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

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SUMMARY

The correct method for calculating the speed of a bicycle chain involves using the formula v = rw, where v is the tangential velocity, r is the radius of the sprocket, and w is the angular velocity in rad/s. In this discussion, the cyclist pedals at an angular rate of 71.5 rev/min, which converts to 7.48 rad/s. The radius of the front sprocket is 0.076 m (15.2 cm diameter), leading to a correct calculation of the chain speed as 0.569 m/s. The error in the initial calculation stemmed from not using the radius correctly.

PREREQUISITES
  • Understanding of angular velocity and its conversion from rev/min to rad/s
  • Familiarity with the formula v = rw for calculating tangential velocity
  • Knowledge of bicycle mechanics, specifically sprocket dimensions
  • Basic arithmetic skills for unit conversions and calculations
NEXT STEPS
  • Learn about angular velocity conversion techniques, specifically from rev/min to rad/s
  • Study bicycle gear ratios and their impact on speed calculations
  • Explore the relationship between pedal crank length and chain speed
  • Investigate the effects of different sprocket sizes on bicycle performance
USEFUL FOR

Cyclists, mechanical engineers, physics students, and anyone interested in understanding the dynamics of bicycle mechanics and chain speed calculations.

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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