Linear RPM vs Time = ? Horsepower

[Sentient]

Linear RPM vs Time = ?? Horsepower

I have graphed some sampled data taken from a car on a level road, traveling its rpm range (from 2000rpm -> 8000rpm) under full acceleration, and the graph shows an almost linear change in rpm over time.

For the sake of example, let us assume RPM = time (secs) * 1000 as this is very similar to the graph i have.

I have not been able to convert this to Horsepower or Torque, although I have the suspicion that because the acceleration is constant, that the horsepower graph would be more curved upward at the high rpm to overcome wind drag. Am I correct in understanding that wind drag is not linear?

Could someone explain how I would graph the horsepower, both corrected and uncorrected for winddrag?

For the graph, please assume the vehicle weight is 1180kg, traveling on a level road at sea level, gear ratio of 2.05, and diff ratio of 3.421.

Thanks
Tony

 

[Sentient]

Opps - also, tyre circumference is 179cm

 

[berkeman]

Wind resistance is definitely nonlinear with velocity. I'm not much help beyond that on your questions, but here's a recent PF thread about dynomometers in case that helps. The Dynojet dynomometer technique uses full-throttle acceleration to measure horsepower and torque, but obviously there is no wind resistance in a dyno test.

https://www.physicsforums.com/showthread.php?t=117800

 

[Sentient]

Thanks berkeman - I have searched the forum and read that post before but unfortunately it did help me. I managed to plot wind resistance on a graph to see its effect, which was wonderful - but I'm still not sure how I would include the figures into a horsepower calculation.

 

[pervect]

As long as your tires don't slip, RPM should be proportional to velocity. However, the conversion factor will depend on what gear your car is in. If you shifted gears or have an automatic transmission, you'll have to account for this factor, otherwise not.

So it seems to me that the first thing you need to do is to convert your RPM figures into velocity figures.

The total work done in accelerating the car will be force*velocity, by definition. There will be several components to the force:

1) Drag forces, due to rolling friction and wind friction, and transmission inefficiencies, that you'll have to model somehow.

2) The force required to accelerate your car, f = ma

So the total force will be

f_total = (mass of car) * acceleration of car + drag force

and the total power will be

power = f_total * velocity

You can compute the acceleration by taking the derivative of the velocity of the car with respect to time. Some smoothing will probably be needed.

 

[Sentient]

Pervect - that is basically what I have been trying to do, but I always get the wrong results. I ignored the drag factor, but my understand is that I will get a lower energy and lower power value (which is fine for now) but I always seems to get a higher value than expected.

at 1 sec, the car is doing 1000rpm so,
velocity = 1000rpm * 60 / (2.05 * 3.421) * 1.79 / 1000 = 15.31kph
*60 to get revolutions per hour
/ (2.05 * 3.421) to get the wheel rph
* 1.79 to get the ground distance in metres
/ 1000 for kilometers

using a unit conversion, i get 15.31kph = 4.25277 meters/sec

by my thinking, since the starting rpm was 0, the starting velocity is 0 so acceleration = 4.25277m/s^2

The mass of the vehicle is 1180kg, so f_total = 5018 (not sure what the units are anymore)

and power now = 5018 * 4.25277 = 21340 (again, not sure of the units - maybe watts?). If its watts, this would give 28hp.

Does my math make sense, or did I go off on a wild tangent somewhere?

 

[Sentient]

I have calculated up to 8000 rpm using the same math as above, and noticed the same problem I've had all along.

1000rpm = 28.62hp
2000rpm = 57.24
3000rpm = 85.87
4000rpm = 114.49
5000rpm = 143.12
6000rpm = 171.74
7000rpm = 200.36
8000rpm = 228.99

I know that in reallife this vehicle produces ~160hp at 8000rpm, so these figures seem very skewed, especially since I am ignoring drag which will increase the figures even more.

What did I do wrong? :)

Thanks
Tony