Είναι κοινά αποδεκτό ότι το μεγαλύτερο σωματικό βάρος αποτελεί πλεονέκτημα στην επίτευξη καλύτερων χρόνων στο κωπηλατοεργόμετρο και συνεπώς οι ελαφρύτεροι αθλητές μειονεκτούν συγκρινόμενοι με τους βαρύτερους σε επίπεδο απόλυτων τιμών. Για την αποκατάσταση αυτής της "αδικίας" έχουν εξελιχθεί διάφορα εργαλεία που συνυπολογίζουν το ΣΒ στον τελικό υπολογισμό της επίδοσης. Μια πρόχειρη αναζήτηση στο διαδίκτυο καταδεικνύει πλήθος άρθρων που δείχνουν ότι όλο και περισσότεροι προπονητές χρησιμοποιούν αυτούς τους υπολογισμούς κατά την επιλογή των αθλητών για τα πληρώματά τους. Το παρακάτω άρθρο του ιστολογίου "The Daily Erg-Rowing Science" αναλύει τον τρόπο υπολογισμού, που μπορείτε να βρείτε στη σελίδα της Concept (http://www.concept2.com/us/training/tools/calculators/weight_adjustment.asp), καθώς και την λογική που κρύβεται πίσω από τις μαθηματικές πράξεις. Ελπίζω να το βρείτε χρήσιμο.
What is it? How is it measured?
The most well-known source of information is the Concept 2 web site, where an online calculator is provided to adjust erg scores. They describe their calculator as "a controlled, measurable way to compare their athlete's potential." This is a better way of putting it - potential - rather than pure ability which would take into account skill on the water.
This calculator works for any distance, but lets look at a 2K race. One athlete (Jimmy) is big and powerful and at 220 lbs. finishes in 6:10. Another (Kenny) is a lightweight, also with a very strong score of 6:20 but at only 155 lb.
Jimmy 220 lb. 6:10
Kenny 155 lb. 6:20
Assuming equal erg scores - who do you want in your boat?
Run them through the calculator and you get the following adjusted scores:
Jimmy 5:53.6
Kenny 5:35.9
The calculator says Kenny should be the faster rower, by a good margin. But what does it mean? Concept 2 says this score represents "how fast you would be able to go in an eight-oared shell if all eight rowers had the same adjusted score as you!" Wow - gimme 8 Kenny's any day!
There is a complicated formula behind this, also reported on the C2 website:
wf=[body weight in pounds/270] ^ .222
In plain english:
weight factor adjustment = (your body weight in pounds, divided by 270) raised to the power of .222
So essentially, you calculate an "adjustment factor" using this formula, and then you multiply your time by it.
For the individual it is much easier to use the online calculator. For coaches looking at many scores, there might be a better way - more on that in a subsequent post.
Where does this come from?
There is no explanation that I have seen on the C2 site as to how their formula was derrived although they do note that the 270 in it used to be 170 and the adjustment was intended to better reflect performance in an eight. If anyone knows more, please leave it in the comments section.
Another great source for this topic is The Physics of Rowing site. It is an amazing resource for those looking for detailed answers to all their questions.
Many people have heard of the "power to weight ratio" suggesting that your power (in Watts - though an erg split is proportional to this) can be simply divided by your weight (typically in kg) to adjust erg scores. The Physics of Rowing site points out that we usually use the "cube root" of weight - or weight to the power of 1/3. The site doesn't explain why this is, but one can assume that since rowing is not a weight bearing sport and because all of your mass does not translate into increased drag on the shell then your mass cannot directly be used. To put it another way your power:weight ratio does not change directly with any increase in weight because that same increase in weight does not slow you down proportionally. If you double your mass you won't double the drag on the shell - it will only go up by some portion of the increase in your mass.
Calculating just a power: weight ratio for our friends in the example above would be done as follows:
First convert their average split from time into watts (there is an excellent explanation in the C2 Training Guide on page 225) but is essentially 2.8 / pace^3 where pace is time in seconds divided by distance. The resulting average wattages for their pieces then would be:
Jimmy = 442W
Kenny = 408W
Divide each by the cube root of their masses to get:
Jimmy = 95.3 W / kg^(1/3)
Kenny = 98.8 W / kg^(1/3)
Kenny has a better power:weight ratio but it does not appear quite as dramatic a difference between them as the C2 formula reports. Using just power:weght and not understanding what it means one might not see clearly the difference between these two athletes. Note that if the units are suitably large this 3.6 W / kg^(1/3) difference may well be very big, but most people wouldn't see it and it converys no information about the effect in a shell.
The Physics of Rowing article goes on to try and evaluate the effect of excess weight on performance on the water. It ends up derriving a formula that deals with the rowers mass in addition to excess deadweight (cox [sorry coxies], oars, cox box etc.) that has to be distributed amongst the rowers - which it pegs at 15 kg per rower - and uses an exponent that takes into account how drag is affected by extra weight. The more weight you add to a shell, the more the wetted surface area increases. But they suggest that this works differently depending on the size of the shell. In the end they end up with a formula that looks like this:
F = (90 / (mass (kg) +15))^0.167
The "factor" that this calculates needs to be divided into the erg score - unlike the C2 formula which is a multiplier. Of course you could just calculate the inverse of this factor(1 / F) and then it becomes a multiplier.
Note that this uses a power of 0.167 which is based on assumptions about wetted surface area in a larger crew boat. The 0.222 used by Concept 2 would come from assumptions linked to a single, where an individuals weight has a larger contribution to the change in wetted surface area. This is how the Physics of Rowing site describes it - but C2 report their formula is for an eight...so who is right? I can't say, but does it really matter?
Let's apply this formula - we see these adjusted scores:
Jimmy: 6:30.7
Kenny: 6:15.7
It still reports Kenny as faster, although not as dramatically. I would wager that if they are decent rowers the C2 formula reports better numbers for an eight.
Why the differences in these three comparisons (we could make it four by changing the exponent in the Physics of Rowing formula, but it makes only a small difference)?
First, all three are just mathmatical models. Appropriate assumptions based on known information is used to compile a formula that is hoped to predict something. These assumptions are based on something but they are just that - assumptions. There is a reason for the 0.167 exponent, for example, but it can't be said to be exact in every case. Not all shells have the same drag in the water or respond to excess mass in exactly the same way. The extra weight carried was also given an assumed value - but is 15 kg per rower correct - no, of course it can't be in all crews and all boats.
The variation in these formulae is to be expected, they are simply different models. Some may be closer to the truth than others, but we would only know for sure through controlled experiements to test the models. In any case the fact that there is variability points out clearly that we cannot rely on any one measure as a "gold standard."
So - to sum it all up - What should you use as a coach?
ASSUMING equal technique:
These formulae strongly suggest that simply picking a crew based on raw erg scores would be a serious error - I hope nobody is doing this anymore???
The fact that the formulae are not perefect models suggests that simply using one of these formulae to pick a crew would also be a mistake - better than a raw score probably, but a mistake.
I would recommend using one or all of these to adjust erg scores to give you a truer picture of your athletes. Doing so might open your eyes up to an athlete with more (or indeed, less) potential than you realized.
DO NOT overemphasize the weight adjusted score. The potential health implications of athletes trying to better their score simply by losing weight cannot be ignored. Point out that for a lighter athlete, losing one pound changes the score by about half a second and there is no way that amount can be a factor in crew selection.
Test on the water! In the end, that's what it really is about isn't it?
A thought for on-water testing:
The Physics of Rowing information suggests that erg scores adjust somewhat less for an eight. There is an additional change in adjustment if you modify the amount of deadweight. If this model is correct it might have implcations for seat racing. Some coaches believe that the pair matrix is the fairest way to select an eight...but is it possible that a larger athlete is penalized more in a pair, perhaps losing in the seat racing when they would indeed have made the eight faster?
The most well-known source of information is the Concept 2 web site, where an online calculator is provided to adjust erg scores. They describe their calculator as "a controlled, measurable way to compare their athlete's potential." This is a better way of putting it - potential - rather than pure ability which would take into account skill on the water.
This calculator works for any distance, but lets look at a 2K race. One athlete (Jimmy) is big and powerful and at 220 lbs. finishes in 6:10. Another (Kenny) is a lightweight, also with a very strong score of 6:20 but at only 155 lb.
Jimmy 220 lb. 6:10
Kenny 155 lb. 6:20
Assuming equal erg scores - who do you want in your boat?
Run them through the calculator and you get the following adjusted scores:
Jimmy 5:53.6
Kenny 5:35.9
The calculator says Kenny should be the faster rower, by a good margin. But what does it mean? Concept 2 says this score represents "how fast you would be able to go in an eight-oared shell if all eight rowers had the same adjusted score as you!" Wow - gimme 8 Kenny's any day!
There is a complicated formula behind this, also reported on the C2 website:
wf=[body weight in pounds/270] ^ .222
In plain english:
weight factor adjustment = (your body weight in pounds, divided by 270) raised to the power of .222
So essentially, you calculate an "adjustment factor" using this formula, and then you multiply your time by it.
For the individual it is much easier to use the online calculator. For coaches looking at many scores, there might be a better way - more on that in a subsequent post.
Where does this come from?
There is no explanation that I have seen on the C2 site as to how their formula was derrived although they do note that the 270 in it used to be 170 and the adjustment was intended to better reflect performance in an eight. If anyone knows more, please leave it in the comments section.
Another great source for this topic is The Physics of Rowing site. It is an amazing resource for those looking for detailed answers to all their questions.
Many people have heard of the "power to weight ratio" suggesting that your power (in Watts - though an erg split is proportional to this) can be simply divided by your weight (typically in kg) to adjust erg scores. The Physics of Rowing site points out that we usually use the "cube root" of weight - or weight to the power of 1/3. The site doesn't explain why this is, but one can assume that since rowing is not a weight bearing sport and because all of your mass does not translate into increased drag on the shell then your mass cannot directly be used. To put it another way your power:weight ratio does not change directly with any increase in weight because that same increase in weight does not slow you down proportionally. If you double your mass you won't double the drag on the shell - it will only go up by some portion of the increase in your mass.
Calculating just a power: weight ratio for our friends in the example above would be done as follows:
First convert their average split from time into watts (there is an excellent explanation in the C2 Training Guide on page 225) but is essentially 2.8 / pace^3 where pace is time in seconds divided by distance. The resulting average wattages for their pieces then would be:
Jimmy = 442W
Kenny = 408W
Divide each by the cube root of their masses to get:
Jimmy = 95.3 W / kg^(1/3)
Kenny = 98.8 W / kg^(1/3)
Kenny has a better power:weight ratio but it does not appear quite as dramatic a difference between them as the C2 formula reports. Using just power:weght and not understanding what it means one might not see clearly the difference between these two athletes. Note that if the units are suitably large this 3.6 W / kg^(1/3) difference may well be very big, but most people wouldn't see it and it converys no information about the effect in a shell.
The Physics of Rowing article goes on to try and evaluate the effect of excess weight on performance on the water. It ends up derriving a formula that deals with the rowers mass in addition to excess deadweight (cox [sorry coxies], oars, cox box etc.) that has to be distributed amongst the rowers - which it pegs at 15 kg per rower - and uses an exponent that takes into account how drag is affected by extra weight. The more weight you add to a shell, the more the wetted surface area increases. But they suggest that this works differently depending on the size of the shell. In the end they end up with a formula that looks like this:
F = (90 / (mass (kg) +15))^0.167
The "factor" that this calculates needs to be divided into the erg score - unlike the C2 formula which is a multiplier. Of course you could just calculate the inverse of this factor(1 / F) and then it becomes a multiplier.
Note that this uses a power of 0.167 which is based on assumptions about wetted surface area in a larger crew boat. The 0.222 used by Concept 2 would come from assumptions linked to a single, where an individuals weight has a larger contribution to the change in wetted surface area. This is how the Physics of Rowing site describes it - but C2 report their formula is for an eight...so who is right? I can't say, but does it really matter?
Let's apply this formula - we see these adjusted scores:
Jimmy: 6:30.7
Kenny: 6:15.7
It still reports Kenny as faster, although not as dramatically. I would wager that if they are decent rowers the C2 formula reports better numbers for an eight.
Why the differences in these three comparisons (we could make it four by changing the exponent in the Physics of Rowing formula, but it makes only a small difference)?
First, all three are just mathmatical models. Appropriate assumptions based on known information is used to compile a formula that is hoped to predict something. These assumptions are based on something but they are just that - assumptions. There is a reason for the 0.167 exponent, for example, but it can't be said to be exact in every case. Not all shells have the same drag in the water or respond to excess mass in exactly the same way. The extra weight carried was also given an assumed value - but is 15 kg per rower correct - no, of course it can't be in all crews and all boats.
The variation in these formulae is to be expected, they are simply different models. Some may be closer to the truth than others, but we would only know for sure through controlled experiements to test the models. In any case the fact that there is variability points out clearly that we cannot rely on any one measure as a "gold standard."
So - to sum it all up - What should you use as a coach?
ASSUMING equal technique:
These formulae strongly suggest that simply picking a crew based on raw erg scores would be a serious error - I hope nobody is doing this anymore???
The fact that the formulae are not perefect models suggests that simply using one of these formulae to pick a crew would also be a mistake - better than a raw score probably, but a mistake.
I would recommend using one or all of these to adjust erg scores to give you a truer picture of your athletes. Doing so might open your eyes up to an athlete with more (or indeed, less) potential than you realized.
DO NOT overemphasize the weight adjusted score. The potential health implications of athletes trying to better their score simply by losing weight cannot be ignored. Point out that for a lighter athlete, losing one pound changes the score by about half a second and there is no way that amount can be a factor in crew selection.
Test on the water! In the end, that's what it really is about isn't it?
A thought for on-water testing:
The Physics of Rowing information suggests that erg scores adjust somewhat less for an eight. There is an additional change in adjustment if you modify the amount of deadweight. If this model is correct it might have implcations for seat racing. Some coaches believe that the pair matrix is the fairest way to select an eight...but is it possible that a larger athlete is penalized more in a pair, perhaps losing in the seat racing when they would indeed have made the eight faster?
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