Height of edge of billiard table

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SUMMARY

The height of the edge of a billiard table must be at least equal to the radius of the billiard ball (r) to prevent the balls from slipping off due to upward forces. A safe recommendation is to set the height slightly higher than r, with optimal initial contact heights ranging between 61% and 64% of the ball's diameter (between 1.22r and 1.28r). This ensures stability and minimizes the risk of the balls bouncing off the table. Reference materials, such as the cushion height guide, provide further insights into these measurements.

PREREQUISITES
  • Understanding of basic physics principles, particularly forces and motion.
  • Familiarity with billiard ball dimensions and properties.
  • Knowledge of calculus concepts related to optimization.
  • Awareness of billiard table design and specifications.
NEXT STEPS
  • Research the physics of motion and forces acting on spherical objects.
  • Explore the relationship between ball radius and table edge height in billiard design.
  • Study calculus applications in optimizing physical dimensions for stability.
  • Review the cushion height guide for billiard tables, focusing on K-66 and K-55 specifications.
USEFUL FOR

Physics students, billiard table designers, and anyone interested in the mechanics of billiard games and ball dynamics.

SlowerPhoton
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Homework Statement


Consider a billiard table with balls of radius r. How high should be the edge of the table to not allow undesirable pressures (and thus slips of the ball)? I.e. if there was no gravity, the billiard ball would still bounce off parallelly to the table plane.

However I do not even understand what exactly it says. Please be easy on me, the last I've taken a class on physics was on high school.

The Attempt at a Solution


My answer would be r because otherwise I can see forces that push the ball off the table (in the upward direction). But that seems like a too easy answer for a calculus class.
 
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You are correct that the height must be r or higher or the balls would fly off the table all the time. And you should have it a little higher to be on the safe side. Here is a reference that shows the height of initial contact to be between 61% and 64% of the height of the ball ( between .61*2*r and .64*2*r ) https://www.pooltablefeltcloth.com/cushion-height-guide-for-k-66-k-55.html
 

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