Space Propulsion - IAP/TU Wien

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limit cycle cont‘d Space Propulsion pulsing properties of attitude – control thrusters Cold-gas -Helium 500 CoId-gas-Nitrogen 50 5 - 10 N 2 H 4 Monopropellant - 500 50 - 100 1200 Bipropellant - N 2 O 4 /MMH Min thrust [mN] 50 10000 Min impulse bit [mN.s] 5 - 10 750 - 1500 Pulsing I sp [m/s] 800 1200 nFL ω = t I v b t c I vΘ = 4 nFLP L w coast time through 2Θ L 4I Θ v L tcy = tc + 2PW = + 2 nLI min P w length of a cycle (from +Θ L to -Θ L ) if minimum impulse bits are used; usually, P W can be neglected nFP mp, cyc = 2 I sp w • m p = 2 2 mp, cyc n IminL ~ propellant consumption per unit time t 2I I Θ cy sp v L
Space Propulsion Example 8: Limit-Cycle Operation A spacecraft with 112.5 kg.m 2 inertia uses 5N thruster pairs mounted at a radius of 0.5 m from the center of mass. For limit-cycle control to Θ L = 0.5 deg (0.008727 rad), what is the propellant consumption rate if I sp is 1900 m/s, the pulse duration is 30 ms, and there are no external torques. ? t 4IvΘL 4*112,5*0,008727 = 2Pw + = 0.06 + = 0,06 + 26,181 26,241 [ s] time for 1 cycle nFLP 2*5*0,5*0,030 cy = w nFPw 2*5* 0.03 m p , cy = 2 = 2 = 0.00032 [ kg / cycle] = 0,32 [ g / cycle] propellant consumed per cycle I 1900 sp • m p, cy 0,00032 −5 m p = = ≅ 1.2x10 [ kg / s] = 1.037 t 26,241 cy [ kg / day] average propellant consumption rate
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Space Propulsion - IAP/TU Wien

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