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# Gear Trains - Bicycle Gearing Calculator

A simple gear can change magnitude and line of action of an effort force.

The effort force is applied to the "driver" and the load is applied to the "follower" .

### Transmission - or Movement - Ratio

Transmission - or movement - ratio can be expressed as

M = n D / n F = t F / t D (1)

where

i M = movement ratio

n D = revolutions of driver (rpm)

n F = revolutions of follower (rpm)

t F = number of teeth on follower

t D = number of teeth on driver

When the same direction of rotation is required for the driver and the follower, an idler wheel is used.

### Gear Calculator

Calculate follower revolutions.

The movement ratio for a gear with an idler wheel can be expressed as

i M = n D / n F = (t I / t D ) (t F / t I ) = t F / t D (1b)

where

t I = number of teeth on idler

### Moment Ratio

The moment - or torque - ratio for a transmission can be expressed as

i T = M F / M L = 1 / (i M μ)                     (2)

where

i T = moment ratio

μ = transmission efficiency

M L = output moment of load from follower (Nm, lb ft)

M F = input moment of force on driver (Nm, lb ft)

### Transmission - Moment Ratio Calculator

The calculator is generic and can be used for SI and Imperial units - output units equals input units.

### Make 3D models of spurs and gears with the Engineering ToolBox SketchUp plugin

Spurs and Gears - Use the awesome SketchUp to make 3D models of spurs and gears

### Typical Gear Ratios

Typical gear ratios for different types of gear sets are indicated below.

Gear Ratios
Type of Gear setTypical Gear Ratios
MinMax
Spur gear, external 1 : 1 5 : 1
Spur gear, internal 1.5 : 1 7 : 1
Helical gear, external 1 : 1 10 : 1
Helical gear, internal 1.5 : 1 10 : 1
Straight bevel gear 1 : 1 8 : 1
Spiral bevel gear 1 : 1 8 : 1
Epicyclic planetary gear 3 : 1 12 : 1
Epicyclic star gear 2 : 1 11 : 1

### Bicycle Gearing

The revolutions of a bicycle wheel when pedaling can be calculated by transforming (2) :

n F = n D t D / t F (3)

where

n F = revolutions of the bicycle wheel (rpm)

n D = revolutions of the pedaling (rpm)

t D = number of teeth in the pedaling sprocket

t F = number of teeth in wheel sprocket

The distance traveled by the wheel can be calculated by multiplying wheel revolutions with wheel circumference:

l = c n F

= c n D t D / t F

= π d n D t D / t F (3b)

where

l = outer wheel traveled length or distance  (m, in)

c = outer wheel circumference (m, in)

d = outer wheel diameter (m, in)

### Example - Bicycle Gear

A mountain bike with 26 inch outer diameter wheels has a 42/34/24T chain-set and a 7-speed 14-34 cassette in the rear wheel.

The outer circumference of the wheel can be calculated as

c = π (26 in)

= 81.7 in

The distance traveled by the wheel in the lowest gear - for one pedaling revolution - using the smallest sprocket in the chainset (24T) and the largest sprocket in the cassette (34T) - can be calculated using (3b) as

l = (1) (81.6 in) (24) / (34)

= 57.7 in

The distance traveled by the wheel in the highest gear - for one pedaling revolution - using the largest sprocket in the chainset (42T) and the smallest sprocket in the cassette (14T) - can be calculated as

l = (1) (81.6 in) (42) / (14)

= 244.8 in

### Bicycle Gearing Calculator

Calculate distance traveled by wheel.

The calculator is generic and can be used for SI and Imperial units - output units equals input units.

bicycle wheel outside diameter - d - (m, mm, in)

number of teeth in chain-set sprocket

number of teeth in cassette sprocket

### Bicycle Gearing Calculator - Template

Make your own graphical Bicycle Gearing Calculator by using this Google Docs template!

## Related Topics

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### Gear Reducing Formulas

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### Gears

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