Question

Bycicles convert force into torque (pedal to axis), torque into force (axis to chain using the front gear), force into a torque (chain to back wheel using back gear), and finally, torque into force (wheel on road), and that accelerates the bike. If you make the front gear smaller, is it easier or harder to pedal (explain in terms of forces/torques)? If you make the back gear smaller, is it easier or harder to pedal?

Answer 1

Bicycles have multiple gears so that it's easier to go up hills, and so you can go faster on level ground. Read this article and in five minutes you'll know how to use your gears.



First, let's get our terms straight so we're on the same page

You can think of gears as the same thing as speeds -- a bike with 18 gears is an 18-speed bike. Bikes generally have 1, 3, 10, 15, 18, or 21 speeds. (10- and 15-speeds are obsolete and you don't see them on new bikes any more.)
Lower numbers are the low gears, and higher numbers are the high gears. First gear is a low gear. Twenty-first gear is a high gear. That's pretty easy, right?

Shifting means going from one gear to another. You shift gears by sliding the shifter on the handlebars. On most bikes this shifts the chain onto a different sized ring. On three-speed bikes the gears are inside the hub of the wheel so you don't see them.

Downshifting means going to a lower gear, and upshifting means going to a higher gear. You can also say shift down and shift up.

How do I tell what numbers my gears are?

If your bike has three speeds then telling the gears apart is easy, because there's only one shifter and it's labeled 1-2-3. You can skip the rest of this section and go on to the next one.
But if your bike has 10 or more speeds then it's just a little bit trickier, because you have two shifters....Let's say you have an 18-speed bike. Your left shifter will be labeled 1-2-3, and your right shifter will be labeled 1-2-3-4-5-6. This means that for each number on the left, you get six different speeds on the right, for a total of 18. Here's how it works:

#1
#2 #3

1 2
3
4
5
6

Right-Hand Shifter
(Rear Ring Set)
1 2
3
4
5
6

Right-Hand Shifter
(Rear Ring Set)
1 2
3
4
5
6

Right-Hand Shifter
(Rear Ring Set)


Shifting puts the chain on a different ring. The left shifter changes the ring where the pedals are. The smallest ring is 1, the middle ring is 2, and the biggest ring is 3. When you downshift with your left shifter, you're moving to a smaller ring.

The right shifter changes the ring on the rear wheel. This is opposite of the front set: On the rear wheel the biggest ring is 1, and the largest ring is 6.

You don't have to worry about the ring sizes if you don't want to, you can just look at the numbers on the shifter. You can downshift with either shifter, moving it from a higher number to a smaller number. You get a bigger change when you shift with the left-hand shifter than when you shift with the right-hand shifter.

Now that you know what the terms mean, let's see how to use our gears

Here's pretty much all you need to know about shifting gears:
If you're going uphill and it's too difficult, shift down.
If your legs are spinning the pedals way too fast (it's too "easy") then shift up.
That's it, in a nutshell. Of course there are nuances but that's 90% of what you need to know.

Here it is with more detail:

Let's say you're on a three-speed bike, in second speed. You start to go up a hill, and suddenly your legs can't spin the pedals as fast. You're barely turning the pedals, pushing hard on them, and you're going so slowly you think you might fall over. The solution? Downshift to first gear.

How does that solve the problem? First gear moves you a shorter distance for each spin of the pedals, which makes it easier to pedal.

Now let's say you've reached the top of the hill, and you start going downhill slightly. Soon you find there's no resistance in the pedals -- you can spin them as fast as you want and you're not really getting anywhere. Solution? Upshift back to 2, and if it's still too easy, then upshift to 3.

This works because the higher gears move you farther for each spin of the pedals, making you do more "work", and making it less "easy".

Advanced gearing

So you've learned the basics: Uphill = shift down, Downhill = shift up. But you have an 18-speed bike and you're wondering which shifter to use, the left one or the right one?
The answer depends on how much change you need. If you need a big change, use your left shifter. If you need a small change, use the right one. As you ride you'll get a feel for whether you need a big change or a small change.

Another thing: Try to keep the chain in a sort-of straight line between the front and rear sets, rather than going at an angle from left to right. For example, in the very lowest gear the chain will be all the way on the left on both sets. In the very highest gear the chain will be all the way on the right. What you don't want to do is to use the left-hand ring in the front and the right-hand ring in the back, which makes the chain go diagonally -- that stretches the chain and wears it out. You also don't want to use the right-hand ring in the front and the left-hand ring in the back. Same thing.