# How to calculate fuel consumption of car (mpg) from speed and accleration knowing mass, drag coeff and rolling resistance?

How can I calculate the current (instantaneous) mpg of my car if I know the speed and acceleration of the car? From reading various answers for the "car going level or up/down hill" question asked earlier by someone, I understand there are 4-5 factors to consider:

1. Rolling resistance (how do I get or calculate this value for my make/model?)
2. Engine resistance (how do I get or calculate this value for my make/model?)
3. Air drag coefficient (assume I know this)
4. Mass of car (assume I know this)
5. "Power curve" of car? What is power curve? Do I need to know this? How do I get or calculate this?
6. Slope of road (assume level for simplification)
-
This qustion seems a little rediculous to me; are you (for example) merely looking for a way to see how much it is costing you to push harder on the accelerator when the light goes green?? I.e. a more instantaneous mpg reading than modern cars currently offer. If so, the simlest answer would be to design a more accurate fuel level guage that took temperature and gaseous pressure in the fuel tank, as well as the actual fuel level, into account. – qftme Apr 28 '11 at 23:55
My car is not a newer model with instantaneous mpg readout. Also, there are some onboard diagonostic meters that may do this for $200-300. I wanted to know of it could be done using physics and engineering. – user3344 Apr 29 '11 at 16:49 How do you think the$200 gadgets work? I don't feel this answers the question. – qftme Apr 30 '11 at 2:50
Some approximate calculation is possible in principle, but it is not clear what would constitute and "answer" to this battery of questions. – dmckee May 30 '11 at 19:00
Sender resistance is missing in the 6 factors given. – Inquisitive Dec 29 '12 at 14:04

You can't. At least, not in any accurate way. The reason being that you have too many variables. Each variable adds a significant amount of error due to inaccuracies in measurement to your calculation. This might be a nice math problem, but as a physics problem, it has little application to the real world. My WAG is that the error in your calculation would probably exceed 50%.

If you want to determine fuel consumption, try just accurately measuring how much fuel is being consumed at any given moment in time. Your engine's fuel pump will "know" this information based on how hard it needs to work. It's a pretty trivial task to convert this information into something usable if you're in the process of designing a car's computer, which is why this feature is included in many newer cars.

As for the math that would give you a "miles per gallon" number, it would go like this:

For argument's sake, consumption rate R is measured by the fuel pump in ml/second. For the time being, let's measure speed (V) in metric as well, since that too is being measured accurately. Speed needs to be reduced to meters/second to match the fuel pump's consumption rate figures, allowing them to cancel out. The amount of fuel used over any distance would be:

Consumption = R / V

and Consumption would be measured in millilitres/meter. Multiply by 1000 for litres/km.

-

No, you cant. Because it is simple to know mpg we have to calculate fuel flow. Only measuring speed and acceleration you know variation distance time and need to calculate fuel flow also.

-