Average Power vs. RMS Power

I'm late to the geek party, but this is a neat debate, so I thought I'd jump in 😄.

Ken, I don't think Bruce is talking about taking an RMS mean of power, but of taking an RMS mean of torque and velocity, just as in electronics you do an arithmetic mean of power but an RMS mean of voltage and current.

I think he's onto something, but RMS isn't the answer. More from the wikipedia article:

Quoted post said:

However it is important to stress that this is based on the assumption that voltage and current are proportional (that is the load is resistive) and is not true in the general case

In a mechanical context, RMS would only be applicable if torque and velocity were proportional, but as frenchyge established, they aren't due to inertia.

However, I think the real point is that, if I understand how an SRM calculates power, Bruce's point demonstrates that the SRM is doing it wrong. If it really does average torque x average velocity for one revolution, then there will be an error when pedal velocity varies over the revolution. A small error, but an error nonetheless. If the higher velocities come where torque is higher than average, then it will be underreporting power. If the higher velocities come where torque is lower, it would be overreporting. If velocity happens to be just out of synch enough with torque, then it might get lucky and the errors would cancel out. But I can't see any reason for that to be the case.

I would assume that pedal velocity would vary most when inertia is low and resistance high -- like on a trainer or a steep hill. So maybe Bruce's original thought is right, that the apparent difficulty of trainer sessions has to do with instrumentation.

ahaile said:

I'm late to the geek party, but this is a neat debate, so I thought I'd jump in 😄.

Ken, I don't think Bruce is talking about taking an RMS mean of power, but of taking an RMS mean of torque and velocity, just as in electronics you do an arithmetic mean of power but an RMS mean of voltage and current.

I think he's onto something, but RMS isn't the answer. More from the wikipedia article:

In a mechanical context, RMS would only be applicable if torque and velocity were proportional, but as frenchyge established, they aren't due to inertia.

However, I think the real point is that, if I understand how an SRM calculates power, Bruce's point demonstrates that the SRM is doing it wrong. If it really does average torque x average velocity for one revolution, then there will be an error when pedal velocity varies over the revolution. A small error, but an error nonetheless. If the higher velocities come where torque is higher than average, then it will be underreporting power. If the higher velocities come where torque is lower, it would be overreporting. If velocity happens to be just out of synch enough with torque, then it might get lucky and the errors would cancel out. But I can't see any reason for that to be the case.

I would assume that pedal velocity would vary most when inertia is low and resistance high -- like on a trainer or a steep hill. So maybe Bruce's original thought is right, that the apparent difficulty of trainer sessions has to do with instrumentation.

Welcome - my previous sherpa has told me I'm on my own here 😉 so any newcomers are most welcome!!

Your last paragraph interests me, because on a steep hill, inertia is also low. So the damping effect of the riders mass is low - hence the dead spots in the rotation would be more pronounced. Although, having said that, the body adjusts it's behaviour when on a steep climb - on my computrainer I get better spinscan results when grinding on a steep climb than when spinning fast - i.e. my power curve becomes more circular. I am conscious that I start pulling up on the pedals in this situation.

I guess the best way to test this would be to get the comms protocol between the measuring device (I have a PT and an Ergomo) and write a PC application that calculates the torque average using RMS and test this out.

I must really be bored - one week off the bike with sinusitus and I'm dreaming up these things!! :o

ahaile said:

Ken, I don't think Bruce is talking about taking an RMS mean of power, but of taking an RMS mean of torque and velocity, just as in electronics you do an arithmetic mean of power but an RMS mean of voltage and current.

I see your point. That I wasn't clear myself.

Quoted post said:

However, I think the real point is that, if I understand how an SRM calculates power, Bruce's point demonstrates that the SRM is doing it wrong. If it really does average torque x average velocity for one revolution, then there will be an error when pedal velocity varies over the revolution.

If it really does average torque and angular velocity over one revolution by taking arithmetic means, then calculate "average" power by multiplying them, I would agree that it is an incorrect algorithm.

But if it samples torque and angular velocity, multiply them to get power, then averages the power values over one revolution (or one second in case of PowerTap), there's nothing wrong about it.

I was always under impression that the latter was the case because the latter is easier and requires less computing power than the former (less semiconductor, less memory, less program steps, less execution time), not to mention the former is utterly incorrect.

Quoted post said:

I would assume that pedal velocity would vary most when inertia is low and resistance high -- like on a trainer or a steep hill. So maybe Bruce's original thought is right, that the apparent difficulty of trainer sessions has to do with instrumentation.

I've never argued (well, disccussed 😉) about apparent difference in PE between road and trainer. I just thought (and still think) application of RMS concept should be unnecessary if PM designers have done it right in the first place.

Ken

Okay Ken - see your point - you are saying the PM should sample instantaneous power many times per revolution (say 70 times) by sampling instantaneous torque and velocity and multiplying the two. Then the 70 instantaneous power samples should be averaged.

Maybe that is the way it is done but I don't think so - the reason why I don't think so it that the powertap gives you the option to use a cadence sensor, or to derive cadence from the hub - they say that using a cadence sensor is more accurate - which is sampled only once per second.

Bruce Diesel said:

Maybe that is the way it is done but I don't think so - the reason why I don't think so it that the powertap gives you the option to use a cadence sensor, or to derive cadence from the hub - they say that using a cadence sensor is more accurate - which is sampled only once per second.

I'm sorry but I fail to see the connection between the two ways PT senses cadence and the algorithm to calculate 1sec average power...

Anyway, I sent email asking this very question to Saris customer service so hopefully we won't have to speculate much longer.

Cheers,

Ken

sugaken said:

I'm sorry but I fail to see the connection between the two ways PT senses cadence and the algorithm to calculate 1sec average power...

Anyway, I sent email asking this very question to Saris customer service so hopefully we won't have to speculate much longer.

Cheers,

Ken

Well, if the most accurate way to get cadence is from the cadence sensor, then cadence (and hence rotational velocity) is being sampled only once per revolution. This value would have to be used when multplying with each torque sample to get instantaneous power.

Will be good to hear what the Saris guys say.

Bruce Diesel said:

Well, if the most accurate way to get cadence is from the cadence sensor, then cadence (and hence rotational velocity) is being sampled only once per revolution. This value would have to be used when multplying with each torque sample to get instantaneous power.

Will be good to hear what the Saris guys say.

Cadence doesn't enter into the PowerTap's calculation of power, which is based on torque and angular velocity measured at the hub.

acoggan said:

Cadence doesn't enter into the PowerTap's calculation of power, which is based on torque and angular velocity measured at the hub.

Okay, so each data sample received contains torque and angular velocity, which are multiplied to get instantaneous power approx 70 times per second. These 70 or so instantaneous power samples are then averaged to give an approximately per second power reading?

If that is the case then my belief is that this is the correct way to do it - but then I'm sure the engineers at Saris would already know that 😎

Bruce Diesel said:

Okay Ken - see your point - you are saying the PM should sample instantaneous power many times per revolution (say 70 times) by sampling instantaneous torque and velocity and multiplying the two. Then the 70 instantaneous power samples should be averaged.

Great discussion guys. A lot of this has been discussed on Topica in the past although using RMS to calculate power is a new one.

Both SRM and PT assume a constant angular velocity for a complete revolution of the crank or hub respectively. This does lead to errors in the computation of the power but normally the error is small. In some cases (like using oval rings) the magnitude is thought to be significant.

The only way to fix this would be to add a high data rate crank or hub position sensor which would add cost and complexity to the system. If I were building a powermeter, that's how I'd do it.

Back to the RMS thing. I'm finding this kind of interesting. I too am an EE about 12 years out of school and haven't thought about that in ages.

In an AC power calculation, the V in the P=VI calculation is in fact Vrms (actually there is a power factor term in there too but I'm not sure how that applies here). How that applies to human power I'm not sure but it is interesting.

beerco said:

Both SRM and PT assume a constant angular velocity for a complete revolution of the crank or hub respectively. This does lead to errors in the computation of the power but normally the error is small. In some cases (like using oval rings) the magnitude is thought to be significant.

Hmmmn, our resident doc feels otherwise.

beerco said:

The only way to fix this would be to add a high data rate crank or hub position sensor which would add cost and complexity to the system. If I were building a powermeter, that's how I'd do it.

The way the ergomo calculcates torque using two perforated disks on either side of the bb axle, then shining an LED through the perforated disks. As the axle twists, so the phase difference between the two square waves changes - hence they are able to calculate torque. But inherent in that is the angular velocity which can be calculated from the period of the square wave. They'd be able to do it.

beerco said:

Back to the RMS thing. I'm finding this kind of interesting. I too am an EE about 12 years out of school and haven't thought about that in ages.

Hurts a bit doesn't it 😉

beerco said:

In an AC power calculation, the V in the P=VI calculation is in fact Vrms (actually there is a power factor term in there too but I'm not sure how that applies here). How that applies to human power I'm not sure but it is interesting.

Yup, that's what got me thinking (which is now hurting even more)

Bruce Diesel said:

Hmmmn, our resident doc feels otherwise.

Well, actually our resident doc (if you mean Andy 😉) doesn't say anything about resolution of angular velocity sensor. That is, how often angular velocity is updated on the hub or the crank.

I'll have to bug whoever gets back to me from Saris on this.

beerco said:

In an AC power calculation, the V in the P=VI calculation is in fact Vrms (actually there is a power factor term in there too but I'm not sure how that applies here). How that applies to human power I'm not sure but it is interesting.

There's your answer Bruce. If you bring the power factor back into the equation to account for the additional imaginary power that some people are expending while riding on the trainer, then that resolves all the perceptions and anecdotes. QED. 😄

The PT senses angular velocity using a reed switch in the hub and a magnet housed in the receiver unit (ie, 1x per wheel rev).

As your original sherpa, I'm not gone now, just lost. 😄

sugaken said:

Well, actually our resident doc (if you mean Andy 😉) doesn't say anything about resolution of angular velocity sensor. That is, how often angular velocity is updated on the hub or the crank.

I'll have to bug whoever gets back to me from Saris on this.

I might have misinterpreted his statement:

acoggan said:

Cadence doesn't enter into the PowerTap's calculation of power, which is based on torque and angular velocity measured at the hub.

Which may in fact have been a misinterpretation of what I said originally. What I meant to say was cadence is used to calculate angular velocity, which in turn is used to calculate power.

Anyway, Saris will provide the answers hopefully.

frenchyge said:

There's your answer Bruce. If you bring the power factor back into the equation to account for the additional imaginary power that some people are expending while riding on the trainer, then that resolves all the perceptions and anecdotes. QED. 😄

The PT senses angular velocity using a reed switch in the hub and a magnet housed in the receiver unit (ie, 1x per wheel rev).

As your original sherpa, I'm not gone now, just lost. 😄

Why then do they even give the option of an external cadence sensor? Since the hub is measuringexactly thesame thing - I'm lost too :eek:

frenchyge said:

There's your answer Bruce. If you bring the power factor back into the equation to account for the additional imaginary power that some people are expending while riding on the trainer, then that resolves all the perceptions and anecdotes. QED. 😄

There you go.😄

Quoted post said:

The PT senses angular velocity using a reed switch in the hub and a magnet housed in the receiver unit (ie, 1x per wheel rev).

Ah, so I won't have to bug the poor customer service rep from Saris, then. Thanks, frenchy.

Ken

Bruce Diesel said:

Why then do they even give the option of an external cadence sensor? Since the hub is measuringexactly thesame thing - I'm lost too :eek:

The "virtual" cadence sensor calculates cadence from torque pattern; if you have two legs to pedal your bicycle, there should be two peaks per revolution of your crank. If your torque pattern has some noises (i.e. more than two peaks per revolution) or is too smooth to have discernible peaks, it might miscalculate your cadence.

OTOH, the pedal cadence sensor is just a reed switch which is turned on by the crank-mounted magnet. You just have to count the pulse per minute or measure the interval between two pulses. Hence it's more accurate than the virtual cadence.

Ken

Bruce Diesel said:

Hmmmn, our resident doc feels otherwise.

No, I'm in agreement with beerco: under most conditions, the 200 Hz sampling rate of the SRM (at the crank) or the 70 (60?) Hz sampling rate of the PowerTap (at the hub) is sufficient to ensure the accuracy of the measurements, even though the data collection is time-based instead of position-based as it technically should be. It's possible (with the SRM) that this approach breaks down when angular velocity varies throughout the pedal cycle more than usual, e.g., due to the use of non-round chainrings (and in fact I believe that I was the first person to point this out), but I don't think it can be said just yet that this has been shown to be true.

BTW, for our wind tunnel study we validated the SRM against a Monark ergometer, which provides a low inertial load comparable to many trainers, and the SRM worked just fine...

sugaken said:

...it might miscalculate your cadence.

MIGHT?? :eek: You've used it right? 😉 (Just kidding, I know what you meant.)

sugaken said:

Hence it's more accurate than the virtual cadence.

...at least more reliable, yes. 🙂

frenchyge said:

The PT senses angular velocity using a reed switch in the hub and a magnet housed in the receiver unit (ie, 1x per wheel rev).

The magnet is actually embedded in the large silver spacer on the left side of the axle - you can see it in the pic here:

http://www.wheelbuilder.com/closeup.asp?cid=25&pid=198&offset=0

If you take your wheel off your bike and turn the slowly turn the axle by hand, you can often hear a faint click a the reed switch closes.

There is another reed switch in the receiver that is used to count wheel revolutions when you use the handlebar computer as a normal cycling computer...maybe that's what you had in mind?