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Homework Help: Speed loss during gear change

  1. Apr 13, 2010 #1

    I have a assignment to produce a excel work book to calculate acceleration time and top speeds for different gear ratios in race cars. I have so far work out time to accelerate to top speed, but I want to add a bit more detail to my graphs by showing the speed loss during gear changes.

    car mass - 600kg
    drag coefficient - 1.3
    density air - 1.225kg/m^3
    frontal area - 0.4m^2
    rolling resistance = 125N
    shift time - 0.5 seconds

    I can work out the momentum and drag forces at the point the clutch is pressed at the start of the gear change using

    momentum = mass * velocity
    = 600v

    drag force = (0.5 * coefficient drag * density air * frontal area * velocity^2)+ rolling resistance
    = 125+0.3185v^2

    Sure it can be work out using calculus but has been many years since I last did that.

    Any help would be greatly appreciated

    Thanks Andy
  2. jcsd
  3. Apr 15, 2010 #2

    Filip Larsen

    User Avatar
    Gold Member

    I'm not sure why you model rolling friction as a constant force. If that is really what you want to do, perhaps you can find some formulas describing speed as function of time in https://www.physicsforums.com/showthread.php?t=393048

    Normally, though, one would model rolling friction as proportional to speed, that is, your equation of motion during gear shift would be

    [tex] m \dot{v} = -k v^2 - c v[/tex]

    where [itex]m, k, c > 0[/itex]. The c constant is the one corresponding to your 125N (at some speed?) If I quickly integrate this (assuming this is not really part of your homework, and if it is, you should figure out to do this integral yourself), I get

    [tex] v = \frac{d}{(1 + d/v_0)\exp(ct/m)-1} [/tex]

    where v0 is the initial speed at t = 0 and [itex] d = c/k[/itex].
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