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Rocket Performance • Te rocket equation • Mass ratio and performance • Structural and payload mass fractions • Regression analysis • Multistaging • Optimal ΔV distribution between stages • Trade-off ratios • Parallel staging • Modular staging © 2016 David L. Akin - All rights reserved http://spacecraft.ssl.umd.edu U N I V E R S I T Y O F Rocket Performance MARYLAND 1 ENAE 791 - Launch and Entry Vehicle Design Derivation of the Rocket Equation V • Momentum at time t: e m-Δm v m M = mv Δm v+Δv v-V • Momentum at time t+Δt: e M =(m − ∆m)(V +∆v)+∆m(v − Ve) • Some algebraic manipulation gives: ! m∆v = −∆mVe • Take to limits and integrate: m V final dm final dv = − ! m ! Ve minitial Vinitial U N I V E R S I T Y O F Rocket Performance MARYLAND 2 ENAE 791 - Launch and Entry Vehicle Design The Rocket Equation mfinal − ∆V • Alternate forms r ≡ = e Ve m initial mfinal ∆v = −Ve ln = −Ve ln r ! !minitial " • Basic definitions/concepts m m – Mass ratio r ≡ final or ℜ≡ initial ! minitial mfinal – Nondimensional velocity change “Velocity ratio” ∆V ⌫ ⌘ Ve U N I V E R S I T Y O F Rocket Performance MARYLAND 3 ENAE 791 - Launch and Entry Vehicle Design Rocket Equation (First Look) 1 Typical Range for Launch to ) Low Earth Orbit initial 0.1 /M nal fi 0.01 Mass Ratio, (M Mass 0.001 0 2 4 6 8 Velocity Ratio, (ΔV/Ve) U N I V E R S I T Y O F Rocket Performance MARYLAND 4 ENAE 791 - Launch and Entry Vehicle Design Sources and Categories of Vehicle Mass Payload Propellants Structure Propulsion Avionics Power Mechanisms Thermal Etc. U N I V E R S I T Y O F Rocket Performance MARYLAND 5 ENAE 791 - Launch and Entry Vehicle Design Sources and Categories of Vehicle Mass Payload Propellants Inert Mass Structure Propulsion Avionics Power Mechanisms Thermal Etc. U N I V E R S I T Y O F Rocket Performance MARYLAND 6 ENAE 791 - Launch and Entry Vehicle Design Cost and Weight Distribution - Atlas V U N I V E R S I T Y O F Rocket Performance MARYLAND 7 ENAE 791 - Launch and Entry Vehicle Design Cost and Weight - Atlas V First Stage propellant mass Propellant mass fraction PMF = total stage mass U N I V E R S I T Y O F Rocket Performance MARYLAND 8 ENAE 791 - Launch and Entry Vehicle Design Cost and Weight - Atlas V Second Stage U N I V E R S I T Y O F Rocket Performance MARYLAND 9 ENAE 791 - Launch and Entry Vehicle Design Basic Vehicle Parameters • Basic mass summary mo =initial mass mo = mpl + mpr + min mpl =payload mass • Inert mass fraction mpr =propellant mass ! m m min =inert mass δ ≡ in = in ! mo mpl + mpr + min • Payload fraction ! m m λ ≡ pl = pl ! mo mpl + mpr + min • Parametric mass ratio r = λ + δ U N I V E R S I T Y O F Rocket Performance MARYLAND 10 ENAE 791 - Launch and Entry Vehicle Design Rocket Equation (including Inert Mass) 1 ) Typical Range for Launch to Low initial Earth Orbit Inert Mass /M Fraction δ 0.1 0 0.05 payload 0.1 0.15 0.01 0.2 0.001 Payload Fraction, (M Fraction, Payload 0 2 4 6 8 Velocity Ratio, (ΔV/Ve) U N I V E R S I T Y O F Rocket Performance MARYLAND 11 ENAE 791 - Launch and Entry Vehicle Design Limiting Performance Based on Inert Mass 5 4.5 Typical Feasible Design Range for V/Ve) 4 Inert Mass Fraction Δ 3.5 3 2.5 2 1.5 1 0.5 0 Asymptotic Velocity Ratio, ( Velocity Asymptotic 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Inert Mass Fraction, (Minert/Minitial) U N I V E R S I T Y O F Rocket Performance MARYLAND 12 ENAE 791 - Launch and Entry Vehicle Design Regression Analysis of Existing Vehicles Veh/Stage prop mass gross mass Type Propellants Isp vac isp sl sigma eps delta (lbs) (lbs) (sec) (sec) Delta 6925 Stage 2 13,367 15,394 StorableN2O4-A50 319.4 0.152 0.132 0.070 Delta 7925 Stage 2 13,367 15,394 StorableN2O4-A50 319.4 0.152 0.132 0.065 Titan II Stage 2 59,000 65,000 StorableN2O4-A50 316.0 0.102 0.092 0.087 Titan III Stage 2 77,200 83,600 StorableN2O4-A50 316.0 0.083 0.077 0.055 Titan IV Stage 2 77,200 87,000 StorableN2O4-A50 316.0 0.127 0.113 0.078 Proton Stage 3 110,000 123,000 StorableN2O4-A50 315.0 0.118 0.106 0.078 Titan II Stage 1 260,000 269,000 StorableN2O4-A50 296.0 0.035 0.033 0.027 Titan III Stage 1 294,000 310,000 StorableN2O4-A50 302.0 0.054 0.052 0.038 Titan IV Stage 1 340,000 359,000 StorableN2O4-A50 302.0 0.056 0.053 0.039 Proton Stage 2 330,000 365,000 StorableN2O4-A50 316.0 0.106 0.096 0.066 Proton Stage 1 904,000 1,004,000 StorableN2O4-A50 316.0 285.0 0.111 0.100 0.065 average 312.2 285.0 0.100 0.089 0.061 standard deviation 8.1 0.039 0.033 0.019 U N I V E R S I T Y O F Rocket Performance MARYLAND 13 ENAE 791 - Launch and Entry Vehicle Design Inert Mass Fraction Data for Existing LVs 0.18 0.16 0.14 0.12 LOX/LH2 0.10 LOX/RP-1 0.08 Solid 0.06 Storable Inert Mass Fraction Mass Inert 0.04 0.02 0.00 0 1 10 100 1,000 10,000 Gross Mass (MT) U N I V E R S I T Y O F Rocket Performance MARYLAND 14 ENAE 791 - Launch and Entry Vehicle Design Regression Analysis • Given a set of N data points (xi,yi) • Linear curve fit: y=Ax+B – find A and B to minimize sum squared error N ! 2 error = !(Axi + B − yi) ! i=1 – Analytical solutions exist, or use Solver in Excel A • Power law fit: y=BxN 2 ! error = ! [A log(xi)+B − log(yi)] i=1 • Polynomial, exponential, many other fits possible U N I V E R S I T Y O F Rocket Performance MARYLAND 15 ENAE 791 - Launch and Entry Vehicle Design Solution of Least-Squares Linear Regression N ∂(error) =2!(Axi + B − yi)xi =0 ∂A i=1 N ∂(error) =2 (Axi + B − yi)=0 ∂B ! N N N i=1 2 A xi + B xi − xiyi =0 ! ! ! N N i=1 i=1 i=1 A ! xi + NB − ! yi =0 i=1 i=1 2 N ! xiyi − ! xi ! yi ! yi ! xi − ! xi ! xiyi B A = 2 2 = 2 2 N ! xi − (! xi) N ! xi − (! xi) U N I V E R S I T Y O F Rocket Performance MARYLAND 16 ENAE 791 - Launch and Entry Vehicle Design Regression Analysis - Storables 0.10 0.08 0.06 0.04 0.02 R2 = 0.0541 0.00 Inert Mass Fraction Mass Inert 1 10 100 1,000 Gross Mass (MT) U N I V E R S I T Y O F Rocket Performance MARYLAND 17 ENAE 791 - Launch and Entry Vehicle Design Regression Values for Design Parameters Vacuum Ve Inert Mass Max ΔV (m/sec) Fraction (m/sec) LOX/LH2 4273 0.075 11,070 LOX/RP-1 3136 0.063 8664 Storables 3058 0.061 8575 Solids 2773 0.087 6783 U N I V E R S I T Y O F Rocket Performance MARYLAND 18 ENAE 791 - Launch and Entry Vehicle Design Economy of Scale for Stage Size 0.20# M 0.18# ✏ = inert 0.16# Minert + Mprop 0.14# 0.12# 0.10# 0.08# 0.06# 0.04# Stage#Inert#Mass#Frac6on#ε# 0.02# PMF =1 ✏ 0.00# − 1# 10# 100# 1,000# 10,000# Stage#Gross#Mass,#MT# Storable#MER# LOX/RPD1# Storables# LOX/LH2# Cryo#MER# U N I V E R S I T Y O F Rocket Performance MARYLAND 19 ENAE 791 - Launch and Entry Vehicle Design Stage Inert Mass Fraction Estimation 0.183 ✏ =0.987 (M kg )− LOX/LH2 stageh i 0.275 ✏ =1.6062 (M kg )− storables stageh i U N I V E R S I T Y O F Rocket Performance MARYLAND 20 ENAE 791 - Launch and Entry Vehicle Design The Rocket Equation for Multiple Stages • Assume two stages ! mfinal1 ! ∆V1 = −Ve1 ln = −Ve1 ln(r1) !minitial1 " ! m ! V −V final2 −V r ∆ 2 = e2 ln m = e2 ln( 2) ! ! initial2 " • Assume Ve1=Ve2=Ve ∆V1 +∆V2 = −Ve ln(r1) − Ve ln(r2)=−Ve ln(r1r2) U N I V E R S I T Y O F Rocket Performance MARYLAND 21 ENAE 791 - Launch and Entry Vehicle Design Continued Look at Multistaging • Tere’s a historical tendency to define r0=r1r2 ! ∆V + ∆V = V ln (r r ) = V ln (r ) 1 2 − e 1 2 − e 0 ! • But it’s important to remember that it’s really ! m m ∆V + ∆V = V ln (r r ) = V ln final1 final2 ! 1 2 − e 1 2 − e m m initial1 initial2 ⇥ • And that r0 has no physical significance, since mfinal2 mfinal1 = minitial2 r0 = ⇥ ⇒ ⇥ minitial1 U N I V E R S I T Y O F Rocket Performance MARYLAND 22 ENAE 791 - Launch and Entry Vehicle Design Multistage Inert Mass Fraction • Total inert mass fraction ! m + m + m m m m δ = in,1 in,2 in,3 = in,1 + in,2 + in,3 0 m m m m ! 0 0 0 0 min,1 min,2 m0,2 min,3 m0,3 m0,2 ! δ0 = + + m0 m0,2 m0 m0,3 m0,2 m0 • Convert to dimensionless parameters ! δ0 = δ1 + δ2λ1 + δ3λ2λ1 • General form of the equation n stages j−1 δ δ λ 0 = ! [ j " ℓ] j=1 ℓ=1 U N I V E R S I T Y O F Rocket Performance MARYLAND 23 ENAE 791 - Launch and Entry Vehicle Design Multistage Payload Fraction • Total payload fraction (3 stage example) ! mpl mpl m0,3 m0,2 λ0 = = ! m0 m0,3 m0,2 m0 • Convert to dimensionless parameters ! λ0 = λ3λ2λ1 • Generic form of the equation n stages λ λ 0 = ! j j=1 U N I V E R S I T Y O F Rocket Performance MARYLAND 24 ENAE 791 - Launch and Entry Vehicle Design Effect of δ and ΔV/Ve on Payload 0.9000.7000.4000.2500.0900.0600.020 0.018 ∆V 0.3500.8000.080 0.0500.600 = 12340.0255 0.7000.0700.2000.016 0.300 Ve 0.0140.500 0.6000.0600.040 0.250 0.1500.012 1 stage 0.400 0.5000.050 2 stages 0.2000.0300.010 3 stages 0.3000.4000.040 0.1000.008 0.150 4 stages 0.3000.0300.020 0.2000.006 0.100 Total Payload Fraction Payload Total 0.0500.0040.2000.020 0.010 0.0500.100 0.0020.1000.010 0.000 0 0.2 0.4 0.60.6 0.80.8 11 Inert Mass Fraction U N I V E R S I T Y O F Rocket Performance MARYLAND 25 ENAE 791 - Launch and Entry Vehicle Design Effect of Staging Inert Mass Fraction δ=0.15 0.25 Single Stage Three Stage Two Stage Four Stage 0.20 0.15 1 stage 2 stage 3 stage 0.10 4 stage Payload Fraction 0.05 0.00 0 1 2 3 4 5 Velocity Ratio (ΔV/Ve) U N I V E R S I T Y O F Rocket Performance MARYLAND 26 ENAE 791 - Launch and Entry Vehicle Design Trade Space for Number of Stages 4 3.5 Solids 3 LOX/RP-1 Four Stage Storables 2.5 Three Stage 2 LOX/LH2 1.5 Two Stage Velocity Ratio DV/Ve Ratio Velocity Velocity Ratio DV/Ve Ratio Velocity 1 Single Stage 0.5 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Inert Mass Fraction U N I V E R S I T Y O F Rocket Performance MARYLAND 27 ENAE 791 - Launch and Entry Vehicle Design Effect of ΔV Distribution
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  • Corporate Profile

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    2013 : Epsilon Launch Vehicle 2009 : International Space Station 1997 : M-V Launch Vehicle 1955 : The First Launched Pencil Rocket Corporate Profile Looking Ahead to Future Progress IHI Aerospace (IA) is carrying out the development, manufacture, and sales of rocket projectiles, and has been contributing in a big way to the indigenous space development in Japan. We started research on rocket projectiles in 1953. Now we have become a leading comprehensive manufacturer carrying out development and manufacture of rocket projectiles in Japan, and are active in a large number of fields such as rockets for scientific observation, rockets for launching practical satellites, and defense-related systems, etc. In the space science field, we cooperate with the Japan Aerospace Exploration Agency (JAXA) to develop and manufacture various types of observational rockets named K (Kappa), L (Lambda), and S (Sounding), and the M (Mu) rockets. With the M rockets, we have contributed to the launch of many scientific satellites. In 2013, efforts resulted in the successful launch of an Epsilon Rocket prototype, a next-generation solid rocket which inherited the 2 technologies of all the aforementioned rockets. In the practical satellite booster rocket field, We cooperates with the JAXA and has responsibilities in the solid propellant field including rocket boosters, upper-stage motors in development of the N, H-I, H-II, and H-IIA H-IIB rockets. We have also achieved excellent results in development of rockets for material experiments and recovery systems, as well as the development of equipment for use in a space environment or experimentation. In the defense field, we have developed and manufactured a variety of rocket systems and rocket motors for guided missiles, playing an important role in Japanese defense.
  • Commercial Orbital Transportation Services

    Commercial Orbital Transportation Services

    National Aeronautics and Space Administration Commercial Orbital Transportation Services A New Era in Spaceflight NASA/SP-2014-617 Commercial Orbital Transportation Services A New Era in Spaceflight On the cover: Background photo: The terminator—the line separating the sunlit side of Earth from the side in darkness—marks the changeover between day and night on the ground. By establishing government-industry partnerships, the Commercial Orbital Transportation Services (COTS) program marked a change from the traditional way NASA had worked. Inset photos, right: The COTS program supported two U.S. companies in their efforts to design and build transportation systems to carry cargo to low-Earth orbit. (Top photo—Credit: SpaceX) SpaceX launched its Falcon 9 rocket on May 22, 2012, from Cape Canaveral, Florida. (Second photo) Three days later, the company successfully completed the mission that sent its Dragon spacecraft to the Station. (Third photo—Credit: NASA/Bill Ingalls) Orbital Sciences Corp. sent its Antares rocket on its test flight on April 21, 2013, from a new launchpad on Virginia’s eastern shore. Later that year, the second Antares lifted off with Orbital’s cargo capsule, (Fourth photo) the Cygnus, that berthed with the ISS on September 29, 2013. Both companies successfully proved the capability to deliver cargo to the International Space Station by U.S. commercial companies and began a new era of spaceflight. ISS photo, center left: Benefiting from the success of the partnerships is the International Space Station, pictured as seen by the last Space Shuttle crew that visited the orbiting laboratory (July 19, 2011). More photos of the ISS are featured on the first pages of each chapter.