I guess we find the same problems in the wild enjoyable. I spent a few nights procrastinating on homework to brainstorm how I could try to find the most efficient walking path between points on campus. I figured that I would need to be able to represent the campus on some sort of plane where each point has a value referring to its elevation, and then finding the geodesic. I figured I could refer to some physiology literature and find if anyone has tabulated average energy expenditures for walking at different grades (downhill, flat, or uphill). Now, my math skills are really sub-par (haven't gotten past single variable calculus), so this question had me asking various physicist friends how to solve the problem. I just found myself learning along the way.
I'm curious how you determined efficiency for each of the candidate walking patterns. Did you compare only the traveled distance, or did you also take into account the energy spent per unit distance? I think that could make a difference if, for example, you had these walking strategies:
Walking strategy S => A "normal" human gait, except you travel in an squiggle path (i.e. not a straight line) to your destination.
Walking strategy T => Do continuous jumping jacks while walking, but continue in a straight path.
S may travel a longer distance, but will exert less energy overall and therefore be more efficient than T. Now, that's a pathological scenario, but I wonder if your walking pattern could have the same issue where you are actually exerting more energy despite walking a shorter distance. It'd be interesting to do more research on the biophysics of how your body moves.
I'm curious how you determined efficiency for each of the candidate walking patterns. Did you compare only the traveled distance, or did you also take into account the energy spent per unit distance? I think that could make a difference if, for example, you had these walking strategies:
Walking strategy S => A "normal" human gait, except you travel in an squiggle path (i.e. not a straight line) to your destination.
Walking strategy T => Do continuous jumping jacks while walking, but continue in a straight path.
S may travel a longer distance, but will exert less energy overall and therefore be more efficient than T. Now, that's a pathological scenario, but I wonder if your walking pattern could have the same issue where you are actually exerting more energy despite walking a shorter distance. It'd be interesting to do more research on the biophysics of how your body moves.