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MAE 4262: ROCKETS AND MISSION ANALYSIS. Rocket Equation and Losses September 4, 2012 Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk. ROCKET EQUATION: IMPORTANT TRENDS. TYPICAL D V MISSION REQUIREMENTS.

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mae 4262 rockets and mission analysis

MAE 4262: ROCKETS AND MISSION ANALYSIS

Rocket Equation and Losses

September 4, 2012

Mechanical and Aerospace Engineering Department

Florida Institute of Technology

D. R. Kirk

typical d v mission requirements
TYPICAL DV MISSION REQUIREMENTS

http://www.strout.net/info/science/delta-v/intro.html

d v capability for various rockets
DV CAPABILITY FOR VARIOUS ROCKETS

REF: Space Propulsion Analysis and Design, by Humble, Henry and Larson

gravity
GRAVITY
  • Remember that gravity on Earth (~ 9.81 m/s2) may be calculated fundamentally
    • Average radius of the Earth ~ 6,378 km or 3,963 miles
    • Mass of the Earth ~ 5.9742x1024 kg
  • Some typical values for Earth:
    • High power amateur model rocket ~ 100,000 ft, 30.5 km, 19 miles
      • g/ge = 99%
    • Shuttle in LEO (altitude of 300 km, 186 miles)
      • g/ge = 91%
    • Satellite in GEO (altitude of 42,000 km, 26,000 miles)
      • g/ge = 1.7%
  • Note that the radius of the moon is about 1,737 km and mass is 7.36x1022 kg
    • So g on the surface of the moon is about 1.62 m/s2
slide10
Variation of lift and drag coefficient with Mach number of V-2 rocket missile based on body cross-sectional area with jet off
comments launch from surface of earth
COMMENTS: LAUNCH FROM SURFACE OF EARTH
  • To get to orbit (or to escape), direction of travel must be parallel to Earth’s surface (not perpendicular)
  • We launch vertically off the surface of the Earth, WHY?
    • Gravity
      • When rocket is vertical, gravity is acting against T and V
    • Drag
      • V2 dependence: Drag ↑ as rocket accelerates
        • Large effect in lower atmosphere
        • Acceleration of vehicle is almost constant even though mass is changing
      • Density dependence: r ↓ very rapidly in atmosphere (r/rS.L. ~ 1% at 100,000 ft)
  • All rocket pass through condition of maximum dynamic pressure (MAX Q)
    • Many rockets stay vertical through this part
    • Get through atmosphere as quickly as possible
    • BUT before rocket really starts to speed up
comments launchers
COMMENTS: LAUNCHERS
  • Need certain velocities to get to space (and stay in space), escape, insertion, transition velocities, etc. → give DV requirements
  • Don’t want to carry fuel (heavy fuel is working against you)
    • Burn fuel early in flight → high accelerations, V2 ↑
    • Atmosphere is counter argument: drag, dynamic pressure
  • Why not launch horizontal?
    • Less gravity loss
    • Drag loss is high, more time in atmosphere
    • Lots of structural stress
    • Launch might look different on moon
  • Vertical launch segment:
    • Get out of dense atmosphere quickly, but still at relatively low speed
    • Don’t spend too much time here (vertical segment contributes nothing to eventual vertical orbital velocity)
    • Highest gravity losses, but sustain them to get lower density then really increase DV
slide14
Variation in air density (r), velocity (V), altitude (h), and dynamic pressure (q) during a Space Shuttle launch