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I can go faster

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JimK:
This is a nice puzzle! It will probably take some experimenting to figure out exactly what's going on!

Here is one fun game I thought about when I was reading Wilson's Bicycling Science: suppose you are on a road that goes up and down every couple feet or so. I think you can propel yourself forwards indefinitely by moving your body around on the bike. Get low on the bike at the top of a hill and then on each down slope push yourself up high. Then on the up slopes you take the weight off the bike by getting low again. There's probably a way to time some back-and-forth swinging motion that will also work, pushing and pulling, working with the varying shape of the road.

It's fascinating to watch skateboarders. I think you can get some turning into the action and make it work. Instead of the road going up and down, you can turn to make your path wiggle back and forth, and then by shifting your weight along with the curves... these BMX bikes have really low seats, the point of which I think is essentially to create more room for getting low, a wider range of rider heights.

I remember back in college, in freshman physics, I was playing with how to pump on a swing. Here was my scheme: stand up on the swing; each time you get to the bottom of the swing's movement, stand up tall. At the top of the swing's movement, both forward and backward, squat down. Wow! You can get going scary high that way, in a hurry! The more usual swinging style is what you were doing on your bike. I confess I have never really figured that out.

The whole business of moving one's body around on a bike and how that affects the bike's motion - it's really fascinating!

Matt2matt2002:
Thanks folks.
I must confess to having discovered this quite a while ago but only thought of bringing it to this forum today having been continually impressed at the quality of technical debate and friendly camaraderie.
All I can add at this point is to recommend that anyone who tries this out to be unsighted from friends and neighbours.

JimK:

--- Quote from: JimK on August 26, 2012, 10:57:15 pm --- Get low on the bike at the top of a hill and then on each down slope push yourself up high. Then on the up slopes you take the weight off the bike by getting low again.

--- End quote ---

This stuff is subtle and I think I got this wrong. A nice general principle: in a frictionless system, if you can figure out how to pump energy in somehow, it just has to turn into motion.

With rolling hills or a twisting path, the force pressing you down varies. If you lift yourself up in the high force region and then let yourself back down in the low force region, then you are doing net positive work around the cycle, and that has to turn into the motion of the bike.

On rolling hills, the high force region is at the bottom of the valley where the road is concave upward. The low force region is at the top of the hill, where the road is concave downward. So to pump the bike forward, push yourself up at the bottoms of the valleys and let yourself back down at the tops of the hills. Just stay high on the up slopes and just stay low on the down slopes.

On a curvy path, the high force region is on the curves and the low force region is on the straight parts or the inflection points where the curve changes directions. Even on an elliptical path you should be able to pump: the high force region is the tightly curved part and the low force region is the less curved part. Lower yourself at the inflection points and stand up high where the tightest part of each curve is. Of course this is for a vehicle where the weight is high up dynamically balanced over a narrow support.

I realize this isn't quite the puzzle originally presented in this thread, but that's how I usually attack these things: I start by looking at similar or related problems that I can get some purchase on. Sometimes it will fertilize a little insight!

JimK:
Another fun way to get a bike going without pedaling is to use the brakes! If fling your body forward and backward on the bike, and apply the brakes at the back to push off forwards but let off the brakes when catching yourself at the front and returning backwards... that ought to be another way to move the bike forward, this time going straight and level. If the road alternated between loose stuff with high rolling resistance and smooth stuff with low rolling resistance, that could work instead of using brakes.

No wonder my girlfriend thinks I am nuts, all this crazy stuff running around in my head. Yeah, I might save the testing for a quieter stretch of road!
 

JimK:
I should say, there is a fundamental law of physics, the conservation of momentum. If some complex system is sailing along with no external forces being applied to it, then the overall speed of the system can't change. If the system falls apart then the individual bits can go any speed as long as the other bits compensate through some sort of recoil. But if the system hangs together however loosely, its speed can't change.

So the fun here is to get around that "no external forces" clause. Mostly the ground just pushes up so that can't affect the forward movement. But hills, curves, rolling resistance... those aren't simply "up", so they create opportunities.

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