (4πA)/λo - α x (L + W)/2 where GdB is the maximum gain of the antenna; A is the area of the antenna; λo is the free space wavelength; α is the attenuation; L is length and W is the width of the patch antenna. No losses where assumed so the formula was reduced to GdB = 10 log 2 (4πA)/λo . A loss of 6dBi will be subtracted from the total calculated gain in an attempt to accurately reflect the antenna performance. The maximum gain was calculated to 36.6dBi, so the gain used in the reflected power calculation was 30.6 dBi. Since we only want to find the ground an antenna beam width of only 1° was used to calculate the ground radar cross 2 2 3 4 section. The return power formula is Pr = PG λo σ / (4π) R α.

Reflected return power calculation:

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P = transmitting power = 250 mW + 23.98 dBm G2 = (antenna power gain)2 = (33.8)2 + 30.6 dBi 2 2 λo = (3.2mm) - 49.9 dBsm σ = ground radar cross section at 2000 meters + 15.83 dBsm α = atmospheric attenuation = .3 dB/km x R x 2 - (+1.2) dB (4π)3 = 1984 - ( + 32.97) dB R4 = (2000m)4 - (+ 132) dBm4

Pr = reflected return power at 2000m - 125.59 dBm

Pr = reflected return power at 50m - 112.53 dBm

The radar cross section of the earth was calculated by using an area of 3826m2 (41,182 ft2) multiplied by a scattering coefficient for deciduous trees of .01. This gives a RCS of 38.26 m2 (411.8ft2) at 2000m. At 50m (164ft) the RCS is .0237 m2 (.255 ft2). The coefficient for deciduous trees is lower than that of grass (.1) and that of wet snow of (1). Therefore the radar will have the lowest reflected power return for deciduous trees.

Appendix H.3: Guidance and Control [J. Martin]

Figure 1. excerpt from Puff Adder Guiance and Control Module from PRODAS’ FCS Builder

The figure above shows the logic required for the firing of one squib; some was shared, but much of it was reproduced for each squib. PRODAS allowed each squib to be fired independently, according to its own properties of thrust, duration, etc. The downside of this mechanism was that each squib was required to be fired independently; because of this, the maximum number of control “blocks” were quickly expended, and only 24 squibs could be implemented. Even so, the Puff Adder was able to accomplish its missions easily, though its true “maximum” potential is still unknown. Due to this restriction, it was also not possible to create a “closed loop” controller for this missile, though our open loop simulations should prove that the concept is at least

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realistic with this missile. The following plots are a demonstration of the possible control authority of this missile, using 24 or fewer squibs.

Trajectory Prediction

This is an example of some calculations that were done to determine how many squibs to fire at the beginning of burn to reach any distance given by a particular mission:

effect of firing multiple squibs to generate lift during motor burn

This plot shows different numbers of squib firings and its overall effect on the distance of the projectile. Each curve represents adding “one more” squib to the picture.

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9400

9200

9000

8800 Series1 Series2 8600

8400

8200

8000 0 2 4 6 8 10 12 14 16 18

comparison of prediction curve versus actual distance traveled

Plotted here are two curves, one the actual distance traveled (vs.# of squibs fired) and the other a curve predicted by the following formula: dist = 776 + c+ p*x + k*e^(tx) + re^(u*(x+q))

This is how the projectile will be able to know how many squibs to fire at the beginning of each flight – since the “model predictive” controller will not be able to accurately predict the outcome of a squib firing this early in the burn, an alternative method must be used. As the graph shows, this method should be sufficient.

The same results can be shown for the crossrange squib pulses:

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results of firing multiple squibs in the crossrange direction at launch

1200

1000

800

Series1 600 Series2

400

200

0 02468101214

actual distance versus the distance of a prediction curve

As in the previous example, a good first order approximation can prepare the missile for its trajectory and make in-flight trajectory tracking much easier

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Appendix H.4: Squibs

The following graphs are presented to illustrate real thrust/pressure profiles from thrusters similar to the ones used by the Puff Adder. Note the obvious repeatability; this is required for guidance and control purposes, because without consistency it would be impossible to adequately predict the impact of a squib firing. These are profiles from different squibs than what the Puff Adder would use, which is why the thrust numbers and durations are different, but they would look approximately the same, since they are similar in size, shape, and composition.

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Appendix I – Trajectory [J. Williams, M. Shannag, S. Strand, J. Martin]

The trajectory discipline of the Viper team was separated into two sections: modeling and simulation. Each member of the team was then broken out into various sub-discipline areas. Each section was then integrated into one master trajectory model. An intense integration effort with precise configuration control was used to maintain the proper amount of oversight on the model. This organization structure is found below in Figure 34.

Trajectory Jason Williams, Integrator

Modeling Team Simulation Team Jason Williams, Lead Mutasem Shannag, Lead

PRODAS Master Modeler BOOM Expert Jason Williams Jason Martin

IDEAS Structural Expert Ricardo Naranjo Guidance Algorithm Expert Jason Martin

IDEAS 3-D Modeler Jason Williams Propulsion Expert Stephen Strand

Aerodynamics Expert Stephen Strand

Figure 34. Trajectory Organization Chart

Modeling Approach [J. Williams]

The key tool used in modeling and simulation aspects of the Puff Adder was PRODAS V.3.2.3©i. The modeling approach was broken into three phases: PRODAS Training, Master Model Creation, and Simulation Integration.

The PRODAS Training Phase was initiated early on in this course. The training was available online from the 2005 PRODAS Technical Symposium conducted in Burlington,

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Vermont.ii This training was broken up into 12 Tutorial Modules that covered PRODAS Introduction, ATM Mass and Aerodynamics Modeling, ATM Guidance and Control, and BOOM Guidance and Control Modules. This was then integrated with the available training tutorials within the PRODAS software itself.

Following the training phase of the course, the mass model could then be created. The mass model would consist of four major assemblies: Nozzle & Fins, M2045 Motor, DACS, and M261 MPSM Warhead. The integrated cross section model of these assemblies can be found in Figure 35.

Figure 35: Puff Adder 2-D Sectioned Model [J. Williams]

This complete view represented in Figure 35 is the complete assembly generated in PRODAS. As mentioned previously several top level assemblies were modeled using given CDD constraints as initial parameters. Refinements were made on each component and element within the assemblies in order to meet our objectives. The final versions of these top level assemblies are elaborated on below.

Modeling Results [J. Williams]

Nozzle and Fin Assembly [J. Williams]

Figure 36: 2-D Nozzle & Fin Assembly [J. Williams]

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The Nozzle and Fin Assembly can be seen in Figure 36. This section is modeled based on the interface with the current M261 launcher referenced in Appendix 2 of the CDD. The nozzle was baselined from the nozzle on the MK66 motor, with similar interfacing to the motor assembly. Moreover, this assembly contains the aft section control surfaces, the fins. This includes a four fin wrapped design for stable flight and is optimized for the Puff Adder. More information on the fin section can be found in Appendix E.

M2045 Motor Assembly [J. Williams]

Figure 37. 2-D M2045 Assembly The M2045 Motor Assembly can be seen above in Figure 37. This section is modeled based on the current MK66 motor. This motor is within the Hydra 70 envelope diameter at 69.85 mm. This mass model includes a ethyl cellulose inhibitor similar to the MK66 inhibitor with a modified grain. More information on the modified grain can be found in the Propulsion section of this report in Appendix F. This section of the Puff Adder interfaces with both the Nozzle and Fin section interface and the DACS section interface. The motor case is modeled as AISI 4340 Steel and further information can be found in the Weight and Structures section of this report in Appendix G.

Divert and Attitude Control System (DACS) Assembly [J. Williams]

Inertial Measurement Unit Divert Thruster Package Thermal Insulator

Thermal Battery Warhead & Fuzing Interface

RADAR Element Processor Element Wiring Element

Figure 38: 2-D DACS Assembly [J. Williams]

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The DACS Assembly can be seen above in Figure 38. This section contains all guidance, avionics, and divert thrusters. This section required detailed research and analysis to complete. As seen above, this section consists of a thermal battery, thermal insulator between the battery and IMU, IMU, RADAR, processor, divert thruster or squib package, warhead and fuzing interface, and the wiring tube and circuitry components associated with the avionics. A more detailed approach and information associated with the Avionics section can be found in Appendix H.

M261 MPSM Warhead Assembly [J. Williams]

Figure 39. M261 MPSM Warhead Assembly

The MPSM Warhead Assembly can be seen above in Figure 39. This section is modeled based on the interface with the current M261 launcher referenced in Appendix 2 of the CDD. This portion of the mass model has remained unchanged throughout as the CDD required that no changes be made to the warhead. This portion of the model was modeled previously in PRODAS by Arrow Tech and presented in one of the training sessions.

In addition to the model represented in PRODAS, a representative 3-D model was generated in IDEAS. No structural analysis was done on this portion of the design as all structural analysis was done in IDEAS 2-D environment. However, an isometric view of the Puff Adder can be seen in Figure 40 below.

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Figure 40. 3-D IDEAS Model

Many of the internal components were modeled to scale in this design; however, if in the future, it is desired to conduct a 3-D structural analysis on this design this version of the Puff Adder will need to be update as such. However, most of the components within the missile are to scale. Below in Figure 41 is one such component, the nozzle represented in its solid and wireframe models:

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Figure 41. 3-D IDEAS Nozzle Model

Figure 42. 3-D IDEAS Nozzle Wireframe

Simulation Approach [M. Shannag]

In this discipline of Trajectory, simulation was performed by using PRODAS V.3.2.3 employing a 6-DOF model. Guidance and control simulation was performed using BOOM, a FORTRAN based program specifically designed to predict the atmospheric flight mechanics of smart projectile systems. Three key sea level atmosphere parameters used in the Puff Adder simulation, were cold, standard, and hot. Our simulation was performed for two launching platforms, helicopter and ground for both a minimum and objected down-ranges of 500 and 8000 meters respectively as well as a launch angle of 20 and 15 degrees respectively for the helicopter mission, and from an altitude of 100 meters.

Simulation Results [M. Shannag]

After many sleepless nights and dedicated hours put in by our BOOM expert, the Puff Adder was ready to take on its mission. I am proud to say that all the required performance parameters set forth in the CDD were met by our Puff Adder and in many cases exceeded such requirements, for both the helicopter and the ground launch missions, as well as for three temperature conditions, cold, standard, and hot. The guided missions used as many as 36 DITs to direct the Puff Adder in its route to target.

Figure 24 shows the Puff Adder reaching its minimum objective downrange of 500 meters, with a the down range as a function of flight time during a guided flight using 24 DITs and a launch angle of 20 degrees for all three temperatures. Each condition designated by a unique color. As can be seen from our data, guided missions provided the Puff Adder with extra range to meet its mission and beyond. Still even if the DITs failed to operate at launch the Puff Adder is able to reach its target and detonate the warhead.

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While figure 25 shows the same platform firing the Puff Adder with a launch angle of 15 degrees during a guided flight, smoothly reaching its objective target 8000 meters away and detonating its warhead in a synchronized performance. The figure shows all three profiles of the three conditions at hand.

Some limitations to the PRODAS simulation code prevented the simulation team from exploring their innovative ideas and apply such ideas to the Puff Adder simulation; they were able to achieve the desired objective of the mission set forth in the CDD.

While for the ground mission scenario of this simulation the missile was launched with an angle of 1.8 and 15 degrees for the minimum and objective down ranges respectively, and from an altitude of zero (0) meters. As can be also seen in figures

Figure 26 on the other hand shows the Puff Adder‘s flight profile of reaching the downrange of 500 meters during a guided flight, this figure shows the downrange as a function of time again for all three conditions simultaneously. This mission is achieved with a ground launch angle of 1.8 degrees and an elevation of zero meters. Once again, in the failsafe scenario, and the DITs fail to fire after launch the Puff Adder easily reaches its target.

Figure 27 on the other hand shows a guided ground mission launch at an angle of 15 degrees and reaching a maximum downrange of 9200meters, which surely exceeds the objective of 8000 meters. This mission was accomplished by using both banks of DITs (24). On the other hand, in the case of a failure of DITs firing after launch, the missile does reach its desired target at 8000 meters, but only in the cases of standard and hot conditions and fails to reach target in cold conditions.

Atmospheric Performance

comparison of the Puff Adder at nominal and extreme altitudes (max ranges)

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Ballistic Trajectories

Air-launched failsafe trajectories for all temperatures (downrange)

Air-launched failsafe trajectories for all temperatures (crossrange)

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Ground-launched failsafe trajectories for all temperatures (downrange)

Ground-launched failsafe trajectories for all temperatures (crossrange)

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Maximum Trajectories

Air-launched “max range” trajectories for all temperatures (downrange)

Ground-launched “max range” trajectories for all temperatures (downrange)

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Appendix J - Platform Integration Radar [J. Dickson, M. Vogan]

The requirements set forth in the CDD for the M261 launcher interfaces are the following:

M261 Launcher: The ATM shall be compatible with the M261 Launcher and its interfaces (App. 2). Launcher Interfaces: The ATM shall be compatible with current M261 Launcher interfaces. Provisions for communication to the guided rocket are allowable (ex: black box attachment).

Description of M261 launcher: The M261 Launcher, shown below, is a lightweight, nineteen-tube, reusable launcher with a detent retention system. The M261 Launcher has the capability of remotely setting warhead fuses through the umbilical connection in the warhead. The aft end of each tube is fitted with a detent retention system. This detent retention system is composed of the detent retainer, launcher contact spring, and contact arm blast paddle. When the motor is inserted into the launcher tube the detent retainer locks onto the motor nozzle, the launcher contact spring sits on the nozzle contact band, and the contact arm blast paddle is in the closed position. To fire the motor a current is sent through the launcher contact spring to the nozzle contact band. When the motor is fired the blast from the thrust moves the contact arm blast paddle to the open position, which through mechanical linkage releases the detent retainer. The retention force is specified between 170 to 700 lbf. The retention force is specified between 170 to 700 lbf.

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the threshold weight specified in the CDD. With 19 Puff Adder missiles, the helicopter launcher platform weight is significantly reduced by 4.56 Kg (10.032 lbs). The Puff Adder employs 4 aerodynamic fins at the base of the rocket motor. The fins are wrapped around the missile body just as the Hydra-70 baseline. The Puff Adder is loaded and retained within the launcher using the same procedure and locking mechanism as the baseline. The launcher cannot distinguish between the two missiles. The Puff Adder's guidance scheme is 100% compatible with the current electrical connections of the launcher. The same interfaces (helicopter or ground-based platform) are used to provide initial GPS coordinates to the Puff Adder.

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Appendix K – Implementation Issues [M. Vogan]

The most significant implementation issue to address in the development and production of the Puff Adder Advanced Tactical Missile is the cost. As discussed in Section 3.1 of the main paper, the cost of the missile was largely determined by its weight, minus the avionics subsection. The components of the avionics subsection were priced individually, as shown in Table 13, below: Table 13. Avionics Subcomponent Pricing List Avionics Component Average Price per Unit IMU – BAE SiIMU02 $2,200 FM-CW Radar $1,200 DIT Squib Block (12x4 squibs @$10.00ea) $500 Processor and autopilot electronics $500 Thermal Battery $100 miscellaneous $500

TOTAL: $5,000

Additional implementation issues concern the timeline for further missile development and production, and the flow of work as the design continues to be refined. As challenges are encountered during the production of the missile – both with the design of the missile and the design of the production process – the hardware and software associated with both will need to be modified and/or reprogrammed. A flow chart shown below in Figure 43 gives a more thorough picture of the flow of this process that was discussed in Section 3.3, and requires continual interaction with the customer to ensure that additional requirements are being met, that the production process continues to fall within reasonable cost limits and appropriate timelines. Assuming the design, as refined with the assistance of the customer, works properly and that no interference from other government priorities or projects with the timeline of production and testing occurs, the activity detailed in the flow chart below should allow the missile to be ready to deploy within 20-23 months from the date of award of the contract.

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Figure 43. Project Development Flow Chart

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Appendix L – Responses to Review Team Questions [S. Strand, J. Martin]

AERODYNAMICS/PROPULSION QUESTIONS [S. Strand]

Your thrusters appear to be the Close to CG? Yes they are initially about 2 to 3 calibers from the CG initially and as the motor burns the thruster ring ends up behind the CG. The ring is always forward of the CP.

In your research did you ever search for or come across the term, Aerodynamic jet interaction? Yes, rolling missile, as well as the natural stability of the missile, minimizes the effects. The flow field around the missile is affected due to the reduction in specific heat of the air downstream of the jet and a Navier-Stokes analysis will be needed to completely understand the effects of the control thruster burn on the missile body and fins. The tools and analysis in this paper did not include this effect on the missile.

Had you guys heard of the LC3 design that used divert thrusters with the Hydra 70 motor and M261 warhead? Did you notice how difficult it was to maneuver with that baseline? No we had not heard of the other design, However, we started with the Hydra70 as our baseline and had to modify both the thrust profile to allow a longer burn time for more pitch angle and the fins, so move the CP much closer to the CG.

Did you find anything in your analysis related to roll rate reversal of a wrap around fin in the transonic region? Yes, we recognize that wrap around fins do have a direction reversal during the transonic period of the flight, but with careful design that can be eliminate using a notch or tab on the trailing edge of the fin. This effect was not analyzed in this paper, neither PRODAS nor DATCOM can truly model wrap around fins. Both tools must use an “effective” cant angle to mimic the curve effect of the fin, but that does not create a spin rate reversal in the simulation runs. The best way to determine the nature and magnitude of this effect is through wind tunnel testing.

GUIDANCE & CONTROL QUESTIONS [J. Martin]

When you said squibs were “non-aerodynamic”… Clarification? – This comment was meant to imply that the squibs do not depend on missile velocity to change the course of the missile. To cite an example, a canard would require the missile to have some forward velocity before its motions could impart a moment or lateral force on the missile. The squibs, on the other hand, do not require this sort of aerodynamic interaction for control authority. It is worth noting, as further explored by Stephen, that the firing of squibs would create an aerodynamic impact on the missile, and particularly on the fins in the rear, but that our analysis tools were insufficient to completely explore this effect – we assumed it to be small enough to be negligible in first order analysis. (Stephen may have notes on this question as well.)

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How have you addressed potential problems associated with squib/radar interaction? – noted as a potential issue, but beyond our ability to analyze at this stage and so assumed manageable. (Jerry may have notes on this question also)

(Comment about LC3 / Motor modification) – It was indeed modification of the motor which allowed us to achieve feasibility with this design. The original motor would not have been sufficient for this purpose – that’s why we used boost-sustained slot design, and changed the fin shape and size. (Stephen might also have comments)

Did they (Pacific Scientific) give a delivery estimate on Squibs? – These squibs are similar to squibs that are currently being manufactured by Pacific Scientific (and others). Delivery time was not specifically quoted, but should be “fast” since it would only require retooling for a slightly new shape, similar to existing shapes, and very little reengineering.

Can a Kalman Filter, when combined with the IMU and Radar, really provide the kind of accuracy required to reach the target? – It is possible that it will not. This analysis (and the skill sets of our team members) did not provide us with the necessary tools to answer this question. However, the very reason that Modified Projectile Linear Theory was chosen was because we believe that this “predictor” will be an accurate enough “guess” for the Kalman filter to accurately filter the other data. Viewing the reports referenced (B. Burchett and M. Costello, "Specialized Kalman Filtering for Guided Projectiles” and “Model Predictive Lateral Pulse Jet Control of an Atmospheric Rocket.”) and the original book on the subject, Modern Exterior Ballistics (McCoy), there seems to be strong evidence that for a missile of this type, the model predictive modified linear controller will be as accurate as a 6DOF simulation. It will be used to calculate the missile’s position on the fly and correcting these “guesses” based on data collected from the two sensor technologies.

Were you actually able to model squibs firing using PRODAS? – Yes; recent additions to PRODAS allow modeling of these effects. However, limitations in the controller aspect of PRODAS limited us to an open loop controller rather than closed loop. The mathematics of guidance combined with specific squib firing logic used too much memory, and PRODAS was unable to handle that situation. It is expected that future releases of PRODAS will not have this restriction.

Are you familiar with the work of Dr. Mark Costello, and did you use it in your control design? – Yes, and we actually discussed it with him personally. Our missile depended heavily upon his research and in fact his writings formed the bulk of our supporting research.

Did you investigate how to manage the scheduling of individual thruster firings and other associated timings? Yes, this question affected us in many ways. Not only did the thrusters have to fired in accordance with the proper positioning during missile spin, but if fired too closely together, they could dangerously destabilize the missile. We found that it was a bad idea to fire more often than “Every third squib.” At slower speeds, the squibs had a greater impact, but at faster speeds, the squibs “became available” sooner. Therefore this number was not very dependent on speed.

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We also allocated different banks of squibs for different “missions” during flight. 24 were for initial “pitching” to coarsely move the trajectory in large steps, and 24 more were used for fine tuning the trajectory during the remainder of flight.

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