What’s the ideal force curve? Peter Mallory

Peter’s excellent book, The Sport of Rowing, includes this advice about force curves

How about parabolas? You make a parabola by slicing a cone . . . or by graphing the formula x² = 4py . . . or by recording Kris Korzeniowski’s force curve while rowing!

Or the force curve of 1920 Olympic Men’s Singles and Doubles Champion John B. Kelly, Sr. Or 1956, 1960 and 1964 Olympic Men’s Singles Champion Vyacheslav Ivanov. Or 1960 Olympic Men’s Coxless-Fours Champion Ted Nash. Or 1967 and 1969 European Men’s Coxless-Pairs Champion Larry Hough and Tony Johnson. Or 1969 European Men’s Doubles Champion John Van Blom and Tom McKibbon. Or 1974 World Men’s Eights Champion Al Shealy. Or 1984 Olympic Men’s Doubles Champion Brad Alan Lewis and Paul Enquist. Or 1988 and 1992 Olympic Men’s Singles Champion Thomas Lange. Or 1996 Olympic Men’s Eights Champion Michiel Bartman. Or 2004 Olympic Men’s Eights Champion Bryan Volpenhein. Or 2004 and 2008 Olympic Women’s Doubles Champions Caroline and Georgina Evers-Swindell.

What’s going on here? For Heaven’s sake, it’s a slice of a cone! What could that possibly have to do with rowing?

If you could ask legendary coach Steve Fairbairn what the ideal force profile would be for moving a rowing shell down the course, he would describe to you a parabola, my friends. As would Charles Courtney of Cornell. And Hiram Conibear of the University of Washington. And Jumbo Edwards of Great Britain. And Karl Adam of Ratzeburg. And Dr. Theo Körner of the German Democratic Republic. And Harry Mahon and Dick Tonks of New Zealand.

Seriously, what is going on here? Why a parabola of all curves?

Coaches have been trying to explain that for 200 years, and I have done my best to include their most eloquent efforts in The Sport of Rowing. My own tongue-in-cheek first effort was in my first book, An Out-of-Boat Experience, and it was this: “God is a rower, and He rows like me!” If I had chosen to be a bit less juvenile back then I might have said something about how when we hear the boat sing beneath us, we truly touch the Divine, that traveling over water relying on our own body power has truly cosmic implications, that only a perfect curve, only a parabola, is good enough for rowers like us.

So if the ideal power curve is a perfect parabola then the ideal peak force position is at 50.0%.  Many single scullers peak here and bigger boats peak at 46-47%.

 

33 thoughts on “What’s the ideal force curve? Peter Mallory

  1. Mel Harbour says:

    Sigh

    Please, let’s have a bit of accuracy. Just because something happens to resemble a parabola to some people doesn’t mean that it’s anything of the sort. A parabola is a very specific mathematical structure.

    This whole article is an exercise in confirmation bias of a hypothesis, full of ludicrous statements and inaccuracies. In the section on Harry Mahon in his book, Mallory talks about the British template being a parabola, but presents a graph of it at the same time, showing something that quite clearly isn’t a parabola. Largely because it isn’t even symmetrical, never mind parabolic.

  2. Peter Mallory says:

    I love Mel Harbour’s reaction. There is nothing more reliable in rowing circles than the inevitable passionate push-back against ideas perceived to be new or counter to established Orthodoxy, so thank you, Mel.

    The British template illustrated in my book was a real-world curve of a particular individual, and it was used by the great Harry Mahon prior to the British VII’s 2000 Olympic Gold Medal. In the real world, every curve of every athlete is absolutely unique. A parabola is an ideal construct. Individual athletes may approach it, but no one could match it exactly. Kris Korzeniowski’s curve shown above is about as close as anybody is going to get, but look closely. It’s not quite perfect, but none of this invalidates my assertion.

    The Sport of Rowing presents no hypotheses at all. Rather, it is a thorough and careful survey of historic evidence followed by an invitation to the readers to draw their own conclusions based on that well-documented evidence. My informally-worded posting above on rowperfect.co.uk is an impassioned invitation to look at history and recognize the overwhelmingly obvious pattern. This is “ludicrous” only to those who are close-minded. My point was: “Don’t take my word for it. Trust the example of the athletes and coaches I have listed.”

    And if you disagree, good for you, but please provide a reasonable and comprehensive alternative rather than merely descending to name-calling. Rebecca invited me to begin a constructive dialogue on her website, so I hope we can carry forward from here on in with great passion but also respect and thoughtfulness.

    • r.d.carver says:

      the tip of the scull travels about 28″ out from the side of the boat during the first half of the stroke till 90 degrees and during this movement the curve of the scull encourages slip towards the stern . some say there is “lift towards the bows” like an aeroplane wing but that only applies to a plane in level flight. the scull is like a plane wing when the aeroplane goes in a curve from climbing to diving when there is no “lift”. However if the curve of the scull is reversed the “slip” is discouraged, and the scull tends to move towards the bows with no slip. After 90 degrees the direction of push is increasingly not towards your stern rudder but towards the start which is more efficient. On the feather, the tips of the sculls point down and not upwards which looks odd. Has anyone done a hydrodynamic test of such a scull.

      • Mel Harbour says:

        Ok, next bit of fairly dodgy mathematics – in this case fluid dynamics. Be careful discussing lift – your intuition will very often be wrong. If an aeroplane has circulation of the airflow around its wings (subtle point – circulation can look pretty like a smooth flow), it will be creating lift. Its flight certainly doesn’t have to be level for that to be the case!

        A curve in a wing (or an oar blade) is to do with delaying separation of the fluid flow at higher angles of attack. Reynolds number effects mean that the lift force generated by an oar blade in the first portion of a stroke is equivalent to the force generated on something about the size of a barn door in a hurricane.

        If you use a scull like you suggest, what you would get is (in order): Early separation of the fluid flow during the first portion of the arc, leading to the blade slipping through the water, and a lack of efficiency; significantly more slippage through the second portion of the arc, where the blade is acting like a parachute; more separation of the fluid flow during the last portion of the stroke.

        In summary, I wouldn’t recommend it.

    • Mel Harbour says:

      Hi Peter,

      I’m certainly not name-calling, and my criticism of your description is based more on my training as a mathematician than it is anything to do with my experience of rowing.

      You say that your post is ‘informally worded’, but at the start pull out a precise definition of a parabola (correctly) as a conic section. If you hadn’t started out by trying to be so precise, I don’t think I would have been that bothered by the post! The point is that what you’ve seen as the pattern is a curve which is, to your eye, a symmetrical ‘hump’. You’ve called that a parabola. But there’s nothing to suggest that this is the case. There are plenty of other classes of curves that look somewhat visually similar. For example, the curve also looks somewhat like a catenary.

      You then seem to have got upset that I’ve called you out for indulging in confirmation bias, but then in your response, you simply further confirm that that’s what is at work. From your work, you’ve gathered some evidence. From this evidence, you’ve spotted what you believe to be a pattern (remember that human brains are exceedingly good at constructing patterns where they may not exist). You’ve then selected examples which appear to confirm your hypothesis, while ignoring those that don’t. You quote Olympic champions that you say exhibit parabolic forces curves. But you ignore all the examples that do not, and gloss over the fact that all your examples actually have force curves which do not either. Even the curve that you begin your article with manifestly isn’t symmetrical – it is biased towards the left hand edge. This process of having a hypothesis and then attempting to make the data fit it is called confirmation bias. I’m not name calling – I’m pointing out the facts of what you’re doing.

      If someone supplies a hypothesis, someone else does not need to supply an alternative theory in order to disprove that hypothesis. You don’t present any actual evidence, or theory, of why a parabolic curve should be optimal. The onus is on the proposer of the theory to back it up with either evidence or theory.

      On a separate strand, I would be astonished if the most efficient curve were a parabola. In the stroke, you have a blade efficiency that is profoundly asymmetrical, biomechanical efficiency that is asymmetrical, and a stroke arc that is not symmetrical about any obvious point (like the perpendicular). I don’t know what the optimum curve is, but a probabilistic argument would immediately suggest that it won’t be symmetrical. Indeed, the factors I mentioned above might suggest that it should be biased towards the front of the stroke. I wonder whether we see that in any of the force curves?

  3. Steven says:

    Has anyone translated this force curve into a speed curve? Given the force of the water against the blades, if the rower pulls with the force curve above it stands to reason that the sculls acceleration with drop at the end of the stroke – even though the speed keeps increasing.

    • Mel Harbour says:

      Steven,

      You should check out BioRow, Valery Kleshnev’s site, which has all the data you’d want. I think you’re finding it tricky to visualise as you need to be clearer about which frame of reference you’re working in.

      Mel

  4. John Sheldon says:

    It makes sense to apply the maximum force when the blade is at right angles to the direction of motion, since at all other angles some work is wasted because the blade is moving water sideways. The rate at which the force builds and decays around this angle, ie the shape of the curve, is unlikely to be significant. Recognition of this feature of the rotary oar was the basis of Steve Fairbairn’s famous short stroke style.

    • Mel Harbour says:

      Hi John,

      Sadly it doesn’t work like that. In fact that point is (purely in terms of the blade efficiency) possibly the least efficient point in the stroke. Essentially, you’re moving a small volume of water quickly at that point, rather than a large volume of water slowly, resulting in wasted energy. You’re referring to the ‘pinching effect’, which has been demonstrated to not occur.

      Mel

      • Me says:

        Pot kettle black methinks. Water is in a general sense not being moved. Rather the blade is locked (or close to it) to a point in the water and the boat levered past it.

  5. Rob McCarthy says:

    I like the thoughts from Mel and Steven, we can’t de nigh physics, its laws etc.
    Fantastic Peter, that we are openly discussing the illusive force cure/s at last. The Top Guns aren’t fools or physicists . Would you pass out your winning edge secrets?
    The traditionalist ( coach ) is closed to the visual knowledge available to us today and sadly many rowers hammer their boat down the course.
    If we piece these Curves [ force, boat speed, seat speed, oar handle speed, power, body speed, acceleration etc ] yes they can be over-layed, we will find the ultimate smooth flow of not that once-in-a-lifetime stroke all rowers seek but many end on end. You too can become a `natural’ .
    By the way a plane’s wing always creates the vortices of lift if air is flowing around it. Unless it stops in `flight’. The vortexes around the blade however do have a direct correlation to the timing and transference of these loads . Providing posture and pitch are spot on. Sorry it a bit full-on but you’ve got me excited.

  6. John Sergeant says:

    An interesting discussion but I would add a small note of caution for those rowing sweep, especially in small boats and particularly in pairs. The tendency of a pair to fish-tail (or “yaw” in aeronautical speak) is not helped by having identical (parabolic or other-shaped) force curves delivered by the two rowers. This is because the torque, relative to the (moving) centre of mass of the boat, varies through the stroke. In other words, a pair travels straighter, and therfore with less wasted energy, if the stroke has relatively powerful legs and the bow has a relatively powerful upper body. This means that the peak of the force curve is reached slightly earlier in the stroke seat and slightly later in the bow seat, reducing the costly tendency to peturb the forward motion of the shell with twisting. I would have thought that this was an obvious and well-understood phenomenon but, every time I have explained it to rowers I have been coaching in small boats, they have treated it like a revalation. Swapping seats so that the athlete stroking the boat has the stronger legs and the one in bow has the stronger upper body can eliminate fish-tailing and thereby make the boat go faster with no increase in effort, assuming both athletes are comfortable acting as stroke. This logic also applies in fours and eights. Don’t be fooled by the fact that larger boats fish-tail less than a pair; it is still using a good deal of energy to turn a big boat, as everyone knows when they try to turn one while docking or at the end of a course. There are also rigging changes that can impact on fish-tailing, but that is probably for another day.

  7. Peter Mallory says:

    We are now developing a great conversation on a crucial aspect of boat moving, just what I suspect Rebecca was hoping for with this posting on her terrific website. Many thanks to her and to all who have contributed so far.

    Let me begin by recognizing the absolute validity of mathematician Mel Harbour’s point that there are many classes of curves that resemble a parabola to a layman such as myself. Mea culpa. When I describe the dominant shape found in champion rowers and scullers as a parabola, I am using the term informally. Most rowers and coaches would recognize what I am getting at, but I have also heard the shape well described as an ice cream cone, a haystack or an upside-down U (Cornell’s Charles Courtney in 1900). Heck, Mel’s use of “symmetrical hump” works just fine for me as well.

    Now on to Harbour’s assertion that I have indulged in confirmation bias by cherry-picking examples from history that confirm my hypothesis while ignoring those that don’t. I am very pleased to report that I anticipated such potential criticism long ago and took the appropriate steps. In my recent book, The Sport of Rowing, I absolutely bent over backwards, spending seven years researching and 2,500 pages documenting 100% of the crews at World and Olympic Championships during the last two decades. One hundred percent! Then I set out the percentages of finalists across both genders and all events, sweep and scull. They range from 90 to 99% in favor of a surging pullthrough over the alternative. No cherry-picking. Zero. None. I’m quite proud of that.

    And I am mystified by Harbour’s assertion that my hypothesis is invalidated simply because humans who row in actual boats create real-world force curves which are not perfectly symmetrical and smooth to the nth degree. I cannot speak for every rower, but I know I have rowed for 53 years now, and I still only briefly approach perfection for a stroke or two on the very best of days. Tomorrow, if I am very lucky, I will get a teeny bit closer, but even if I don’t, it will be well worth the effort to try.

    On to other interesting musings:

    Mel states that his analysis “might suggest that [the optimum curve] should be biased toward the front of the stroke.” This seems perfectly reasonable, don’t you think? In fact, there are a lot of people who would agree, a whole lot. The trouble is that race results do not support this hypothesis. Few championships at the international level have ever been won with a strong front-end bias. Even the very best hypotheses must give way to overwhelming empirical evidence to the contrary.

    Now one must remember that the two force application strategies to which we are referring, Kernschlag, the German Democratic Republic term for a “solid stroke with a hard beginning,” and Schubschlag, the GDR term for a more-or-less symmetrical “thrust stroke,” are two points on a continuum. Examples of each blend into the other in the real world, so there is indeed room for interpretation, for confirmation bias on my part. I concede that another observer might come up with an 85-15% split instead of my 95-5% results. I won’t argue that I am perfect, but the conclusion stands.

    Incidentally, I am pleased to report that Mel and I have resolved in separate emails any apparent conflict between us. Passion comes with any discussion between rowers. It’s healthy and envigorating.

    John Sheldon speculates that “the shape of the curve is unlikely to be significant.” This also seems reasonable. It turns out that the shape of the curve is absolutely everything!! It’s all about the organic whole.

    John further states that “it makes sense to apply the maximum force when the blade is at right angles to the direction of motion.” I believe it is useful to look at things from another perspective. No one point, not even the point of maximum efficiency at mid-stroke, has any relevance at all except as it relates to the points immediately before and after it. In other words, each point during the pullthrough (after the theoretical initial point) is only relevant if it builds on the cumulative effort of all that has preceded it and in turn forms the foundation for the next point in the pullthrough. It’s all about the stroke as a whole. So it is enter, and then build, build, build boat speed all the way to the release. There are no prizes for effort in the front half, no prizes for effort at the mid-point. As far as force application is concerned, the boat is judged only on the cumulative acceleration imparted to the hull by the release of each stroke. Surge, surge, surge and send the boat.

    As Steven says, “the speed keeps increasing.”

    That’s the real world lesson to be learned from history, not a theory that seems reasonable or fits a hypothesis derived from physics or mathematics. In the case of Sir Isaac Newton, the apple came first, and then the laws were developed to attempt to further explain the observed real world phenomena. In rowing, the success of Schubschlag crews comes first, and if Mel Harbour or some other scientist way smarter than I can establish that the best mathematical curve that describes what actually works in the real world is a catenary rather than a parabola, then I say hooray!

    John Sergeant’s discussion of pair rowing reminds us that any ideal force application strategy must be adapted to the particular boat and the particular athletes in that boat. I would add one thing to your spot-on analysis, John. You associate front-half bias with strong legs and a strong second half with upper body strength. This is correct only to a point. I would respectfully suggest that you focus instead on the athlete as a whole. The three major muscle groups, legs, back and arms, should work in harmony with one another. If you place athletes in front of a screen displaying their force curves in real time, such as with the excellent Rowperfect system, they can change their curves in relatively short order, but I have found it is better to ask them to focus on the stroke and on their bodies as organic entities. For instance, if you say, “Drive harder with your legs,” or “Emphasize the finish,” you risk getting a segmented stroke. Better to say, “Push your haystack a bit to the left,” or “Push it more to the right,” and let their subconscious minds guide them to make the adjustments you desire. (Many of you will recognize this as the Fairbairn approach.)

    p.s. Rob, you’re my hero. Whether we are athletes, coaches or scientists, it will always be the poets amongst us who get closest to the truth.

    • Mel Harbour says:

      Hi Peter,

      Only seems fair to continue the debate!

      Can you inform me of your methodology of collecting the force/angle data for all these Olympic and World Champions? I’m not sure that that data is normally available. Obviously some examples exist, where people have rowed on a Rowperfect or been measured in a biomechanics rigged boat, but I don’t think the coverage is anything like 100%.

      You say that few champions have won with a strong front end bias. But the data clearly doesn’t support that statement. Take as a very small subset of data the ideal curve for the GB Men’s eight you quote above. It has a front end bias. Indeed, if you look at the work of Valery Kleshnev, who I would guess has built up more data on elite level rowers than almost anyone else out there, he finds that the recommended position of the maximal force is between 32% and 40% of the way through the stroke. If that’s not a front end bias, I don’t know what is! His data is built on measurements he has taken of people winning at World and Olympic level. I would argue that the number of champions he has measured exhibiting those sort of force parameters provides the requisite level of counter-example to invalidate your hypothesis that 90%+ of champions exhibit a symmetrical force curve, or even something very close to it.

      You say, as a rather throwaway remark, ‘the point of maximum efficiency at mid-stroke’, with again no justification. You’re making a really big statement there, especially, again, in the face of both theory, and empirical data to invalidate it. If that were the case, it would logically suggest that the arc should be symmetrical about the perpendicular. But yet that’s not the case – people row with a front-end-biased arc.

      And I suppose I’d better put myself out there in terms of my personal opinions on what the ‘ideal’ force curve should be. My answer is “it’s complicated”! You’re dealing with a complex, multi-variate system. We have many competing effects, such as the efficiency of the blade, the efficiency of a person’s body, the relative strength of their muscle groups, the relative mass of their body segments, and their mass relative to the boat, the conditions (wind speed, direction, water temperature), the equipment, the speed of the hull, the rig of the boat. I could go on…

      I think you can come up with general guiding principles, but I actually don’t think that it’s possible to define a perfect force curve for all situations and all people. I guess that’s where I do align quite closely with something you say, Peter. It’s known, for example, that there is a strong correlation between the point at which the force curve achieves 70% of its maximum value and the speed of the boat. But obviously we can ‘cheat’ in all sorts of ways that don’t actually make the boat go faster!

      Mel

      • Mel Harbour says:

        And to reply to myself – of course it isn’t neccesarily proven that there is only one ‘best’ force curve. There’s an assumption in there as well.

  8. Peter Mallory says:

    This is great stuff, Mel. Here are my responses to your thoughtful points in no particular order:

    Let me say that, unlike you, I do believe that there is an ideal rowing force curve, and that is the curve that most efficiently and effectively converts human muscular effort into boat speed cumulatively between entry and release of every pullthrough. That curve is smooth, and it emphasizes no one portion of the pullthrough, not the beginning, not the middle, not the end, but instead focuses on the pullthrough as an organic whole. I have rowed with people like that. I have become a rower who rows like that, and when you feel it, you immediately understand. (Not very scientific, I’m afraid. I wish we could go out in a double and I could show you.)

    You are absolutely right that there is a myriad of ways to achieve this ideal, and the specific ways that will work for tall heavyweight men versus short lightweight men, for instance, can vary considerably. (Current U.S. Coach Tim McLaren has a lot of experience in this, having coached the 1992 Australian Olympic Champion Men’s Double, two lightweights, and the huge coxless-four that dethroned the Oarsome Foursome a few years later.) There is also the fact that some athletes thrive rowing short and high while others excel at long and low. Nevertheless, the shape of the ideal curve remains the same. So I agree with you: “It’s complicated.”

    My methodology: Forty years ago, Olympic and World Champion U.S. Coach Allen Rosenberg told me he could look at any athlete for a few strokes and discern all he needed to know. No need for seat racing or ergometers. I thought he was bluffing. I thought it was impossible. Now after fifty-three years in the sport and seven years of analyzing film frame-by-frame for hours each day, I realize that Allen was not bluffing. All it takes is a very educated eye (though I admit I still look at ergs and still believe in seat racing).

    But my eye is not all I have to judge with. I have rowed all over the world using a myriad of styles with a myriad of teammates. I have rowed with World and Olympic Champions, and I have rowed with novices on their first day in a boat. I have coached by rowing alongside my crews for decades.

    I have benefitted from the many force curves collected by Cas Rekers, the inventor of the Rowperfect rowing simulator. I have recorded several hundred curves on my own. I have amassed what is probably the largest database of rowing force curves of elite rowers in the world.

    I put all that together and made a visual survey of 100% of the finalists in every World and Olympic Regatta back to 1994 (and every other year where film evidence has survived going back to the dawn of outdoor action film technology). The evidence is clear and consistent, and I have reported it in detail in The Sport of Rowing.

    Now before you accuse me of the egregious absence of scientific rigor in my reliance on a visual survey, let me remind you that even scientists are forced to work with the evidence at hand, and I defy you to name anyone on Earth who has expanded the information database more than I have.

    And really the job at hand is not that hard. The challenge is to discriminate between a front-end explosive pulse, easily identified by legs going flat at 50-60% of the pullthrough, and an emphasis on the organic pullthrough as a whole, also easily identified by legs going flat at 80-100% of the pullthrough. Is there a clear demarcation between the two? Most of the time, but not always. There are a few hybrid intermediate examples you and I could debate and end up disagreeing on.

    Are my eyes perfect? Is my judgment infallible? Am I foolproof? Of course not! But Mel, I bet that you and I could sit down together and survey one year’s DVD, and even if our counts differed by 10% or 20%, you’d still be astonished at the overwhelming number of Schubschlag over Kernschlag crews we would both identify.

    You would find that the preponderance of data does indeed support my thesis.

    You keep coming back to the Mahon-authorized curve used by the 2000 British Men’s Eight not being exactly symmetrical. Harry brainstormed his ideal curve with Rowperfect’s Cas Rekers and 1982 World Champion bow-man Tony Brook. I know Harry’s intent because the conversation was described to me by both Cas and Tony. The Atrill curve used as a template was essentially a symmetrical haystack with a bit of a tail due to late arm draw, but the character of the pullthrough as an organic whole remained. I encourage you not to get so hung up on small deviations from an ideal. Focus on the general personality of each rowing stroke. Believe me, a true front-end bias curve looks nothing like the Atrill curve. Take Mahe Drysdale. He is a great example of a competent and successful front-halfer, but he is also nearly unique in history.

    I’m glad you mentioned my good friend, Valery Kleshnev. He and I have had a long discussion about this very subject, and I cover it in great detail in The Sport of Rowing. Valery has written repeatedly that he has tested more than 5,000 individuals and that around 85% of them front-half their pullthroughs. When I began my own research, I expected to confirm Valery’s results by finding similar percentages, and after all, if you go to a high school or small college championship or a masters regatta in the United States, that’s pretty much what you would tend to see. Well, when I looked at international regattas, I was shocked to discover not 85% front-halfers but more like 5-10% front-halfers. This begged for an explanation.

    First I questioned my data. I went back over my analysis and kept surveying more years, more regattas. My results remained consistent. I interviewed athletes and coaches. I rowed with athletes myself. I tested athletes. No inconsistencies. They were all confirming what I was seeing.

    Then I thought to myself. Every how-to rowing book in the world (with the exception of Steve Fairbairn’s books) describes the pullthrough as a sequence of legs first, then back swing, finishing with arm draw, so it is not surprising that most rowers begin their careers rowing sequentially. I am glossing over a lot of detail here, but sequential rowing often leads to front-half emphasis. At the lowest levels of our sport, perhaps the percentage of front-halfers even exceeds 85%. This is the group that Valery has often worked with both in Australia and now in Britain, not World and Olympic Champions as you state. As the athletes progress from local to regional to national to international levels, there is a natural winnowing out process. Only the most successful progress to the next level. By the time athletes reach World and Olympic finals, we discover there are hardly any front-halfers left, which is yet another argument in favor of the superiority of surging Schubschlag pullthroughs.

    What never ceases to amaze me is the way that true-believers cling to their orthodox beliefs in so many corners of human culture, but none more than rowers. How do you explain the preponderance of our greatest coaches of history describing and/or teaching surging force application? In America, Charles Courtney, Hiram Conibear and his immediate followers, Frank Muller, Joe Burk, Frank Cunningham, Tom McKibbon, Harry Parker (after the 1960s), Steve Gladstone, and now Mike Teti, Tom Terhaar. In world rowing, Fairbairn, Karl Adam, Körner, Janousek, Klavora, Korzeniowski, Spracklen, Buschbacher, Mahon, Jutta Lau, Grobler, Tonks, Paul Thompson? Are you really able to dismiss the lessons of all these coaches and their crews? The GDR juggernaut? Redgrave’s crews? The Oarsome Foursome? The Evers-Swindells? Brian Volpenhein and the 2004 Olympic Champion U.S. Men’s Eight? Olympic Champion Scullers from Kelly to Beresford to Ivanov to Scheiblich to Karppinen to Lange to Karsten to Tufte?

    I keep repeating this: Don’t take my word for it, Mel. Listen to the great coaches of our past and present, and look carefully at their athletes and crews. Learn from history. That’s what my book does. Go read it.

    Here’s some homework. Off the top of my head I can think of five individuals in the last 50 years who won Olympic titles while front-halfing: Martin Cross, Xeno Muller, Rob Waddell and a couple of guys in the 2004 U.S. Eight (and I’m not so sure about Xeno even though he tests that way). See if you can come up with a few more.

    Have a great weekend.

    • Mel Harbour says:

      Some interesting statements of not-quite-fact in your post, Peter…

      In order to invalidate Valery’s data, you basically intimate that the quality of the athletes he recorded and worked with were low level. “This is the group that Valery has often worked with both in Australia and now in Britain, not World and Olympic Champions as you state.” in your words. So the periods when he’s been working with the AIS, and in particularly people like James Tomkins and Drew Ginn, or the period when he was working for the EIS and the British team, or currently, when he’s working with the Danish lightweights don’t count as being high level? Interesting…

      So, from your process, your ‘evidence’ that top level rowers produce symmetrical force curves is that you’ve measured film/video of lots of them, and attempted to back calculate the force curve from that data. Unfortunately, that’s a totally flawed methodology. You simply can’t do that. There are other input variables that are changing at any point, that mean that it fundamentally does work. Secondly, with a sampling rate (for video) of around 25 frames per second, your data sampling rate is actually very low. So, from a scientific perspective, while your data is better than nothing, in comparison to properly, and directly, measured biomechanical data, it should be ignored.

      Let’s look at something slightly more concrete that you do quote. Rowperfect force curves. You’ve collected presumably more than are ‘publicly available’. But, so everyone’s on the same page, let’s just work with the ones that are available publicly. These are mostly taken from successful high level rowers (Olympic and World Champions). If we look at the ones that Rowperfect distribute, every single one of them has the power peak somewhere in the first half of the stroke, and shows a bias of the area under the curve towards the front end of the stroke. In other words they are all front end biased. So, sadly for you, the facts are running very much counter to what you’d like to believe.

      Now let’s look at proper biomechanical data generated by direct measurement on the water. What we see from that is that in both crews with a late power peak, and an early power peak, we see a handle speed curve that increases through the drive and peaks in the second half. In other words, we have direct proof that the method you are using to ‘calculate’ the force curve is fatally flawed, and produces data that is wrong. Indeed, scientifically, when you generated that data in the first place, and found it to be out of alignment with existing data, what you should have done is not question the validity of the other data, but rather question your collection method (and theirs). If you had done so, you would have seen that your collection method does not stand up to scrutiny.

      As I mentioned above, you’re saying that the data Valery records is of lower standard rowers. Here’s a link to the latest newsletter. The data he is presenting is from the Danish LM4-. Not exactly lower standard rowers, I’m afraid! Look at figure 1a. What do we see? Oh look, force curves heavily front-end biased, with the power peaks in the first half. Again, in line with Valery’s recommendations for elite level targets. For reference, you can find these targets here (last page). Note the prognostic times – he’s talking about elite level crews, not beginners here (unless you’ve seen beginner eights targetting 5:18!). Looking just at the LM4- targets in that document, he’s talking about a power peak 35% through the arc, achieving 70% max force after 13 degrees, and dropping down below 70% 20 degrees from the end of the stroke. That is profoundly not a symmetrical stroke.

      So, in summary, I have shown that you data collection method is flawed. I’ve shown that the available data, and summaries of that data for elite level athletes show the opposite conclusion to the one you’d like to see. You’re left trying to argue your case without any data that has been collected via a solid method. Scientifically, you now have no choice, but to accept that reality is different to what you want it to be, and to redraw your conclusions. Of course, you can continue with your view, but by doing so you’d be joining the ‘flat earth society’, and choosing to ignore the evidence to the contrary.

  9. Alistair Potts says:

    I’m pleased Rebecca’s found a topic that’s generated some healthy chat, although this is pretty much the equivalent of inviting Mystic Meg onto Thought for the Day.

    Really, this is pretty silly. You start of by telling us how we can see a parabola (among others) “by recording Kris Korzeniowski’s force curve while rowing!” I presume that’s what the graph is you’ve chosen to show. It’s nothing like a parabola. The ratio of the area under each side of the midpoint is 8:7 , in other words the left side is nearly 15% bigger than the right. Since you evidently can’t recognise a parabola, I can’t really take your assertion that everyone from John Kelly to the Evers-Swindells also parabolises very seriously.

    You’re welcome to think that the rowing well has ‘cosmic implications’. But to infer that one of those implications is that the perfect stroke must follow a simple mathematical formula is not just fallacious but lazy. You must go into a rage at seeing the front wing of an F1 car. And shaving in the morning must be particularly onerous as you gaze at your own head, so cruelly not a perfect sphere. (Mine isn’t either.)

    Then you list off a bunch of coaches from the who’s-who of 20th century rowing, some of whom are dead, and suggest they would readily sign up to your quasi-religiously-inspired notion. That’s the point where your innocuous nonsense becomes pretty obnoxious. And trying to defend it by rubbishing your naysayers are reactionary just marks your zealotry out for what it is, I’m afraid.

    • Peter Mallory says:

      Alistair –

      You seem to be directing your comments directly at me, so let me respond directly . . . and let me attempt to maintain a civilized and constructive tone.

      Look again at the Korzeniowski curve. The vertical center line was arbitrarily drawn by the primitive compter program I was using when the curve was generated more than 25 years ago. If you adjust the placement of that line, then the Korzo curve will be easily recognized as about as symmetrical as you will find in the real world.

      As for my being able to recognize a parabola, My mistake is that 1) I have been using the term informally and without scientific rigor, and 2) any nonscientist not intent on discrediting me would immediately understand what I was getting at. That has turned out to be a dreadful strategy when dealing with you and Mel, so I have no one to blame but myself. This discussion has degenerated into the Spanish Inquisition, and it deserved better. I’m sorry.

      You accuse me of being a zealot. I consider myself a rower first, an historian second, and an observer of human nature perhaps most of all. Your abusive language would fit extremely well into virtually any period of rowing history, and so I applaud your passion and your faith in your beliefs.

      Let’s just agree to disagree from this point forward.

      • Mel Harbour says:

        Peter,

        Alistair’s comments about the symmetry (or rather, lack thereof) aren’t based on the position of the centreline drawn. It’s just a statement of fact about the curve. It’s not symmetrical. It’s nothing like symmetrical. Just like every other force curve. And ‘about as symmetrical as you find in the real world’ is a nonsensical statement – that’s like saying ‘well the Earth is nearly flat, so it must actually be flat’.

        Your statement that this has descended into an inquisition shows your misunderstanding of the process that we’re following. You have proposed a theory. Like any theory, it may or may not be true. It is entirely correct, and not in any way offensive for others to attack the theory, and work out whether there are any weak points in it. The first time Andrew Wiles put forwards his proof of Fermat’s Last Theorem it was (after some debate) ‘returned to sender’ – it was proved to be wrong. It’s a fact of scientific life – that’s what we do. And it’s a useful, constructive exercise. The problem arises because you’ve seen your theory demolished, and unfortunately you’re too attached to that theory and hence see the attacks as personal. They’re not – they’re attacks on the (flawed) logic of your theory and the way you’ve built it up. They’re only personal in the sense that we’re getting frustrated that you’re hanging onto the theory in the face of overwhelming evidence and logic to the contrary.

        Mel

  10. Rob McCarthy says:

    For The Fun of Rowing.
    To through a spanner in the works. Try this little game with your crew on your Rowperfect.
    This helps each rower to create cosmic connectedness in the 4th dimension. Possibly on club night!

    On the RP each rower in turn.
    Rating- 18 -25
    Effort – 40% – 60% only
    5 Strokes to compose one’s thoughts ( No noise from the on-lookers)
    The next 4 strokes must be the most – parabuolickularily and diametrically shaped humps ever created whilst rowing
    After LOL recovery by all
    Re Play (scroll) the 4 strokes for the crew to cast their vote ( 0 -10 ) 10 points Being the 4 most outrageous
    Repeat for each rower
    Talley the points and enter names on the ladder chart

    Tip for curves, Left bias, right bias , loaf of bread, ice-cream cone, jiggery ( uncoed), C4 detonation, etc.
    Objective: To have rowers who can think for themselves and aware of their actions
    Have Fun!!! Winning is a bonus.

  11. Steven says:

    Don’t we need to consider the optimal force per energy expended curve and not just the optimal force to move the boat?

    That is. A curve that moves the boat most efficiently may not be effective use of the body.

    An example. Say we were to say that the catch where the most efficient time to drive the boat forward. (not the case, just hypothetical). However, the legs at the catch have the least leverage and so significantly more energy is required to drive the oar at that point. To experience this. Try your max leg press weight at close to your legs locked. Now try that weight when your legs are at at 90 degrees.

    • Peter Mallory says:

      For me, it’s all about the organic whole, not one ideal point or another, but you are absolutely brilliant in repeating the assertion that efficiency and effectiveness must both he achieved in the quest for a workable force application strategy, and this would be true for a specific boat or specific athletes or even an abstract and possibly imaginary ideal.

  12. Jim says:

    Why are we getting hung up on precise mathematical definitions when the assertion seems to be put the blade in, accelerate to the finish and release? I don’t really see how you can argue against that. The problem isn’t that the equations which govern the mechanics are particularly complex, but that the interaction of the components in the system make it so (hence the shape of that F1 wing). In a crew boat, in the real world, the curve is always going to be a fudge because (unless you have a four of quadruplets) the athletes are not biomechanically identical and you will need to find the best compromise.
    I do like the idea of an organic approach, because as soon as you start to impose dogma you are losing sight of what you are trying to achieve, a winning boat. The system (equipment and crew) doesn’t care how you think a boat should be rowed, just what it needs to move.
    Going back to some earlier posts, my fluid mechanics may be very rusty but I would have thought an analysis of the blade action would be more like a centrifugal impeller rather than a wing, especially not a delta wing shedding vortices to create lift. Yes? No?

    • Mel Harbour says:

      Jim,

      As far as the vortex shedding part goes, if you look at some good photos of a blade from above, you’ll see precisely the vortex shedding that you’d expect to see to indicate the circulation associated with creating lift.

      Mel

      • Jim says:

        Fair point. I am on shaky ground here as it has been quite a few years but don’t you see the same vortices at the tips of impellers? Aren’t they here a negative byproduct, being associated with the slip factor rather than the actual mechanism of imparting energy?
        If you were to somehow prevent the vortices from forming (by preventing water transferring front to back around the edge of the blade) would that make the blade less efficient?

        Jim

  13. Peter Mallory says:

    Mel –

    What can I say? This whole exchange is becoming less and less stimulating for me, but I started the discussion, so it doesn’t seem right for me to back away just because it’s become increasingly unpleasant.

    Let’s agree that neither of us is going to convince the other of the rightness of our positions on the subject of force application in rowing, but let’s see if we can at least show some mutual respect and a little dignity. I suggest we both try to keep the personal attacks to a minimum and see if we can make our discussion something that other readers can actually learn from, or at least be entertained in the process. Maybe we can even sell a couple of Rowperfect systems along the way.

    Let me be clear. I never once suggested that Valery Kleshnev’s data was invalid. I only stated that I could not confirm his percentages by specifically sampling athletes at any recent World Championships. Valery does great work and has worked with many great athletes. The entire world rowing community, myself included, has benefited from his research and continues to do so.

    You mention James Tomkins. To get a sense of what it is like to row with him and what his philosophy of force application is, read Chapter 156 of my book. Tomkins is a Schubschlag rower, by the way.

    You mention Danish Lightweights. Three-time Olympic Champion Eskild Ebbesen’s recorded curve is a slightly left-leaning haystack. Rasmus Quist’s recorded curve is more-or-less symmetrical. You also could have cited the Italian Lightweights of the ‘80s and ‘90s, perennial World Champions and well known for their explosive catches. There are other pockets of Kernschlag believers all over the world. I wouldn’t be surprised if the majority of rowers on Earth, including Valery Kleshnev and Alistair Potts, another passionate contributor to this discussion, agree with you and not me on force application. My only point is that history indicates that Schubschlag has found more success than Kernschlag, and by a wide margin. It is also the consensus of the majority of the great coaches throughout history.

    You call my inference of force application from close visual observation and stop-frame analysis a “flawed strategy.” I call it working with the only data available, and I have supplemented it with interviews with athletes and coaches and with actually rowing with a number of Olympic Champions. What have you done besides reading Valery Kleshnev?

    But let’s agree that we would both prefer to work with recorded force curves from every athlete at every World Championship. If only such data existed!

    As for the publically available Rowperfect curves, you unequivocally state that “every single one of them has the power peak somewhere in the first half of the stroke.” First of all, I’m sure you mean “force” and not “power” since as a scientist I don’t have to explain to you that power is always increasing from catch all the way to release because of the increase in the speed of the hull during that period. But second and more importantly, your statement is incorrect. Of Rekers’ curves of world-class athletes, those of Mahe Drysdale, Eskild Ebbesen, Frans Goebel, and Derek Porter could be classified as left-leaning Kernschlag force curves. Peter Haining actually hits the second half of his pullthrough. Thomas Lange and Greg Searle have more-or-less symmetrical Schubschlag force curves. Then there are the curves of Louis Atrill, Sebastien Casset, Vaclav Chalupa, Jean Christophe Roland, Niels van der Zwan, Sarah Winkless, Henk-Jan Zwolle (and Cas Rekers himself). All are Schubschlag rowers who break their arms late and/or employ a ferryman’s finish. What this generates is a curve that looks a lot like a near-symmetrical haystack but has a little tail at the end. As a rigorous scientist, you apparently classify these curves as having a front-end bias, and I would say to you: Bravo! But as a rower, I would say these athletes surge smoothly through the first 90+% of the pullthrough before their effort at boat moving literally “tails off.” From this point of view, one could seriously consider adding Drysdale and Ebbesen to this category, and maybe even Goebel, leaving only Derek Porter in the true Kernschlag camp.

    By the way, I spoke at some length with Derek about his force application, and this is part of what he told me: “I do tend to row more leg drive and hang off with the back and then finish at the end rather than more concurrent, which would be like a Thomas Lange. That is the technical change I was trying to make between 1996 and 2000. I wanted to initiate the back drive a little bit earlier and engage that concurrent movement so that I would finish my arms, back and legs more together.” (He never managed to successfully make that change.)

    Mel, I’m so regretful that I ever mentioned the words “parabola’ or “symmetrical.” You have shaped them into clubs and mercilessly beat me over the head with them. Just think Kernschlag or Schubschlag, pound the catch or surge to the finish, and maybe someday we can actually have a constructive and illuminating conversation.

    You then say that “proper biomechanical data generated by direct measurement on the water” provides “direct proof” that my method is fatally flawed. What data? Where’s your data? And you go on to state that my collection method does not stand up to scrutiny? What scrutiny? Your scrutiny? No specifics from you, just absolutist conclusions.

    Now let’s take a deep breath and review your discussion of the latest Rowing Biomechanics Newsletter, figure 1a. You keep using the scientific term “power” when you mean “force,” a serious mistake I would not expect from a scientist. Regardless, what figure 1a shows is that the bow-, 2- and 3-seats are indeed Kernschlag rowers with an initial pulsing leg kick followed by a separate second effort by the upper body, producing a 2-part pullthrough. If this is your ideal force application protocol, Mel, you would find little support amongst successful international-level rowers and coaches anywhere in the world and any time in history. The stroke-seat is a Schubschlag rower with late arm draw, a trait he shares with his three boat mates.

    You characterize this boat as “heavily front-end biased,” and while there is a lot more than that going on, I won’t debate this further with you because the distinction you are making is meaningless to me. What counts is surge to the release, and in this boat the stroke does it quite well while the others are less effective. Please forget I ever mentioned symmetricality. I get the impression that you have no interest in trying to get past my poor choice of words to the essence of what I am trying to convey.

    Now it is interesting to note that Valery only identifies the boat as a “top international four” and that he got the information from Eskild Ebbesen and the Danish Rowing Federation. Ebbesen’s curve does indeed resemble the curve of the athlete in stroke, but it would be interesting to ask who the athletes tested actually were and if any of the various historic Olympic Champion Danish Lightweight Coxless-Fours ever had such a marked disparity of force application within them.

    Now to your summary. You state you have proved your points to your own satisfaction.. Oh my yes, I get that. You are the enlightened scientist, and I am the member of the flat-earth society. I get that, too. That is why this discussion is becoming increasingly tedious. Do you have some sort of origin story that explains the strength of your conviction? Do you have some in-boat anecdotes to back up your view of how best to move boats and how you came to embrace it so passionately? Because it’s really all about sitting in a boat and rowing, not lab testing or theorizing. It’s all about what works out there in the world, not what makes sense or fits your preconceptions or mine.

    More than once you have accused me of confirmation bias, that I already had my mind made up and then went out in search of data to back up my pre-existing world view. If you only knew? I was taught to row the technique you must have been taught as well, and I followed those teachings with messianic zeal . . . until I could ignore no longer the fact that I was being beaten by others doing it a different way. It took me years. I fought hard. I indeed searched hard for explanations that did not involve letting go of my fundamental beliefs about rowing. If you had known me back then, 35 or 40 years ago, you would have been absolutely right about me and confirmation bias.

    But no longer. During my seven years of research for The Sport of Rowing, I had to give up several fundamental beliefs because history clearly showed they didn’t work, a humbling experience, I can tell you. Today for me it’s all about what works in boats.

    Let’s agree that your world view works just fine for you. I respect that, so keep holding on to it. You are upholding a long and storied tradition in rowing. I salute you.

    • Mel Harbour says:

      Sorry it’s taken me a while to reply, but I’ve been quite busy, and struggling to find the motivation to pick your answer apart again, when you don’t seem to want to listen. I have two aims here – firstly, I want to try and open your eyes to the ridiculous nature of a lot of what you are saying, secondly I want to open other people’s eyes to the same problems, so that further myths about rowing are not sent out there unchallenged.

      You again say that I’ve engaged in ‘personal attacks’. I have done no such thing. I have observed a lack of scientific rigour that you are displaying, which is simply a statement of fact. Nothing personal about it.

      Let’s first separate what rowers and coaches think they are doing, and what they are actually doing. You started this whole discussion as one of force curves. This is measurement of what they are really doing. It’s perfectly possible that they need to think they are doing something different in order to achieve this. A classic example is the need of racquet sport players to think about ‘hitting the ball slower’ sometimes – not what they’re actually going to do. Within our own sport, it’s frequently the case that people thinking about being too fast in the blade entry are often actually slower due to tense muscles. So the two are profoundly different. You wanted to talk about reality though, with bringing up force curves.

      So, force curves. Yes, I used the term power curve, which is wrong, and you are right to pull me up on it (as an aside, see what it looks like when someone doesn’t get offended by having their mistakes pointed out!). It wouldn’t actually make a difference though – the power curve is a modulation of the force curve. I don’t quite understand why you think that it would rise all the way to the finish. Since force falls to zero by the finish, clearly power does too!

      The point of my ‘flawed analysis’ comments is to try and educate you that the visual analysis you have conducted does not allow you to conclude anything about the force curve at all. It’s a nice idea that it might, but the reality is that it doesn’t. It’s not dissimilar to the idea that erg scores would be a predictor of boat speed. There’s a correlation, sure, but erg scores do not account for anything like the total variability in boat speed. And I doubt that you, or anyone else, would suggest that we should choose erg scores over boat speed! My point about your method being fatally flawed is that I can easily identify factors that influence the force curve that are not observable from a side-on series of pictures. For example, you take no account of the fluid dynamics of the blade in the water, and whether it will be slipping more or less at any point. As such, while you can use the pictures as a partial proxy, you are unable to use them to draw any actual conclusions. What you are observing is something that closer approaches handle velocity (with respect to the hull).

      Peter Haining might be a good example to pursue. Look at his force curve. It categorically PEAKS (highest force) in the first half of the stroke. He actually then has a slightly unusual second half of the force curve, showing a marked flattening of the curve, probably related to a strong arm draw in some way. But that doesn’t change the fact that his force curve peaks in the first half (markedly so) and is about as far from a parabola, or anything symmetrical as you can see in a top class rower/sculler!

      You cling, both here and in your book, to your chosen method of classification of rowing stroke, namely ‘kernschlag’ and ‘schubschlag’. But you then conflate the concepts of what’s actually happening, with what the rower is feeling is happening. If we’re talking about force curves, only the former is relevant.

      As I said above, your data is actually that of handle velocity relative to the boat. It might be instructive to look at (again) some directly measured data on this. Let’s go with the latest biomechanics newsletter (http://www.biorow.com/RBN_en_2012_files/2012RowBiomNews05.pdf). Let’s in particular look at sculler 2 (blue line). He’s got a 2k on the water of 6.34, which certainly narrows down who it can be! There’s a fairly full set of data there to look at. In particular, we can see a couple of things:

      * The force curve once again peaks in the first half of the drive
      * The force curve has a strong bias towards the front half of the drive – there is significantly more area under the curve in the first half than the second.
      * The handle velocity curve biases towards the second half.

      Again a very strong counter-example to your theory that the perfect force curve is anything like symmetrical.

      Unfortunately you betray yourself in your reply to me though. Having to deal with the fact that the information being presented strongly contradicts what you’d like to believe, you resort to a classic argument, namely ‘but have you got any direct experience or opinion to back this up?’. In other words, you are asking me to move away from data that can tell us what actually happens, and back into the world of anecdote, which is exactly where we are trying to get away from by being able to actually measure what’s going on.

      I don’t understand why you can’t just do what is the only reasonably logical conclusion to this discussion, and issue a statement at the top of the article retracting it, as the information contained within is demonstrably not sound. I’m not for a minute suggesting that the work that you’ve done in collating all the information contained in your book is anything short of incredible. I have much enjoyed the free chapters that have been available on Row2k over time. But this article in particular is sadly flawed.

  14. Rob McCarthy says:

    Cograt’s Peter , you have two chapters for you new book. Cheers

    Here’s a thought provoker for you: A Rower only needs an oar to get down the slide (to the back-stops) . This thought encompasses physics we’ve been too frightened to comprehend .

    More on Force Curves come on [ from the catch to the peek of a `humped curve` – half of the force applied is wasted……]
    What if that first portion is hollowed[ a hollowed force curve ]?. There is no wasted force .

    • Peter Mallory says:

      Think about it, Rob.

      Nevertheless, you bring up an interesting point about the shape of rowing force curves. The climb of the curve from the catch to the peak does not represent force wasted. It is merely overcoming inertia, like a heavy rocket seeming to take forever to inch away from the launch pad and clear the gantry as it slowly gathers speed. Meanwhile, the force being applied by its motors remains constant. As for the curve’s shape, convex or concave, humped or hollowed, it turns out that as long as the curve remains convex, the boat is accelerating organically. Whenever it turns concave, you have an interruption of the acceleration. This can occur at midstroke, as in the Kernschlag curves of three members of the Danish four discussed above, or toward the end of the stroke if the athlete employs delayed arm draw or a ferryman’s finish. All this is discussed at great length in my book. Not mentioned in my book is my personal preference for maintaining convexity from catch to release, but I provide plenty of examples of successful athletes who have chosen to follow other paths.

      And thanks for your tone, Rob. It is a breath of fresh air.

  15. Philip says:

    Everyone who has wasted their time here reading and responding to nonsense when none of our opinions are changing (aren’t they?) needs to go out for a long, quiet row.

    I’d say more, but I’m afraid I now am one of the people I was talking about and need to go take my own advice. I encourage you to do the same.

  16. David Harralson says:

    Very interesting set of comments so far. However, I would submit that there is no “perfect” force curve, it varies from athlete to athlete and depends largely on their physiology.

    Also, this talk about a “perfect” force curve has applicability only in the single. Every multi-rower boat has much more complex requirements.

    I will illustrate with a personal example. I started to row at 70 and am a lightweight at 1.8 m (5’11”). My coach is an ex-world cup lightweight. One day, he asked me to row with him after practice, and I had him rig our rec double as a pair. As we pulled away from the dock, the boat “wiggled”. I said to myself “Aha, I know what is causing that!”. I envisioned what his force profile might be like and adjusted my force profile to what I judged to be a more compatible profile. Voila! The boat straightened out and my SpeedCoach app said our check/bounce was below 10 and we were rowing as quickly as when I coxed our eight.

    In our first race, with only two practices, we had a faster time than our 4+, and at the same stroke rate.

    Now, I will not draw conclusions from one example. However, I think I can fairly state some or all of the following:

    Each rower will have an optimal force profile that somewhat depends on leg length, thigh length, upper body length, arm length, and various muscle attachment points to the skeleton that determines the efficiency at which muscle force can be translated to real force at the foot stretcher/oarlock.

    Every multi-person boat has much more complex force profile requirements. The prototypical example of this is in the pair, where “magic pairs” row faster than pairs that out erg them. This can be extended to the four and eight where the best ordering of rowers will produce a happier and faster boat. But this is also true in sculling boats. The SpeedCoach check/bounce readings change whether I row in bow seat or as stroke in a double, and depending with whom I scull.

    The check/bounce readings also vary widely depending on with whom I row in the pair despite my attempts to be compatible with my partner. One guy and I are much smoother together, and I notice that coach often has us paired together in the four and eight. I think that the best coaches have the implicit ability to determine these optimum pairings.

    In conclusion, as a mathematician I appreciate the attempt to derive mathematical explanations for our rowing endeavors. As a pseudo athlete I realize the ultimate futility in other than the most general conclusions being reached.

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