Vehicle Design and Performance
You may solve either question (a), which deaIs with the design of a communications satellite or
question (b), which deals with the design of an unmanned aeriaI vehicle (UAV). Both questions
are equivaIent in terms of degree of difficulty and methodology.
(a) Spacecraft Design Problem
You should assist in the design of a communications satellite at geosynchronous altitude S , see Figure 1.
The performance requirement is a transmission data rate of &, = 100 [Mbps]&20% at a
radio frequency of f = 2 [GHz]'. The satellite is made up of a solar panel of area A [m2] with
efficiency m,a standard bus that consumes Pbuspower, and a parabolic antenna of diameter D [m]
with transmission efficiency qt.
Earth
1-78
Satellite
sdar
[km]
c=3 .lo8
W,= 1358
speed of light
w/m2] solar constant
solar panel efficiency
bus power
transmission efficiency
[J-'1
link constant
[m/s]
Ph, =300
= 0.8
a = 2.4 . 10"
(h]
GEO altitude
S=35786
Figure 1: Geosynchronous communications satellite with important constants
Tt is your job to negotiate between the power and payload teams to find a solution for the design vector
x = [DA]" that will satisfy the performance requirement fie*,
while not violating any constraints.
Some equations that might be useful are given below, where A is the electromagnetic wavelength [m]
and PA is the power generated by the solar panel:
data rate [bps]
transmission power [W]
parabolic antenna gain
path loss
[-I
1-3
R=cr-Pt.Gt.Ls
Pt = PA - Phs
7T2D2*
Gt = A2
=
-
2
(A)
(al) Assuming 45 degree incidence of sunlight onto the solar panel, find Pt = f ( A ) . Compute a lower
bound Ama for Pt = 0.
~ [I 5JT. Compute the
(a2) The two subsystem teams suggest an initial design x, = [DA ] =
performance R(x,). Does this design meet the requirement? Explain.
(a31 If design x, meets the requirement, set X I = x, and continue directly with (a4). Otherwise,
x, as a starting point for finding an acceptable design $1. Plot your path from x, to X I in the
(D,A)-design space. The space is bounded by 0,5 5 D 5 3 [m]and Amin 5 A 5 12 [m2j. Hint: Plot
the (D,A)-spwe on a, separate sheet.
use
(a41 Management likes your design X I ,but points out that it is not unique. Find a second acceptable
design, X Z , at some distance from XI. Sketch the line that corresponds to the requirement &, = 100
[Mbps] in (D,A)-space (isoperformance contour).
(a51 The accounting department gives you the cost estimation relationships for the antenna CD =
2500 . D 2[$I and solar panel CA= 12000 ( A 1) [$I, respectively. Find a design x3 that will minimize
the total cost CA CD and meet the requirement Keq.
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(86) YOU think you are all done. Unfortunately, now the attitude control system (ACS) team is
complaining about your design 23. What is their problem? Hint: Think about; the effect of D on the
beamwidth 8.
'1 [Mbps] is one million bits per second
(b) Unmanned Aerial Vehicle (UAV) Design Problem
You should assist in the design of a UAV to be used for reconnaissance missions. The'performanee
requirement is an endurance Ereq of 20 [hours]&10%. Your job is to find a good design,
represented by the vector x = [f ,331, where f is the fuel mass fraction and LR is the wing aspect ratio.
Figure 2 shows a side and top view of the UAV along with important constants.
q = 0.8
I-I
c = lo-"
b-I1
CL= 1.2
Coo= 0.05
m,=220
p = 0.6
zv
wing
mw
V=4Q
g=10
propeller efficiency
specific fuel burn
lift coefficient
zero lift drag coefficient
airframe mass (exclud;ng wl'ng)
air density at 6500m
cruise speed
gravitational acceleration
[-I
[-I
[kg1
Pg/m3J
b/sJ
[m/s2J
fuel
mf
Figure 2: UAV design with important constants
The aspect ratio is At = B/b, while the wing area S is equal to S = Bb and remains fixed. The m a s
of the wing is dependent on the aspect ratio as rn, I&) = (m,/l8)At.
Some other useful equations for
solving this problem are:
E = c s . ~ ; l - ( d m - 1)
Endurance [secJ
total drag coefficient
empty mass [kg]
[-I
c:
CD = CD,+ n AE
m1=rn,+m,=m,(I+At/18)
(bl) First compute the constant a used in the endurance equation: a = 29743 / ( c V ) . Then compute
the wing area S [m2], assuming that f = 0.25 and AZ = 6. Hint: The lift is 1; = (p/2)~2SCr.
and
L = g - m, during straight and level flight.
(b2) Compute the performance E(xo:,)for the initial: dmign vector xo = [f 4 = [0.25 61. Does this
design meet the performance requirement Ere,?
(b3) If design x, meets the requirement, set X I = x, and continue directly with (b4). Otherwise, use
x, as a starting point for finding an acceptable d ~ i g nXI. Note that the design space is bounded by
0.1 5 f 5 0.5 and 5 5 AZ 5 16, respectively, Hint: Try adjusting the fuel mass fraction, f.
(b4) Management like your design X I ,but points out that it is not unique. Find a second acceptable
design, x2, at some distance from XI. Hint: This time, try adjusting AZ, starting from design x,.
(b5) Plot your path from x, to X I and 2 2 in the (j,&) design space. Sketch the line that carresponds
to the requirement Ere, = 20 [hours], i.e. the ist~endurancecontour.
(b6) The UAV lifecycle cost is the sum of the production coat C, = 1000 P T E ~and the total fuel cost
Cj = 5000 - y - f - ml . Which design, X I or x2, has the Iower lifecycle cost C, Cf,
given that y = 4
[$/kg]? Briefly explain the tradeoff between both designs.
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MIT OpenCourseWare
http://ocw.mit.edu
16.842 Fundamentals of Systems Engineering
Fall 2009
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