# Calculating Power from Acceleration

• precisionpete
In summary: So, as Stan says, the car weighs 3307 lbs and it's weight is 3307 lbs. You have 1500 kg of mass. This means that if you apply a force of 1500 kgf (1500 * 9.8 Newtons) to one side of a scale, and the car on the other, the car will lift off the scale. The scale now reads 1 tonne. (for the benefit of those who prefer Imperial units, 1500 kgf is about 3307 lbs of force).On the other hand, your car also weighs 3307 lbs in Imperial units. That is, it exerts a force of 3307 lbs onto the ground. (
precisionpete
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?

Thanks

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.

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.

Thanks

Last edited:
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:
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.

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

precisionpete said:
I'm still not clear on why I didn't need to use the gravitational constant? ... a 1500kg car .
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.

## What is the formula for calculating power from acceleration?

The formula for calculating power from acceleration is power = mass x acceleration x velocity.

## How is power related to acceleration?

Power is directly proportional to acceleration. This means that as acceleration increases, power also increases.

## What are the units for power and acceleration?

The units for power are Watts (W) and the units for acceleration are meters per second squared (m/s^2).

## Can power be negative when calculating from acceleration?

Yes, power can be negative when calculating from acceleration. This occurs when the direction of the acceleration is opposite to the direction of the velocity.

## What are some real-life applications of calculating power from acceleration?

Calculating power from acceleration is used in various industries, such as automotive and sports. It is used to measure the performance of vehicles and athletes, as well as in designing efficient machinery and equipment. It also has applications in physics and engineering research.

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