- #1

expn

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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:[tex]f\left(n,\,t\right)=\frac{P_{mt}}{m_{n}}=I_{n}+x_{n}\times y_{n}^{t^{z_{n}}}.[/tex]

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

But, this is done based on 4 variables, strictly associated with individuals; Where:

[itex]I_ {n}[/itex] is the last line value, from the table above, corresponding to category [itex]n[/itex]; and represents the result of the function [itex]f\left(n,\,\infty\right) [/itex];

I know nothing about the variables [itex]x_ {n}, y_ {n}[/itex] and [itex]z_ {n}[/itex], 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:

[tex]I_{0}=1.8, x_{0}=56.0547, y_{0}=0.3147,z_{0}=0.2934[/tex]

[tex]I_{51}=6.4, x_{51}=9.7124, y_{51}=0.8556, z_{51}=0.7245[/tex]

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...

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:[tex]f\left(n,\,t\right)=\frac{P_{mt}}{m_{n}}=I_{n}+x_{n}\times y_{n}^{t^{z_{n}}}.[/tex]

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

But, this is done based on 4 variables, strictly associated with individuals; Where:

[itex]I_ {n}[/itex] is the last line value, from the table above, corresponding to category [itex]n[/itex]; and represents the result of the function [itex]f\left(n,\,\infty\right) [/itex];

I know nothing about the variables [itex]x_ {n}, y_ {n}[/itex] and [itex]z_ {n}[/itex], 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:

[tex]I_{0}=1.8, x_{0}=56.0547, y_{0}=0.3147,z_{0}=0.2934[/tex]

[tex]I_{51}=6.4, x_{51}=9.7124, y_{51}=0.8556, z_{51}=0.7245[/tex]

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...

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