In Treadmill vs. Real Hill: Which is harder to run, Steve Mould and Jared Reabow ran an interesting experiment: does it take more energy to run up a hill or to run in place on a treadmill with the same inclination? The result was interesting, but also a bit of a let-down: the treadmill run used 9.1 W, while the ramp run used 10.1 W, 11% more. More research is clearly needed 😅! What could improve the experimental setup?

The friction of a regular treadmill and a wooden slope is going to be different, so using the same surface material would eliminate that option. Using a hard surface material would also reduce friction, but could increase the amount of slip. We can avoid the slip by using a rack railway, which would also allow testing with much bigger inclines, even beyond 45°. A Lego treadmill should work beautifully for this: run on the treadmill for the stationary test, and lay the tread out on an incline to do the moving test.

Comparing with different inclinations should also help. If we see an X% difference between the energy use on the treadmill and the stationary surface both at a positive angle and when running horizontally, we can conclude that the difference is not because of the incline. A bigger incline would also be interesting.

Even a negative incline could be interesting, if instead of running the engine we used engine breaking to generate power. Would this result be relevant for the experiment? I’m not sure, but intuitively I would expect the power use on a slope of X° to be similar to the power generated on a slope of -X°. Unfortunately this result would probably be dominated by the engine/dynamo efficiency, which are both going to be much less than 100%. The engine and dynamo efficiencies could also be completely different, say, 80% and 50%.

Another easy win would be to use an aerodynamic vehicle to minimise differences due to air resistance. In a similar vein, a heavy vehicle would make the air resistance a smaller factor of the total energy use. And since drag is proportional to the square of the speed, using a slow speed would further reduce the contribution from air resistance. Slowing down would also reduce the risk of transferring extra energy to the vehicle because of rattling in the treadmill system itself (thanks Adon!).

In summary and conclusion, I’ll need about 500,000 moon dollars for Lego parts, a to-be-negotiated sum to contract a friend to “find a Lagrangian and minimise the action”, and three months to produce a Git repo and YouTube video with the results.