Everybody knows intuitively how athletic performances evolve with age. They start by improving steadily during the first two decades of life then taper off and start gradually decreasing with advancing age. What is astonishing is that, barring injuries and/or illness, the evolution is particularly smooth.
Below I give the evolution of best performances with age for high jump. Both branches follow roughly straight lines and the ratio of the slopes is around 5: as I have already explained young athletes progress five time faster than old athletes slow down.
My friend D. Harder, the author of the excellent "Sports comparisons: you can compare apples to oranges" monograph, has computed age indices for the various athletics' disciplines. You can see below his results for high jump. Quite expectedly they are following the world record evolution i.e. dividing the record by the index should give a performance more or less constant throughout the various ages of life.
Of course, the natural question is whether these findings are specific to athletics. So I decided to try the same approach for something quite different, namely swimming. Before presenting the results, some background is in order. What is the physical quantity one must use in order to characterise performances? As I have explained in my publication "The physical basis of scoring the athletic performance" which appeared in New Studies in Athletics 22 (2007) page 47, the best candidate is the amount of energy that can be converted into work, necessary in order to produce the performance. For jumps and throws the result, be it length or height, is directly related to the kinetic energy of the athlete. For races, the energetic cost is a linear function of the velocity (with the exception of very short races, where a quadratic term does play a role). So it makes sense for athletics to discuss the performances in terms of the velocity for track events and in terms of the distance (horizontal or vertical) for the field ones. When it comes to swimming, things are more complicated. The energetic cost is definitely not a linear function of velocity. However it is neither a cubic function of velocity, as a naïve application of hydrodynamics would suggest. Thanks to the pioneering work of di Prampero we know now the energetic cost of swimming is a smaller power of the velocity. This can be explained by the fact that the swimmer is not a rigid body but optimises his shape while swimming. In the graphic below I opted for a power of 2.6 (but the results would not have been substantially different had I used a cubic power). The graphic is based on the US age records (which are the only ones I could easily find).
Again, just as in athletics, the two branches are essentially linear and the ratio of the slopes again around 5. This is a most interesting result. It shows that the curve of rise and fall of the athletic performances with age is universal.
Whatever the discipline, whatever the sport, one expects that the evolution of performances will statistically follow the "rise & fall" curve above. Notice that the curve passes through 0 at an age of zero and again at around 125 years. As I explained in a previous post of mine this is the theoretical maximal life span, i.e. an age that no human can expect to exceed.
Of course the universality of the rise & fall curve must be understood as an abstraction. When we talk about a specific individual one expects deviations form the curve (even under optimal conditions health-wise). Thus the performances of a given population are expected to vary within bounds which will roughly follow the universal curve. This corresponds to the shaded part delimited by the two curves as shown in the diagram below.
And then there is another particularity, that of the 'late bloomers'. Not all individuals age at the same speed. So it may happen that some athletes, who are not distinguished when young, start excelling at a later age. This is illustrated by the red line in the diagram above. Unfortunately, just as late bloomers exist, so do "early witherers", people who are among the top tier when young but who regress faster than the average person. But, whatever the scenario, one expects the evolution of the performances of any individual to be governed by the universal curve: one can never stray very far from it either in the positive or in the negative sense. The only thing that can disrupt this regularity are health problems and/or accidents. (Unfortunately, both are quite common).
Below I give the evolution of best performances with age for high jump. Both branches follow roughly straight lines and the ratio of the slopes is around 5: as I have already explained young athletes progress five time faster than old athletes slow down.
My friend D. Harder, the author of the excellent "Sports comparisons: you can compare apples to oranges" monograph, has computed age indices for the various athletics' disciplines. You can see below his results for high jump. Quite expectedly they are following the world record evolution i.e. dividing the record by the index should give a performance more or less constant throughout the various ages of life.
Of course, the natural question is whether these findings are specific to athletics. So I decided to try the same approach for something quite different, namely swimming. Before presenting the results, some background is in order. What is the physical quantity one must use in order to characterise performances? As I have explained in my publication "The physical basis of scoring the athletic performance" which appeared in New Studies in Athletics 22 (2007) page 47, the best candidate is the amount of energy that can be converted into work, necessary in order to produce the performance. For jumps and throws the result, be it length or height, is directly related to the kinetic energy of the athlete. For races, the energetic cost is a linear function of the velocity (with the exception of very short races, where a quadratic term does play a role). So it makes sense for athletics to discuss the performances in terms of the velocity for track events and in terms of the distance (horizontal or vertical) for the field ones. When it comes to swimming, things are more complicated. The energetic cost is definitely not a linear function of velocity. However it is neither a cubic function of velocity, as a naïve application of hydrodynamics would suggest. Thanks to the pioneering work of di Prampero we know now the energetic cost of swimming is a smaller power of the velocity. This can be explained by the fact that the swimmer is not a rigid body but optimises his shape while swimming. In the graphic below I opted for a power of 2.6 (but the results would not have been substantially different had I used a cubic power). The graphic is based on the US age records (which are the only ones I could easily find).
Again, just as in athletics, the two branches are essentially linear and the ratio of the slopes again around 5. This is a most interesting result. It shows that the curve of rise and fall of the athletic performances with age is universal.
Whatever the discipline, whatever the sport, one expects that the evolution of performances will statistically follow the "rise & fall" curve above. Notice that the curve passes through 0 at an age of zero and again at around 125 years. As I explained in a previous post of mine this is the theoretical maximal life span, i.e. an age that no human can expect to exceed.
Of course the universality of the rise & fall curve must be understood as an abstraction. When we talk about a specific individual one expects deviations form the curve (even under optimal conditions health-wise). Thus the performances of a given population are expected to vary within bounds which will roughly follow the universal curve. This corresponds to the shaded part delimited by the two curves as shown in the diagram below.
And then there is another particularity, that of the 'late bloomers'. Not all individuals age at the same speed. So it may happen that some athletes, who are not distinguished when young, start excelling at a later age. This is illustrated by the red line in the diagram above. Unfortunately, just as late bloomers exist, so do "early witherers", people who are among the top tier when young but who regress faster than the average person. But, whatever the scenario, one expects the evolution of the performances of any individual to be governed by the universal curve: one can never stray very far from it either in the positive or in the negative sense. The only thing that can disrupt this regularity are health problems and/or accidents. (Unfortunately, both are quite common).
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