Gear Ratio Calculations #26 BackToList Print

*A comprehensive document to back up mention in other places*

1. Preface

2. Low Gear

3. High Gear

4. Other Calculations

5. Friction Comparison

6. Terminology Summary

7. Deraileur Compatibility

8. Power Output

1. Preface

This document goes with the Bike Transmissions Reference Database.

The simplest way to calculate gear ratios is to just divide the number of teeth on the current front cog with the number on the rear. Could be called "cog ratio". For example if your chain is on a 26 tooth sprocket on the front and a 36 tooth sprocket on the back, the ratio is 26/36 = 0.72.

To take into account the diameter of the wheel, a common measurement is to multiply each of the above "cog ratios" by the wheel diameter in inches. That gives you "gear-inches". A typical 700c wheel is 27 inches in diameter. So the gear-inches of the above 0.72 ratio is 19.4 gear-inches.

Another ratio often quoted is the overall "gear range", which is the highest to the lowest. Eg: On the Trek 520, the highest gear is 48/11 and the lowest is 26/36.

High Low Range

Fraction Ratio Ratio Percent ------------------------------------------------ Trek 520 48/11 4.4 0.72 610%

2. Low Gear

(Lowest Gear by cog ratio) here are two main ways to compare low gears: (1) Cog ratio and (2) Gear Inches. Gear Inches takes into account the wheel diameter. The cog ratio is just the ratio of the cogs, without regard for the wheel size. "Low Gear" by cog ration is is the ratio of the smallest chain ring on the front and the largest cog on the back cassette. Front/Back. If you've got a 24 tooth chain ring on the front and a 36 tooth cog on the back, your low gear is 24/36 teeth =.66 to 1. One turn of the crank turns the wheel .66 of a revolution.

On touring bikes, you definitely want your low ratio to be less than 1 to 1. For example, the Surly Long Haul Trucker comes with a 50/39/30 on the front and a 11-36 on the back. So the lowest gear ratio is 30/36 which is 0.83. My Miyata 1000 has 50/40/28 and a 14-30 on the back, giving 0.93, and my Rocky Mountain is 42/32/22 and 12-32 giving 0.69.

Of course, the gear ratio alone doesn't quite tell the whole story, because it doesn't take into account the diameter of the wheel and tire. There is a measurement called "Gear Inches" which just multiplies the above ratio times the diameter of the tire. eg: A 1.00 cog ratio with a 26 inch wheel would be 26 gear-inches. That is a handy number to compare if you are trying to compare two radically different sizes of wheels, such as a foldup bike and a road bike. If you really want to be fancy, you could factor in the crank length, and make adjustments for the actual tire diameter you have.

As a practical matter, if you are looking at buying a bike, simply calculating the cog ratio is good enough. Below are a few low gear statistics:

--Cog Ratio------

Bike Fraction Decimal WheelD Gear-Inches -----------------------------------------------------

Surly LHT 30/36 0.83 27" 22.4

Miyata 1000 28/30 0.93 27" 24.2

Rocky Mountain 22/32 0.69 26" 17.9

3. High Gear

The gear ratio is a ratio between the number of teeth. Could be called "cog ratio". It is calculated by dividing the number of teeth on the largest chainring by the smallest cog on the cassette. Eg: 52 teeth on the front divided by 11 teeth on the back. 52/11=4.7 (4.7 to 1)

4. Other Calculations

There are numerous gear calculators on the internet that calculate all sorts of other statistics. I don't find many of them useful these days to help with actual buying decisions. However you may find them interesting. For example, Sheldon Brown has a "Gain Ratio" calculator.
https://www.sheldonbrown.com/gear-calc.html

Some of these calculations were more useful back in the days when we used to individually pick each cog in a cassette.

Another statistic is called "Rollout" or "Development". Sheldon Brown talks about. It is the distance the bicycle travels for one crank revolution, and is usually measured in meters. Development can be calculated by dividing the chainwheel size by the rear sprocket size, multiplying the result by the wheel diameter and by pi (3.1416). See also gear inches and gain ratios.

So the rollout for the 0.72 ratio we multiply by 700cm x 3.14159

I don't think this is very useful, although one could use it to compare riding to walking I suppose.

5. Friction Comparison

This website did a comparison of losses between a 1x and 2x system.
[a href=https://www.velonews.com/gear/gear-issue-friction-differences-between-1x-and-2x-drivetrainsVelo News[/a]

The 2X drivetrain had lower frictional losses in every gear than the 1X system—with the caveat that the chainrings matched up with the ideal cogs in the rear. The average friction within the 1X drivetrain was 12.24 watts. This was computed as the sum of the drivetrain power losses in each of the 11 gears divided by 11. The average friction of the 2X drivetrain was 9.45 watts, computed as the sum of the power losses in each of the 15 optimal gears divided by 15. This is just under a three-watt average difference between the two drivetrains.

The frictional losses of the system were highest for each chainring when the chain ran on the smallest cog. This is also where the difference in frictional losses were greatest between the two drivetrains: at the highest gear ratio (4.8) the 48 X 10-tooth combination consumed six watts more than the 53 X 11-tooth combination.

6. Terminology Summary

In my database, the various statistics have short code names like "Front" or "Rear" that require longer names if you were referring to them in a conversation or article.

Calculator Article

Name Name --------------------------------------Front FrontCogs Front Chainrings

Rear RearCogs

LowGear Low Gear Cog Ratio

HighGear High Gear Cog Ratio

LowInch Gear Inches - Low Gear

HighInch Gear Inches - High Gear

A typical conversation might be: Compare the "LowGear" on the Miyata 1000 with the Trek 520.

The ratio of the number of teeth between front and back. There are two cog ratios: Low Gear and High Gear.

This is the typical spec you see in online catalogs. Eg: 11-34 It is usually accompanied by the number of speeds. Bike X has an 11-34 9 speed cassette. Only the two ends of the range are specified.

These words always refer to gears. Eg: In a car you might say "put it into Low".

Low Gear Ratio. The ratio between the crank and the axle. In my stuff I usually mean Low Gear Ratio if I just say "Low gear". But if I was sending an email I might say "what is the low gear ratio on that bike? Or what is the internal low gear ratio on a Rohloff hub? (Reduction ratio)

7. Deraileur Compatibility

In general, all touring bikes require the Shimano SGS (long cage) deraileurs, due to having low gears. SGS is Shimano code for "long cage".
Shimano MTB rear derailleurs last letters will be GS or SGS, which stand for "Short cage" or SGS for long cage. A XTR rear derailleur will be RD-M970-GS (for short cage) or RD-M970-SGS (for long cage)

There should also be entry in deraileur database.

Park Tools Rear Derailleur Adjustment

This article goes thru how to set the rear derailleur all three screws: H, L and B.

8. Power Output

Why do you need low gears? Because you need to keep spinning in your efficient range. A 20 inch low gear is 0.508 meters forward. If on a 1% slope, that is 0.005 meters up. Raising 1 kg 1 meter/second takes 10 watts. Raising 1 kg

So if spinning at 80 rpm,

To raise 1 kg a distance of 1 meter takes 10 newton.meters (joules)

to raise 1 kg a height of one meter in 1 second would take 10 watts of power (a watt is 1 joule/second)

- to raise 100 kg a distance of 1 meter in 1 second takes 1000 watts of power at 150 watts, you can raise 1 kg

If the hill is

- One watt is 1 joule/second

One watt will raise
So 100 watts

If going at 80 rpm and 150 watts, you can climb ? 80

GearInch Meters
-------------------------------

1" 0.0254

24" 0.609

20" 0.508

80 rpm in a 20" gear is 80 x 0.508 meters/minute

= 40.6 meters/minute

= .67 meters/second

With a 1% grade, each meter forward raises you 1 cm or 1000m would raise you 10 meters, which would require With a 6% grade, 1000m raises you 60 meters,

With a 6% grade, 0.508 meters would raise you .0304 meters