---
title: "Calculated Metrics"
slug: "fv-calculated-metrics"
updated: 2025-03-19T06:37:52Z
published: 2025-03-19T06:39:04Z
canonical: "docs.1080motion.com/fv-calculated-metrics"
---

> ## Documentation Index
> Fetch the complete documentation index at: https://docs.1080motion.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Calculated Metrics

## F₀ and v₀

The main output of a force/velocity profiles are the two numbers $F_0$ and $v_0$. Together, they describe the physical abilities of the runner:

- **F₀ (Force Intercept):** $F_0$ 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):** $v_0$ is the theoretical maximum sprinting speed that the athlete could achieve if the force output dropped to zero. Although no athlete actually reaches $v_0$, 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 $v_0$ *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* ($v_0$). A smaller $\tau$ means the athlete accelerates to a significant portion of their top speed more quickly, indicating a more explosive start, while a larger $\tau$ 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:

$v(t) \;=\; v_0 \,\bigl(1 - e^{-\,t/\tau}\bigr)$

where:

- $v_0$ is the theoretical max speed,
- $t$ is time,
- $\tau$ (tau) is the time constant that dictates how quickly $v(t)$ approaches $v_0$.

If you substitute $t = \tau$ into the equation, you get: $v(\tau) \;=\; v_0\,\bigl(1 - e^{-1}\bigr)$

That value of $1 - e^{-1}\approx 0.632$ 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 $RF_{max}$ 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 ($F = ma$).

**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 ($F = ma$), this becomes an indirect measurement of acceleration ability.