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

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Homework Help Overview

The discussion revolves around calculating the speed of a bicycle chain, given specific parameters such as wheel diameter, pedal crank length, and angular rate of pedaling. The problem involves understanding the relationship between angular velocity and linear speed in the context of bicycle mechanics.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss converting revolutions per minute to radians per second and applying this to the radius of the front sprocket to find the speed. There are questions about whether the length of the pedal crank should be considered in the calculations.

Discussion Status

Some participants are actively engaging with the calculations, identifying potential errors in the approach. There is a recognition of a mistake related to calculating the radius from the diameter, and participants are collaboratively exploring the implications of this oversight.

Contextual Notes

There is a mention of the need to calculate the speed of a link of the chain relative to the bicycle frame, which adds context to the calculations being discussed. The original poster's attempts are noted, but there is no explicit resolution or consensus on the correct method yet.

freeurmind101
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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.

Homework Equations


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?
 
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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.

Homework Equations


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?
 
(1min/60sec)*(71.5revs/min)*(0.152m)*(2*pi rad/1rev)=1.138
 
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!
I should have noticed I had half your answer.
 

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