In-Car Dynomometers...math!

[Nelson David E]

At one time, Brian Lane said:
> 
> On Fri, 11 Aug 1995, Ric Rainbolt wrote:
> 
> > At the risk of getting flamed, I would like to say "me too".  I would like
> > to include a 3-axis acceleromter circuit on the ECU I'm currently designing
> > and it would be nice to exploit them as much as possible.  Someone mentioned
> > having worked out the math for G's <--> HP (given mass and time, I guess)
> > and I would definately like to see that math, if possible.
> 
>   Well the basic HP formula is:
> 
>     Weight(in lbs) x Acceleration(in Gees) x Speed (in MPH)
>     -------------------------------------------------------
>                             375
> 
>   The Auto Math handbook is also useful for various formulas.
> 
>    Brian

What a conincidence, I worked out the eq. for mass, accel., dist, time 
last night.  Here's the run down:
   Force=Mass*Accel which has units Newtons => ((Kg)(m))/s^2
   Work =Force*Dist which has units NewtonMeters => ((Kg)(m^2))/s^2
   Power=Work/Time  which has units NewtonMeters/Second => ((Kg)(m^2))/s^3
   Power also has units of Joules/Second => Watts
   Joule's units are ((Kg)(m^2))/s^2
   Taking the units for Power=Work/Time, and subst. in Joules, we end up 
with Joules/Second which is what we are after.
   1 HP = 746 Watts.
   HP = Mass*Accel*Distance/(Seconds*746)
Since we are dealing with power, all we need to do is add/subtract the 
relavent powers. Define "+" power as "stuff to make the car go" and "-" 
power as the "stuff that makes us not go as fast as we would really want".

Granted, I know there will be drag coeff., rolling resistance, frictions 
etc. adding to the negative power.  But I figure that wind resistance is 
the greater contributor to this at least above 35-40 mph.  Any comments 
out there on that one? 

Ok, so here goes, set up your little accelerometer/cpu.  I was thinking of
triggering off the lead weight of the rim (assuming only one was there)
that way I could get the distance.  Now here is a thought, measure the
change of velocity of the lead weight and we have acceleration...hmmmmm. 
Some aftermarket cruise controls place a magnet on the drive shaft, I
don't see why that can't be used, just use their sensor/magnet setup. 
First I'd take the vehicle up to, say, 100 mph, set it in neutral and
start logging data every .5-1 second.  This will give you the HP required,
"-", to maintain that speed.  Do this two times, once in the wind and once
with the wind and average them.  (Mayby a couple of times would be 
better).  BTW, doing this while a weather system is
coming in probably isn't the best idea either. Now do some time trials
with the vehicle in one gear.  I guess 2nd or 3rd and collect the data. 
Now, HPwheel(mph)=HPaccel(mph)-HPdecel(mph).  The HPdecel is gathered from
the first run from 100 -> 20 mph. Once we have the numbers and knowing 
the tranny/transaxle/rear axle ratios we can calc. the HP vs. RPM and thus 
torque vs. RPM.  HP=Torque*RPM/5150 (roughly).

Other thoughts, I don't know how automatics would react/work with this 
setup.  Don't spin your tires when you punch it (although the numbers 
would look GREAT!).  I don't know how much tires "grow" during highway 
speeds.  If you make any body changes, drag. coef could be looked at 
also.  Remember, the units above are in SI units not the good 'ol 
English units.  And most of all, don't get a ticket :).

Any comments/suggestions/laughter out there????

-- 

David /\/elson
D-Nelson at taiu.edu

	Disclaimer: The above thoughts/feelings do not necessarily represent 
		those of my employer nor my other personalities.

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