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Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
Ae2104 orbital-mechanics-slides 13
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Ae2104 orbital-mechanics-slides 13

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These are the lecture slides to the ninth lecture of the course AE2104 Flight and Orbital mechanics.

These are the lecture slides to the ninth lecture of the course AE2104 Flight and Orbital mechanics.

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  • 1. Flight and Orbital Mechanics Lecture slides Challenge the future 1
  • 2. Flight and Orbital Mechanics AE2-104, lecture hours 25+26: Launchers Ron Noomen October 1, 2012 AE2104 Flight and Orbital Mechanics 1|
  • 3. Example: Ariane 5 Questions: • what is the payload of this launcher? • why does it have 2 stages and 2 boosters? • what are the characteristics of each stage? • …. [Arianespace, 2010] AE2104 Flight and Orbital Mechanics 2|
  • 4. Overview • • • • • • Ideal single-stage launcher Ideal multi-stage launcher Real single-stage launcher (gravity, atmosphere) Real multi-stage launcher (idem) Overall performance (Pegasus) Design (Pegasus) AE2104 Flight and Orbital Mechanics 3|
  • 5. Learning goals The student should be able to: • derive, describe and explain Tsiolkovsky’s equation • describe and explain the concept of a multi-stage launcher and quantify its performance • describe and quantify the performance of a launcher in realistic conditions, i.e., under the influence of gravity and drag • make a 1st-order design of a new launcher from scratch • …. Lecture material: • these slides (incl. footnotes) AE2104 Flight and Orbital Mechanics 4|
  • 6. Principles Principles + performance ideal rocket: partial recap of ae1-102 AE2104 Flight and Orbital Mechanics 5|
  • 7. Principles (cnt’d) before during after w • • • • vehicle contains payload, structure, propellant exhaust velocity propellant w conservation of momentum of system vehicle accelerates AE2104 Flight and Orbital Mechanics 6|
  • 8. Principles (cnt’d) • system = launcher + expelled propellant • momentum system = constant dV M dt dM   w dt Solidification Principle: F • • • • dV  Ma  M dt  mw M = instantaneous mass of rocket [kg] m = expelled (gaseous) mass per unit of time, or mass flow [kg/s] V = inertial velocity of launcher [m/s] w = relative exhaust velocity of expelled propellant [m/s] AE2104 Flight and Orbital Mechanics 7|
  • 9. Ideal single stage rocket Equation of motion (vacuum, no gravity): dV M dt dM   w dt Integration: V  M begin    w ln   M   end  Tsiolkovsky’s Equation (a.k.a. ”the rocket equation”) Note: w = Isp g0 AE2104 Flight and Orbital Mechanics 8|
  • 10. Ideal single stage rocket (cnt’d) Characteristic parameters: • thrust-to-weight ratio: 0  • mass ratio:   So: • burn time: tb  • end velocity Vend • burnout altitude: send F M 0 g0 M begin M end M begin  M end m  I sp  1 1   0     I sp g0 ln   2 g0 I sp  ln    1   1   0    AE2104 Flight and Orbital Mechanics 9|
  • 11. Ideal single stage rocket (cnt’d) “normal” Λ impulsive shot * Mbegin / Mend tb (Isp / Ψ0) (1 – 1/Λ) 0 Ψ0 F / (M0 g0) ∞ Vend send Isp g0 ln(Λ) g0 Isp2 / Ψ0 (1 – (ln(Λ)-1)/Λ) 0 *: impulsive shot: all propellants are ejected in 1 instant AE2104 Flight and Orbital Mechanics 10 |
  • 12. Ideal single stage rocket (cnt’d) Do not forget (cf. ae1-102): • Ψ0 > 1 • structural loading at burnout AE2104 Flight and Orbital Mechanics 11 |
  • 13. Ideal multi-stage rocket (cnt’d) Definition of parameters: • Mtotal = total mass (i.e., before firing) • Mpayload = payload mass ( ) • Mconstr = construction mass ( • Mprop = propellant mass ( ) ) • Mbegin = Mtotal = Mpayload + Mconstr + Mprop • Mend = Mpayload + Mconstr AE2104 Flight and Orbital Mechanics 12 |
  • 14. Ideal multi-stage rocket V V   M total g0 I sp ln   M  total  M prop   M total g0 I sp ln   M  constr  M payload M constr M payload  M total M total           V   exp   I g   sp 0   AE2104 Flight and Orbital Mechanics 13 |
  • 15. Ideal multi-stage rocket (cnt’d) Example 1: ΔV = 10 km/s, Isp = 400 s, Mconstr/Mtotal = 8 %, Mpayload = 500 kg  • Mtotal = Mbegin = ??? • Mprop = ??? • Mconstr = ??? AE2104 Flight and Orbital Mechanics 14 |
  • 16. Ideal multi-stage rocket (cnt’d) Example 1 (cnt’d): AE2104 ! NO SOLUTION Flight and Orbital Mechanics 15 |
  • 17. Ideal multi-stage rocket (cnt’d) Options: • reduce required Mpayload • use engine/propellant with higher Isp • use lighter construction • multi-staging AE2104 Flight and Orbital Mechanics 16 |
  • 18. Ideal multi-stage rocket (cnt’d) Example 2: ΔV = 10 km/s, Isp = 400 s, Mconstr/Mtotal = 8 %, Mpayload = 250 kg AE2104 Flight and Orbital Mechanics 17 |
  • 19. Ideal multi-stage rocket (cnt’d) Example 3: ΔV = 10 km/s, Isp = 500 s, Mconstr/Mtotal = 8 %, Mpayload = 500 kg  AE2104 Flight and Orbital Mechanics 18 |
  • 20. Ideal multi-stage rocket (cnt’d) Example 3 (cnt’d): ΔV = 10 km/s, Isp = 500 s, Mconstr/Mtotal = 8 %, Mpayload = 500 kg  • Mpayload/Mtotal = 0.0502 • Mtotal = Mbegin = 9960 kg • Mconstr = 797 kg • Mprop = 8663 kg • Mprop/Mtotal = 87.0 % AE2104 Flight and Orbital Mechanics OPTIMAL SOLUTION? FEASIBLE SOLUTION? 19 |
  • 21. Ideal multi-stage rocket (cnt’d) Example 4: ΔV = 10 km/s, Isp = 400 s, Mconstr/Mtotal = 4 %, Mpayload = 500 kg  AE2104 Flight and Orbital Mechanics 20 |
  • 22. Ideal multi-stage rocket (cnt’d) Example 4 (cnt’d): ΔV = 10 km/s, Isp = 400 s, Mconstr/Mtotal = 4 %, Mpayload = 500 kg  • Mpayload/Mtotal = 0.0382 • Mtotal = Mbegin = 13089 kg • Mconstr = 524 kg • Mprop = 12065 kg • Mprop/Mtotal = 92.2 % AE2104 Flight and Orbital Mechanics OPTIMAL SOLUTION? FEASIBLE SOLUTION? 21 |
  • 23. Ideal multi-stage rocket (cnt’d) Example 5: no construction mass ……….. AE2104 Flight and Orbital Mechanics 22 |
  • 24. Ideal multi-stage rocket (cnt’d) Example 6a: ΔV = 5 km/s, Isp = 400 s, Mconstr/Mtotal = 8 %, Mpayload = 500 kg  • Mpayload/Mtotal = 0.1997 • Mtotal = Mbegin = 2504 kg • Mconstr = 200 kg • Mprop = 1804 kg • Mprop/Mtotal = 72.0 % AE2104 Flight and Orbital Mechanics OPTIMAL SOLUTION? FEASIBLE SOLUTION? 23 |
  • 25. Ideal multi-stage rocket (cnt’d) Example 6b: ΔV = 5 km/s, Isp = 400 s, Mconstr/Mtotal = 8 %, Mpayload = 2504 kg  • Mpayload/Mtotal = 0.1997 • Mtotal = Mbegin = 12,539 kg • Mconstr = 1003 kg • Mprop = 9032 kg • Mprop/Mtotal = 72.0 % AE2104 Flight and Orbital Mechanics OPTIMAL SOLUTION? FEASIBLE SOLUTION? 24 |
  • 26. Ideal multi-stage rocket (cnt’d) Add numbers examples 6a+b: Example 6a Example 6b total ΔV [km/s] 5.0 5.0 10.0 Mprop [kg] 1804 9032 10836 Mconstr [kg] 200 1003 1203 Mpayload [kg] 500 2504 500 Mtotal [kg] 2504 12539 12539 stage 2 stage 1 AE2104 Flight and Orbital Mechanics 25 |
  • 27. Ideal multi-stage rocket (cnt’d) Compare examples: Example 1 Example 3 Example 4 ΔV [km/s] 10.0 Mpayload [kg] Example 6a+b 500 Isp [s] 400 500 400 400 Mconstr/Mtotal [%] 8 8 4 8 # stages 1 1 1 2 Mprop [kg] n.a. 8663 12065 10836 Mconstr [kg] n.a. 797 524 1203 Mtotal [kg] n.a. 9960 13089 12539 AE2104 Flight and Orbital Mechanics 26 |
  • 28. Ideal multi-stage rocket (cnt’d) Compare examples: Conclusion: 50% gain in payload (ratio) !! AE2104 Flight and Orbital Mechanics 27 |
  • 29. Ideal multi-stage rocket (cnt’d) Multi-staging: Advantages: • no need to accelerate total construction mass until final velocity  upper stages perform more efficiently o more payload capacity o more ΔV capacity Disadvantages: • more complexity (engines, piping, …) AE2104 Flight and Orbital Mechanics • more risk (jettison, ignition, …) 28 |
  • 30. Ideal multi-stage rocket (cnt’d) Definition of parameters: • Mtotal,i = total mass of stage “i” (i.e., before firing) • Mpayload,i = payload mass of stage “i” • Mconstr,i = construction mass of stage “i” • Mprop,i = propellant mass of stage “i” • Note: Mpayload,i = Mtotal,i+1 AE2104 Flight and Orbital Mechanics 29 |
  • 31. Ideal multi-stage rocket (cnt’d) green = payload Stage 1 2 3 4 AE2104 Flight and Orbital Mechanics 30 |
  • 32. Ideal multi-stage rocket (cnt’d) Tsiolkovsky, single stage : V  M begin    I sp g0 ln   M   end  define p  M payload / M begin   M constr / M prop then M begin M end  M payload  M constr  M prop M payload  M constr  1 p  so V  1  I sp g0 ln   p       (after [Fortescue, Stark & Swinerd, 2003]) AE2104 Flight and Orbital Mechanics 31 |
  • 33. Ideal multi-stage rocket (cnt’d) Derivation of 4th equation on previous sheet: M payload  p M begin and   M prop M constr so M begin  p M begin  M constr  M prop which becomes (1  p ) M begin  M constr  M prop  (  1) M prop or 1  M prop 1 p mass ratio for Tsiolkovsky's equation : 1 M prop M begin 1 p  1  M end p M prop   M prop 1 p M begin   1  1 p 1  p  1 p  1 p(1   )   (1  p )  1 p  p    p AE2104 Flight and Orbital Mechanics  32 | 1  p 
  • 34. Ideal multi-stage rocket (cnt’d) stage "i" only :  1  i   I sp ,i g0 ln    p   i  i total launcher : Vi Vtot   Vi    1  i  I sp ,i g0 ln    p   i  i assume I sp ,i  I sp i  s so Vtot    1 s  I sp g0 ln    p  s   i (after [Fortescue, Stark & Swinerd, 2003]) AE2104 Flight and Orbital Mechanics 33 |
  • 35. Ideal multi-stage rocket (cnt’d) by definition : Ptot  p1  p2  p3  ..... p N   pi optimal solution (w.o.derivation ) : pi  N Ptot so Vtot  I sp g0 N {ln(1  s )  ln( s  N Ptot )} (after [Fortescue, Stark & Swinerd, 2003]) AE2104 Flight and Orbital Mechanics 34 |
  • 36. Ideal multi-stage rocket (cnt’d) N • #stages typically 3 or 4 • single stage: ΔV/(Ispg0) 1.7 – 2.4 (factor 1.4) Véronique 1 Ariane-4 2 P 0.044 0.02-0.03 • 4 stages: ΔV/(Ispg0) 2.0 – 5.5 (factor 2.8) • staging very attractive (for modest P) AE2104 stages for Ariane• high P: gain multi-staging limited ( 2Flight and Orbital Mechanics 5, Delta IV, Titan V, …) real challenge! 35 |
  • 37. Ideal multi-stage rocket (cnt’d) Question 1 The performance of a rocket (i.e., the ΔV that can be obtained) is determined by the ratio Mbegin/Mend, amongst others. New parameters ”p” and ”σ” can be defined: p=Mpayload/Mbegin and σ=Mconstr/Mprop. Derive the following equation: Mbegin/Mend = (1+σ)/(p+σ) AE2104 Flight and Orbital Mechanics 36 |
  • 38. Ideal multi-stage rocket (cnt’d) Question 2 The performance of a rocket (i.e., the ΔV that can be obtained) is determined by the ratio Mbegin/Mend, amongst others. New parameters ”pi” and ”σi” can be defined for each possible stage “i”: pi=Mpayload,i/Mbegin,i and σi=Mconstr,i/Mprop,i. Derive the following equation which holds for an arbitrary number of stages N (where it is assumed that the parameters σi are equal to “s” for all stages, and the payload fractions of all stages pi are equal to (N)√Ptot (i.e., the Nth root of Ptot): Vtot  I sp g0 N {ln(1  s)  ln( s  N P )} tot AE2104 Flight and Orbital Mechanics 37 |
  • 39. Ideal multi-stage rocket (cnt’d) Question 3 Given the equation Vtot  I sp g0 N {ln(1  s)  ln( s  N P )} tot 1. What do the various parameters represent? 2. What does the equation express? 3. Make a sketch of the behaviour of ΔVtot/(Isp g0) as a function of parameter N, for the case Ptot = 0.001 and the case Ptot = 0.010 (parameter “s” is equal to 10%). Clearly indicate the (range of) numerical values for ΔVtot/(Isp g0). 4. Discuss the consequences of increasing N for both cases of Ptot. AE2104 Flight and Orbital Mechanics 38 |
  • 40. Real single-stage launcher [Fortescue & Stark, 1995] In direction of flight: M dV/dt = F cos(α+δ) – M g sin(γ) - D AE2104 Flight and Orbital Mechanics 39 |
  • 41. Real single-stage launcher (cnt’d) In direction of flight: M dV/dt = F cos(α+δ) – M g sin(γ) – D 1. Thrust misalignment: α+δ ≠ 0° (α needed to counteract gravity, δ for steering  cannot be avoided) 2. Gravity loss: γ ≠ 0° (launcher lifts off in vertical direction  unavoidable) 3. Drag loss: D ≠ 0 (first part of trajectory through atmosphere  unavoidable) AE2104 Flight and Orbital Mechanics 40 |
  • 42. Real single-stage launcher (cnt’d) vertical flight : dV  w dM D  g dt  dt M M integratio n : Vend dM D  g dt  dt M M  Vend ,ideal  Vg  Vd   where Vend ,ideal Vg   w     I sp g0 ln(  ) g0 tb AE2104 Flight and Orbital Mechanics 41 |
  • 43. Real single-stage launcher (cnt’d) velocity at burnout : Vburnout   1  1  I sp g0 ln(  )  1    0     • including gravity losses • w/o drag losses altitude at burnout : hburnout  2 I sp g0  ln(  )  1  1  1 2  1  1    0    2 0       altitude at culminatio n : hculm  2 I sp g0  1 1  0 ln 2 ( )  ln(  )   1  0  2   time until culminatio n : tculm  I sp ln(  ) AE2104 Flight and Orbital Mechanics 42 |
  • 44. Real single-stage launcher (cnt’d) Data: • specific impulse Isp = 300 s • Ψ0 = 1.5 •Λ=5 Results: w/o gravity burn time [s] with gravity 160.0 burnout velocity [m/s] 4736.6 3167.0 burnout height [km] 281.4 155.8 culmination time [s] - 482.8 culmination height [km] - 667.0 culmination height for impulsive shot [km] - 1143.5 AE2104 Flight and Orbital Mechanics 43 |
  • 45. Real single-stage launcher (cnt’d) Culmination altitudes of single-stage launchers, for Isp = 200 s (left) and 400 s (right). Maximum acceleration = 10g. AE2104 Flight and Orbital Mechanics 44 |
  • 46. Real single-stage launcher (cnt’d) Gravity loss: minimize by shifting to horizontal flight a.s.a.p. Drag loss: minimize by reducing trajectory through atmosphere CONFLICT !! Solution 1: start in vertical directory, then turn to (more) horizontal direction. Solution 2: use air-launched vehicle. AE2104 Flight and Orbital Mechanics 45 |
  • 47. Example: Pegasus Requirements [OSC, 2003]: • maximum payload 455 kg into LEO • cost-effective • reliable • flexible • minimum ground support • multiple payload capability • short lead time • (released at 12 km altitude) [OSC, 2010] AE2104 Flight and Orbital Mechanics 46 |
  • 48. Example: Pegasus (cnt’d) Pegasus XL mission profile [OSC, 2007] AE2104 Flight and Orbital Mechanics 47 |
  • 49. Overall performance [OSC, 2000] Can we (easily) reproduce these numbers? AE2104 Flight and Orbital Mechanics 48 |
  • 50. Overall performance (cnt’d) Specific energy (i.e., energy per unit of mass): Eorbit = Epot,begin + Ekin,eff – ΔEpot • Eorbit = total energy in orbit (sum of kinetic+potential) • Epot,begin = potential energy at launch • Ekin,eff = effective kinetic energy • ΔEpot = gain in potential energy AE2104 Flight and Orbital Mechanics 49 |
  • 51. Overall performance (cnt’d) Substitution:   2a    R e  hlaunch 1   V0  V1  V2  V3  Vd  g 2  2        a R e  hlaunch   • μ = gravitational parameter Earth • a = semi-major axis of orbit • hlaunch = altitude of launch platform • V0 = velocity of launch platform • ΔV1,2,3 = velocity increment delivered by stage 1,2,3 • ΔVd+g velocity loss due AE2104 Flight and Orbital and gravity50 | to atmosphere Mechanics
  • 52. Overall performance (cnt’d) velocity Earth velocity L1011 Pegasus carrier: V0 cos(i )  0.463 cos( launch )  0.222 cos( launch ) Pegasus vehicle: stage Isp [s] Mprop [kg] Mconstr Mbegin [kg] [kg] 3 289.3 770 126 Mpayload+Mprop,3+Mconstr,3 2 291.3 3925 416 Mbegin,3+Mprop,2+Mconstr,2 1 295.9 15014 1369 Mbegin,2+Mprop,1+Mconstr,1  a = f(i, δlaunch, hlaunch, payload mass) AE2104 Flight and Orbital Mechanics 51 |
  • 53. Overall performance (cnt’d) [Wertz&Larson, 1991]: • Drag+gravity losses 1.5-2.0 km/s • Drag loss: 0.3 km/s Pegasus: small launcher  • Drag+gravity losses 1.5 km/s • Drag loss 0.3 km/s • Gravity loss 1.5 – 0.3 = 1.2 km/s AE2104 Flight and Orbital Mechanics 52 |
  • 54. Overall performance (cnt’d) Results for launches due East from KSC (δ=28.5°) and WTR (δ=34.6°): AE2104 Flight and Orbital Mechanics 53 |
  • 55. Overall performance (cnt’d) Orbit altitude as a function of carrier velocity (Mpayload = 300 kg, launch at equator): AE2104 Flight and Orbital Mechanics 54 |
  • 56. Design Can we (easily) reproduce the overall layout of a launcher? Example: Pegasus AE2104 Flight and Orbital Mechanics 55 |
  • 57. Design (cnt’d) Some data and assumptions: • 3 stages • Isp identical for all stages (290 s) • Mconstr/Mtotal identical for all stages (0.08) • Vc = 7.784 km/s at h=200 km • Vearth = 0.464 km/s at equator • Vcarrier = 0.222 km/s w.r.t. Earth •  Vpegasus,initial = 0.686 km/s AE2104 Flight •  ΔVideal = 7.784 – 0.686 = 7.098 km/sand Orbital Mechanics 56 |
  • 58. Design (cnt’d) • Drag loss 0.3 km/s • Gravity loss 1.2 km/s 1st order approach: • ΔVideal equally distributed over 3 stages • Drag loss on account of 1st stage • Gravity loss equally distributed over 3 stages  • Stage 1: ΔV = 2.366 + 0.3 + 0.4 = 3.066 km/s AE2104 Flight and (each) • Stage 2 and 3: ΔV = 2.366 + 0.4 = 2.766 km/sOrbital Mechanics 57 |
  • 59. Design (cnt’d) Tsiolkovsky’s rocket equation: V V   M total g0 I sp ln   M  total  M prop   M total g0 I sp ln   M  constr  M payload M constr M payload  M total M total           V   exp   I g    sp 0  AE2104 Flight and Orbital Mechanics 58 |
  • 60. Design (cnt’d) Stage 3: Mpayload = 455 kg, Isp = 290 s, Mconstr / Mtotal ~ 0.08: so: • Mtotal = 1526 kg • Mconstr = 122 kg • Mpayload = 455 kg • Mprop = 949 kg Next: total mass of stage 3 is equal AE2104 Flight andmass of stage 2. to payload Orbital Mechanics 59 |
  • 61. Design (cnt’d) stage 3 stage 2 stage 1 re-eng real Δ re-eng real Δ re-eng real Δ [kg] [kg] [%] [kg] [kg] [%] [kg] [kg] [%] payload 455 455 0.0 1526 1351 12.9 5116 5692 -10.1 constr. 122 126 -3.1 409 416 -1.6 1572 1369 14.8 prop. 949 770 23.2 3181 3925 -19.0 12961 15014 -13.7 total 1526 1351 12.9 5116 5692 -10.1 19649 22075 -11.0 AE2104 Flight and Orbital Mechanics 60 |
  • 62. Further reading • Koelle, D.E., Cost Analysis of Present Expendable Launch Vehicles as contribution to Low Cost Access to Space Study. In: (2nd ed.), Technical Note TCS-TN-147 (96), TransCostSystems, Ottobrun, Germany (December 1966). • Parkinson, R.C., Total System Costing of Risk in a Launch Vehicle. In: 44th International Astronautical Congress (2nd ed.), AA-6.1-93-735 (16–22 Oct., 1993) Graz, Austria . • Isakowitz, S.J.. In: (2nd ed.), International Reference Guide to Space Launch Systems, American Institute for Aeronautics and Astronautics, Washington DC (1991). • “ESA Launch Vehicle Catalogue”, European Space Agency, Paris, Revision 8: December 1997. • http://www.orbital.com info on Pegasus, Taurus and Minotaur • users.commkey.net/Braeunig/space/specs/pegasus.htm • http://arianespace.com/english/leader_launches/html • http://www.boeing.com/defence-space/space/delta/record.htm) AE2104 Flight and Orbital Mechanics 61 |

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