Trying to understand SPM

[Carl Watts]

Most of the Concept2 maths (from the days of PM2s on model Bs) is discussed in some detail at http://www.atm.ox.ac.uk/rowing/physics/ergometer.html

Nice math.

As I thought the power is a cubic law, to spin the flywheel twice as fast you need 8 times the power.

Of interest was the difference between the static and dynamic Erg set-ups.

Also the effect on rating...

13. Effect of Rating

Note that the rate appears as a cube term: changing the rate from 30 to 36 (a factor 1.2) results in a factor (1.2)3 = 1.7 increase in power loss. Similarly, rating 24 rather than 30 consumes (0.8)3 = 0.5 - only about half as much power is lost.

What is also clear is that say if you can row continuiously at 2:00ave/500M pace at say 19 SPM you have a definate advantage over rowing the same pace at say 32 SPM.

With my weight at 100kg and the above rates, the saving are significant with wasted power dropping from 60W down to just 13W (just to move my body back and fourth on the slide not even holding the handle) for my 19SPM 2:00ave/500M 60min training rows.

Interesting stuff, thanks for the link Citroen.

[Tinus]

What is also clear is that say if you can row continuiously at 2:00ave/500M pace at say 19 SPM you have a definate advantage over rowing the same pace at say 32 SPM.

It would be the other way around. Anu Dudhia assumes inelastic ends of the stroke. This assumption is not true in practice and the energy losses accompanied with the body acceleration are much less. If you assume a loss of only a fraction say 25% and you take into account the effect that the smaller speed variations of the flywheel accompanied with higher stroke rate are more efficient (analog to section 10), then the most efficient stroke rate is in the high twenties or low thirties.

At 19 SPM one looses too much energy because of the higher speed fluctuations of the flywheel. At 32 SPM the effect of the energy loss due to the inelastic component of the bouncing motions at the catch (and in lesser amount at the release) is not yet very large enough to dominate the equation. So, rowing the same pace at 32SPM instead of 19SPM costs less power.

[Tinus]

The flywheel does more like 40 rps.

I was wrong here. The flywheel does only a third of this number. 40 rps would be an enormous speed.

I confused the number with the magnetic sensor. The flywheel contains three magnets used to measure the rotation of the wheel. So the number of magnets passing the sensor is three times higher as the rps of the flywheel. (Add to this that the relation between one magnet passing and the moved handle distance is also close to three, when expressed in centimeters)

[NavigationHazard]

The top pink curve in this ErgMonitor screenshot shows flywheel rpms. The blue curve is handle force, the blue line is average handle force, the green curve is handle speed, and the dark red line is instantaneous watts.

Flywheel rpms on this non-trivial stroke peak at about 1750 rpm, or about 29 rps. To some extent they'll vary according to drag factor. This stroke was DF 138.5. At a lower DF flywheel revolutions would be somewhat faster....



On this rather less extreme stroke, flywheel rpms peak at about 1600, or about 26.7 rps.
Offhand I'd say that peak flywheel rpms most of the time for most people are going to be closer to 20 rps than to 40. A peak of 40 is possible, I think, but you're probably going to need the handle-force of something in the order of 1:10 pace at a reasonable sprint rating. I would be astonished if it could be done from a dead fan.

[NavigationHazard]

I happened to have this ErgMonitor screenshot lying around so I thought I'd share it as well. The purple curve is handle force (what you'd see on a PM force-curve display). The dark red curve is instantaneous watts over the entire duration of the stroke. It peaks at about 800w just before the finish. I've extended the graph to show what happens to instantaneous watts as the flywheel slows down on the recovery. Average watts for the whole stroke are 336.6.

The point is that input to the flywheel happens only on the drive. As soon as that ends (as a practical matter, as you brake your hands at the finish to avoid thwacking yourself in the chest), the flywheel starts to decelerate. The longer the recovery, the more it will keep spinning and the more revolutions you'll get 'for free.' On the other hand, the more the flywheel slows down the lower your average watts over the entire stroke cycle are going to be. Drag Factor complicates matters a bit: at higher drag you get higher instantaneous watt values, but the flywheel is harder to accelerate at the catch and also slows faster on the recovery. Physiology also matters: at low ratings you need high peak force on the drive to compensate for the extra recovery time; at high ratings the short recoveries compromise your ability to sustain high peak force. Somewhere you need to find a balance.

As Tinus says, the upshot is that for any given rower and a given drag factor, given constant rower input (handle force, drive:recovery ratio) there's going to be an optimum rate that balances average watts you can sustain during the drive against average watts over the recovery. I quite agree that for many purposes for most people, efficiency defined this way is likely to entail ratings in the high 20s-low 30s (maybe 27-33 spm or so).

[slwiser]

Great charts and good discussions...maybe I am learning something, but so far not sure what.

[Carl Watts]

Results from where I sit currently at my level of strength & cardio fitness line up pretty close with the following:-

2:21 @ 10SPM
2:13 @ 12SPM
2:06 @ 14SPM
2:01 @ 16SPM
1:56 @ 18SPM
1:52 @ 20SPM
1:49 @ 22SPM
1:46 @ 24SPM
1:43 @ 26SPM
1:40 @ 28SPM
1:38 @ 30SPM
1:36 @ 32SPM

Rating at less than 9 SPM with enough power per stroke the other day had the PM4 all confused and the SPM went to 78 and the pace was 1:55.

Everyone's figures are going to vary considerably from one end of the spectrum to the other, i.e. Elite rower to the other end, the newbie ex-couch potato. The learning curve for me has between being able to balance rating and generating the power per stroke AND being able to sustain that power for the full duration of the event so as to avoid a DNF at all costs.This really only comes with a whole lot of experience and only being about 6 months into some decent training there is a long way to go yet.