# Does anyone know the formulas for determining power output?

#### jmocallaghan

##### New Member
I've watched a lot of people discuss power output, have a polar myself and use of a powertap. looking at the srm and the polar, mechanically they are very simple devices. does anyone here know the formulars to determine power output, specifically the polars?

has anyone tried to build a power meter yet on their own?

jmocallaghan said:
I've watched a lot of people discuss power output, have a polar myself and use of a powertap. looking at the srm and the polar, mechanically they are very simple devices. does anyone here know the formulars to determine power output, specifically the polars?

has anyone tried to build a power meter yet on their own?

For rotating machinery, Power = Torque x angular velocity

As measured at the cranks:
Power (watts) = Pedal Force (Newtons) x crank length (meters) x Cadence (rpm) x 2*pi/60

This assumes that the pedal force is the net force applied tangentially to the cranks, and that each leg applies force for one-half the circle.

The Polar meter measures chain tension as a way of determining the amount of torque being applied to the cranks.

11ring said:
Oh and cadence is RevsPerSec. nor RPM, so divide by 60 from your normal RPM measure.

jmocallaghan said:
I've watched a lot of people discuss power output, have a polar myself and use of a powertap. looking at the srm and the polar, mechanically they are very simple devices. does anyone here know the formulars to determine power output, specifically the polars?

The polar uses what is similar to an electric guitar pickup to determine the vibrating frequency of the chain, measures the speed of the chain through the derailler, and the cadence of the right crankarm.

jmocallaghan said:
I've watched a lot of people discuss power output, have a polar myself and use of a powertap. looking at the srm and the polar, mechanically they are very simple devices. does anyone here know the formulars to determine power output, specifically the polars?

has anyone tried to build a power meter yet on their own?
The Polar formulas can be found from the US Patent Office web pages. Search e.g. with "Polar" or "Power measurement device" or whatsoever until find the right patent application.

WarrenG said:
The polar uses what is similar to an electric guitar pickup to determine the vibrating frequency of the chain, measures the speed of the chain through the derailler, and the cadence of the right crankarm.
And you put this response and one from above together and you get the total answer. Power=torque*angular velocity. Torque is force times distance, so if you measure vibration, you can back out force and ultimately torque.

Interesting, thank you. If this is the case, and we know that most riders do not produce power across 50% of the revolution, how accurate is this formular?

frenchyge said:
For rotating machinery, Power = Torque x angular velocity

As measured at the cranks:
Power (watts) = Pedal Force (Newtons) x crank length (meters) x Cadence (rpm) x 2*pi/60

This assumes that the pedal force is the net force applied tangentially to the cranks, and that each leg applies force for one-half the circle.

The Polar meter measures chain tension as a way of determining the amount of torque being applied to the cranks.

jmocallaghan said:
Interesting, thank you. If this is the case, and we know that most riders do not produce power across 50% of the revolution, how accurate is this formular?
It's not really the formula that would induce inaccuracy, but rather the data collection methodology. All but the Polar collect data with strain gauges and I think the sampling frequency is ~72 per second for the PT. I'm not sure about the SRM and Ergomo. The PT averages these discrete observations over a 1.26 second duration. I think the question you are asking is whether this methodology induces error or bias, given a typical cadence of 70-110rpm.

jmocallaghan said:
Interesting, thank you. If this is the case, and we know that most riders do not produce power across 50% of the revolution, how accurate is this formular?
We know that? For people pedalling with both legs, I think there's at least some force being applied at most points of the circle.

Power meters tend to integrate the torque applied during the 1 or more crank revolutions, and then display the average power produced. That evens out the varying power produced at different points in the stroke.

It's not really the formula that would induce inaccuracy, but rather the data collection methodology. All but the Polar collect data with strain gauges and I think the sampling frequency is ~72 per second for the PT. I'm not sure about the SRM and Ergomo. The PT averages these discrete observations over a 1.26 second duration. I think the question you are asking is whether this methodology induces error or bias, given a typical cadence of 70-110rpm.
Just a little correction... It would be great if the PT did average over that period, but it doesn't. It just grabs a single value at the set recording frequency. This is why PT's are a bit sketchy when it comes to short power durations, and why there are 'magic' cadences. In practice this isn't really a problem, but does explain why many people can get 5sec powers significantly higher on a PT than any other PM =).

All the other power meters do average over their sampling interval.

Scott

scotmart said:
Just a little correction... It would be great if the PT did average over that period, but it doesn't. It just grabs a single value at the set recording frequency. This is why PT's are a bit sketchy when it comes to short power durations, and why there are 'magic' cadences. In practice this isn't really a problem, but does explain why many people can get 5sec powers significantly higher on a PT than any other PM =).

All the other power meters do average over their sampling interval.

Scott
I realize that the PT computer grabs every nth observation for recording frequencies other than 1.26s. But, I'm talking about the function of the strain gauges themselves. Are you saying that the strain gauges do not average ~90 discrete observations (72 x 1.26) within the hub? I would be very surprised at that.

I realize that the PT computer grabs every nth observation for recording frequencies other than 1.26s. But, I'm talking about the function of the strain gauges themselves. Are you saying that the strain gauges do not average ~90 discrete observations (72 x 1.26) within the hub? I would be very surprised at that.
Well, suprise!

No averaging, just current value at all recording intervals.

Scott

scotmart said:
In practice this isn't really a problem, but does explain why many people can get 5sec powers significantly higher on a PT than any other PM =).

A 5sec power number is an average over 5 seconds whether that consists of 5 samples or 100 samples, so even if the PT gets only one measurement for each 1.x seconds the average for 5s is still good, right? IME with a PT, I'm not seeing abnormal jumps (>~20-40 watts) from one 1.x second sample to the next at high power levels.

scotmart said:
Just a little correction... It would be great if the PT did average over that period, but it doesn't. It just grabs a single value at the set recording frequency. This is why PT's are a bit sketchy when it comes to short power durations, and why there are 'magic' cadences. In practice this isn't really a problem, but does explain why many people can get 5sec powers significantly higher on a PT than any other PM =).

All the other power meters do average over their sampling interval.

Scott

RapD is right that torque is averaged over 1.26 seconds and with the recording interval set at 1s (really 1.26s), there's no data discarded. Only longer recording intervals will discard data, but there's scarcely need for other recording intervals.

The reason PT has aliasing, or "magic" cadences as you put it, has nothing to do with the recording interval but with sampling interval. Regardless of what recording interval you set, the PT averages torque over 1.26s; that is, it is time-based instead of based on one crank revolution. Therefore, the sampling interval may contain, for example, two peaks in torque because of the variation over the pedal circle. The next sample will probably have two troughs and so on.

That's why PT data is a bit noisy, but over the long term the numbers are good.

scotmart said:
Well, suprise!

No averaging, just current value at all recording intervals.
Don't the strain guage meters (like the PT) integrate the electrical current passed through the strain guage circuit over the entire sampling period, and then report that total at the end of the sampling period? The electrical resistance of the strain guages varies with the torque being produced at any given instant. If what you're saying is true, then it should be possible synch up the PT so that the reporting is alway done at the deadspot. I'm pretty sure that'd be a noticeable problem.

I thought the 'magic cadence' phenomenon was due to the number of downstrokes that were being included in the sampling period (ie, some samples only include 2 downstrokes, but every e.g, 3rd sampling period will include 3 instead).

jws said:
The reason PT has aliasing, or "magic" cadences as you put it, has nothing to do with the recording interval but with sampling interval. Regardless of what recording interval you set, the PT averages torque over 1.26s; that is, it is time-based instead of based on one crank revolution. Therefore, the sampling interval may contain, for example, two peaks in torque because of the variation over the pedal circle. The next sample will probably have two troughs and so on..

This explanation certainly fits with PT's manual that says that cadences over 140 rpm's may not be measured correctly unless they're measured with the crank arm magnet and cadence sensor. Without the cadence sensor the PT is looking at peaks in the strain to determine when you're pushing _down_ on the pedals. Two peaks per sample would be confusing...

WarrenG said:
This explanation certainly fits with PT's manual that says that cadences over 140 rpm's may not be measured correctly unless they're measured with the crank arm magnet and cadence sensor. Without the cadence sensor the PT is looking at peaks in the strain to determine when you're pushing _down_ on the pedals. Two peaks per sample would be confusing...
It typically sees at least 2 peaks per sample (one from each leg), but at very high cadences the peaks and valleys would be very closely timed, and pretty non-distinct (ie, more circular force application).

But, this certainly supports the idea that the PT is looking at torque over the entire sampling period, and not just picking the instantaneous value at report time. Otherwise, it would never know when the peaks and valleys occurred.

frenchyge said:
It typically sees at least 2 peaks per sample (one from each leg), but at very high cadences the peaks and valleys would be very closely timed, and pretty non-distinct (ie, more circular force application).

But, this certainly supports the idea that the PT is looking at torque over the entire sampling period, and not just picking the instantaneous value at report time. Otherwise, it would never know when the peaks and valleys occurred.

Yes, and might miss some peaks and valley.

I do some standing starts at high torque and if the sample was based on one instant every 1.2x seconds it could miss some downstrokes and I'd be seeing jumpy torque readings in the file, but I don't.

And why would it take 72 samples every 1.2 seconds but only use one sample instead of averaging many (all 72?) samples before sending that average to be saved in memory? -Simple for a microprocessor to do.

I think the sampling frequency is ~72 per second for the PT.

i'm fairly confident it's 60 x's per second.

ric

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