Physiological, aerodynamic and geometric constraints of flapping account for bird gaits, and bounding and flap-gliding flight strategies.

Aerodynamically economical flight is steady and level. The high-amplitude flapping and bounding flight style of many small birds departs considerably from any aerodynamic or purely mechanical optimum. Further, many large birds adopt a flap-glide flight style in cruising flight which is not consistent with purely aerodynamic economy.

Inverted pendular running: a novel gait predicted by computer optimization is found between walk and run in birds.

Idealized models of walking and running demonstrate that, energetically, walking should be favoured up to, and even somewhat over, those speeds and step lengths that can be achieved while keeping the stance leg under compression. Around these speeds, and especially with relatively long step lengths, computer optimization predicts a third, 'hybrid', gait: (inverted) pendular running (Srinivasan & Ruina 2006 Nature 439, 72-75 (doi:10.1038/nature04113)).

Why not walk faster?

Bipedal walking following inverted pendulum mechanics is constrained by two requirements: sufficient kinetic energy for the vault over midstance and sufficient gravity to provide the centripetal acceleration required for the arc of the body about the stance foot. While the acceleration condition identifies a maximum walking speed at a Froude number of 1, empirical observation indicates favoured walk-run transition speeds at a Froude number around 0.5 for birds, humans and humans under manipulated gravity conditions.