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Unformatted text preview: derive equations that relate these quantities via energy balance:
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msi+1 + mghi+1 = ms2 + mghi + ηfi − dCD s2 ,
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2i i = 1, . . . , N, where g = 9.8 is the gravitational acceleration. The lefthand side is the total vehicle energy (kinetic
plus potential) after it passes through knot point pi+1 ; the righthand side is the total vehicle energy
after it passes through knot point pi , plus the energy gain from the fuel burn, minus the energy
lost to drag. To set up the ﬁrst vehicle speed s1 requires an additional initial fuel burn f0 , with
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ηf0 = 2 ms2 .
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Fuel is also used to power the onboard system of the vehicle. The total fuel used for this purpose is
fob , where ηfob = T P , where P > 0 is the (constant) power consumption of the onboard system.
We have a fuel capacity constraint: N fi + fob ≤ F , where F > 0 is the total initial fuel.
i=0 The problem data are m, d, h1 , . . . , hN +1 , η , CD , P , and F . (You don’t need the knot points pi .) (a) Explain ho...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.
 Fall '13
 F.Borrelli
 The Aeneid

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