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QUESTION: I donít know if this is more of a math question but how do bike gears work? I think the gears attached to the peddles are sprockets and the smaller gears on the rear wheel are cogs. Now if I choose a smaller cog in back I would think it would be harder to turn but will produce more speed per resolution? I assume all benefit of having relatively different sized gears between peddles and rear wheel is to manage a tork/speed relationship? If that is the case why have more than one sprocket? Why not a middle sized sprocket and a great range of cogs? It seems more complex than needed.

ANSWER: Hello James,

Let me start with a discussion of a single-speed bike. One revolution of the pedals yields more than one revolution of the rear wheel. Assume you have marked one of the links of the chain so you can measure how far the chain went. If you measure the radius of the chain as it follows the curve of the front gear, you can calculate the circumference of that gear. For one revolution of the pedals, the chain must move a distance equal to the circumference of the front gear. You can verify that using the mark on the chain. Since the rear gear is smaller, it has a shorter circumference. So it rotates more than one revolution while the pedals rotate once. That is what I referred to in my 2nd sentence. If those 2 gears were the same radius, you could not move your feet fast enough to drive the bike at what is your full speed as it actually is configured. You are correct in your statement of the benefit of multiple gear options. In a single-speed bike, the size chosen for the front and rear gears is a compromise intended to yield a reasonable torque/speed relationship. Emphasizing one factor puts you at a disadvantage when the other factor is needed.

When you are climbing a hill, it is beneficial to be able to adjust the relative size of the gears so that the rear gear is larger than with the above compromise. That increases the torque delivered to the rear. And increases the speed your feet must go.

What you are suggesting would eliminate the need for a derailleur at the front. But there is a practical limit to the number of gears you can mount at the rear. The most I have seen is 6. The chain has to go to either side to get those gears on the end. That increases the risk that the gear alongside of the one selected will go tick-tick-tick on the chain. It might even snag the chain and force it to change gears.

I am no more than a casual Sunday afternoon rider. So that is about as much as I know on the subject.

I hope this helps,

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QUESTION: My bike has 3 sprockets and 8 cods giving it 24 speeds. But I fail to see the need for that many options. My concern is "cross chaining" and making the chain go too far diagonally. If it had one sprocket with the petals, and maybe 6 cogs in the back with even greater range in sizes shouldn't that do as well? I currently keep my peddle sprocket in the middle to reduce pull in the back either way, but still can't think of a smooth way to go from one extreme to the other safely.

Hello James,

My bike has 3*7=21 speeds. I, like you, seldom get out of 2nd gear in the front cluster of gears. But some serious riders keep adjusting gearing in order to keep feet going at an optimum speed. It seem obsessive to me - but I am not a serious rider.

I have read about a transmission for cars in which there are 2 cones, an input cone and an output cone, with a heavy belt connecting the 2. The cones are oriented with fat ends opposite so that the belt is the correct length no matter where the belt is. The position is adjusted smoothly over its range as the car's speed changes so that the engine continues to run at a magic rpm that was found to be its most efficient. It seems logical that there would be some benefit in efficiency - but I doubt it is very significant.

To answer your question: "If it had one sprocket with the petals, and maybe 6 cogs in the back with even greater range in sizes shouldn't that do as well?" I have to give those serious riders mentioned above a benefit of a doubt, so my answer to you is: "almost as well".

I apologize for being slow to answer. I hope this helps,


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Steve Johnson


I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.


I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University

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