[Diy_efi] BHP calculations

[Brian Dessent]

Hugh Keir wrote:

> I need help with the formula to calculate acceleration BHP.
> 
> I know the weight of the car and the change in engine RPM over time.

I'd say there are a number of ways to go about this.  However you do it,
the hardest part will be keeping consistent units.  Decide on a common
set of units and convert everything to those units.  Don't try to mix
units!

Power equals force times velocity.

With a given constant K (that represents gear ratio, final drive, and
effective tire diameter) you have:

v(t) = K*RPM(t)

If you numerically differentiate that (i.e. (v(n+1) - v(n))/deltaT)
you'll get a(t).  Note that you'll probably want to do a bit more than
simple numerical differentiation, since the result is very "noisy."  You
could apply a moving average filter to the data first, or average your
resulting acceleration values.  Or, if you want to get really fancy try
curve-fitting (like a high order polynomial fit) v(t) and then
mathematically differentiate the equation.  I have an example of doing
this in Excel using an 8th order polynomial and the LINEST() function.

So then convert a(t) to F(t) by dividing by mass.  Now you have v(t) and
F(t), multiply and you have power, P(t).  You can get torque by dividing
power by RPM and a constant which will depend on the units in which you
are working.  Now plot these verses RPM, and you have dyno-like graphs.

Note that, depending on the speed that you were moving, you might want
to incorporate a correction factor into 'K' above for the effective tire
diameter increasing as the tires expand at higher speeds.  Do a google
search, there are a bunch of web pages with these types of equations,
and a lot of them have javascript calculators worked out as well.

Brian

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