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MIT16_842F09_assn4_sol - Assignment#4 Solutions 16.899...

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Assignment #4 Solutions 16.899 – Fundamentals of Systems Engineering Part I. Vehicle Design and Performance (Aeronautics) 1) In Figure 1, what physical effects cause R to increase as m is increased from 1kg to about 20000kg? What causes the slight decrease as m increases beyond 20000kg? Hint: examine the variables of the Breguet range equation. There are several ways to explain this. This is just one of them: In looking at the BRE, there are three main factors that affect range; engine performance (PSFC), aerodynamics (C L /C D ), and fuel fraction (m fuel /m). From the engine’s perspective, in general a) the less power it has to produce in cruise, the lower the PSFC. At the same time, one wants to b) maximize C L /C D which we know, from the drag polar, occurs when parasite drag equals drag-due-to-lift. Typically, if the aerodynamic condition is satisfied, we’ve done as good as we can in minimizing the power required. Finally, we want c) as much fuel as possible without overstressing the a/c. When the aircraft is very light, the best improvement we can make is in terms of c) since the stress limits are easily avoidable by adding relatively low amounts of reinforcement (in terms of mass), and it is relatively easy to meet a) and b). This is true for a range of mass that continues upward until stress limits become very costly to increase (i.e. the amount of mass required to reinforce is no longer worth the range gained by the increase in fuel mass). This is related to the square-cube law as described below in the answer to number 3. At this point, it is also no longer easy to meet the requirements of a) and b). That
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