Why do front gears become harder when the cassette becomes larger but opposite for the rear ones?

Question

I noticed on mine and other road bikes that the "big" front gear becomes "harder" (more distance per revolution) when it switches to the bigger cassette. That makes sense, larger revolution of the chain. But this seems to be the opposite with the rear gears. Here, it becomes "harder" when switching to the smaller cassettes. I always thought I was seeing things until I saw this video:

where at 2:48, they confirm it.

Another thing I always wondered was why the gear shifters on each side seem to be opposite to each other as well. On a road bike, there is a "large shifter" and a "small shifter". The right hand, which controls the back cassette makes it "harder" when pushing the small shifter. The left hand which controls the front cassette makes it "easier" when pushing the small shifter.

Are these two things related? And what is the reason for the shifters and cassettes apparently contradicting each other.

Answer 1

What makes a combination hard is the ratio between the size of the front sprocket and the rear one (front divided by rear). The higher this ratio is, the harder the combination is.

To make the ratio higher, you can either increase the numerator (= increase the front size), or decrease the denominator (=decrease the rear size).

Answer 2

An example with numbers: Let’s say the chainring (front sprocket) has 40 teeth and your currently selected cassette sprocket in the rear has 20 sprockets.

For every turn of the chainring the chain moves by 40 links. So the rear sprocket (and therefore the rear wheel) has to make two full revolutions. So your rear wheel turns twice as fast as your cranks.

Now imagine you shift to a smaller rear sprocket with 10 teeth. Suddenly you make four full wheel revolutions for every crank revolution. So you go twice as fast in this gear and need a corresponding increase in leg power (assuming you keep pedaling at the same cadence).

The size and arrangement of the shift paddles is just a result of the derailleur spring pulling towards the smaller sprocket (on both the front and the rear derailleuer) in most modern systems. There have been systems in the past where the rear derailleur spring pulled towards the bigger sprockets.

Answer 3

Renaud's answer succinctly covers the gear ratio part of your question, so I'll address the gear shifter part.

To start from basics, bicycle chain-based transmissions "change gears" when devices called "derailleurs" dislodge the chain from one sprocket and laterally move it to another. This movement is accomplished via spring tension in one direction, and in most cases cable tension in the other (electric shifters are outside the scope of this answer). In modern transmissions, the spring acts in the direction of smaller sprockets, whereas the cable acts towards larger sprockets. Hence, you need two control inputs per sprocket cluster, one for each of these actuators.

Note that with this arrangement, the cable not only needs to shift the chain, but also must fight the spring. Hence, the "large" shift paddle is used to actuate the cable--you get a larger surface to push on (in addition to more leverage) to accommodate for this dual action. In comparison, the "small" shift paddle is all that's needed to allow the spring to do its job, since that is pretty much automatic. You'll notice that this design of "large paddle moves chain towards larger sprockets and vice versa" exactly lines up with your observations.

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Note again: not every mechanical road shifter on the market uses a two-paddle system like this. There's other ways to implement bicycle shifter operation. The fundamental principle is the same throughout though: something is operating a cable-spring combination.

Answer 4

And finally I'd like to address the third part of your question, if I understand it correctly: Why do the large chain rings in the front grow from the inside out (the outermost chain ring is the largest), while the little sprockets in the back cassette shrink (the outermost one is the smallest)?

The reason is that one tries to avoid running the chain "diagonally", that is, on the innermost chain ring in the front and the outermost in the back, and vice versa. In such a configuration, the chain must bend a lot because it runs "straight" (parallel to the bicycle) over the "sprockets" but at an angle from the front to the back. This quickly wears the teeth of the sprockets which take on the lateral force as well as the chain which works with the least friction when straight.

Since the highest gear results from using the largest front chain ring together with the smallest back sprocket, ordering the sprockets/chain rings the same way in the front and in the back would require the chain to run diagonally since the largest chain ring and the smallest sprocket would be opposed. The same is true in reverse for the smallest gear. These extreme gears would be unavailable for regular operation, and the adjacent gears would also need to be avoided for longer use.

Ordering the sprockets anti-parallel, by contrast, makes those extreme gears available with a straight chain, which is desirable. Shifting the chain both in the front and in the back in the same direction changes the transmission ratio; if the sprockets were ordered the same way, it wouldn't really change much because the ratio stays similar if you reduce (or increase) both the nominator and denominator at the same time. As depicted with the extremes, you'd need to increase "diagonality" of the chain in order to change the transmission ratio, which is undesirable.

Answer 5

Another thing I always wondered was why the gear shifters on each side seem to be opposite to each other as well. On a road bike, there is a "large shifter" and a "small shifter". The right hand, which controls the back cassette makes it "harder" when pushing the small shifter. The left hand which controls the front cassette makes it "easier" when pushing the small shifter.

Conventional shifters use a cable to control the derailleurs. Cables are good at pulling, but not very good at pushing. So a spring it used to push the derailleurs in the direction opposite to the cable's pull. On most derailleurs the springs push the cables to the smaller sprockets and the cables pull the derailleurs onto the larger sprockets. As you have noticed, smaller cogs in the front make for a lower, easier gear ratio and smaller cogs in the back make for a higher, harder gear ratio. I believe that they work this way because the cable's pull is more powerful than the spring's pull and it's easier to push the chain onto the smaller cogs than the larger cogs.

Not all derailleurs work this way. My 1961 Rudge's Cyclo rear derailleur has a conical spring that pushes the derailleur onto the the larger cogs and the cable pulls the derailleur onto the smaller cog. Some older front Suntour derailleurs use the spring to push the chain onto the larger chainwheel and the pull of the cable pushes it onto the smaller chainwheel.

Answer 6

It's easiest to think about chain speed.

A big sprocket means slow rotation of its shaft corresponds to a given chain speed.

A small sprocket on the other hand means fast rotation of its shaft corresponds to a given chain speed.

Big gear is when the rear wheel rotates fast but the bottom bracket spindle rotates slow. Now, for fast rotation of the rear wheel for a given chain speed, you would select a small rear sprocket. And for slow rotation of the bottom bracket spindle, you would use a big front sprocket (called chainwheel).

Small gear is opposite: rear wheel rotates slow but the bottom bracket spindle rotates fast. Everything is reversed now. For slow rotation of the rear wheel, you would select a big rear sprocket. And for fast rotation of the bottom bracket spindle, you would select a small front sprocket (called chainwheel).

How derailleurs operate (low-normal / high-normal) is entirely unrelated to this. Both low normal and high normal rear derailleurs have been built.

Answer 7

The physics of simple machines like gears or pulleys is related to levers: pulling on the longer end of a lever is easier, pulling on the shorter end is harder (shorter lever arm).

The "levers" that give a mechanical advantage are

• Length of the pedal cranks compared to the radius of the chainring (front gear). You're pushing on the long end (the pedal at the end of its crank), and changing front gears changes how short the other end of the "lever" is, taking more or fewer turns to pull the chain the same linear distance.
• The rear wheel radius compared to sprocket radius: you are pulling (via the chain) on the short end of that lever to move the rear wheel. A smaller rear gear makes the short end of the lever even shorter.

The net effect of front+rear gears is to create a ratio of number of turns of the pedals to turns of the rear wheel. The more times the rear wheel has to turn for one rotation of the pedals, the harder the gear ratio. Smaller rear gears turn more times for the same length of chain moving past them.

(Since the chain meshes with teeth, we usually count number of teeth around the circumference instead of talking about radius, but those are of course directly related. Gears connected by a chain work just like gears where the teeth mesh directly, in terms of gear ratios.)

If you want more examples and explanations of levers, pulleys, and gears, you can google "simple machines pulleys gear ratio" or something like that. I tried but I don't know if any of the articles, videos, or physics/engineering tutorials that came up are good or not.