Geometric adjustments
Interesting. But I think the best method is called experience.
You could show someone exactly how you do it, as far as applying side spin based on a geometric solution, and if the person has the same stroke quality as you, and they use your cue to shoot each shot as instructed, then your method will work for them in the same manner it works for you. But if they have a better stroke than you, no steering flaws, etc... or if they have a worse stroke than you, unable to consistently strike the cb where they intend to strike it, then the method you show them will not be very consistent for them. And since their cue may cause more or less cb deflection than your cue, the method you show will have to be tweaked to work with a cue of different deflection than yours.
Compensating for english is a very subjective process that players learn through experience, through trial and error. Sure there are some basic methods that can be used to roughly adjust for this, like using bhe or fhe. But these aren't one-size-fits-all type methods because of the difference in individual strokes and individual cues. A player must experiment with his/her own playing cue in order to find the right bridge length that works for using bhe. And even that variable changes when the cb and ob are separated by a greater distance. So in the end it boils down to experience, to table time. But it would be interesting to see this geometric method you speak of, and to see how it can be adapted to different players and different cues.
All of this is true, when it relates to divergent english. People already use perceived geometric ratios, like 1/2 ball and 1/4 ball, in their thinking. Meanwhile, when the effect of throw and deflection are all but eliminated, the primary adjustment that needs to be made concerns the new cue angle created by moving the cue into position, to apply the side. The adjustment that needs to be made differs based on whether the side converges from the inside side of the shot or whether the convergence comes from the outside side.
Outside converging side moves the cue line into a fat hit relative to the ghost ball line. Inside converging side moves the cue line into an overcut position relative to ghost ball. As a result, the aim line needs to be adjusted for each. In order to simplify and keep the adjustment simple, a geometric fact was used.
Since the cue line and the ghost ball line cross, the choice of where to cross, allows for a consistent ratio of 1:1 to be used. If the cue line originates from a point beside the center of mass and meets the reference aim line at its midpoint the amount of offset at the impact area is equal to the torque line created at the cue ball center. An elongated X crossing in the middle has equal distances between the ends of the lines. That is a 1:1 ratio. It’s a measurable amount of adjustment
regardless of length of shot.
If a torque line the width of 2 dimes is used and crosses the ghost ball line at its midpoint and the converging side is inside side, the ball will be overcut into the far side of the pocket. To compensate for the overcut, the original aim line is adjusted to the undercut side of the pocket. Conversely if the converging side is outside side, the initial compensating aim is to the overcut side of the pocket.
The next post will focus on the reasons that convergent side might be chosen over center ball or divergent side.