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Calculating Power from Acceleration

  1. Dec 22, 2011 #1
    I am designing a dynamometer app for a phone and am having trouble with the math.

    The goal is to measure acceleration with the built-in accelerometer then calculate velocity, position, horsepower, etc. It's mostly working but I think I am messing up the units. I get plausible values for velocity and position. But power does not look right. I am filtering the acceleration to remove noise.

    I need instantaneous values so they can be plotted over time.

    I'm using...

    accelerationG[n] = measured (Gs)
    accelerationMss[n] = accelerationG[n]*9.8 ... in m/s^2
    dt = sample time in s

    I am numerically integrating values for...
    velocity[n] = velocity[n-1] + (accelerationMss[n-1] + (accelerationMss[n] - accelerationMss[n-1])/2)*dt;
    position[n] = position[n-1] + (velocity[n-1] + (velocity[n] - velocity[n-1])/2)*dt;

    weight = 1500 ... kg
    mass = weight/9.8 .. kg
    force = mass*accelerationMss[n]
    power = force*velocity[n] ... should be in KW?

    In a simulation, I get plausible values for velocity and position but the power number seems very very large. I suspect I am messing up the units.

    Can anyone please point out where?

  2. jcsd
  3. Dec 22, 2011 #2
    Welcome to PF.

    Yes, when you have acceleration instrumentation, you can figure out all kinds of usefull parameters.

    Your power is basically as you have shown:

    Power = mass X acceleration X velocity

    Lets plug in some reasonable numbers:

    Power = 1500 kg X (9.8/2) m / s^2 X 18 m/s = 1.32 X 10^5 watt = 132 kW = 177 horsepower.

    I have assumed the measured accleration of the car is g / 2 which is reasonable for today's cars.

    You can see your units are kg-m^2 / s^3 which equals watts.
  4. Dec 22, 2011 #3
    Okay... so it was almost working. I think I was converting weight to mass when I should have left it alone as kg.

    Now I need to figure out and subtract aerodynamic drag etc.

    Maybe I should go dig in the basement for an old physics textbook.

    Last edited: Dec 22, 2011
  5. Dec 22, 2011 #4
    Through some work with horsepower I came to the conclusion at 100% efficiency 32 hp will lift or accelerate 555 pounds at one G, since one HP is defined as lifting 555 pounds one foot in one second, That seems to me to be 1/32 g of acceleration, say in space and one g is defined as 32 feet per second squared.

    It seemed to me to require 32 hp to keep accelerating that 555 pounds at 32 feet per second squared, say, in space. Using those figures I come up with a HP rating of 138 hp, since you are accelerating 1500 Kg(2400 pounds) at one g, with is about 4.34 to one ratio compared with 555 pounds, that works out to 138 hp(4.3 times 32=138) in this system. What do you think of that line of reasoning?

    In space, wouldn't the amount of power be the same to go from say 1 meter per second to 100 meters per second as from 101 meters per second to 200 meters per second, eliminating the velocity factor?
    Last edited: Dec 22, 2011
  6. Dec 22, 2011 #5
    I'm still not clear on why I didn't need to use the gravitational constant? i.e. a 1500kg car should have a mass of 1500/9.8 = 153kg. Or is the mass actually 1500kg and the weight is 1500*9.8 Fg. I guess I am also confused between weight and mass.
  7. Dec 22, 2011 #6


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    Homework Helper

    1 horsepower is usually defined equal to 550 lb ft / sec (not 555).

    The cars mass is 1500 kg, and it weighs 1500 kg * 9.8 newtons/kg = 14700 newtons. In english units, the cars mass is 102.8 slugs and it weighs 102.8 slugs * 32.174 lbs / slug = 3307 lbs.
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