Then it's wrong, I'm afraid.
Some guy in the states somehow managed to get a PhD out of it a couple of years ago, but it's pretty obvious Newtonian physics. When you walk, you keep your legs mostly straight, and your center of gravity rides along fairly smoothly on top of your legs. In running, you jump from one foot to the other. Each jump raises your center of gravity when you take off, and lowers it when you land because you bend the knee to absorb the shock. This continual rise and fall of our weight requires a tremendous amount of Newtonian force, essentially to work against gravity, on both takeoff and landing, which doesn't happen in walking.

That's before you even get into the biology aspect of efficiency of anaerobic vs aerobic respiration (anaerobic is more common in running and is less efficient) and issues of wind resistance, although that's a function of speed and you are talking about running vs walking at the same speed so you're correct, that doesn't matter)
( the mighty badger Aphrodite, on a bar stool, by your side, Mon 18 Apr 2011, 10:08, 1 reply, 15 years ago)

not having done biology ever
and purely working from the physics point of view, that is fairly obvious
( Vipros. clever got me this far, then tricky got me in, Mon 18 Apr 2011, 10:10, Reply)

I've done plenty of biology
and by that I mean, I've fucked your mum.
(PsychoChomp, Mon 18 Apr 2011, 10:16, Reply)

I've fucked yours
but she's so fat it was more like astronomy
( Vipros. clever got me this far, then tricky got me in, Mon 18 Apr 2011, 10:18, Reply)