Assuming that 6 degrees is the optimum angle for throwing strikes, below is a table that traces the ball path at the breakpoint for the ideal strike line.

Board....Length (feet)
1........46.78
2........47.63
3........48.47
4........49.31
5........50.16
6........51.00
7........51.84
8........52.69
9........53.53
10.......54.37
11.......55.22
12.......56.06
13.......56.91
14.......57.75
15.......58.59
16.......59.44
17.......60.28

Below are my assumptions:
1. Lane width is 41.5 inches.
2. There are 39 boards.
3. The pocket is located at x = 17.75 inches, y = 60.433 feet.

If anybody else has calculated this and come up with different results, I would appreciate an explanation of how you came up with the values.

That is assuming the ball will hit the breakpoint, turn to a 6* angle with respect to the lane, and roll out. Such is not the case - the ball's angle w/respect to the lane will gradually increase as it hooks toward the pocket. Also, the values Slowinski used were based on 5% entry angle, because you had a good chance to strike if you ended up with 4-6%.

I probably should not have used the word "breakpoint", as the ball could break at various distances and angles, and ultimately merge with this "optimum entry angle" for lack of a better word.

At this point, I am primarily concerned with validating that my math is correct.

Haha Dennis. Joe and I bowl together, its a running joke we have about another bowlers excuses for not striking or bowling good.

You really do need to see lanes up close. The pits and tracks, the lifted areas, the tilts. The shallow gutters, the weak side boards, the pin deck tilt. Your mathematics are in a perfect world, but bowling lanes are not .

Erin

I thought that is what the pattern length -31 trick was for or the pattern length - 35+4.. and based on that your numbers are off a bit. 32 feet of oil would have the ball at the 1 board when it makes a straight line to the pocket from there...

but maybe you are accurate and they are off cause if you have a 50 ft pattern slowinski's formula gives you an pattern exit point of 19 board which can't be accurate..

I'm leaning towards you having the correct numbers...interesting..
can anybody else back up his numbers.. I could but feel kind of lazy to do all the math on it right now..

My bad for using the word "breakpoint". It seems to have caused some confusion.

The pattern length minus 31 is to help find the optimum exit point for an oil pattern. The numbers I posted represent where the ball would have to be before it hits the pins to obtain a 6 degree entry angle. These are not contradictory. On different oil patterns the ball path should merge with the 6-degree entry angle at different points. For example, Cheetah (36-feet) might merge on the 5 board at 50.16 feet, while the Shark (44-feet) might merge on the 13 board at 56.91 feet.

Erin, you are a great recruiter. If I am ever in California, I will look you up to help with the USBC certification process. For now, the numbers are based on standard lane dimensions, and should apply in most situations.

I'm still hoping somebody can verify my math is correct. It has been a long time since I have had to do any trigonometry. The next step is to calculate the precise boards where to stand on the approach, and aim at the foul line and arrows to merge with the optimum strike entry angle at the 2.5 board, 7.5 board, and 12.5 board. This is something I have never seen spelled out anywhere, and should be useful for adjusting to a variety of conditions.

But that's just it Joe, every bowling lane in existance has wear and tear. Some much more then others. Old wood lanes are not going to perform like new synthetics, especially where it comes to taking a specific pattern like Cheetah etc..... That's why USBC put in allowances in their Sport rules for such lanes.

I agree that bowlers will always need to adjust to lane conditions. My goal is to map out a system of adjustments that gets the ball to what is recognized as the optimum strike entry angle on different conditions. A lot of people throw the ball well. They just don't know how to line up. Hopefully, this will help.

I don't think there is any way you will ever find the pocket if your ball is on the 5 board at 50 feet on the Cheetah.

The problem is that the ball will continue to hook, adding entry angle, up until it reaches the pocket (on an ideal shot). This means that it might look more like

35 feet: -2* entry angle
40 feet: -1* entry angle
45 feet: 0* entry angle
50 feet: 2* entry angle
55 feet: 4* entry angle
60 feet: 6* entry angle

So, you cannot try to fit the ball path to a straight line coming from the pocket at 6*. It will be a curve, and the shape of that curve will be different depending on things like oil pattern, axis rotation, coverstock, lane surface, etc.