Will you PM an overview of what you have so far? I'm a Physicist so would be quite interested... Either way, you are lifting your weight through the same height, so the work done in the vertical should be similar. The horizontal component would be different however, for the reasons explained above.
A play off between the training effect and the risk of injury is a good point to consider. I think the additional stimulation required from the hamstring and glueal muscle groups (due to the gait being active on the road), in addition to the greater irregularity, would result in local muscular acidosis and therefore more stress on the cardio vascular system. This results in more overload as a training effect.
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[Will you PM an overview of what you have so far? ] Nah - post it on here Chris. The forum needs a bit of livening up - a lynchin'... or summat.
Well, if you take this to its logical conclusion then running on a horizontal treadmill would be zero effort as you are merely letting the belt move beneath you. Clearly this isn't the case and it is undoubtedly harder running on an inclined treadmill than a horizontal one so it must be somewhat like running up a hill. Your body probably does in fact move up and down quite a bit on a steep treadmill but quite what the equivalent road incline would be I don't know.
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I read somewhere that if running on a treadmill, to compensate for the belt moving underneath you and the lack of wind resistance etc, you should put it on a 1% incline. This apparently is the equivalent to running on the flat outside.
Whether that makes 12% on the treadmill equivalent to 13% outside or not I don't know.