accelerometer based dyno ideas

[Orin Eman]

> At 11:07 AM 1/28/99 -0800, Orin Eman wrote:

> >> At 08:24 AM 1/28/99 -0500, Dan Llewellyn2 wrote:
> >
> >> >you can get up to speed are rare.  If they incorporated the data
> >> >from a G-field measuring device, like an Analog Digital ADXL05,
> >
> >Yes, but you still need the speed input since the accelerometer
> >cannot tell the difference between acceleration and gravity...

> Yeah, sort of. There are a lot of intermediate levels depending on
> how many simplifying assumptions you make. If you require the road
> to be flat (not necessarily level) and suspension travel to be
> effectively nil, you can subtract out the known constant 1g gravity
> vector. (This assumes a 2-axis accelerometer, which the adxl202 is.)

Sure, assuming a flat level road etc., you only need one axis.
With an additional axis, vertical thru the car (a_p), you can measure
the angle of the car to the horizontal - it's cos-1(a_p/g)
The the force required to overcome gravity is m* g * sin(angle to horizontal).
The total force produced by the car is now the above plus
m * measured acceleration.

All in one - power is:

m * v * (forward accel + g * sin(cos-1(vertical accel/g)))

That's messy, so I looked at the vector diagram instead and found
you can replace the g * sin/cos-1 mess with square_root(g*g - a_p*a_p)

> If you try to solve the more realistic problem, and allow nonflat
> roads and suspension travel, it gets trickier. For my own amusement
> I've tried to see how much of that you could reliably factor out,
> but haven't gotten too far.

I'll think about that one later, though my guess is the above
correction gets most of it... if your sensors are at the center
of gravity of the car that is.

Actually, the inclination of roads changes fairly slowly,
so you could filter out most of the suspension movement
on the 'vertical' sensor and just get a reading of the
angle to horizontal.

> >As far as the horsepower calculation is concerned, you would
> >use the acceleration from the accelerometer and the speed from
> >another sensor...

> If you have the speed, from RPM, VSS or whatever, I guess you could
> use that info in combination with the accelerometer info to
> compensate for nonlevel (and perhaps nonflat?) roads. I haven't
> really thought about this yet.

> In any case you still need mass plugged in as a given, right?
> To get horsepower rather than acceleration I mean.

You always need mass... the formula is m * v * a 
mass times velocity times acceleration.

It comes from force * distance / time.  Distance / time is speed.
Force from mass * acceleration.  All is fine if all the force
is used accelerating the car.  If some is used to overcome the
effect of gravity, that's when we get inaccurate.

> >> One thing I was gonna mention is the Analog Devices ADXL202, a
> >> second generation, 2 axis +/- 5g accelerometer. It's even easier
> >
> >I looked at it when it first came out and the specs didn't look
> >very good to me.  It's bad enough getting .01g resolution out
> >of an ADXL05 with any reasonable bandwith and the 202 looked worse
> >to me.

> I agree that getting a high resolution*bandwidth product out of the
> xl05 is not easy, but I don't see how it's any worse for the xl202.
> The noise spec is exactly the same for both parts. Maybe if you needed
> to use the PWM output on the xl202 that would make it tougher, but
> the raw analog signal is easily available too.  I'm not trying to
> irritate anyone here, maybe there's just something I'm missing?

I looked at the PWM signal and couldn't see any reason to use
it over the ADXL05 with some filtering and a 10 bit AtoD.
I didn't look at the analog output specs for the '02.
The '05 output is d*mn noisy looking at the signal on the scope though!

I must admit that the Analog packaging options always seem
to put the part I want in the most irritating package - the
ADXL05 in the silly can and the AD597 either $15 in ceramic dip
or $4 in surface mount.  I solder surface mount for that difference!

Orin.