Gear ratio requirement (RPM --> km/h)

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SUMMARY

The discussion centers on calculating the required gear ratio for a vehicle with wheels of 58 cm diameter powered by motors with a maximum speed of 6024 RPM, aiming for a maximum speed of 190.2 km/h. To find the gear ratio, participants suggest first determining the RPM of the wheels at maximum velocity. The relationship between wheel diameter and radius is emphasized, as well as the conversion of RPM to radians per second for accurate calculations. The final answer must be a unitless value, rounded to two decimal places.

PREREQUISITES
  • Understanding of gear ratios and their significance in vehicle dynamics
  • Knowledge of RPM (Revolutions Per Minute) and its conversion to radians per second
  • Familiarity with basic geometry, specifically the relationship between diameter and radius
  • Ability to perform unit conversions between speed measurements (km/h to m/s)
NEXT STEPS
  • Calculate the RPM of the wheels at the vehicle's maximum speed of 190.2 km/h
  • Learn about the formula for gear ratio calculation in mechanical systems
  • Explore the relationship between wheel size and vehicle speed
  • Study the conversion techniques between different speed units, such as km/h to m/s
USEFUL FOR

Students in mechanical engineering, automotive engineers, and anyone involved in vehicle design or performance optimization will benefit from this discussion.

D.B0004
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Homework Statement


A vehicle having wheels with a diameter of 58cm, is powered by motors that have a maximum speed of 6024 rpm. Each motor is coupled to the wheel using a gear mechanism as shown in figure 2-14. Calculate the required gear ratio if the vehicle's maximum speed is 190.2 km/hr.

Note: Answer is a unitless value, correct upto two decimals.

Homework Equations


No clue. C = 2 * PI * R?

The Attempt at a Solution


I converted 6024 rpm to radians per second hoping I could do the same with hm/hr, but I do not know the radius of the tire? See photo attache for diagram. Thanks for help.
 

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D.B0004 said:

Homework Statement


A vehicle having wheels with a diameter of 58cm, is powered by motors that have a maximum speed of 6024 rpm. Each motor is coupled to the wheel using a gear mechanism as shown in figure 2-14. Calculate the required gear ratio if the vehicle's maximum speed is 190.2 km/hr.

Note: Answer is a unitless value, correct upto two decimals.

Homework Equations


No clue. C = 2 * PI * R?

The Attempt at a Solution


I converted 6024 rpm to radians per second hoping I could do the same with hm/hr, but I do not know the radius of the tire? See photo attache for diagram. Thanks for help.
... but you know the diameter of the wheel. How is diameter related to radius?...
 
I converted 6024 rpm to radians per second...

I would start "at the other end of the problem". eg Work out the rpm of the wheel at max velocity.
 

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