How is power on PM5 calculated?

[JaapvanE]

Erger Power is the average energy loss rate of the fan when not driven, as observed during the erger's rest time.

No, it isn't. This is a fundamentaly wrong perception of the entire measurement of power. Although at the end of the session, all energy has dissapated through the flywheel, this is NOT how the physics and power measurement work on any rower. It simply can't work that way. Although there are way too many things completely wrong with this approach, I'll name the most important ones

1. This would make a decelerating stroke stronger as more energy is dissapated, and a short accelerating one weaker. Even more extreme, it would make the first recovery (and thus stroke) the weakest, and the last recovery (and thus stroke) the most powerful by far, by definition, as most energy is put in the flywheel at the start to accelerate at the start (and not much is lost) and all the flywheel's energy must be dissapated at the end of the last drive. And this is regardless of what the rower does. Where typically, at the start a lot of power is produced (which is underreported by both the PM5 and ORM), and the last stroke can be an extremely weak one.
2. Energy is also dissapated by the flywheel throughout the drive. Drag is still drag, energy is still lost because of it. Because we put more energy in than we lose, the flywheel will accelerate. But despite its acceleration, we are not allowed to ignore the energy that is lost during the drive due to drag, especially as the biggest portion of the top-speed (and thus maximum drag) is in that section of the stroke: during the arm pull forces balance out and the flywheel is in equilibrium, maintaining its top-speed.
3. It completely ignores the fact that flywheels can be (and are) used to store energy. By equating the power produced by the rowing subject to the energy dissapated, this fraction is ignored (this, in fact is where the fraction "I ( ∆ω / ∆t ) ∆θ" comes from: this is the energy stored in the flywheel). So energy that is stored in the flywheel by accelerating it further, is completely missed. This is in fact the underlying issue of point 1: you accelerate a flywheel in the beginning, storing a lot of energy in it, only to get it back at the end of the session.

As it is the rowing subject produces the power during the drive, one MUST measure what happens during the drive as well. That is why P = k * ω^3, where ω is the average speed across the entire stroke (i.e. drive AND recovery) is a decent approximation.

[jamesg]

I'm saying what it is, not how it's measured. But if you can get the data out, you could use it. You only need the two highest and lowest speeds and their times.

The energy lost by a flywheel in a certain time, divided by that time, in the absence of any input work, is the average Power loss, by definition.

[JaapvanE]

I'm saying what it is, not how it's measured. But if you can get the data out, you could use it. You only need the two highest and lowest speeds and their times.

That is indeed C2's current (and mistaken) approach to stroke detection. It is flawed, as at the begin and end of a drive, a force can be present that is weaker than the dragforce, so the flywheel decelerates despite being powered. The only good approach is to calculate the dragfactor and see if the deceleration is consistent with the dragforce being the only force present.

The energy lost by a flywheel in a certain time, divided by that time, in the absence of any input work, is the average Power loss, by definition.

You are measuring the wrong thing. A flywheel can store energy (this is in fact the industrial application of flywheels). So if you are measuring power, you should measure the power the rowing subject puts into the flywheel. And law of conservation of energy teaches us that this is "the energy stored in the flywheel" + "the energy lost throughout the entire stroke". You completely ignore the effect of storing energy in the flywheel.

[iain]

That is indeed C2's current (and mistaken) approach to stroke detection. It is flawed, as at the begin and end of a drive, a force can be present that is weaker than the dragforce, so the flywheel decelerates despite being powered. The only good approach is to calculate the dragfactor and see if the deceleration is consistent with the dragforce being the only force present.

I agree that an "ergometer" ought to measure the energy, but this is also the case in a boat. It starts at rest and finishes with kinetic energy built up on the row, but arguably the "useful work" does not include this as it is used to carry the boat forward after the race is over!

- Iain

[JaapvanE]

I agree that an "ergometer" ought to measure the energy, but this is also the case in a boat. It starts at rest and finishes with kinetic energy built up on the row, but arguably the "useful work" does not include this as it is used to carry the boat forward after the race is over!

Measuring the energy stored in a flywheel is actually quite easy, all you need is its Inertia and the slowest angular velocity. Measuring the energy stored in boat is as simple. This is far from rocket science, even in a real life measuring scenario. But people should not say that "the power produced by a rowing person is equal to the power disapated during the recovery". It is a fundamentally wrong approach to measuring power as it ignores the energy lost in the drive and the energy stored in the flywheel itself.

When you know the average angular velocity across the stroke and the dragfactor you can do a quick but fairly accurate estimation of power, and if you want to be precise you need the Flywheel Inertia, the instantaneous angular velocity and instantaneous angular acceleration. These instantaneous values are volatile, so should be avoided if possible, but it is doable.

So when you measure the flywheel it is extremely easy to measure the power that is put into it, a long as you measure the right thing and don't ignore over 50% of the power produced.

[jamesg]

completely ignore the effect of storing energy in the flywheel.

Certainly. As Iain notes, at the start of a race, KE is zero. At the finish, KE is whatever say 100kg at 5m/s amounts to. Presumably C2 machine behave the same way.

It is a fundamentally wrong approach to measuring power as it ignores the energy lost in the drive

Incorrect. You confuse Work and Power. C2 rowing machines have a fan, which makes it possible to measure the energy loss rate (= Power) at every stroke during the recovery, when no other work is being done on the flywheel. This Power is the same during recovery and pull, since it depends only on fan characteristics, so only needs to be measured once per stroke.

[JaapvanE]

Certainly. As Iain notes, at the start of a race, KE is zero. At the finish, KE is whatever say 100kg at 5m/s amounts to. Presumably C2 machine behave the same way.

You are confusing linear and rotational physics. The energy stored in the flywheel is a function of Flywheel Inertia and ω in rad/sec.

It is a fundamentally wrong approach to measuring power as it ignores the energy lost in the drive

Incorrect. You confuse Work and Power. C2 rowing machines have a fan, which makes it possible to measure the energy loss rate (= Power) at every stroke during the recovery, when no other work is being done on the flywheel. This Power is the same during recovery and pull, since it depends only on fan characteristics, so only needs to be measured once per stroke.

So I get back to my original post:

The precise calculation to calculate the work done (see the Physics of Ergometers, formula 8.2):
∆E= I ( ∆ω / ∆t ) ∆θ + k ω^2 ∆θ
where I is the flywheel inertia, k the drag, ω is the angular velocity and θ is angular distance.

and then formula 8.3 tells us:
P = E / t

As Power = Work / Time, where in rowing it is common to use the stroketime.

The thing you keep ignoring is that you want to measure power on the handle that is produced by the rowing person. Nobody gives a rat's @ss about the way the energy is removed from the system. We do care about how hard people are working. The only reason we measure at the flywheel at all is to measure the effort of the person doing the rowing. And measuring the energy stored in the flywheel is doable without any extra measurement, also for C2 (the calculation of the force curve requires calculation of instantaneous a Torque and thus of instantaneous angular acceleration).

Please also observe that we've used the approximation algorithm for over 3000K on several C2's and we've consistently been within 0.05% of the PM5 results. You can hypothesize all you want, but we implemented this, had it verified by people with an experimental physics Phd, and tested it to great lengths. So the approximation algorithm is the one most likely been used in the C2 PM5 as stroke to stroke consistency isn't my strongest point.

It actually would be incredibly foolish to measure anything during recovery as even the approximation algorithm yields better results, is much simpler to implement and is robust against both measurement noise and stroke detection errors. Only thing you really need to measure during recovery is drag, time and angular distance. In fact, all open source applications I've investigated use the simplified method (aside Dave's solution).

Dave Venrooy actually showed that the precise algorithm is doable (he calculated the work done during drive using a discrete intergation approach) and with our approach to rotational physics it might even scale to non-perfect machines.

[iain]

The thing you keep ignoring is that you want to measure power on the handle that is produced by the rowing person.

I think what most people in the early days wanted to know was how the speed of a boat would be affected by a similar stroke, as despite calling the machine an ergometer, it was designed as an aid for OTW training. That is why the readings are designed to approximate to the behaviour of a boat.

[JaapvanE]

I think what most people in the early days wanted to know was how the speed of a boat would be affected by a similar stroke, as despite calling the machine an ergometer, it was designed as an aid for OTW training. That is why the readings are designed to approximate to the behaviour of a boat.

True, but that is why the approximation is a decent approach: when accelerating the average angular velocity rises so does reported power, but the university of Ulm has shown that the PM5 doesn't give you enough credit for it. For example, in the first five strokes, the PM5 underreports power as it seems to ommit an explicit acceleration/deceleration component.

This makes the C2 perform well when stroke-to-srroke consistency is high (which IMHO is a good thing for a training tool), but people get punished by underreporting power when the consistency is lacking. I'm not certain the latter is a bad thing from a training perspective, but when seeing it as a competition machine, it is a thing really to keep in mind when sprinting.

[jamesg]

The thing you keep ignoring is that you want to measure power on the handle that is

Why would I want to do that? I only need reasonably consistent data describing the physical results of what I do. Flywheel speeds mirror this all too close enough for decrepit me.

If you want to add on the total kinetic energy of the flywheel, you already have data enough: the flyweel speed measured in the last stroke of the race. But what's the point?

Varying speed during a race is a technical fault, since it certainly takes more power than constant speed. We know this, so we don't do it. I've seen a swimmer miss a gold medal simply by going a little too fast in the first length of a 400m. Still got a silver.

[JaapvanE]

The thing you keep ignoring is that you want to measure power on the handle that is

Why would I want to do that?

Why bother making a force curve then? That is all defined from the handle, not on the flywheel.

I only need reasonably consistent data describing the physical results of what I do. Flywheel speeds mirror this all too close enough for decrepit me.

Aside from creating a discrepancy in definitions if you'd ommit it (as the forces and force curve are also defined at the handle), a gradual slowdown would result in a higher indicated power.

And if you want consistent results, using any instantaneous angular velocity is extremely foolish: they are quite volatile due to measurement noise, vulnerable to stroke detection errors and have fundamental issues with the discrete measurement. So they deliver unstable results (I know this by experience, as we have experimented with this quite extensively). The alternative is much simpler, and isn't unstable.

[Nomath]

...Varying speed during a race is a technical fault, since it certainly takes more power than constant speed. We know this, so we don't do it. I've seen a swimmer miss a gold medal simply by going a little too fast in the first length of a 400m. Still got a silver.

I want the erg to calculate and display my energy input as accurately as possible, whether I row very clumsily and unsteady or like a metronome athlete.

It is clear, as JaapvanE pointed out, that for calculating the work in a stroke you have to take into account the average flywheel speed during the whole stroke, not only during the recovery as you suggested earlier. Otherwise you would probably miss a quarter or half of the true energy input

... P = k * ω^3, where ω is the average speed across the entire stroke (i.e. drive AND recovery) is a decent approximation.

I did several computer simulations using force profiles published in the scientific literature. The graph below shows the calculated flywheel speed during 4 strokes with the force profile measured by the Ulm University. I normalized the peak power to 600N, which is roughly what a trained, non-elite rower generates in a 5K run. Stroke rate was set at 25 spm. Drive distance was set to 1.50 m. Flywheel speed is in radians per second.
The vertical lines are at the start of the stroke.



In this simulation, the true power input is accurately known, viz. the integral of the force over the travel distance of the handle. To check whether the results of the formula
Power P = k * ω^3 (note : ω is the average radial velocity during the stroke)
is accurate, I deliberately did prior strokes (not shown in the graph) using the same force profile but with a shorter recovery.
The result is that the flywheel speed starts higher than in a stationary situation at 25 spm. After about 2 strokes the speed profile is seen to stabilize to the steady input. The above formula leads to a considerable overestimation for the first 2 strokes in the graph. The true power in each stroke is 211W ; the estimated power for the 4 strokes shown is 232W - 217W - 212W - 211W, respectively.

Hence, to my surprise, the above formula is quite accurate for a stationary stroke pattern. However, it is not accurate with stroke-to-stroke variations in force or stroke rate.

[jamesg]

Otherwise you would probably miss a quarter or half of the true energy input

Incorrect. The fan Power to air constant (drag) is measured during recovery, when possible. Drag is the same over the entire stroke, so using the complete stroke time and the flywheel speeds, gives the total stroke energy loss to air.

Bikes with strain gauges for power no doubt measure total input through the pedals; but speed is not derived from power on bikes. Other systems have to be used to measure speed, thanks to wind and slopes.

The Rowerg has only one system, so it has to target speed, not total input, since rowing is a sport.

[jamesg]

I want the erg to calculate and display my energy input as accurately as possible, whether I row very clumsily and unsteady or like a metronome athlete.

Then use HR, if that doesn't cover all work done, what can?

[JaapvanE]

I want the erg to calculate and display my energy input as accurately as possible, whether I row very clumsily and unsteady or like a metronome athlete.

Then use HR, if that doesn't cover all work done, what can?

Because quite interesting metrics originate from the (changing of the) relation between external power produces and internal stress. For example VO2Max, but also other metrics.