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Estimating maximum velocity of a car

  1. Mar 7, 2005 #1

    Asking for some help here. :smile:

    I've been working on a speadsheet to estimate the top speed of a car and am running into difficulties. I'm trying to take as much into account as possible, for example aerodynamic drag, drivetrain loss, rolling friction, etc, which probably isn't helping the issue. I've made a fair amount of progress but it's certainly not correct yet.

    I've found a few web pages that do something similar, but they don't take as much into account and they tend to use all kinda of weird and wonderful imperial units that make it a nightmare to work anything out with.

    If anyone could take a look and give me some pointers, that would be awesome.

    Many thanks in advance


    Attached Files:

  2. jcsd
  3. Mar 8, 2005 #2


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    You should use the actual torque curve of the car that you're looking at rather than just the peak power.

    Also, drivetrain efficiency is a complicated thing that really can't be estimated very well a priori (it is highly dependent upon speed, gear choice, load, temperature, lubrication types, etc).

    You would probably want to find a chassis dyno measurement of the car, which will already "take into account" a lot of the losses. A problem with that is that they aren't necessarily measuring brake power (i.e. power delivered to a "brake" allowing zero acceleration). Most dyno's allow the car to accelerate fairly quickly, so you also have "losses" that go into spinning up the various drivetrain components. The acceleration in these tests has nothing to do with what a car would experience in real life, so this is problematic. Anyway, near top speed, you want measurements that are as close to brake power as possible.

    Also, since you seem to like a lot of detail, take into account changes in the air density. This affects both drag and power output. Tires also "grow" a bit at high speeds.

    I also don't think your ram air calculation is correct. It probably scales as v^2, and I doubt it would be significant on a car without specially designed intakes (such as an F1 car). "Ram air" intakes on street cars are really just meant to bring in colder air from outside the engine compartment, which is a completely different effect.
  4. Mar 8, 2005 #3
    Cheers for your reply. I was beginning to wonder if anyone was going to bother.

    I know it's quite a lot to look over, so is a lot to ask really, but seemed easier than lots of seperate threads getting each detail right.

    I'm more concerned about getting the spreadsheet to work reasonably well with the given data then getting 100% accurate data in the first place, as that's just damn awkward for the majority of cars, particularly if you want to go into detail. Torque curves would be one such problem, although I could simplify it by having it linear between the two known points (at max torque and max power) - I'll add that later.

    Since attaching it here I've done a little bit more work to it and cleared up a few issues. I did indeed switch to using a square law for the ram air affect, since the data was for the McLaren F1 I suspect it uses all kinds of wizardy to be as fast as it is (it didn't cost a million dollars for nothing). Also I needed this to get the last few mph in the estimation. I've probably still over-estimated it's affect, as although it's only giving a 2.5% boost around 100mph, by the time the vehicle is travelling at 240mph the ram air device is increasing power by 14%. Normally I would ignore this however, it was just for this example.

    I've also added temperature related air density, and used a warmer temperature to get the speed up the last few mph. How the air density affects power is something I would have to completely ignore, as I haven't the faintest idea how to do it, if the electronics are advanced enough to detect and adjust the mixture for it, and what density the engine was measured under in the first place. A nice thought still.

    What else: tyre "grow". Hmm, yes, this would be complicated to get working accurately I'd imagine, but you can get around this by guessing the pressure the hot air would would increase the tyre to in the first place. I don't know anything about rubber expansion with temperature, but I'm assuming any such affect would have a negligable affect on the rolling radius.

    Anyway cheers for looking and commenting, it's mainly just acceleration I need to get working now, think I'll take a break for a couple of days and come back fresh.

    I can attach the improved spreadsheet if anyone would be interested.


  5. Mar 9, 2005 #4


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    A couple more comments:

    You don't want to interpolate the torque linearly between the torque and power peaks. The slope of the torque curve at its peak is zero (obviously), but decreasing quite rapidly at the power peak. You can actually find the slope at the power peak just by knowing the power and rpm there. So you can get a quadratic fit using only these two data points.

    There are actually standardized empirical formulae relating an engine's output under different atmospheric conditions. When power is stated as SAE or DIN or whatever, those are supposed to represent numbers 'corrected' back to some standard condition. Dyno operators do these calculations (or their computers do), so it should be possible to find the equations online.

    As for tire growth, I think the main effect is from centrifugal forces, not temperature. It can actually be quite significant on racing tires, but less so otherwise. If you're looking for a couple mph, the effect might be large enough even on street tires (especially at Mclaren F1 speeds).
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