MAE 4262: ROCKETS AND MISSION ANALYSIS

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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

Rocket Equation and Losses

September 4, 2012

Mechanical and Aerospace Engineering Department

Florida Institute of Technology

D. R. Kirk

TYPICAL DV MISSION REQUIREMENTS

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

DV CAPABILITY FOR VARIOUS ROCKETS

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

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
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
• 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
• 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
Variation in air density (r), velocity (V), altitude (h), and dynamic pressure (q) during a Space Shuttle launch