Equations · equation
Cue-to-Ball Speed Transfer
Billiards
- Equation
- v_ball ≈ v_cue · 2 m_cue / (m_cue + m_ball) · (1 + e)/2
- Field
- Billiards
Symbols
v_cue the cue's speed at impact · m_cue the mass that actually follows through — the cue, or on a loose grip mostly its front end · m_ball 170 g · e tip–ball restitution, about 0.7–0.9
Significance
A heavy cue on a light ball gives the ball more speed than the cue had: with a 540 g cue and a 170 g ball the ideal is about 1.5 times, less the tip's losses. Which is why a firm stroke is about cue speed, not muscle, and why the grip's tightness changes the effective mass but not much else. Momentum conservation and Newton's law of impact, nothing more.
Open on the Equations shelf — the interactive card, the filters, and everything alongside it.