Indoor rowing competitions: 'heavy-shell' vs 'light-shell' format
Posted: October 9th, 2021, 5:36 pm
This longish post presents an idea for an alternative indoor rowing competition. A competition maximally inclusive towards athletes with a wide variety of body sizes, and a competition that effectively eliminates the need for weight classes.
I am afraid it’s going to be a bit technical/mathsy, but bear with me, the end result (a recipe for an alternative competition) is pretty straightforward.
The Concept2 rower continuously measures two quantities: the power P delivered to the flywheel and the time t that passes. The PM5 translates these two quantities into distance D covered as function of time t using the equation P = c (D/t)^3. Here the quantity c emulates the drag on the rowing shell that occurs in on-the-water conditions. This drag is dominated by wetted surface friction. The wetted surface will depend on the weight M of the rower(s), and therefore c should increase with increasing M. For the Concept2, however, the quantity c is taken to be a constant independent of the rower weight M: c = 2.8 (units: kg/m). One might argue that this emulates the situation of a rowing shell much heavier than the rower(s) in it. As in this situation the rower(s) hardly influence the total weight, the wetted surface stays roughly constant with varying M. This, however, does not create a scenario fully consistent with the choice c = 2.8, as for a shell much heavier than the rower’s mass, c would be considerably larger than 2.8. Yet, as this ‘heavy shell’ scenario does correspond to the case c = constant, I will refer to the choice c = 2.8 as the ‘heavy shell’ choice.
It should be clear that the choice c = 2.8 boils down to no more than a practical choice: it eliminates the need for data on rower’s weights. The downside of the c=constant choice is that this form of indoor rowing favors the heavyweights more strongly than on-the-water rowing. One could opt for a function c(M) that is much more consistent with the physics of wetted surface friction for on-the-water rowing shells carrying rowers of total weight M. Here I will not go this route of optimizing c(M) so as to stay closest to on-the-water conditions. Rather, I treat competitive indoor rowing as a sport in its own right, and aim to optimize c(M) such that a competition originates that is maximally inclusive towards rowers of a large range of body weights.
I will not dive into the nitty-gritty of the problem and I will spare you the allometery considerations (google ‘Kleiber’s law’ if you are interested in this), but just state here that a vast body of research results indicate that metabolic rates scale with body mass via a power law with exponent ¾. Statistically, for a population of indoor rowing athletes, one would therefore expect the power P to be proportional to M^(3/4). To maximize indoor rowing competitiveness over the widest range of body weights, it follows that c should be proportional to M^(3/4). More specifically, I normalized c as follows: c = (14/135) M^(3/4). This ensures that for a rower with M = 81 kg we recover c = 2.8. For lighter rowers c drops below 2.8 (corresponding to a smaller wetted surface), while for heavier rowers c increases beyond 2.8 (corresponding to a larger wetted surface).
It should be clear that rendering c proportional to M to the power ¾ corresponds to the situation of a very light rowing shell. This follows from the fact that when M drops to zero, c also drops to zero. In the case of a rowing shell with non-negligible mass, when M drops to small values one would expect the wetted surface (and hence c) to approach a finite value. Therefore, I will refer to the case of c proportional to M^(3/4) as the ‘light shell’ scenario.
The net result of the above is two distinct competitions: a heavy-shell indoor rowing competition (the current competition) and a light-shell indoor rowing competition (proposed here). The first avoids the need for weight information for the rowers, but favors the very heavy. The second requires weight information, but allows for a tight competition between athletes with vastly different body sizes. The first is implemented into the PM5 algorithms, and the second obviously isn’t. This doesn’t mean it is currently infeasible to set up a light-shell indoor rowing competition. It is actually pretty straightforward to do so. You simply have to absorb the weight-dependent c(M) into a correction factor for the distance covered in the race.
This works as follows (I take the example of a 2000m race):
1) All rowers are weighted prior to start
2) For a rower weighting in at M kilograms, the distance correction factor (M/81)^(1/4) is calculated (calculate M/81, take the square root of the result, and square root once more)
3) The PM4 for each rower is programmed for a single distance of 2000m times his/her correction factor computed in step 2. (For example: a 95 kg rower would need to complete 2081 m, while a 75 kg rower will finish when completing 1962 m.)
4) If such a competition is organized, it helps when the spectators shout “500!” once the rower they are spectating completes 500 m times his/her correction factor, and “1000!” once the rower completes 1000 m times the correction factor, etc. This makes all participant and all spectators aware of how tight the race is.
Personally I have a weight that is rather ideal for a lightweight (spot on 75 kg), and I guess that in a light shell indoor rowing competition I will meet a much stronger competition from very fit athletes in my age category who are much lighter than me. I think this makes the sport much more interesting. Arguably, the biggest problem indoor rowing masters competitions currently face is the fragmentation over a multitude of categories. A light shell competition would eliminate the need for weight categories. That is one step towards less fragmentation.
But that is just me. Question is: would you welcome such a light shell indoor rowing competition?
I am afraid it’s going to be a bit technical/mathsy, but bear with me, the end result (a recipe for an alternative competition) is pretty straightforward.
The Concept2 rower continuously measures two quantities: the power P delivered to the flywheel and the time t that passes. The PM5 translates these two quantities into distance D covered as function of time t using the equation P = c (D/t)^3. Here the quantity c emulates the drag on the rowing shell that occurs in on-the-water conditions. This drag is dominated by wetted surface friction. The wetted surface will depend on the weight M of the rower(s), and therefore c should increase with increasing M. For the Concept2, however, the quantity c is taken to be a constant independent of the rower weight M: c = 2.8 (units: kg/m). One might argue that this emulates the situation of a rowing shell much heavier than the rower(s) in it. As in this situation the rower(s) hardly influence the total weight, the wetted surface stays roughly constant with varying M. This, however, does not create a scenario fully consistent with the choice c = 2.8, as for a shell much heavier than the rower’s mass, c would be considerably larger than 2.8. Yet, as this ‘heavy shell’ scenario does correspond to the case c = constant, I will refer to the choice c = 2.8 as the ‘heavy shell’ choice.
It should be clear that the choice c = 2.8 boils down to no more than a practical choice: it eliminates the need for data on rower’s weights. The downside of the c=constant choice is that this form of indoor rowing favors the heavyweights more strongly than on-the-water rowing. One could opt for a function c(M) that is much more consistent with the physics of wetted surface friction for on-the-water rowing shells carrying rowers of total weight M. Here I will not go this route of optimizing c(M) so as to stay closest to on-the-water conditions. Rather, I treat competitive indoor rowing as a sport in its own right, and aim to optimize c(M) such that a competition originates that is maximally inclusive towards rowers of a large range of body weights.
I will not dive into the nitty-gritty of the problem and I will spare you the allometery considerations (google ‘Kleiber’s law’ if you are interested in this), but just state here that a vast body of research results indicate that metabolic rates scale with body mass via a power law with exponent ¾. Statistically, for a population of indoor rowing athletes, one would therefore expect the power P to be proportional to M^(3/4). To maximize indoor rowing competitiveness over the widest range of body weights, it follows that c should be proportional to M^(3/4). More specifically, I normalized c as follows: c = (14/135) M^(3/4). This ensures that for a rower with M = 81 kg we recover c = 2.8. For lighter rowers c drops below 2.8 (corresponding to a smaller wetted surface), while for heavier rowers c increases beyond 2.8 (corresponding to a larger wetted surface).
It should be clear that rendering c proportional to M to the power ¾ corresponds to the situation of a very light rowing shell. This follows from the fact that when M drops to zero, c also drops to zero. In the case of a rowing shell with non-negligible mass, when M drops to small values one would expect the wetted surface (and hence c) to approach a finite value. Therefore, I will refer to the case of c proportional to M^(3/4) as the ‘light shell’ scenario.
The net result of the above is two distinct competitions: a heavy-shell indoor rowing competition (the current competition) and a light-shell indoor rowing competition (proposed here). The first avoids the need for weight information for the rowers, but favors the very heavy. The second requires weight information, but allows for a tight competition between athletes with vastly different body sizes. The first is implemented into the PM5 algorithms, and the second obviously isn’t. This doesn’t mean it is currently infeasible to set up a light-shell indoor rowing competition. It is actually pretty straightforward to do so. You simply have to absorb the weight-dependent c(M) into a correction factor for the distance covered in the race.
This works as follows (I take the example of a 2000m race):
1) All rowers are weighted prior to start
2) For a rower weighting in at M kilograms, the distance correction factor (M/81)^(1/4) is calculated (calculate M/81, take the square root of the result, and square root once more)
3) The PM4 for each rower is programmed for a single distance of 2000m times his/her correction factor computed in step 2. (For example: a 95 kg rower would need to complete 2081 m, while a 75 kg rower will finish when completing 1962 m.)
4) If such a competition is organized, it helps when the spectators shout “500!” once the rower they are spectating completes 500 m times his/her correction factor, and “1000!” once the rower completes 1000 m times the correction factor, etc. This makes all participant and all spectators aware of how tight the race is.
Personally I have a weight that is rather ideal for a lightweight (spot on 75 kg), and I guess that in a light shell indoor rowing competition I will meet a much stronger competition from very fit athletes in my age category who are much lighter than me. I think this makes the sport much more interesting. Arguably, the biggest problem indoor rowing masters competitions currently face is the fragmentation over a multitude of categories. A light shell competition would eliminate the need for weight categories. That is one step towards less fragmentation.
But that is just me. Question is: would you welcome such a light shell indoor rowing competition?
). In my case, it also provides motivation to work harder to keep up with the younger and larger people within my broad category.