# Mass + time + acceleration => watts

1. Nov 5, 2009

### andpe

Hello, this is my first real post here =)

I'm working on an in-car-accelerometer that I want to display
Torque, Horsepower and more..
I can do all the calculations when I calculate power, but here is the thing :

Power(w) from acceleration(in m/s^2) im not sure about.

I plan to sample data from the accelerometer about four times per sec and calculate speed, distance and power from every sample.

P = Fm

Would it then be correct if I say :

power(w) =weight*acceleration*(previous speed+(acceleration*(time-previous time) ??

lets say that my accelerometer tells me that the acceleration at this moment
is 5,77 m/s^2, and that time since last reading is 0,222 seconds - given a weight of the car at 1500 kilograms, and that last recorded speed was v0 = 0 :

power(w) = 1500 * 5,77 * (0 + (5,77 * 0,222) = 11086,5watts

The power the eqation above gives me, (is this correct btw?) is this the average power over the last 0,222 seconds?

Can I then add all the samplevalues for power to get the total power? If yes, then I plan to display the value that has the largest value.

Anyone? I'm I on the right track here?

Thanks

Andreas from Norway

2. Nov 5, 2009

### Bob S

Andreas-
Force times distance = work
Force times distance over time = Force times velocity = power

F dx = joules

F dx/dt = F v = m a v = joules/second = watts

Bob S

Last edited: Nov 5, 2009
3. Nov 5, 2009

### andpe

Ok, so what youre saying is?

power = force * velocity
force = mass * acceleration ?? 1500kg * 5,77 m/s^2 = kg m / s^2
velocity = v0 + (at) ?? 0 + (5,77m/s^2 * 0,222s) = 0 m/s + 1,28m/s = 1,28 m/s (hmm?)
power(watts) = 8655 kg m/ s^2 * 1,28 m/s = 11078 kg m^2 / s^3

Or what? am I doing it wrong?

What equation for power would you use, Knowing the variables time between samples, speed, and acceleration at this time?

Thanks

Andreas

Last edited: Nov 5, 2009
4. Nov 5, 2009

### diazona

Yep, that calculation looks fine to me.
$$\langle P \rangle \approx m a^2 \Delta t$$

Of course, to find the "true" power exerted you would have to have continuous acceleration data, which is impossible - in reality, as you know, you can only sample the acceleration at finite intervals (like every 0.222 seconds in your example). So the true average power over each 0.222 second interval may be slightly more or less than the value you will calculate. If you add up the powers from a whole bunch of these intervals, then all the discrepancies add up, and sometimes that makes your total power pretty far off.

If you'd like to learn more about how you can do a more accurate calculation, do some research into the field of numerical integration. There are a lot of resources out there that can get you started; the book Numerical Recipes is a classic. For reference, if I remember my names right, what you described in your post is called the Euler method, and the best general-purpose method (which you may want to look into) is the Runge-Kutta method.