# Mass Estimating Relations

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1 Review of iterative design approach (MERs) Sample vehicle design analysis David L. Akin - All rights reserved

2 Akin s Laws of Spacecraft Design - #3 Design is an iterative process. The necessary number of iterations is one more than the number you have currently done. This is true at any point in time. 2

3 Vehicle-Level Prelim Design - 1st Pass Single Stage to Orbit (SSTO) vehicle V=9200 m/sec 5000 kg payload LOX/LH2 propellants Isp=430 sec (Ve=4214 m/sec) M o = M l δ=0.08 λ r = e V Ve = λ = r δ = = 153, 000 kg M i = δm o = 12, 240 kg M p = M o (1 r) = 135, 800 kg 3

4 System-Level Estimation Start with propellant tanks (biggest part) LOX/LH2 engines generally run at mixture ratio of 6:1 (by weight) LH2: 19,390 kg LOX: 116,400 kg Propellant densities ρ LOX = 1140 kg m 3 ρ LH2 = 71 kg m 3 4

5 Propellant Tank Regression Data Tank Mass (kg) y = x R 2 = y = x R 2 = Tank Volume (m^3) LH2 Tanks LOX Tanks RP-1 Tanks Linear (LH2 Tanks) Linear (LOX Tanks) 5

6 Propellant Tank MERs (Volume) LH 2 tanks M LH2 T ank kg =9.09V LH2 m 3 All other tanks M T ank kg = 12.16V prop m 3 6

7 Propellant Tank MERs (Mass) LH 2 tanks = 71 kg m 3 = M LH 2 LOX tanks ρ LH2 ρ LOX = 1140 kg m 3 = M LOX T ank kg =0.0107M LOX kg RP-1 tanks T ank kg =0.128M LH2 kg ρ RP 1 = 820 kg m 3 = M RP 1 T ank kg =0.0148M RP 1 kg 7

8 Cryogenic Insulation MERs M LH2 Insulation kg =2.88A tank kg m 2 M LOX Insulation kg =1.123A tank kg m 2 8

9 LOX Tank Design Mass of LOX=116,400 kg M LOX T ank =0.0107(116, 400) = 1245 kg Need area to find LOX tank insulation mass - assume a sphere ( VLOX V LOX T ank = M LOX = m 3 ρ LOX 3 r LOX T ank = =2.90 m 4π/3 A LOX T ank =4πr 2 = m 2 M LOX Insulation =1.123 kg m 2 (105.6 m2 ) = 119 kg 9 ) 1

10 LH 2 Tank Design Mass of LH 2 =19,390 kg M LH2 T ank kg =0.128(19, 390) = 2482 kg Again, assume LH 2 tank is spherical r LH2 T ank = M LH2 ( VLH2 4π/3 V LH2 T ank = M LH 2 = m 3 ρ LH2 ) 1 3 =4.02 m 10 A LH2 T ank =4πr 2 = m 2 Insulation =2.88 kg m 2 (203.6 m2 ) = 586 kg

11 Current Design Sketch Masses LOX Tank 1245 kg LOX Tank Insulation 119 kg LH 2 Tank 2482 kg LH 2 Tank Insulation 586 kg LOX r=2.90 m LH2 r=4.02 m 11

12 Other Structural MERs Fairings and shrouds M fairing kg =4.95 ( A fairing m 2 ) 1.15 Avionics M avionics kg = 10 (M o kg ) Wiring M wiring kg =1.058 M o kg l

13 External Fairings - First Cut A cone = πr r 2 + h 2 Payload Fairing A frustrum = π(r 1 + r 2 ) (r 1 r 2 ) 2 + h 2 Intertank Fairing LOX r=2.90 m LH2 r=4.02 m A cylinder =2πrh Aft Fairing/Boattail 13

14 External Fairings - First Cut Assumptions P/L fairing h 7 m P/L fairing r 2.9 m I/T fairing h 7 m I/T fairing r m I/T fairing r m Aft fairing h 7 m Aft fairing r 4.02 m Payload Fairing Intertank Fairing LOX r=2.90 m LH2 r=4.02 m Aft Fairing/Boattail 14

15 Fairing Analysis Payload Fairing Area m 2 Mass 645 kg Intertank Fairing Area m 2 Mass 1624 kg Aft Fairing Area m 2 Mass 1902 kg LOX r=2.90 m LH2 r=4.02 m 15

16 Avionics and Wiring Masses Avionics M avionics kg = 10 ( 153, 000) = 744 kg Wiring M wiring kg = , 000(21 m) 0.25 = 886 kg 16

17 Propulsion MERs Liquid Pump-Fed Rocket Engine Mass M Rocket Engine ( kg) = T( N) + Solid Rocket Motor T( N) A e A t + 59 M Motor Casing = 0.135M propellants Thrust Structure Mass M Thrust Structure ( kg) = T( N) 17

18 Propulsion MERs (continued) Gimbal Mass M Gimbals Gimbal Torque τ Gimbals kg P 0 (Pa) ( ) = T(N).9375 ( N m) = 990,000 T(N) P 0 (Pa)

19 Propulsion System Assumptions Initial T/mg ratio = 1.3 Keeps final acceleration low with reasonable throttling Number of engines = 6 Positive acceleration worst-case after engine out Chamber pressure = 1000 psi = 6897 kn Typical for high-performance LOX/LH2 engines Expansion ratio A e /A t =30 Compromise ratio with good vacuum performance 5 (1.3) = >

20 Propulsion Mass Estimates Rocket Engine Thrust (each) Rocket Engine Mass (each) M Rocket Engine ( kg) = ( 324,900) ,900 Thrust Structure Mass (each) M Thrust Structure T( N) = m 0g( T / W) 0 n engines = 324,900 N ( ) = 373 kg ( kg) = ( 324,900) = 497 kg 20

21 First Pass Vehicle Configuration LOX r=2.90 m LH2 r=4.02 m 21

22 Mass Summary - First Pass Initial Inert Mass Estimate 12,240 kg LOX Tank 1245 kg LH2 Tank 2482 kg LOX Insulation 119 kg LH2 Insulation 586 kg Payload Fairing 645 kg Intertank Fairing 1626 kg Aft Fairing 1905 kg Engines 2236 kg Thrust Structure 497 kg Gimbals 81 kg Avionics 744 kg Wiring 886 kg Reserve - Total Inert Mass 13,052 kg Design Margin % 22

23 Modifications for Second Pass Keep all initial vehicle sizing parameters constant Pick vehicle diameter and make tanks cylindrical to fit Redo MER analysis 23

24 Effect of Vehicle Diameter on Mass Margin 35 Inert Mass Margin (%) Vehicle Diameter (m) 24

25 Effect of Mass-Optimal Diameter Choice Mass-optimal vehicle has diameter=1.814 m Mass margin goes from -6.22% to +33.1% Vehicle length=155 m Length/diameter ratio=86 approximately equivalent to piece of spaghetti No volume for six rocket engines in aft fairing Infeasible configuration 25

26 Effect of Diameter on Vehicle L/D 1000 Length/Diameter Ratio Vehicle Diameter (m) 26

27 Second Pass Vehicle Configuration 27

28 Mass Summary - Second Pass Initial Inert Mass Estimate 12,240 kg 12,240 kg LOX Tank 1245 kg 1245 kg LH2 Tank 2482 kg 2482 kg LOX Insulation 119 kg 56 kg LH2 Insulation 586 kg 145 kg Payload Fairing 645 kg 402 kg Intertank Fairing 1626 kg 448 kg Aft Fairing 1905 kg 579 kg Engines 2236 kg 2236 kg Thrust Structure 497 kg 497 kg Gimbals 81 kg 81 kg Avionics 744 kg 744 kg Wiring 886 kg 1044 kg Reserve - - Total Inert Mass 13,052 kg 9960 kg Design Margin % % 28

29 Modifications for Iteration 3 Keep 4 m tank diameter Change initial assumption of δ iteratively, with resulting changes in m 0 and m i, to reach 30% mass margin Modify diameter to keep L/D 10 and iterate again for optimal initial mass estimate 29

30 Vehicle-Level Prelim Design - 3rd Pass Single Stage to Orbit (SSTO) vehicle V=9200 m/sec 5000 kg payload LOX/LH2 propellants Isp=430 sec (Ve=4214 m/sec) M o = M l δ= λ Diameter=4.2 m L/D=9.7 r = e V Ve = λ = r δ = = 169, 800 kg M i = δm o = 14, 130 kg M p = M o (1 r) = 150, 700 kg 30

31 Mass Summary - Third Pass Initial Inert Mass Estimate 12,240 kg 12,240 kg 14,130 kg LOX Tank 1245 kg 1245 kg 1382 kg LH2 Tank 2482 kg 2482 kg 2755 kg LOX Insulation 119 kg 56 kg 62 kg LH2 Insulation 586 kg 145 kg 160 kg Payload Fairing 645 kg 402 kg 427 kg Intertank Fairing 1626 kg 448 kg 501 kg Aft Fairing 1905 kg 579 kg 626 kg Engines 2236 kg 2236 kg 2443 kg Thrust Structure 497 kg 497 kg 552 kg Gimbals 81 kg 81 kg 90 kg Avionics 744 kg 744 kg 773 kg Wiring 886 kg 1044 kg 1101 kg Reserve - - Total Inert Mass 13,052 kg 9960 kg 10,870 kg Design Margin % % % 31

32 Mass Budgeting Estimates Budgeted Margins Initial Inert Mass Estimate 14,131 kg 14,131 kg LOX Tank 1382 kg 1589 kg 207 kg LH2 Tank 2755 kg 3168 kg 413 kg LOX Insulation 62 kg 72 kg 9 kg LH2 Insulation 160 kg 184 kg 24 kg Payload Fairing 427 kg 491 kg 64 kg Intertank Fairing 501 kg 576 kg 75 kg Aft Fairing 626 kg 720 kg 94 kg Engines 2443 kg 2809 kg 366 kg Thrust Structure 552 kg 634 kg 83 kg Gimbals 90 kg 103 kg 13 kg Avionics 773 kg 889 kg 116 kg Wiring 1101 kg 1267 kg 165 kg Reserve 1630 kg Total Inert Mass 10,870 kg 12,500 kg 32

33 References C. R. Glatt, WAATS - A Computer Program for Weights Analysis of Advanced Transportation Systems NASA CR-2420, September I. O. MacConochie and P. J. Klich, Techniques for the Determination of Mass Properties of Earth-to-Orbit Transportation Systems NASA TM-78661, June Willie Heineman, Jr., Fundamental Techniques of Weight Estimating and Forecasting for Advanced Manned Spacecraft and Space Stations NASA TN-D-6349, May 1971 Willie Heineman, Jr., Mass Estimation and Forecasting for Aerospace Vehicles Based on Historical Data NASA JSC-26098, November

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