cushioncrawler

05-02-2011, 07:13 PM

In The Science Of Pocket Billiards by Jack Koehler 1989. Koehler's Table 4-1 (page 48) shows the angular permissible errors for straight-in corner pkt shots. For 24" to cnr-pkt and 48" to Oball the permissible error for a straight-in shot iz 0.48dg -- ie 0.24dg left of center, and 0.24dg right.

Koehler's table suggests that a pot iz most diffikult if the Oball iz halfway to the pkt.

Koehler's table allso suggests that a 24" pot from 48" haz nearnuff the same permissible error az a 48" pot from 24", ie that the permissible error for an Oball X" from the Qball iz the same as the permissible error for an Oball X" from the pkt.

I think that Koehler's figures are based on komputations based on simple geometry, and dont inklood friktion effekts, ie throw, however this duznt affekt the following matters.

I drew my own drawings (on komputer) showing the geometry of permissible error and theze agreed with Koehler's rezults.

Geometry shows that the equation for komparativ permissible error iz......

KPE = 4(x-x^2).

Where x = dist of Qball to Oball kompared to Qball to pkt, eg 1/8 if 10"/80".

If Oball iz halfway tween the Qball and the pkt then x=4/8ths, and the KPE = 16/16ths (ie 1.00), ie halfway iz the most diffikult pozzy for the Oball (ie 1.00 iz the max).

My figures are....

0/8th = 0/16ths. If the Oball iz touching the Qball u karnt miss (say).

1/8th = 7/16ths.

2/8th = 12/16ths.

3/8th = 15/16ths.

4/8th = 16/16ths. Halfway tween Qball & pkt iz most diffikult, the KPE iz 16/16, ie 1.00.

5/8th = 15/16ths.

6/8th = 12/16ths.

7/8th = 7/16ths.

8/8th = 0/16ths. If the Oball iz on the edge of pkt u karnt miss (say).

If the Oball iz halfway tween Qball and pkt (and straight-in), and u moov the Oball halfway closer to the Qball (ie now 2/8ths instead of halfway), u enlargen the PE, the KPE goze from 16/16 to 12/16. In other words, u hav made the PE larger by 16 kompared to 12, or 4/3.

If u moov that Oball halfway closer again (ie now 1/8th instead of halfway), the KPE goze to 7, ie u hav now made the PE larger by 16 kompared to 7, or 16/7.

The size of the difference might be a surprize for some.

mac.

Koehler's table suggests that a pot iz most diffikult if the Oball iz halfway to the pkt.

Koehler's table allso suggests that a 24" pot from 48" haz nearnuff the same permissible error az a 48" pot from 24", ie that the permissible error for an Oball X" from the Qball iz the same as the permissible error for an Oball X" from the pkt.

I think that Koehler's figures are based on komputations based on simple geometry, and dont inklood friktion effekts, ie throw, however this duznt affekt the following matters.

I drew my own drawings (on komputer) showing the geometry of permissible error and theze agreed with Koehler's rezults.

Geometry shows that the equation for komparativ permissible error iz......

KPE = 4(x-x^2).

Where x = dist of Qball to Oball kompared to Qball to pkt, eg 1/8 if 10"/80".

If Oball iz halfway tween the Qball and the pkt then x=4/8ths, and the KPE = 16/16ths (ie 1.00), ie halfway iz the most diffikult pozzy for the Oball (ie 1.00 iz the max).

My figures are....

0/8th = 0/16ths. If the Oball iz touching the Qball u karnt miss (say).

1/8th = 7/16ths.

2/8th = 12/16ths.

3/8th = 15/16ths.

4/8th = 16/16ths. Halfway tween Qball & pkt iz most diffikult, the KPE iz 16/16, ie 1.00.

5/8th = 15/16ths.

6/8th = 12/16ths.

7/8th = 7/16ths.

8/8th = 0/16ths. If the Oball iz on the edge of pkt u karnt miss (say).

If the Oball iz halfway tween Qball and pkt (and straight-in), and u moov the Oball halfway closer to the Qball (ie now 2/8ths instead of halfway), u enlargen the PE, the KPE goze from 16/16 to 12/16. In other words, u hav made the PE larger by 16 kompared to 12, or 4/3.

If u moov that Oball halfway closer again (ie now 1/8th instead of halfway), the KPE goze to 7, ie u hav now made the PE larger by 16 kompared to 7, or 16/7.

The size of the difference might be a surprize for some.

mac.