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MIT16_842F09_assn2_sol - Vehicle Design and Performance...

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Vehicle Design and Performance Master Solution - CONFIDENTIAL - January 2002 This paper contains the master solution for the vehicle design and performance question for the doctoral qualifying examination in the Department of Aeronautics and Astronau- tics at MIT. This paper is to be used for grading purposes only. (a) Spacecraft Design Problem (al) Assuming 45 degree incidence of sunlight onto the solar panel, find Pt = f (A). Compute a lower bound Amin for Pt = 0. The power generated by the solar panel is the solar constant times the area A times the efficiency times the cosine of the incidence angle, thus: In order to cor~lpute the transmission power as a furlctiorl of A, we have to subtract the bus power and substitute the constants: The lower bound Amin is found by setting Pt = 0 as: (a2) The two subsystem teams suggest an initial design x, = [D AIT = [I 5IT. Compute the performance R(x,). Does this design meet the requirement? Explain. We substitute the three last equations from the problem formulation into the link budget equation for the data rate R and obtain: where p = 93703.3 [J-1m-2] is a constant. Thus, the performance goes linearly with solar panel area A and quadratically with antenna diameter D. Substituting the values lor x, in the above equation we obtain R(xo) = 25.9 [Mbps]. This design does not meet the requirement (80-120 [Mbps]) and is significantly underdesigned. We need to increase the data rate R by increasing D, A or both. (a3) If design x, meets the requirement, set XL = x, and continue directly with (a4). Otherwise, use x, as a starting point for finding an acceptable design xl. Plot your path from x, to x1 in the (D,A)-tradespace. Note that the tradespace is bounded by Dmin 5 D 5 Dmax and Ami, 5 A 5 A,, respectively. Hint: Plot the (D,A)-tradespace as large as you can on a separate sheet.
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Starting from x, we can find xl by increasing the antenna diameter D. The question is by how much? A sensitivity analysis can help determine a good step size: Substituting the values for x,, we obtain a sensitivity dR/dD = 51.5 [Mbps/m]. Thus the step size is found as: Thus, we attempt the new design point
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MIT16_842F09_assn2_sol - Vehicle Design and Performance...

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