Estimating Torque from Power over Time

[Zipper]

I am looking at electric motor performance data for a vehicle motor with a torque limited output that is unknown. The performance of the motor is shown below. The vehicle weighs 2150kg. Is there a way to estimate the torque from the power over time?

I know how to calculate torque at any given time from power and velocity. This result is suspect, likely because the velocity data is rounded integer data and not as accurate.

But intuitively I believe that the torque could be calculated from the change in power over time. Something like change in kinetic energy = average power * time.

Any advice? I have read through several related torque threads here, mostly concerning calculating torque from one point of power and velocity.

Time Speed (mph) Distance (ft) Power
sec mph ft kW
0.00 0 0.0 48
0.25 6 0.0 109
0.50 11 4.6 196
0.75 18 13.7 250
1.00 23 18.3 342
1.25 30 27.4 401
1.50 34 58.5 489
1.75 41 67.9 528

 

[russ_watters]

Do you know the equation relating torque and power? Can you relate speed to it using the physical properties of your device (which you have not provided...)?

 

[Zipper]

The formula I know is Torque = Power / Angular Speed

which in this case for the second sample of 6 mph and 109 kW I believe to be

(109*1000)/((63360*6*9.73)/(60*86.9)*2*PI()/60) or 1467 Nm

where 63360 is inches per mile, 9.73 is the fixed gear ratio, 60 converts hours to minutes and 86.9 is the tire circumference in inches.

But I suspect that this 1467 Nm number overestimates the actual torque because of errors in recorded velocity. I suspect that the final entry of 41 mph and 528 kW which gives 1040 Nm is closer to the actual torque, but that the torque is actually constant for this range and the error in velocity can be worked around by instead using the change in power over time. But I don't know how to do that.