## 3 Experiment 2
### Discussion  
First, participants running on a treadmill while being presented with a moving virtual scene were asked to match the visual speed of the VR scene to their actual running speed. Participants set visual speed significantly higher than the actual running speed, i.e., treadmill speed. In other words, the visual scene had to move significantly faster than the treadmill speed for the two speeds to be perceived as equivalent, indicating and underestimation of visual speed relative to treadmill speed. Then, spatiotemporal gait parameters and HR were measured with participants running on a treadmill at their preferred running speed while being presented with different optical flow conditions. At the end of each condition, perceived effort was recorded. We did not observe any significant difference between optical flow conditions regarding the spatiotemporal gait parameters. However, we observed an effect of the time (i.e., minute) of acquisition. In addition, the HR was significantly different in the noOF condition than in the VR conditions, while there was no difference between conditions regarding perceived effort. Our results confirm the general tendency to underestimate visual speed relative to locomotor speed in virtual environments, both when walking [18; 44; 45; 46] and running [47; 48; 49]. Compared to previous work with running participants, our results show that visual speed underestimation relative to running speed also occurs with participants running at their preferred running speed. Specifically, previous work was always based on imposed running speeds [47; 48; 49], which were not necessarily in the range of preferred speeds of all participants. Here, every participant selected his/her running speed, reducing a possible influence of fatigue. This likely also reduced the attentional demand and fear of falling off of the treadmill [50] thanks to an increased felt safety compared to an imposed running speed. Figure 6: Mean heart rate. The bars represent the means and the error bars the 95% confidence interval of those means. Previous studies on walking showed that the manipulation of the optical flow can significantly affect locomotor patterns [15; 17; 21; 22]. In particular, optical flow can modulate parameters known to be reflective of gait instability, such as step width, step length, stride cycle, and stride velocity variability [51; 52]. Our results show that this influence on locomotor patterns cannot be extended to individuals running on a treadmill. In fact, none of the spatiotemporal gait parameters (i.e., step length, step duration, step frequency, and step width) was significantly affected by the optical flow condition. This suggests that when running at a self-selected speed, the presence and manipulation of the optical flow has no stabilizing or destabilizing effect. The difference between our results and those previously reported with walking participants could be linked to the fact that running seems to be characterized by a higher automatization and a lower cortical control compared to walking [25; 29]. The observed effect of the minute of acquisition could be linked to treadmill running accommodation, which can be different from individual to individual [53]. Moreover, our results show that the presence and manipulation of the optical flow does not influence this accommodation process, since no difference was found between the four optical flow conditions. Even if there was no significant effect of the optical flow conditions on spatiotemporal running parameters, VR seems to influence HR. Specifically, we found significant differences between the noOF and the VR conditions. Because the order of presentation of the conditions was randomized, exercise intensity was the same for each subject in all conditions, and starting HR did not differ between blocks. Therefore, the observed difference should not be linked to the running task per se. The higher HR values in the VR conditions may therefore be linked to an emotional activation, HR being a possible indicator of excitement [54].