## 2 Methodology
### Mesures  
The spatio-temporal parameters (STP) were recorded at an acquisition frequency of 60 Hz. The Stryd sensor was connected to the Suunto 9 (Susunto, Vaanta, Finland) watch via Bluetooth(r). Before each test, the mass and height of the runner was entered into the \"Stryd\" application (version 6.0.1). The mass of the subject is essential for power calculation. The Stryd uses four parameters which are (1) mass of the subject entered in the application, (2) acceleration, (3) percentage of slope inclination, and (4) speed of the subject obtained with the accelerometers and the gyroscope to estimate the power developed. The STP that were measured throughout the test included:  
* Ground Contact Time (GCT, in seconds): the time between the first moment the foot touches the ground and the last contact of the shoe before the toes lift off the ground. * Cadence (SF, in steps/min): number of times the foot is in contact with the ground per minute. * Vertical oscillation (VO, in cm): variation in the vertical position of mass' center during the run. * Leg stiffness (Kleg, in kN/m): indicator of a runner's ability to restore the force applied to the ground. * Flight Time (FT, in seconds): the period between toe-off and the next foot contact. During this phase, the athlete makes no contact with the ground, therefore in essence is in flight. (e.g., right-left). * Step length (SL, in meters): The distance between the landing of one foot and the next landing of the opposite foot. * Step time (ST, in seconds): corresponds to the time between the start of the step cycle (placing the foot) and the end of the cycle (placing the same foot again). Based on previous studies [24] with GCT, SF, ST and running speed, the authors calculated the FT and SL using the following formula:  
\[\text{ST (s)}=\frac{60}{\text{SF (step.min}^{-1})}\]  
\[\text{FT(s)}=\text{ST (s)}-\text{GCT (s)}\]  
\[\text{SL (m)}=\frac{\text{velocity (m.min}^{-1})}{\text{SF (step.min}^{-1})}\]  
* Force (N): is the mechanical action exerted by one object on another. * Distance (m): correspond to the length that separates two points. * Work (J): corresponds to the application of a force (N) over a distance (m). * Acceleration (m.s\({}^{-2}\)): corresponds to a vectorial physical quantity, representing the modification of the speed of a movement as a function of time. * Velocity (m.s\({}^{-1}\)): a variable that measures the ratio of an evolution to time. Power (P, in W): the mechanical measurement of the effort and intensity of the run. It corresponds to the work done per unit of time [26]. \[\text{Power (W)}=\frac{\text{Work (J)}}{\text{Time (s)}}\]  
The work is equal to the force (N) applied multiplied by a distance (m). \[\text{Work (J)}=\text{Force (N).Distance (m)}\]  
Therefore, power can be written as:  
\[\text{Power (W)}=\frac{\text{Force (N).Distance (m)}}{\text{Time (s)}}\]The distance divided by a time corresponds to velocity, which is more commonly referred to as \"speed\". \[\text{Power }(\text{W})=\text{Force }(\text{N}).\text{Velocity }(\text{m.s}^{-1})\]  
The force being equal to the mass of an object multiplied by its acceleration, the previous equation can be written as:  
\[\text{Power }(\text{W})=\text{Body }\text{masse }(\text{kg}).\text{ Acceleration }(\text{m.s}^{-2}).\text{Velocity }(\text{m.s}^{-1})\]  
Normalized Power (NP, in W/Kg): it is the ratio between a power and a mass  
The heart rate was recorded at an acquisition frequency of 1 Hz. Average heart rate (bpm): corresponds to the average heart rate recorded during the test. The parameters relating to the runner's speed of movement were:  
Time (min): corresponds to the total time taken by the subject to complete the course. Speed (km/h): corresponds to the ratio of a distance traveled over a period. Pace (min/km): corresponds to the ratio of a time over a distance. Climbing speed (m/h): corresponds to the number of meters of positive elevation gain over one hour.