Equations · equation
Ghost-Ball Aim
Billiards · 1835
- Equation
- aim the cue ball's centre at the point 2R from the object ball's centre, on the line to the pocket; ball-hit fraction f = 1 − sin θ
- Field
- Billiards
- Year
- 1835
Symbols
R ball radius · θ cut angle · f the fraction of the object ball's width the cue ball covers at contact: 1 for a full hit, ½ for a half-ball, ¼ for a quarter-ball
Significance
Picture the cue ball frozen where it must be at contact — touching the object ball on the far side from the pocket. Its centre is one ball's diameter from the object ball's centre along the pocket line; send the real cue ball there. The fraction the two overlap when seen from the cue is 1 − sin θ, which is why a half-ball hit is a 30° cut and a quarter-ball is 48.6°. Pure geometry; throw adds a correction on top.
Referenced by
equation
skill
Open on the Equations shelf — the interactive card, the filters, and everything alongside it.