## 3 Experiment 2
### Methods
#### 3.2.3 Procedure  
As in Experiment 1, prior to the running task, the participants filled out a custom-made questionnaire about their sports activity. For this experiment, also the short version of the International Physical Activity Questionnaire (IPAQ--French version) was used. At the beginning of the experiment and prior to the testing phase, the participants spent 4 min familiarizing themselves with treadmill running. During this phase, they were instructed to \"select an exercise intensity that you prefer and can be sustained for 20 min\" [39; 40]. The selected running speed was then used for the subsequent testing phase. To ensure that the participant's speed selection was solely based on perception, the speed display on the treadmill was covered so that it was only visible to the investigator. Self-selected running speed was used to reduce inter-individual differences, because fitness level and running experience have an influence on the parameters measured for this study. The first part of the experiment allowed us to assess the visual speed perceived as matching the chosen running speed for each participant. Participants were presented with the visual scene while running at their preferred running speed. They were instructed to estimate if the optical flow was slower or faster than the actual running speed. Four consecutive tests were proposed in a random order using a one up-one down staircase method [41; 42]. The optical flow started two times at a higher speed than the actual treadmill speed (+4 km/h) and two times at a lower speed (\(-\)4 km/h). The order of starting speed was randomized. The speed of the visual scene was adjusted according to the one up-one down staircase method, with an increase/decrease of the visual speed of 0.5 km/h until the first inversion of the participant's response, followed by steps of 0.3 km/h. This allowed us to determine the perceptual threshold that indicated the visual speed perceived as matching the actual running speed, i.e., the point of subjective equality (PSE). Prior to the task, participants were familiarized with the experimental setting and task using a training program. The single trials started with the participant running at the previously chosen speed. The visual scene was presented for 2 s before the participants were challenged with a black screen presenting the question \"up or down\", thus asking them to decide if they wanted to increase (i.e., up) or decrease (i.e., down) the speed of the visual scene. For each trial, participants gave their response while continuing their treadmill run by pressing a switch put on top of a light custom-made plastic cylinder (\(115\times 30\) mm, \(15\) g) they were holding in each hand. The responses (i.e., left for up and right for down) were sent to the computer via Bluetooth and directly integrated into the staircase test. Once the participant pressed the chosen button, the graphics returned to the visual scene of the following trial (see Figure 4). Each staircase ended when \(15\) inversions of the responses were reached and the participants were free to take a pause before starting the subsequent test. The second part of the experiment consisted of 4 different blocks in which the participants were asked to run at constant speed for 3 min and 30 s while being presented with different optical flow conditions. The reference value for the optical flow speed was personalized for each participant using the PSE found with the staircase test. The four conditions were:  
* no optical flow (noOF)
* matching optical flow with a visual speed corresponding to the PSE (matchOF)
* faster optical flow with a visual speed that was 40% higher than the PSE (fastOF)
* slower optical flow with a visual speed that was 40% lower than the PSE (slowOF). The order of conditions was randomly assigned. At the end of each block, the participants took a 2-min pause before starting the next block.