we all know that cycling is a hilarious amount more efficient than pedestrian travel. however, my introductory understanding of physics leads me to believe that there should be some hill grade at which walking is more efficient. my reasoning is that on level ground, a bicycle has to overcome air resistance, the inertia of the wheels, rolling resistance and the friction within the bike's components, but on a hill the bike also has to overcome gravity. when you're on foot, ironically its gravity that provides the normal force that opposes my sliding down the hill. i.e. on a steep hill, on foot i dont have to exert any force to stay put, whereas on a bike i do. this may be a completely skewed understanding of the physics of biking... but when i'm churning up a hill at a snail's pace, the only thing keeping me from walking is my road shoes. either way, i need to get in better shape (or get mountain shoes), but is my logic on the right track here?