Scientists have explained mathematically why the famous "silly walks" of Monty Python's John Cleese have never caught on in the long history of Homo sapiens.

The giant, leg-twirling strides of silly walks may enable an individual to leap around swiftly but are simply too expensive in metabolic energy compared to conventional locomotion, according to a paper published on Wednesday by Britain's Royal Society.

Manoj Srinavasan and Andy Ruina, researchers in applied mechanics at New York's Cornell University, drew up a geometrical model of human walking and running.

They found that, in essence, each leg is a "telescoping actuator" that can change its length.

In walking, the body vaults forwards in circular arcs, driven forward by the pendular swing of the legs, with the toe and heel providing the push-off and landing point for each movement. In running, though, the body travels from one parabolic arc to the next, with a bounce in between.

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Srinavasan and Ruina then factored in the metabolic cost of three drains on energy on both movements.

These are the energy expenditure required to keep the body's basic functions ticking over; the cost of swinging the legs; and the cost incurred when a leg is in contact with the ground.

Their equations showed emphatically that walking and running are the most energy-efficient gaits for our species, honed by millions of years of evolution.

"Inverted pendulum walking is energetically optimal at low speeds and step lengths, and impulsive running is energetically optimal at higher speeds," they say.

Silly walks gathered cult status in the British TV comedy show Monty Python's Flying Circus, when the gangling Cleese, dressed in a pin-stripe suit and bowler hat, cavorted around as a bureaucrat in a "Ministry of Silly Walks."

The research, which appears in Proceedings of the Royal Society A, is potentially useful in biomechanics and robotics, where scientists need to understand mathematically how humans (or their robot mimics) move, and the energy cost of doing it.