Colin Colenso said:
...If they work on the CB to OB test, it is probably because the spin transfering throw puts the OB back on the straight track, ....
Good point. Technically, if the OB is hit straight on (pivoting at exactly the cue's pivot point) the cueball should not sit spinning in place but because of throw it should move over to the side the english was applied, by about an inch. The object ball should be thrown in the opposite direction. However, having it spin in place only introduces a small error, less than an inch in the apparent pivot point location.
I'm wondering if both of you (you and Mr. Page) aren't right here, since you haven't actually tested the same cues. If any of you wish to try yet another method, here is one way of doing it. It's pretty much like the test you described but tends to eliminate swerve, and doesn't require one to pivot at some awkward location down the shaft. It's also based on the geometric principle Mike has been describing, so it's like a conglomeration of both your methods.
Place the cueball (or better, a striped ball) at the third diamond from a corner pocket and a quarter ball away from the cushion. Shoot the cueball toward the corner pocket using a quarter ball of "outside" english while aiming parallel to the cushion. Note where the ball contacts the cushion and place the tip of the cue there. The pivot point will then be at the point where the cue crosses the third diamond.
As an aid to the parallel aiming, you can use the edge of a ball frozen to the cushion near the corner pocket, or the edge of a cube of chalk placed on top of the end rail.
To place the ball a quarter ball from the cushion, use a striped ball as the cueball and freeze two balls to the cushion ahead of it, and two behind it. Orient the stripe so that it is aligned with the outer edges of the four balls. If the stripe appears to be approximatley perpendicular to the bed of the table, that's good enough. (If it's 10 degrees off for instance, the edge of the stripe
will still be less than a hundreth of an inch off at the equator.)
This assumes that the stripe is a half-ball in width, which isn't necessarily true. To check this, freeze the striped ball to two other balls (forming a triangle) with the stripe perpendicular to the line-of-centers of the other two. If the edges of the stripe run through the contact points, then it is a half-ball wide.
The reason for using the third diamond is that the butt of most cues will clear the far end rail, making a level stroke possible. With a butt diameter of 1.25" and your fingers rubbing on top of the cloth, the centerline of the cue should be very close to a half-ball above the surface. You can then stroke fairly softly without any appreciable swerve affecting the results.
To apply a quarter ball of english, i.e., to make the actual contact point at the edge of the stripe, you can use your judgement or the following table. It lists the additional offset of the centerline of the cue from the edge of the stripe.
Tip Curvature Additional Offset
Dime..............11/64" (quarter of a dime's diameter)
Nickel............13/64" (quarter of a nickel's diameter)
Quarter..........15/64" (quarter of a quarter's diameter)
Here is a Wei table diagram. In the center, the 13-ball's stripe is being checked.
START(
%AE1D0%BB8[6%CB3[7%DB5[9%EZ5O6%FZ4N3%GB8[3%HB6[8%IB8[9%JC0[9
%KU2D3%LB9[8%M[6N9%NB7[7%OB8[7%PB9[7%WW6D8%Xq6D7
)END
This test gave consistent results with aim-n-pivot on my cue, 18" (to answer your original question). The tip of my cue is pretty thin, ~12 mm, so that may account for this length to some extent.
Jim