The mechanical cost of transport of fast running animals

• At high speeds, mechanical cost of transport is proportional to ground forces ratio (Fx/Fy).
• Fast running requires maximizing (Fx/Fy) and minimizing ground contact time.
• At low speeds, animals choose (Fx/Fy) to be mechanically and metabolically efficient.

Regarding running animals, algebraic expressions for the horizontal (ωx) and vertical (ωy)(ωy) components of the mechanical cost of transport are deduced for a ground force pattern based on the Spring–mass model. Defining μ˜ as the maximum ground forces ratio μ˜=max(Fx)/max(Fy), the analysis shows that the mechanical cost of transport ωx+ωyωx+ωy for fast running animals is approximately proportional to μ˜, and to the relative contact length, and positively correlated to the limb take-off angle and the collision angle. The vertical cost ωy is shown to approximate to zero for fast running animals. Sustained top running speeds are predicted to require the largest possible values of μ˜ and therefore relatively large horizontal propulsive forces, as well as a minimum possible ground contact time. The equations also show that animals running relatively slow would tend to prefer certain interval of values for parameter μ˜, which would minimize both their mechanical cost of transport and their metabolic cost of transport. Very large animals are suspected to be less capable of developing large values of μ˜, which possibly renders them incapable of developing great speeds.