[ODE] Gearbox and engine??

[Nate W]

On Wed, 14 Aug 2002, Keshav wrote:

> I know the values for gear ratios, differential ratio, engine torque
> curve, for a given car.  I also know the radius of the wheels.
>  
>     1. How do I calculate RPM of an engine, given, I know how fast it's
> drive (torqued) wheels are turning?

First you need the total ratio of the entire drivetrain (gearbox plus
differential).  To combine ratios, multiply them: total_ratio =
gearbox_ratio * diff_ratio.  Thus, if the gearbox ratio is 2:1 and the
differential ratio is 4:1, then the total ratio is 8:1.

If the wheels are turning at 500 RPM, then the engine is turning at 250 *
total_ratio = 4000 RPM.

>     2. How do I calculate, the maximum speed (how fast the wheels turn),
> given, I know the engine RPM, engine torque, gear ratio, etc.

Given only the data above, you can figure out a theoretical maximum wheel
RPM, e.g. if the redline is 8000 RPM and the ratio is 8:1 then the wheels
will turn at a maximum of 1000 RPM...  Given the radius of the tire, you
can compute the circumference of the tire, then multiple that
circumference by the wheel RPM to get the car's linear speed at that wheel
RPM.

You're missing a couple of bits of data, though... you need to know things
like rolling resistance, aerodynamic drag, and so on.  The practical top
speed is the speed at which the engine force balances against those
losses.

Here's where the missing data becomes important: if, at the theoretical
top speed compute above, the rolling resistance and aerodynamic drag (and
drivetrain losses, and maybe other losses) would eat up more force than
the engine can supply at that RPM, then the car will never actually reach
that theoretical top speed.

I'm not sure of a good way to find the speed at which the forces balance
out, other than the iterative approach - build some tables of available
engine power vs. losses at different speeds and gear ratios.  There could
be a better approach though... A google search is probably in order at
this point.  

I hope this helps.

-- 

Nate Waddoups
Redmond WA USA
http://www.natew.com