Equations · equation
Throw
Billiards
- Equation
- throw angle ≈ atan(μ v_t / v_n), up to about 5°
- Field
- Billiards
Symbols
μ ball-to-ball friction — not a constant: the shot lab uses Alciatore's measured fit μ = 0.01 + 0.108·e^(−1.088 v), which runs from about 0.12 at a crawl to 0.02 at speed · v_t the relative speed of the two surfaces across the contact — from the cut angle, from side spin, or both · v_n the closing speed along the line of centres
Significance
During the fifth of a millisecond the balls touch, friction drags the object ball a little off the line of centres, toward the direction the cue ball's surface was sliding. A cut throws the object ball forward of the geometric line (cut-induced throw); side spin throws it left or right (spin-induced throw). Slow shots throw more — the friction has more time relative to the speed — and it saturates once the surfaces stop slipping. Chalk on the contact point can double it. Nobody pockets long, slow cuts without allowing for it.
Referenced by
equation
skill
Open on the Equations shelf — the interactive card, the filters, and everything alongside it.