Power Output Calculation from Force Curve

[eng]

Does anyone know how the PM5 monitor calculates power output for each stroke. In particular, does it take into account the rest phase of each stroke?

In other words take the example of two athletes: A & B. Both have identical force curves for their respective strokes, however rower B has a lower duty cycle - or has a very long rest phase between strokes. Will the PM5 calculate a lower "power output" per stroke for athlete B?

Thanks.

[sander]

Does anyone know how the PM5 monitor calculates power output for each stroke. In particular, does it take into account the rest phase of each stroke?

In other words take the example of two athletes: A & B. Both have identical force curves for their respective strokes, however rower B has a lower duty cycle - or has a very long rest phase between strokes. Will the PM5 calculate a lower "power output" per stroke for athlete B?

Thanks.

I have no insight in the inner workings of the PM, but here is what I understand from reading about the C2 on the web. Measuring acceleration and deceleration of the flywheel, the PM calculates the drag factor. Using the drag factor combined with the flywheel mass/rotational inertia, the PM calculates the energy transferred (work) to the flywheel through the chain on each stroke. Average power during the stroke is then simply the Work done to the flywheel divided by the total duration of the stroke. By the way, there is no need to use the "force curve" for that, as the energy delivered can be calculated simply from the angular velocity at the catch and the angular velocity at the finish.

The PM only registers work delivered to the flywheel through the chain.

Identical force curves at different duty cycles are an ideal that cannot be achieved in reality. The flywheel dynamics will result in different rotational velocity of the flywheel at the catch, so the stroke will be "heavier". Think about the first stroke you take from a standing start. At the same stroke length, the duration of that stroke is different then when you have the flywheel going.

[jamesg]

The C2 is an ergometer: a device that measures Work.

Power as shown by the PM at the end of each stroke, is the overall Work done by the brake fan divided by the time of the complete stroke, recovery included.

Flywheel Work is seen from release to catch, the speed loss of the flywheel and its inertia; adding the estimated Work done by the fan during the pull, catch to release.

This system is made possible by the recovery phase, when we do no work but the flywheel does, and its behavior can be observed.

[Carl Watts]

Concept 2 have kindly done all the hard work for you and know how much power is required for the flywheel through the range of rpms and it automatically factors in the drag factor by looking at the rate of flywheel deceleation. Its some complex math that we don't need to worry about including the mass of the flywheel and rotational inertia etc that make the Concept 2 monitor unique as it self calibrates so you result is directly comparable to someone elses on another Concept 2 rower.

The power on the monitor will be average power or Watts which is quite different from the peak power that goes in during the drive. Dropping the rating or spm has a huge effect on the power required during the stroke to maintain a given pace. The power on the monitor will be the average power per stroke that includes the recovery.

Simplified if the force curve looked like a square wave with a flat top at 20 spm that was a 1 sec drive and a 2 second recovery at 2:00.5 pace, that's 200W on the monitor so your drive would be a total of 600W to average out to 200W because for 2 seconds during the recovery there is no power going into the flywheel. From this you can see that dropping the rating requires considerably more power during the drive to maintain a set pace.

By my logic 2:00.5 pace is somewhere near 600W average during the drive at 20spm but I have always welcomed Concept 2 to jump in here and clarify my simplified explanation. Because the human body doesn't produce an ideal force curve, the peak power during the drive could be 800W that averages out by calculating the area under the force curve to 600W.

[jamesg]

To first approximation, the force curve is a half sine wave, so multiplying the average power by the total/pull time ratio and by 1.4 gives the peak power. This can reach almost 6 times the average at rate 20. The power calculation is just basic engineering: Work delivered to the flywheel equals Work done on the atmosphere, which is speed difference x inertia x total/recovery time.

If an oarsman pulls 100 kg at peak handle speed 2m/s, his peak power at that moment is 100 x g x 2 = 2000 Nm/s: 2kW, almost 3 hp.

[eng]

Thank you for the detailed and informative responses. I now understand the mechanism by which the C2 calculates work done. It seems that the consensus is that Watts(average) is calculated by total Work (joules) divided by total period (stroke period + recovery period) - or perhaps to be more precise I should say total period is recovery period + stroke period since the Average Watts is updated at the end of each stroke phase.

[Carl Watts]

You have pretty much got it.

As above if the force curve was half sinewave your peak power is 1.4 of say 600W average which is 840W peak. The ideal force curve would be as flat as possible and building to maximum power as soon as possible with that maximum sustained, which is a square wave.

The monitor produces a nice "Picture" or graph of your power to help with your technique, the maths is calculating the area under the graph to give you an actual number in Watts.

[c2jonw]

Here's a reference I frequently give out to this sort of question:
http://eodg.atm.ox.ac.uk/user/dudhia/ro ... sics.html/
Enjoy! C2JonW