ventolin^3 wrote:
fisky wrote:Thanks, but I'm still confused. Under the above formula, once a runner reaches a constant speed, no further work is done since horizontal acceleration is zero.Example: If mass = 60kg and displacement = 1 mile, but acceleration = zero, then 60x1x0=0
it is not acceleration we are concerned about
it is kinetic energy as starter
that is given as 0.5mv^2
that has to be modified because of drag
at equilibrium pace = flat-out from gun-to-tape, you are limited from physics only by drag
( & only by actual physical leg-turnover speed if running on moon with 0kg scuba in 0kg pressurised suit ) :
0.5mv^3
http://scienceworld.wolfram.com/physics/DragPower.html
Energy is not power, and you can't just multiply KE by v "because of drag".
Also, your assumption that a runner is only working to overcome drag at a steady pace is bogus. If you've run in a tailwind, you probably know this. If not, work through the drag power equation you linked to with some reasonable assumptions:
P = .5*rho*Cd*A*v^3 with rho = 1.2 kg/m^3, Cd = .6, A = .5 m^2, v = 5 m/s
so power to overcome drag for at least one human is 23 W at 5:22 pace. 23 watts is nothing, but most people have trouble maintaining 5:22 pace for extended periods of time. so, there's more to the story than drag.
What's missing? In every step of a run:
-We decelerate a bit when our foot touches down.
-We catch ourselves from the brief moment of airtime (freefall) by exerting a large force on the ground.
-We reaccelerate at toe off.
-We launch ourselves back up into the air.
-We soar through the air (100-150 milliseconds or so)
This cycle repeats 2.5 to 3 times per second. This is where the energy goes.