Bicycle gear system's Input-Output ratio?

In summary, a person weighing 60 kg exerts 30 kg of thrust on a pedal (crank) x 2 pedals = 60 kg of force per Revolution. The ratio per 1 RPM of the pedal crank to wheel is 2.571. The Pedal (Crank) size is Radius 165mm and circumference of 1036.7mm or (70 teeth simplified). The Main Driver cog is Radius 90mm and circumference of 565.5mm or (38 teeth). The Secondary cog (driving the back wheel) is Radius 35mm and circumference of 219.9mm (18 teeth). The back wheel is Radius 340mm and circumference of 2136.3mm (
  • #1
Stevengouws
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TL;DR Summary
What is the output of Torque on the driver wheel of a bicycle(where it meets tar), verse the input of torque on the pedal. I have all the sizes and forces, yet the correct formula eludes me.
A person weighing 60 kg exerts 30 kg of thrust on a pedal (crank) x 2 pedals = 60 kg of force per Revolution. Let's say @ 30 RPM.
What is the output kg of force per RPM on the back wheel where it meets the tar.
I have all the sizes and forces, yet the correct formula eludes me.
Bicycle Input out Ratio.png

The ratio per 1 RPM of the pedal crank to wheel is 2.571

The Pedal ( Crank ) size is Radius 165mm and circumference of 1036.7mm or ( 70 teeth simplified )
The Main Driver cog is Radius 90mm and circumference of 565.5mm or ( 38 teeth )
The Secondary cog ( driving the back wheel ) is Radius 35mm and circumference of 219.9mm ( 18 teeth )
The back wheel is Radius 340mm and circumference of 2136.3mm ( 144 teeth )
Please see image to clarify

I am not interested in resisting forces or frictional forces - rather let's say these do not exist for this exercise, call it a perfect system.( I am still learning )

The online Gear generator Tool I found is a free useful tool for anyone interested:
https://geargenerator.com/#300,450,...,0,0,0,0,3,1,144,12,12,27,0,0,0,0,0,0,1,3,609
 
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As a side note this is NOT for professional cycling purposes
 
  • #3
Without cleats, a 60 kg person will put all their weight = 60 kg force on the pedal.
The crank radius is 165 mm. Large gear is Radius 90 mm.
Chain tension is 60 kg * 165 / 90 = 110 kgf.
Small gear is radius 35 mm. Wheel radius is 340 mm.
Force from tyre along the road = 110 kg * 35 / 340 = 11.323 kgf.
 
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  • #4
Baluncore said:
Without cleats, a 60 kg person will put all their weight = 60 kg force on the pedal.
The crank radius is 165 mm. Large gear is Radius 90 mm.
Chain tension is 60 kg * 165 / 90 = 110 kgf.
Small gear is radius 35 mm. Wheel radius is 340 mm.
Force from tyre along the road = 110 kg * 35 / 340 = 11.323 kgf.
Awesome, thank you so much.
 

1. What is the input-output ratio of a bicycle gear system?

The input-output ratio of a bicycle gear system refers to the relationship between the force applied to the pedals (input) and the resulting rotation of the rear wheel (output). It is typically expressed as a ratio, such as 2:1, meaning that for every two rotations of the pedals, the rear wheel will rotate once.

2. How is the input-output ratio affected by different gear combinations?

The input-output ratio can be affected by changing the gear combination on a bicycle. By shifting to a higher gear, the input-output ratio increases, meaning that more force is required to turn the pedals but the resulting rotation of the rear wheel is greater. Conversely, shifting to a lower gear decreases the input-output ratio, requiring less force to turn the pedals but resulting in a smaller rotation of the rear wheel.

3. Is the input-output ratio the same for all bicycles?

No, the input-output ratio can vary between different bicycles depending on the gear system and components used. Some bicycles may have a wider range of gear options, resulting in a higher input-output ratio, while others may have a more limited range and a lower input-output ratio.

4. How does the input-output ratio impact cycling performance?

The input-output ratio can greatly impact cycling performance, as it determines the amount of force required to pedal and the resulting speed and power of the bicycle. A higher input-output ratio can be beneficial for riding on flat or downhill terrain, while a lower ratio may be more suitable for climbing steep hills.

5. Can the input-output ratio be adjusted on a bicycle?

Yes, the input-output ratio can be adjusted on a bicycle by changing the gear combination. This can be done manually by shifting gears on a traditional bicycle, or automatically on a bike with electronic shifting. Some bicycles also have the option to customize the gear ratio by changing the size of the front or rear gears.

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