# What is the correct method for calculating the speed of a bicycle chain?

• freeurmind101
In summary: It's always good to get a reality check.In summary, the conversation was about finding the speed of a link of a chain relative to the bicycle frame, with given values for the bicycle's wheel diameter, pedal crank length, and angular rate of pedaling. The attempted solution involved converting the angular rate to rad/s and using it to calculate the tangential velocity at the front and back sprockets, but the answer was incorrect due to forgetting to divide the diameter by 2 to get the radius.
freeurmind101

## Homework Statement

A bicycle has wheels 67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclist pedals at a steady angular rate of 71.5 rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 6.45 cm in diameter.

v=rw

## The Attempt at a Solution

I converted the revs/min to rad/s and then used that value times the radius of the front sprocket and got 1.138 m/s but this is wrong. I then tried to calculate the tangential velocity at the back sprocket with the same rate of pedaling and that radius and added it to the value I got from the front sprocket but this was wrong as well. Do i need to take into account the length of the pedal crank?

Welcome to PF, Free.
Looks interesting, but there is no question. What are you trying to find?

freeurmind101 said:

## Homework Statement

A bicycle has wheels 67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclist pedals at a steady angular rate of 71.5 rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 6.45 cm in diameter. (a) Calculate the speed of a link of the chain relative to the bicycle frame.

v=rw

## The Attempt at a Solution

I converted the revs/min to rad/s and then used that value times the radius of the front sprocket and got 1.138 m/s but this is wrong. I then tried to calculate the tangential velocity at the back sprocket with the same rate of pedaling and that radius and added it to the value I got from the front sprocket but this was wrong as well. Do i need to take into account the length of the pedal crank?

Sorry lol, I forgot to include the question. (a) Calculate the speed of a link of the chain relative to the bicycle frame.

I converted the revs/min to rad/s and then used that value times the radius of the front sprocket and got 1.138 m/s but this is wrong.
The method sounds good, but I don't agree with the answer!
Can you show the details of the calculation so we can look for the error?

Wow, I just realized I forgot to divide the diameter by 2 to get the radius lol. I'm such an idiot lol.

Ah, I knew it had to be some little thing. Easy to do!

## 1. What affects the speed of a bicycle chain?

The speed of a bicycle chain is affected by several factors, including the gear ratio, the chain length, and the condition of the chain and gears. The gear ratio determines how many times the pedals must rotate to turn the rear wheel once, while the chain length affects how smoothly the chain moves. A well-lubricated and properly maintained chain and gears can also contribute to a faster speed.

## 2. Does the material of the chain affect its speed?

Yes, the material of the chain can affect its speed. Generally, a lighter chain made of materials such as titanium or carbon fiber will allow for faster acceleration and a higher top speed. However, these types of chains may be more expensive and may not be as durable as heavier chains made of steel.

## 3. How does the speed of a bicycle chain compare to other modes of transportation?

The speed of a bicycle chain can vary greatly depending on the rider's strength and the terrain. On average, a cyclist can maintain a speed of 10-12 mph on flat ground, while professional cyclists can reach speeds of 25-30 mph. This is significantly slower than cars or trains, but may be comparable to walking or running speeds.

## 4. Can the speed of a bicycle chain be increased?

Yes, the speed of a bicycle chain can be increased with proper maintenance and adjustments. Keeping the chain well lubricated and free of debris can reduce friction and improve speed. Choosing the right gear ratio for the terrain can also help maximize speed. Additionally, regular tune-ups and replacing worn out components can also contribute to a faster speed.

## 5. Is there a limit to how fast a bicycle chain can go?

The speed of a bicycle chain is ultimately limited by the strength and endurance of the cyclist. However, factors such as aerodynamics, terrain, and the condition of the bike can also play a role in the maximum speed achievable. In general, professional cyclists can reach speeds of over 40 mph, but the average cyclist may have a maximum speed of around 25 mph.

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