2.2.2. Stride Time

Cavanagh et al. described the relationship between running velocity, stride length, and stride frequency [5]. Stride frequency is an inverse measure of the stride time and describes the number of strides per minute. They showed that runners can increase their running velocity either by increasing their stride length or by increasing their stride frequency, thus decreasing the stride time. For lower velocities, runners tend to increase the stride length, while for higher velocities, they tend to increase the stride frequency. Thus, both the stride time and stride length have no linear dependency on running velocity. Furthermore, it has to be noted that runners control their velocity individually. The stride length and therefore the velocity also depend on other parameters like the gender and the height of the runner. Male runners show greater stride lengths compared to female runners. The stride length increases with the body height [5].

We used these biomechanical relations to build an algorithm that estimates stride length and velocity. Cavanagh et al. [5] provided averaged values for the non-linear correlation between the stride time *tstride* and a relative stride length *dstride*,*rel*, which is calculated by dividing the absolute stride length *dstride* by the runner's height *h*. We looked for further publications describing this relationship and came up with two step functions for males and females that discretized the underlying non-linear relationship between stride time and stride length for each gender. The definition of the functions for both male and female runners can be found in Table 3.

**Table 3.** Definition of step functions for the relative stride length *dstride*,*rel*[*tstride*] for (a) male and (b) female runners for the *Stride time* algorithm.


The stride time *tstride* was obtained by dividing the number of samples of one stride *Nstride* by the sampling frequency *fs*.

$$t\_{stride} = \frac{N\_{stride}}{f\_s} = \frac{(n+1)\_{IC} - n\_{IC}}{f\_s} \tag{4}$$

*Nstride* was computed by subtracting the indices of two consecutive initial ground contacts (*n* + 1)*IC* and *nIC* obtained from the stride segmentation algorithm. After obtaining the relative stride length *dstride*,*rel* of the runner based on the gender and the stride time, the absolute stride length *dstride* was computed by multiplying *dstride*,*rel* from the table and the runner's height *h* in meters.

$$d\_{stride} = h \cdot d\_{stride,rel} \tag{5}$$

The running velocity *vstride* was then calculated using the stride time and the stride length.

$$v\_{stride} = \frac{d\_{stride}}{t\_{stride}}\tag{6}$$

Thus, the *Stride time* algorithm is solely based on the stride time. Gender and body height are usually known in all applications.
