Bicycle gear system's Input-Output ratio?

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Discussion Overview

The discussion centers around calculating the input-output force ratio of a bicycle gear system, focusing on the forces exerted by a cyclist and how these translate to the back wheel. The inquiry involves theoretical aspects of mechanics and gear ratios, without considering friction or resistance forces.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • A participant describes the force exerted by a 60 kg person on the pedals and calculates the thrust as 60 kg per revolution at 30 RPM.
  • The same participant presents a calculated input-output ratio of 2.571 for the pedal crank to the wheel.
  • Another participant discusses the force exerted on the pedals without cleats, suggesting that the entire weight of the cyclist contributes to the force applied.
  • This participant calculates chain tension based on the crank radius and gear sizes, arriving at a force of 110 kgf transmitted through the gears.
  • The force exerted by the tire on the road is further calculated as approximately 11.323 kgf, based on the gear ratios and wheel radius.

Areas of Agreement / Disagreement

There is no consensus on the correct formula for calculating the output force at the back wheel, as participants present different calculations and interpretations of the forces involved.

Contextual Notes

Participants explicitly state that they are ignoring resisting forces and friction for the purpose of their calculations, which may limit the applicability of their results in real-world scenarios.

Stevengouws
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TL;DR
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
 
Engineering news on Phys.org
As a side note this is NOT for professional cycling purposes
 
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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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.
 

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