Bicycle gear system's Input-Output ratio?

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SUMMARY

The discussion centers on calculating the input-output ratio of a bicycle gear system, specifically focusing on a scenario involving a 60 kg rider exerting 30 kg of thrust per pedal. The calculated output force at the back wheel is approximately 11.323 kgf per RPM, derived from the gear ratios and sizes provided. Key components include a pedal crank radius of 165 mm, a main driver cog radius of 90 mm, a secondary cog radius of 35 mm, and a back wheel radius of 340 mm. The ratio of pedal crank RPM to wheel RPM is established at 2.571.

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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
 
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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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