Originally Posted by dmpi
Physics wise there is no energy usage difference between you running at a constant speed on the treadmill and you running the same speed on the ground. Where the difference is when you accelerate. It takes more energy to accelerate on the ground than on the treadmill because on the treadmill youíre not really accelerating, rather the belt is and the treadmill is doing the work. On the treadmill it only takes seconds to accelerate to the speed your going to run at so this is largely a non-issue.
As otherís have mentioned wind resistance pays a slight role. However a fan blowing against you can most compensate for this, with the added benefit of cooling you off.
Another difference is the treadmill surface is springy and itís almost impossible to find a similar surface outside. A rubberized high school track is close. While running on hard surfaces the energy is absorbed by the ground and you have to work harder to lift your legs. On a treadmill the energy of the foot strike is given back to you and your leg just bounces up.
Every article that I have ever read and I have read quite a few contradicts you. From: www.posetech.com/training/archives;00188.html
The scientific data and experience known to us say that treadmill running is easier then overground running. "It has generally been found that overground running does incur greater metabolic costs compared to treadmill running, particularly at faster speeds of running. At the present time the extent that other differences in running mechanics between overground and treadmill running affect oxygen uptake is not known" (Biomechanics of Distance Running, 1990, Editor P.Cavanagh, Human Kinetics, p.276).
My personal experience also suggests that treadmill running is easier. A favorite workout is mile repeats at a 5:30-6:00/mile pace with a 1/4 mile rest jog in between. I find it much easier on a treadmill than on the track. (See above about about effect at faster speeds) Although I cannot rule out pacing, psychological effects, etc. as confounding variables I am convinced that there is a difference. Also I don't think that the acceleration and deaccelerations are the cause.
I think that my "real" experiment plus the experience of many others trumps your thought experiment