For any shot, this finds where to strike the cue ball so its sidespin cancels throw at contact, then lines the cue up back-hand-english style so squirt cancels too.
Drag the balls or click a pocket.
shot lineghost ballcuebridgepaths that pocket
Physics assumptions
Where the tip strikes
The cue ball from behind. Filled circle: the tip. Hollow ring: the line-of-centers point. Tick: the 40% rule. Dashed circle: the miscue limit.
How it works
Gearing.Throw comes from the cue ball's surface sliding sideways across the object ball during contact. That sliding speed is v·sin φ, where v is the cue ball's speed at contact. Outside sidespin with R·ω = v·sin φ stops the sliding, so the balls roll on each other like gears and there is no throw. Once the sideways sliding is gone, topspin or draw can't add any; without gearing, they reduce throw.
From spin to tip offset. A level hit at offset b gives R·ω = 2.5·v0·b/R. If the ball arrived with its starting speed and spin, this gives b = 0.4·R·sin φ, which is Dr. Dave's 40% rule.
What changes on the way. Hit at center height, the ball slides and then rolls, and settles at 5/7 of its starting speed, so it needs less sidespin. Rolling resistance slows it further. Cloth friction also slowly removes sidespin, so it needs more to start with. The page combines these for the speed and distance you set. The sidespin decay rate is an estimate; adjust it under Physics assumptions.
Squirt and the bridge. Squirt is modelled with the pivot-length rule: squirt angle = atan(offset ÷ pivot length). The cue lies on the aim line at the bridge, so it points atan(offset ÷ bridge distance) toward the english side. Set the bridge distance equal to the pivot length and they cancel. Set them differently to see the error.