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. + - + (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. + + MIT OpenCourseWare http://ocw.mit.edu 16.842 Fundamentals of Systems Engineering Fall 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.