## Difficulty level of the road

What is the difficulty level of the road that you will mainly use?

- Straight and level
- Some lightly inclined long distance hills
- Some short distance inclined hills
- Damn, I live in mountains!

This question will influence the kind of transmission system you will need on your bicycle. We are going to talk about gear ratios in the next table. We are jumping here in a more advanced topic. A gear ratio is the difference between the front and rear gear sizes. Why do we need that? Well, lets go back to some mathematical notions here. When two gears are linked together with a chain, they both turn of course since the chain propagate energy from one gear to the other. Thought, they will not necessarily turn the same way, depending on their radiuses. Lets illustrate this concept:

So we know that to determine the speed of rotation of two gears linked together by a chain, we can compute the ratio of their radiuses like this:

Front gear radius / Rear gear radius = rotation speed factor of the rear gear with regard to the front gear rotational speed.

So if the front gear turns at 60 RPM (rotations per minute), a common cyclist cadence, then the rear gear will turn at:

(20 cm / 10 cm) * 60 RPM = 2 * 60 = 120 RPM

So the rear gear will turn twice as fast as the front one. This is the basis of how a cyclist can change the speed at which its bicycle is going while keeping the same pedaling cadence. In the current discussion, this is very important as it will determine the maximal and minimal speed at which a given bicycle will go, with respect to a similar cyclist cadence.

What is important to see here, is that the higher this gear ratio is, the harder it is on your legs muscles. Indeed, it is not simply a fact of multiplying the rotation speed of one gear with respect to an other. It is related to the fact that the bigger this multiplying factor is, the more lever effect the gears creates on the mechanical system.

If you followed so far, you can now understand that the gear ratio of any given bicycle will have a great impact on its effective speed limits, as well as the effort you will have to provide to make it move forward in various road conditions.

Fortunately for us, we can use a sort-cut method to compute these ratios. All gears uses the same gear teeth spacing and dimensions. This is logical since the same chain must run around any of them. Since the gear teeth geometry is constant over all gears, we can use the teeth count on any given gear to compute the gear ratios. In our last example, let's say the front gear had 50 teeth, the rear gear must have had ... 25 teeth. So we could have simply counted each gear teeth count and compute the ratio this way:

(50 teeth / 25 teeth) * 60 RPM = 120 RPM for the rear gear

The following table list approximate ranges of recommended gear teeth counts for the rear and front gear of a bicycle, according to the road you will typically use.

Road difficulty level |
Gear teeth count |
Gear ratio |

Straight and level |
Front: 39 to 54 |
Lowest: 1.44 Highest: 4.91 |

Some lightly inclined long distance hills | Front: 30 to 52 Rear: 13 to 30 |
Lowest: 1 Highest: 4 |

Some short distance inclined hills | Front: 28 to 48 Rear: 13 to 30 |
Lowest: 0.93 Highest: 3.69 |

Damn, I live in mountains! | Front: 22 to 48 Rear: 15 to 35 |
Lowest: 0.63 Highest: 3.20 |

As you can see in that table, the gear are adjusted so that the lowest gear ratio decreases as the road condition gets harder for the cyclist. We also note that the range (from lowest to highest values) gets narrower for mountain conditions while its wider for straight and level conditions. These values basically describes typical race bicycles (at the top of the table) to the other end which are MTB bicycle (at the bottom of the table).

Keep this in mind as you shop your bicycle. You can either ask for the technical data sheet of the bicycle you are interested in, or you can simply count the number of teeth present on the biggest and smallest front and rear sprockets and quickly compute the ratios like we just explained above.

In an other section of this site, we will use the same principles to compute the bicycle speed and traveled distance with respect to the cyclist pedailing cadence. This can be quite useful when riding in groups of cyclist.