How Is the Velocity of Bicycle Pedals Calculated?

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SUMMARY

The discussion focuses on calculating the velocity of bicycle pedals based on given parameters, including the speed of the bicyclist at 20 km/h, the radius of the back wheel at 0.33 m, and cog wheel radii of 0.035 m and 0.085 m. The angular velocity is derived using the formula v = r * omega, leading to a pedal velocity of approximately 3.99 km/h. The conversation highlights the need to understand pedal velocity in relation to the ground, noting that it varies based on the pedal's position in the rotation cycle.

PREREQUISITES
  • Understanding of angular velocity and its relationship to linear velocity
  • Familiarity with bicycle mechanics, specifically cog wheel and wheel radius
  • Basic knowledge of kinematics and motion equations
  • Ability to perform unit conversions between km/h and m/s
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  • Research the effects of gear ratios on bicycle performance
  • Learn about the dynamics of pedal stroke and its impact on cycling efficiency
  • Explore the relationship between angular velocity and linear velocity in different mechanical systems
  • Investigate the physics of motion in cycling, including forces acting on the cyclist
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Cyclists, mechanical engineers, physics students, and anyone interested in understanding the mechanics of bicycle motion and pedal dynamics.

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Homework Statement


A bicyclist travels in a light head wind on a level, horizontal road. The bicyclist keeps a constant speed of v = 20 km per hour. He pedals evenly. The back wheel has a radius of r = 0.33 m. The back cog wheel has a radius of r = 0.035 m. The front cog wheel has a radius of r[f] = 0.085 m. Each pedal arm has the length L = 0.16 m, measured from the center of the front cog wheel.

Find an expression for the maximum and minimum value of the pedal velocity based on the given radii, L and the velocity v.

Homework Equations


v=r*omega

The Attempt at a Solution


I have assumed that the angular velocity of the front and back wheel must be the same.
I have assumed that the angular velocity of the pedals must be the same as the front cog wheel.

Hence:
omega[front cog wheel & pedals] = v/radius of wheel * radius of rear cog wheel/radius of front cog wheel
omega[front cog wheel & pedals] = ((20 km/hr) / (0.33 m)) * ((0.035 m) / (0.0085 m)) = app. 24.96 km/hr*m

v[pedal] = (0.16 m) * (24.96 km/hr*m) = app. 3.99 km/h

Does anyone have an explanation for why the pedal velocity should have a maximum and minimum value and not just be constant?

Any help is much appreciated.


tsrgb
 
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You wrote,


Does anyone have an explanation for why the pedal velocity should have a maximum and minimum value and not just be constant?

I think they want the velocity of the pedal with respect to the ground. When the pedal is at the top it moves forward with greatest velocity, a sum of two motions.
 
Thank you.
I'll try that.tsrgb
 

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