Table 1.

Parameters and equations of a collision-based analysis, plus dimensionless speed and individual limbs cost of transport.

force vector (N), F
velocity vector (ms−1), V
instantaneous angles (radians): θ denotes force, λ denotes velocity and ϕ denotes collision
is mean forward velocity; h is hip height; g is acceleration of gravity on the Earth; x is a multiplier of gravity; n is the number of samples in the stride period; m is body mass
dimensionless speed (the square root of Froude number)		equation (1.1)
instantaneous force angle, where unit vector a is normal to the substrate and upward		equation (1.2)
force angle determined by force-averaging over the contact periods of the stride		equation (1.3)
instantaneous velocity angle, where unit vector b is parallel to the substrate and in the direction of travel		equation (1.4)
velocity angle determined by velocity-averaging over the contact periods of the stride		equation (1.5)
instantaneous collision angle determined from the dot product of force on velocity—the arcsine rotates this angle by π/2 such that it quantifies the deviation from		equation (1.6)
collision angle determined by force- and velocity-averaging over the contact periods of the stride		equation (1.7)
mechanical cost of motion is a normalized absolute value of CoM power equivalent to Φ when ; the small angle approximation of equation (1.6) is substituted into equation (1.7)		equation (1.8)
for small vertical and lateral oscillations		equation (1.9)
for small fore–aft and lateral forces		equation (1.10)
individual limbs cost of transport is a normalization of the absolute value of individual limb power [20], where and indicate the force vectors of each limb		equation (1.11)
mechanical cost of transport is a normalized absolute value of CoM power equivalent to when the conditions of equations (1.9) and (1.10) are met		equation (1.12)
impulse angle for the stride, where I is the impulse vector and unit vector a is normal to the substrate and upward		equation (1.13)
collision fraction determined by force- and velocity-averaging over the contact periods of the stride		equation (1.14)