Exploring the Variation in Movement Capacity of Individuals

[expn]

Hello to all forum members, I came here in an attempt to find a solution to a problem that has been "haunting" me for some years.

I have been trying for some time to understand mathematically the variation in the movement capacity of individuals, based on their effort. In other words, I would like to know why we use up our energy over short distances, when we travel at high speed; but we are able to travel much longer distances when, if we do it more slowly.

Although I really like physics, my knowledge is limited to what I learned in school, many years ago; and I couldn't find a formula that describes this relationship by looking on the Internet. The closest I got was a table, which lists the maximum power that cyclists in different categories at time intervals predefined. When searching for publications by the author of the table, I found a lot about physics applied to cycling, but I couldn't find any formal explanation about the phenomenon registered in it.

Finally, I tried to deduce a formula, based on the table above, using numerical methods; but I got an equation with several variables, which I can't relate to any real-world metrics:$$f\left(n,\,t\right)=\frac{P_{mt}}{m_{n}}=I_{n}+x_{n}\times y_{n}^{t^{z_{n}}}.$$

As far as I can understand, this function obtains the maximum power $P_ {mt}$ over the mass $m_ {n}$ of a “category” $n$ individual in a time interval $t$.

But, this is done based on 4 variables, strictly associated with individuals; Where:
$I_ {n}$ is the last line value, from the table above, corresponding to category $n$; and represents the result of the function $f\left(n,\,\infty\right)$;

I know nothing about the variables $x_ {n}, y_ {n}$ and $z_ {n}$, unless different values are found for each category formula deduction.

For example, for categories 0 and 51, which correspond to the last and first row of the table, respectively:

$$I_{0}=1.8, x_{0}=56.0547, y_{0}=0.3147,z_{0}=0.2934$$
$$I_{51}=6.4, x_{51}=9.7124, y_{51}=0.8556, z_{51}=0.7245$$

I believe that the phenomenon in question is well described, in some relatively accessible book, and can even be considered too simple for the proposal of this forum; but given my difficulty in finding reasonable answers, even among physics and physical education students, I believe that the solution tends to have a relevant didactic value for many others as well...

 

[russ_watters]

I think the issue you are having is that you think this is a physics question when in reality it is a biology question.

Thread moved.

 

[jrmichler]

It's not that simple. There is a good discussion of the physiology of exercise effort vs duration in Lore of Running, Fourth Edition, by Tim Noakes: https://www.amazon.com/dp/0873229592/?tag=pfamazon01-20. This book is an excellent resource. Some information in it is hard to find, so you really need to read through the entire book. Over 900 pages of good information, plus another 100 pages of references.

Some people's bodies are more suited for shorter term higher power, while others are more suited for longer term lower power. As an example, my 5K time at age 57 predicted that I should have been able to run a 3:30 marathon. My marathon time that year was 3:51, even though my training was oriented towards the longer distance. My body just works better at shorter duration higher power efforts.

Now, at age 69, I'm a lot slower. I ran my last marathon in October 2019, where a young woman ran with me for a while, then took off and left me in her dust. She did this with no training at all. Every person's body is different, so any equations must have large standard deviations.

 

[Ygggdrasil]

Look up the difference between aerobic vs anaerobic exercise (specifically, with regard to lactic acid and the Cori cycle). Basically, up to a certain threshold of activity, the body is has enough oxygen flux to be able to metabolize energy normally. However, during very high activity where metabolic activity exceed oxygen supply, the body switches to anaerobic metabolic pathways that build up lactic acid, which builds up in muscles and contributes to fatigue.

 

[Eric Bretschneider]

Now, at age 69, I'm a lot slower. I ran my last marathon in October 2019, where a young woman ran with me for a while, then took off and left me in her dust. She did this with no training at all. Every person's body is different, so any equations must have large standard deviations.

I believe you may have meant that the parameters may have large standard deviations.