Space Propulsion - IAP/TU Wien

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1 – axis maneuvre, cont‘d Space Propulsion total angle of rotation is rotation during coasting is Θ m = Θ (accelerating) + Θ (coasting) + Θ (braking) Θ = ωtc the coasting rotation angle is Θ = nFL t I v b t c ω = nFL I v t b total rotation during acceleration, coasting and braking is Θ m ⎛ nFL = 2 ⎜ t ⎝ 2I v 2 b ⎞ nFL ⎟ + t ⎠ I v b t c = nFL I v 2 ( 2t + t t ) b b c Θ = nFLt 2I v 2 b maneuver time is t m = t C + 2t b accel. minimum rotation time is a fully powered maneuver with zero coast time t min = 2t b = 2. Θ m I nFL v thrust level required for each thruster at given minimum rotation time F Θ m v 2 min I = 2 nLt propellant required for a one-axis maneuver is twice the single burn consumption m p nFt b = 2 = I sp nFt I sp min nFt b m p = = I sp H LI sp
Space Propulsion Example 6: One-Axis Maneuver Find the minimum time required for a spacecraft to perform a 90-deg turn about the z axis with two thrusters if the spacecraft has the following characteristics: Mass of S/C = 500 kg, Radius of S/C = 0.75 m Moment of inertia about the z axis ≅(2/5)M S/C. L 2 = 112.5 kg.m 2 Moment arm = 0.75 m Thrust of each engine = 10 N and Θ m = π/2 = 1.5708 rad t 2. Θ I m v min = = = nFL 2*1.5708*112.5 2*10*0.75 4.854 s How much propellant was consumed by the maneuver if I sp = 1900 m/s ? nFt m 2 * 2 *10 * 4.854 m p = 2 = = 0. 102 I 1900 sp kg
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Space Propulsion - IAP/TU Wien

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