Unless you are driving a hybrid car, where the energy normally lost in decelerations is stored as electric energy to be used in successive accelerations, speed increases of your vehicle are associated to extra fuel consumption. A few years ago we showed that the inherent increases/decreases of total mechanical energy of the body centre of mass during constant speed walking could explain the surprising invariant metabolic cost of transport when walking at oscillating speed. Here we present metabolic results of running at constant and oscillating speeds (11 ± 0, ± 1, ± 2, ± 3, ± 4 km.h-1), with an acceleration/deceleration cycle lasting 6 s, performed by 9 subjects both on a motorized treadmill and on a 68 m diameter circular path as set by a moving spot projected by a laser attached to a motorized telescope, driven by a customly written software.

It is expected from physics and physiology that such running protocol would imply an extra metabolic cost of transport C (J*kg^-1*m^-1) = 4.8 dv*dt^-1, where dv is the speed change (m*s^-1) and dt is its duration (3 s). Surprisingly again, we obtained substantial cost invariance even at the widest speed oscillation (C = +6.6 ± 7.4 % rather than +41.9%). Differently from walking, running mechanics include a portion of the total mechanical work related to the elastic energy (stored and) released by tendons. By taking this into account, it can be shown that the maximum speed oscillation compatible with cost invariance should be ± 4.5 km*h^-1.