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# lecture4 - MECH 6521/498D Space Flight Performance Basic...

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MECH 6521/498D Space Flight Performance Gemini 3 - Titan II • Basic relations of motion • Multistage rocket • Space flight (orbital mechanics) Reading: Sutton and Biblarz Chapter 4 and Chapter 3

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Rocket Fundamentals - Summary Revisit Newton’s third law and conservation of momentum - Rocket thrust model - Rocket equation for an ideal rocket engine Define different performance parameters - Effective exhaust velocity - Specific impulse - Energy efficiencies - Impulse or thrust to weight ratio Define different masses and their ratios = Δ MR I g V sp 1 ln 0 F = m e V e + p e A e p A e () Ties mission requirements and system requirements together to accomplish a particular mission (given by Δ v), the system has to deliver specific characteristics.
2. Rocket Fundamentals 1. Rocket technology 3. Space Flight Trajectories

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Space Flight Performance So far, we only look at the ideal rocket equation i.e. Gravity-free, drag-free space flight - drag, gravity, and burn time effects Applications of the rocket equation to: To model launch trajectories Multi-staging concept Understanding different factors involved in designing launch trajectories Space flight - orbital transfers, and other maneuvers = Δ MR I g V sp 1 ln 0 F = m e V e + p e A e p A e ()
Space Flight Trajectory The rate of acceleration of the vehicle is: dt g dt M D M dM c dV e θ cos = C e is the effective exhaust velocity of the vehicle or the thrust divided by the exhaust mass flow rate Look at forces on rocket in flight again: V For example, another simple particular case: - flight direction and thrust are co-linear - life forces are negligible for wingless vehicle with zero angle of attack α - constant thrust, stationary earth, no wind

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Space Flight Trajectory D f C A V D 2 5 . 0 ρ = where atmospheric density above earth varies roughly as: ( ) 5 . 1 exp ) ( bh a h = With density in kg/m 3 and h is meters, a = 1.2 and b =2.9x10 -5 Roughly, density at 30,000 meters is about 1% of its sea-level value Aerodynamic force or drag D Equivalently you can write down similar expression for the lift L, dynamic force acting in a direction normal to the flight path.
Lift and Drag Variation of lift and drag coefficient with Mach number of the German V-2 missile based on cross-sectional area with jet off and without exhaust plume effects at several angle of attack α .

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Space Flight Trajectory 2 + = h R R g g e e e At 100 miles above the surface the change from the surface is still only about 5%. To calculate velocity increment for acceleration near the earth (or any other large mass), we will generally assume g to be constant. But be sure to state it as an approximation!!! Gravitational force
Space Flight Trajectory The rate of acceleration of the vehicle is: dt g dt M D M dM c dV e θ cos = Neglecting the air drag and gravity terms, we get the ideal rocket equation M dM c dV e = For space launch vehicles, the drag loss is typically 5% to 10% of the final vehicle velocity increment Δ v. Very

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## This note was uploaded on 12/12/2010 for the course MECH 351 taught by Professor Chekhov during the Fall '10 term at Concordia Canada.

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lecture4 - MECH 6521/498D Space Flight Performance Basic...

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