Critical Power/Speed Calculator
About
I built this app to make it easy for athletes to determine their critical power or critical speed.
Physiological Background
The sustainable duration of exercise is dependent upon the intensity (i.e., power or speed) at which the exercise is performed. This fundamental concept is known as the intensity-duration relationship, and for exercise durations of ~2–40 minutes, can be modeled by a two-parameter hyperbolic equation (see methods below). The critical intensity (power or speed) is the highest intensity that can be sustained primarily by aerobic metabolism while still achieving a metabolic steady state. The critical intensity is also a metabolic threshold such that exercising at intensities (powers or speeds) above the threshold will cause increased reliance on anaerobic metabolism and a greater accumulation of fatigue-inducing metabolites. For a given intensity above the threshold, the time until task failure is dependent on the magnitude of the curvature constant (W’ or D’), suggesting that curvature constant can be viewed as a fatigue buffer (or fatigue constant).
Methods
Cycling
The data are fit using a two parameter hyperbolic model according to the equation below:
\[ t = \frac{W'}{P - CP} \ \]
where t is the performance time (s), W’ is the curvature constant (Joules), P is the performance power (W), and CP is the Critical Power (W).
Two additional variables that are calculated in the application are:
- 5 minute Power - An estimate of the highest power that can be sustained for 5 minutes.
- 20 minute Power - An estimate of the highest power that can be sustained for 20 minutes.
Running
The data are fit using a two parameter hyperbolic model according to the equation below:
\[ t = \frac{D'}{S - CS} \ \]
where t is the performance time (s), D’ is the curvature constant (m), S is the average speed (m/s), and CS is the critical speed (m/s).
Two additional variables that are calculated in the application are:
- Mile - Estimated one mile performance.
- 5,000 m - Estimated 5K performance.
Use
Use the app here: https://timfulton.shinyapps.io/critical_power_speed_calculator/
Check out the GitHub repo here: https://github.com/timfulton1/intensity_duration_app
