According to a thread at Bowling Community,
"You would have 0 flare at a Pin to PAP distance of 0 and 6 3/4. Flare will increase from 0 to 3 3/8 and then decrease from 3 3/8 to 6 3/4"
The whole thread is here:http://www.bowlingcommunity.com/b/ubbth ... o_PAP.html
Essentially, think of the core in 3 dimensions; if the pin was on your PAP (0" distance), the core would be rolling on its side when you threw the ball like a barrel or a bat rolling along the floor. If the pin was 6 3/4" from your PAP, the core would be tumbling exactly end over end.
Everything else is just between laying down and standing up. Maximum instability occurs at the midpoint, 3 3/8" a 45* degree angle from either position.
Producing length from a layout in a symmetrical cored ball is a function of pin to PAP layout and surface. As you add distance past the 3 3/8" up to 6", you are essentially decreasing the amount of track flare (stabilizing the core somewhat, or rather putting less violent imbalance in the core position relative to the track). When the core is stable longer, it will skid more in the oil, saving more of the rotational energy applied by the bowler for the backend, producing a more abrupt change in direction.
For Asymmetrical balls, length is controlled primarily by surface prep and the drill angle. As Justin has helped me understand (I believe from Mo Pinel's teachings), the amount of flare in an asym ball is relatively the same from 3" to 6", but when the ball makes it's second transition, the amount of forward roll increases as the pin to pap length is increased.
Maybe Justin can chime in, too, if I've made this as clear as mud.
Someday I would like to write in the same clarity I see things in my head.
Hope this helps!