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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 [J1m2] 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 (80120 [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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View Full Document 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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This note was uploaded on 11/08/2011 for the course AERO 16.810 taught by Professor Olivierdeweck during the Winter '07 term at MIT.
 Winter '07
 OlivierdeWeck
 Aeronautics, Astronautics

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