Here’s a question posed by the Scientific Indian regarding bicycle balance. Given my new found love for bike riding (see breaking out the bike) I figured I’d give this one a go.

Here’s the question:

Which is easy: To maintain your balance when cycling uphill, or when cycling downhill? Assume you maintain a constant speed of 6 km/hr and the inclination is constant. If you like to challenge your proficiency in physics, assume further that you are negotiating a bend.

Here’s my answer (feel free to add your own). In terms of balance, it doesn’t make a difference, assuming a constant speed. However, due to a property of physics called torque, the speed it takes to travel uphill and downhill is rarely going to be the same, and that’s due to gravity.

Torque is what causes rotation in the wheels of the bike when you pedal, and is analogous to an angular force. Pushing the pedals creates torque. The pedals are a lever that turns the main cog, which pulls the chain, which cause rotation of the gear, which is attached to the wheel.

Most bicycles today consist of a gear shift that changes the gear ratio depending upon the speed. Different combinations of gears creates a different effect, by controlling the relative size of the front and rear cogs. A high gear ratio should be used on a flat surface, turns the wheel multiple times for each turn of the pedal. When traveling uphill, a lower gear ratio should be used, which results in having to pedal a lot to get the wheel to turn once.

However, what I’ve noticed from my own experience, is that the gears, when traveling uphill, will shift only when the bicyclist starts pedaling faster. If the biker tries to maintain the same pedal speed, the force of gravity will slow you down dramatically, you won’t have enough torque to keep the wheels moving at the same speed, momentum is lost and you lose balance. You have to pedal a lot harder and faster against gravity, so that the gear will shift to maintain speed.

The advantage to this, is that when you’re traveling on a flat surface, it would get tiring to have to pedal 5 times just to turn the wheel once (for example). But, when you’re going uphill, with gravity slowing you down, pedalling faster will help you keep momentum, and prevent falling over. If you tried to bike uphill on a high gear ratio, I suspect, your wheels would try to turn faster and travel than gravity allow, and you would slip backwards or simply tip over.

When traveling downhill, however, you have gravity on your side. The acceleration due to gravity maintaings your speed, without having to put much force into pedalling. Travelling fast, momentum is maintained, sometimes without having to pedal at all, depending on the steepness of the hill. A low gear ratio is maintained simply by virtue of the acceleration due to gravity.

The second part of your question is a simple matter of centripetal motion. When negotiating around a bend (which is just really traveling a fraction of a circular path, there’s some interesting physics at work.

At any given moment, the direction of the velocity will be straight ahead, but the force and acceleration will be pointing along the radius of the circle, towards the center. So, while turning, the body wants to move along the path of the velocity, and you’ll wind up leaning that way, making maintaining balance a little trickier.

Another interesting affect about turning while on a bicycle is called “counter-steering.” If you were to travel along a straight path and simply turn the wheel to the right, you’d simply fall over. This is because the center of mass must be under the bicycle in order to remain upright. Turning the wheel moves the center of mass out from under the bike. In order to successfully turn, you must first lean steer the bike slightly in the opposite direction of the turn in order to shift the center of mass to the correct position so you can later lean for the turn. It’s the same principle as balancing any object on your hand. You have to move the bottom of the object to the direction that the top of the object is falling, in order to reposition the center of mass. While this lean slight turn in the opposite direction is necessary for all speeds, it’s more noticable at high speeds, which is why decreasing velocity for a tighter turn in a good idea. But, if you decrease the speed too much, momentum will be lost (to friction) and the bike and rider will fall over. (thanks to Felstatsu for the correction)

I hope this answered The Scientific Indian’s question, and I hope all the physics is right. Please post any further questions or [hopefully no] errors.

This entry was posted on Friday, June 6th, 2008 at 12:19 pm and is filed under musings, physics. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.