Limey UK runner wrote:
Like others have said walking a mile takes less energy because it is more efficient. Air resistance increases with the square of velocity, running oscillates your centre of mass against gravity to a greater extent, more energy is spent doing work to accelerate the limbs to higher velocities, energy losses during inelastic collisions and losses during elastic return, there are loads of factors. I can't be bothered to do the numbers to find out which factors dominate. Instinct tells me it is acceleration of the centre of mass against gravity.
This is one of those very old myths that will probably never go away.
^This.
It's a matter of input work vs. output work. The output work is the movement of the mass over a displacement, which is independent of path and time. So it takes the same amount of output work to go a mile at any pace as long as you're talking about the same person (same mass).
The input work can vary greatly, and it depends on your body's ability to radiate heat, its ability to return elastic energy on contact with the ground, extent of vertical displacement of the body, wind resistance, not to mention an individual's unique mechanics that may waste different amounts of energy. This is where the difference between walking and running the mile come into play.