Questions on more bike physics

This continues the series I started the other day, answering questions about the physics of bicycles.  Well, now I have some questions of my own.  Questions that need answers.  Answers that are worth millions of Shrute bucks.

I made some observations while on my daily bike ride today that I couldn’t explain the physics of.  It was related to this statement I wrote in my previous post:

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 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 slight turn in the opposite direction is necessary for all speeds, it’s more noticeable 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.

Given that this is true (and I believe that it is) I wanted to test some other aspects of leaning versus steering control.  I found that leaning is necessary to alter your course by small angles, when traveling on a relatively straight path.  However, for 90 degree turns, simply leaning is not going to get the job done.

I tried to simply turn the front wheel via the handlebars in the direction I wanted to make such a 90 degree turn, while traveling a straight path.  I noticed that I soon as a turned the handlebars even slightly I felt the bike start to tip.  Almost immediately following that, however, the back part of my bike seem to “catch up” with the front wheel, causing me to continue on a straight path.

My question is if this is some physical property (perhaps my momentum?) which makes the bike want to continue on a straight path, or is it some unconscious steering on my part?  I assume it has to do with the repositioning of the center of mass, so that the bike doesn’t tip, but is this because I don’t want it to tip, or because the bike can’t physically tip when traveling forward at a significant velocity?

What I find interesting, as well, is that it is impossible to turn without first steering in the opposite direction of the turn and then leaning to make the turn.  This seems to be the only possible way to reposition your center of mass in order to make a successful turn.  Is this also true?

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Bicycle Physics

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.

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