| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
Anyone know of a formula that produces a reasonably accurate estimate of the miles per gallon of a car traveling at approximately constant speed ? I'm less interested in numbers than in a form for the function that can be applied across many models of car and is reasonably empirically accurate. The constants should hopefully be relatively easy to estimate from measurements. As usual, the smaller the number of experimentally determined constants, the better. Example: (1) miles_per_gallon( speed ) = k1*speed - k2*speed^2 k1 and k2 are constants determined by the car make (and perhaps weak functions of car mileage). This model would correctly predict that miles per gallon is zero while idling, peaks at some speed (in this model, = k1/[2*k2]) and drops off above this speed. It's probably not realistic in that it predicts that miles per gallon drops back to zero at some critical high speed. The real plot tapers off to zero asymptotically (I guess). It would be possible to identify the parameters from mileage data in this example by measuring the slope of miles per gallon against speed near speed = 0 (where mpg ~= k1) and then to compute k2 by back substitution into (1), or from applying least squares on sets of (mpg, speed) pairs. ------------------------------------------------------------------------ Even better would be a functional that maps speed (as a function of time) into total gas consumption over that time. An accurate model might not be able to neglect the mass of the car since power consumption during acceleration is probably sensitive to the mass. Since it's relatively easy to determine the weight, it would be OK for the model to incorporate the mass. It's probably legitimate to neglect the effect of engine temperature on the functional. I propose to neglect engine temperature, not because I think it has no effect, but because I have no good way to measure it, or even know what to measure (and, of course, I hope I can get away with it!). For a similar reason, factors like road surface composition, tire material, etc. should be neglected. By accurately measuring the speed history and total gas consumption, it should be possible to identify the included parameters using something like least squares. ------------------------------------------------------------------------ Even plots (for real cars) of mpg against speed might be helpful.
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1022.1 | CTCADM::ROTH | If you plant ice you'll harvest wind | Fri Feb 03 1989 22:40 | 22 | |
Miles per gallon has a broad maximum as a function of car speed,
so it is approximately quadratic near the maximum.
However, I know of sane basis for deriving such a formula, except
possibly for fitting some plausible function to measured data.
The problem is the *many* factors involved - wind resistance,
hills, atmospheric pressure, gas octane, extra vehicle weight,
timing and tuning of the engine, etc etc...
I played around with measuring the mileage of my car years ago.
A company out in Seattle called Flo Scan had a fuel flow meter for sale,
and I used it to measure the gas consumption. Heathkit also had one
but I don't know if it worked or not. It's a real problem to measure
fuel flow in a car, due to the pulsating pressure of the fuel pump,
the nature of the carburetter float regulator, and so on. On a car
with fuel injection which recirculates the fuel, you would have to
rig up some sort of reseviour. All a real pain. You could browse
through the index to the journal of the Society for Automotive Engineers
for some ideas.
- Jim
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