A spherical satellite has 12 identical monopropellant thrust chambers for attitu

Question

A spherical satellite has 12 identical monopropellant thrust chambers for attitude control with the following performance characteristics: thrust (each unit): 5 lbf; ls (steady state or more than 2 sec); 240 sec; ls (pulsing duration 20 msec): 150 sec; ls (pulsing duration 100 msec): 200 sec; satellite weight: 3500 lbf; satellite diameter: 8 ft; satellite internal density distribution is essentially uniform; disturbing torques, Y- and Z-axes: 0.00005 ft-lbf average; disturbing torque, for X-axis: 0.001 ft-lbf average; distance between thrust chamber axes: 8 ft; maximum allowable satellite pointing position error: ±1 °. Time interval between pulses is 0.030 sec.
(a) What would be the maximum and minimum vehicle angular drift per hour if no correction torque were applied?

Explanation / Answer

According to the given problem,

Answers : 0.466 and 0.093 rad/hr.

Ma = 2/5 m*r^2 3500

lbf = 1587.6 kg; 8 feet = 1.22 m

Ma = 2/5*1587.6*1.22^2

Ma = 945.2 kg/m2 or 697.14 slug/ft^2

T = Fl = Ma*angle 0.001 = 697.14*a

A = 1.43*10^-6 degree/s^2

W = a*t W = 0.00000143*3600 = 0.0052 deg/s = 0.327 rad/hr 0.00005 = 697.14a

Angle = 7.2*10^-8 deg/s^2

W = a*t

W = 7.2*10^-7 * 3600 = 0.00026 deg/s = 0.016 rad/hr

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