# Calculating net power of a RC car?

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Hi,

could anyone explain to me how to calculate the net wheel-power of a radio-controlled car, when I know the following things:

- Acceleration between a few different distance points, graph as a curve (time taken between the different points)

- weight of rc car

- maximum speed

Any suggestions?

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Hi,

could anyone explain to me how to calculate the net wheel-power of a radio-controlled car, when I know the following things:

- Acceleration between a few different distance points, graph as a curve (time taken between the different points)

- weight of rc car

- maximum speed

Any suggestions?

I'm not really sure what you mean by the net wheel-power. So for now, I'll simply assume that you want to calculate the maximum power of the car. If that's the case, then perhaps one way of doing this would be to design an experiment, where you accelerate the car from rest to the maximum speed as fast as possible. Then the energy that the car uses is simply the change in the kinetic energy, which is 1/2mv^2 (where 'm' is the mass of the car, & 'v' is the maximum speed). Take that energy and divide it by the time it takes, and you'll get the maximum power.

I doubt that this is what you really ask though, since it looks so simple. Perhaps you want to elaborate a bit on what you mean exactly by the net wheel-power?

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Hi,

could anyone explain to me how to calculate the net wheel-power of a radio-controlled car, when I know the following things:

- Acceleration between a few different distance points, graph as a curve (time taken between the different points)

- weight of rc car

- maximum speed

Any suggestions?

I'm not really sure what you mean by the net wheel-power. So for now, I'll simply assume that you want to calculate the maximum power of the car. If that's the case, then perhaps one way of doing this would be to design an experiment, where you accelerate the car from rest to the maximum speed as fast as possible. Then the energy that the car uses is simply the change in the kinetic energy, which is 1/2mv^2 (where 'm' is the mass of the car, & 'v' is the maximum speed). Take that energy and divide it by the time it takes, and you'll get the maximum power.

I doubt that this is what you really ask though, since it looks so simple. Perhaps you want to elaborate a bit on what you mean exactly by the net wheel-power?

By net wheel-power I am meaning the power that is used to move the car forward

The maximum power would be the power produced by the engine excluding frictional force in drivetrain, but I am interested in the power pulling the car forwards.

But if I calculate the maximum kinetic energy and then divide it by the time it takes, will that not just give me an average?

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Maximum power may not necessarily refer to engine power only.Without knowing the characteristics of the engine and transmission efficiencies all you can obtain is maximum power of a vehicle, i.e. force to overcome all resistive forces outside a car at maximum speed. This is because the engine will produce various power outputs at various engine speeds and there is no fixed value of net power, but rather a graph of power at any given instant. Also, especially when something so light is starting from rest, the power comming to the wheels will be higher than what we might see from acceleration of a car because of slipping. So the easiest thing to do is calculate maximum power of the vehicle (not the engine), and what Vioh wrote is the best way to find it.

Edit: I edited the "within a car" part out as it was falsr, I was too hasty in typing to think what I was doing.

Edited by Slovakov

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Maximum power may not necessarily refer to engine power only.Without knowing the characteristics of the engine and transmission efficiencies all you can obtain is maximum power of a vehicle, i.e. force to overcome all resistive forces (within and outside a car) at maximum speed. This is because the engine will produce various power outputs at various engine speeds and there is no fixed value of net power, but rather a graph of power at any given instant. Also, especially when something so light is starting from rest, the power comming to the wheels will be higher than what we might see from acceleration of a car because of slipping. So the easiest thing to do is calculate maximum power of the vehicle (not the engine), and what Vioh wrote is the best way to find it.

I now that the power I will measure is not the potential max power by the engine, due to resistive forces just like you mentioned. But what I was going to do was to use P = IV to get potential max power of the car, and then measure practical maximum power and try to estimate the size of the sum of the total resistive forces.

I had a plan, which was to set up a distance, lets say 20m, then I would measure the acceleration between for example every 2 meters, so I could graph a acceleration - time graph.

Then I would somehow calculate the power used to move the car from the accelerations measured and compare it with the theoretical power produced by the engine (excluding the resisitive forces), the difference would then be the sum of all the resisitive forces acting on the car.

Would this work/be a good idea? I had btw planned to measure the acceleration between the points using a video-camera and analyse the tape to get a accurate estimate of the time

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Your main concept sounds nice - the comparison of electrical power of the engine and tractive power seems like a good idea. But calculating it from the graph of acceleration vs time would be somewhat tricky - from this graph you could obtain the tractive force at any instant, and in order to find power at this instant, you would also need speed at the same time. (since at an instant $P=F*v$ ). Or otherwise, you could have a graph of acceleration vs distance $x$ covered by a car. Then obtain graph of force by multiplying the results of acceleration by $m$, and then you can find the total work done by the car by integrating over $dx$. Then power over this distance is this integral divided by time of acceleration. (well, it should be a derivative over time, but let's not be too precise.. or actually, we should be this precise .). In any case though you need quite a lot of data and some work to process it in a proper way.

And again, power will not be constant over the entire time of acceleration; in fact it may not even be linear, this will depend on the kind of motor used. And you will not know whether the power you've measured over 20m is maximum power for the vehicle unless you find the power characteristics of motor you used, or you're sure the car reached its top speed on this distance

Therefore using Vioh's experiment would still be the best way to find tractive power, which is what you are looking for (assuming no slipping). Then comparing these results to theoretical power of the motor will tell combined motor and transmission efficiency. This way all you need to know it the top speed of a car and time to reach it... which seems a bit easier to do.

Edited by Slovakov

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Your main concept sounds nice - the comparison of electrical power of the engine and tractive power seems like a good idea. But calculating it from the graph of acceleration vs time would be somewhat tricky - from this graph you could obtain the tractive force at any instant, and in order to find power at this instant, you would also need speed at the same time. (since at an instant $P=F*v$ ). Or otherwise, you could have a graph of acceleration vs distance $x$ covered by a car. Then obtain graph of force by multiplying the results of acceleration by $m$, and then you can find the total work done by the car by integrating over $dx$. Then power over this distance is this integral divided by time of acceleration. (well, it should be a derivative over time, but let's not be too precise.. or actually, we should be this precise .). In any case though you need quite a lot of data and some work to process it in a proper way.

And again, power will not be constant over the entire time of acceleration; in fact it may not even be linear, this will depend on the kind of motor used. And you will not know whether the power you've measured over 20m is maximum power for the vehicle unless you find the power characteristics of motor you used, or you're sure the car reached its top speed on this distance

Therefore using Vioh's experiment would still be the best way to find tractive power, which is what you are looking for (assuming no slipping). Then comparing these results to theoretical power of the motor will tell combined motor and transmission efficiency. This way all you need to know it the top speed of a car and time to reach it... which seems a bit easier to do.

So If I then have a acceleration - distance graph, probably not linear, can I then somehow calculate the horsepower at a specific instant where the gradient of the tangent is the steepest, ie the acceleration at that instant is largest.

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So I assume you've already done the experiment and only need help on data processing? Well then... looking for the simplest solution

As I said, to obtain power from acceleration, you first need to turn it into force (just multiply by mass of a car). What you can do next is:

a) If you have measured both speed and acceleration at your measurement points (or you can obtain speed from acceleration vs time graph), you can put the force and speed in a table or plot them and find the highest value of $F*v$. This will be your maximum power for the measurement period. (remember this will only mean max tractive power when the car has reached its top speed). Or...

b) If you only measured acceleration, but know the distances at which you've taken your measurements, plot force against this distance. The integral i.e. area under graph is the total work done by a car to cover the distance. In fact this is the same as change in kinetic energy. And here again there are 2 options:

- if you've calculated the indefinite integral and now have a function in terms of distance, it would be good to express it in terms of time. Then you can find the steepest point on this new curve and this gradient will be your maximum power....

- or if you've plainly got your area under graph, just divide it by the total time. This result won't be as precise in real world, but I guess it should be enough for the IA and I'd personally pick this one. (again in case b) just as a) this will only show max tractive power of a car if it's reached top speed).

I know it all sounds complicated but honestly, I can't see any simpler way to do this with the data you have (there's also a way using momentum but it's similar to what's above) . The gradient of acceleration itself - be it relative to distance or time - won't show you power at all, not to mention maximum power. And highest rate of acceleration doesn't mean highest power output of the car, but highest output relative to resistive forces. In reality this means that the highest rate of acceleration (steepest tangent) will be somewhere below the middle of the speed range - when air drag is still low but when rolling resistance isn't too significant anymore. But the car will still have a lot of spare power at this moment.

If it's still unclear, drop me a PM and I'll try to put it in more mathematical language, so it probably will make more sense then.

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