Long-term constant acceleration can be sustained freely in running via stochastic short-term corrections

In the same way that most of the robots and advanced mobile machines are designed to optimize their energy consumption or the smoothness of their motions, it has been demonstrated that competitive runners tend to exhibit smoother strides than recreational runners during running and fast walking. Here, we describe the statistical mechanics of Humans trying to self-pace a constant acceleration,  by studying the statistical properties of the accelerations of the runner's center of mass. Furthermore, it has been checked that this could be even achieved in a state of fatigue during exhaustive 3 self-pace ramp runs. For that purpose, we analyse a small sample of 3 male and 2 female middle-aged, recreational runners ran, in random order, three exhaustive self-paced acceleration trials (SAT) perceived to be "soft", "medium" or "hard".  A statistical analysis shows that Humans can be able to self-pace constant accelerationin some exhaustive runs, by continuously adjusting the instantaneous accelerations. The variations of accelerationsaround the mean are  ARMA stationary processes, which are similar,whichever acceleration levels and runners. The rangeof constant acceleration is very similar between runners and withinthe acceleration level.  This work is the first stepfor understanding the Human optimisation of self-pace processes inexhaustive tasks such as running until exhaustion.