Calculated Metrics

  • Updated on Mar 19, 2025
  • Published on Mar 6, 2025
  • 2 minute(s) read
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F₀ and v₀

The main output of a force/velocity profiles are the two numbers and . Together, they describe the physical abilities of the runner:

  • F₀ (Force Intercept):
    represents the theoretical maximal horizontal force the athlete could produce when starting from rest (i.e., at zero velocity). This value reflects the athlete’s force-producing capability.

  • v₀ (Velocity Intercept):
    is the theoretical maximum sprinting speed that the athlete could achieve if the force output dropped to zero. Although no athlete actually reaches , it serves as a benchmark for their speed potential.

These two values, together with the athlete's body weight and height, can then be used to calculate all the remaining metrics.

Max Speed Unloaded

While is a measurement of speed capacity, it does not represent what the person could actually achieve.

A better value is the estimated max unloaded speed which is calculated by adding the effects of air resistance. This value represents a speed that the runner is expected to be able to reach.

Power

Max Power (Pmax): Greatest power (product of force and speed) a sprinter can generate during the acceleration phase. It reflects overall explosiveness, with higher values indicating better sprint performance.

Relative Max Power: Max power adjusted/normalized to body weight, which allows for a better and more fair comparison between athletes of relative explosiveness.

Acceleration

Tau (𝜏): Defined as the time taken to reach 63% of the top speed (). A smaller means the athlete accelerates to a significant portion of their top speed more quickly, indicating a more explosive start, while a larger suggests a more gradual build-up of speed.

This is a relative acceleration measurement and as such can be hard to compare between individuals in a team. To get an absolute measurement of acceleration ability, the various prediction tables can be used (e.g. time to 5 m).

Why 63%?

The value 63% of the top speed might seem arbitrary but there is a mathematical explanation for it.

In sprinting, velocity as a function of time can be described by this first-order exponential function:

where:

  • is the theoretical max speed,
  • is time,
  • (tau) is the time constant that dictates how quickly approaches .

If you substitute into the equation, you get:

That value of which is commonly rounded to 63%.

Ratio of Force

RF Max (Maximum Ratio of Force): This measurement represents how much of a sprinter’s total force (percentage) is directed horizontally during the start of a sprint. A greater means better and more effective force application for explosive horizontal acceleration. Thus, this is an indirect measurement of early acceleration ability based on Newton´s second law ().

DRF (Decrease in Ratio of Force): This measurement is the rate at which a sprinter’s ability to apply horizontal force drops as they gain speed. A lower DRF means the athlete is better able to maintain a horizontal force application during acceleration. Based on Newton´s second law (), this becomes an indirect measurement of acceleration ability.