Calculate combustion engine torque

[anycast]

Hi,

I'm currently doing a small racing game where I allow players to tweak their car's engine (control number of cylinders, cylinder bore/stroke, turbo chargers, etc).

I've understood the very basics of how combustion engines work but I'm still struggling on how to calculate engine torque given RPM, # of cylinders and cylinder bore/stroke.

From here: http://www.thecartech.com/subjects/engine/engine_formulas.htm I get that it's possible to calculate torque based on the parameters I mentioned above + something called indicated mean effective pressure (imep). I reckon imep is dependent on rpm, and rpm is most likely dependent on the amount of fuel and air going into the cylinders, but I still haven't found a way to calculate imep.

Is there a shortcut I can take to create a believable rpm/torque graphic just based on RPM, # cylinders and cylinder bore/stroke?

Thanks,
Alex

 

[jack action]

Is there a shortcut I can take to create a believable rpm/torque graphic just based on RPM, # cylinders and cylinder bore/stroke?

No.

IMEP is the average pressure within the cylinder. It depends mostly on the amount of air-fuel mixture that goes into the cylinder, the combustion efficiency and the efficiency of the thermodynamic cycle. The last two are relatively constant throughout the rpm range. The amount of air can be calculated based on engine size, rpm and volumetric efficiency. The volumetric efficiency changes with the mean piston speed (which is directly related to rpm). It usually peaks out at a point near maximum torque, being lower before and after that point. The curve's shape greatly depends on the intake-camshaft-exhaust design. That is the very complicated thing to calculate.

But, as the piston goes down, friction will take some force away that will not be converted to torque. That loss is usually converted into an equivalent «pressure» loss from your IMEP, i.e. a friction mean effective pressure (FMEP). It has been found that FMEP is also directly related to mean piston speed. Fortunately, compared with volumetric efficiency, it has a more linear relationship with mean piston speed.

To get the true output torque, you need the brake mean effective pressure (BMEP) in your equation. BMEP is simply the FMEP subtracted from IMEP.

So, in mathematical form, the equation for BMEP across the rpm range would look like:

BMEP = IMEP - FMEP
BMEP = A * f(MPS) - (B + C * MPS)

Where A is a constant mostly depending on the engine cycle & combustion efficiencies, some basic dimensions (total bore area, actually) and engine & fuel characteristics. f(MPS) is a function based on the mean piston speed. B & C are constant for estimating FMEP. And MPS is defined as:

MPS = RPM * Stroke / π

Where π is the crankshaft angular displacement for one stroke (in radians).

That is the f(MPS) that makes it difficult to create a shortcut.

and rpm is most likely dependent on the amount of fuel and air going into the cylinders

Actually, the opposite would be closer to the truth, i.e. the amount of fuel and air going into the cylinders is most likely dependent on the rpm.

 

[anycast]

Thanks for your very well layed out answer. I just went to your site and I'll be spending some time in it :).

Actually, the opposite would be closer to the truth, i.e. the amount of fuel and air going into the cylinders is most likely dependent on the rpm.

Isn't the throttle pedal just a way to increase air and fuel ammounts going into an engine? And isn't this what make the engine vary its RPM?

 

[jack action]

Isn't the throttle pedal just a way to increase air and fuel ammounts going into an engine? And isn't this what make the engine vary its RPM?

Not necessarily. When more air and fuel goes into the cylinder, engine torque will increase. That sudden increase in torque will accelerate the engine rpm IF the engine load is not changed. But if the engine load is increased at the same time, the rpm could remain the same (or even drop if the load increase is larger than the torque increase).

For example, if you drive on a flat road and run into a hill, your speed (and rpm) will reduce because the engine load increases. If you open the throttle just the right amount, the speed (and rpm) will be maintained. Open it more and your car (and engine) will accelerate.

No matter what, when you are stuck in a given rpm, a maximum air flow rate can be achieved once your throttle is wide open. If you want more, you will need to go to a higher rpm (usually by changing gears).

 

[anycast]

Thanks!

 

[Nidum]

An alternative approach to getting engine data for your racing game would be to get the dimensions and performance characteristics for a range of real commercial engines .

Most manufacturers publish extensive data on their products .