In the last issue, I discussed the importance of entry angle and how USBC testing has shown that six degrees is the optimum angle of entry into the strike pocket.

We looked at two charts, one showing six degrees versus four and two degrees and the other showing that higher average bowlers typically have greater entry angles. The charts also showed that the increase in just one degree of entry angle, while seemingly immaterial, has a significant impact on scoring and your overall average.

All this talk stemmed from a math equation that I was thinking about as I lay in bed in the middle of the night. The equation was based on a conversation I had with USBC Coaching Certification manager Cary Pon. Illustrations from the USBC Coaching Silver level certification manual shown here relate to playing short and long oil patterns. Many people don't realize that typically it is best to play a short pattern further right (for a righthander) and a long pattern further left, toward the pocket. The reason this can be difficult to understand is that on a short pattern, bowlers see the ball hook and believe they must move deeper.

The X's represent where your breakpoint should be to best play the patterns. If you connect these two Xs - as in the third diagram in Figure 1 - you should have a line that goes to the pocket. As USBC Specification and Certification research has noted, the optimum entry angle for a strike ball is six degrees and the perfect strike occurs when the center of the ball is at the 17.5 board when it hits the pocket side of the headpin (at that same six-degree angle).

My 3 a.m. thought was that an equation exists based on this line drawn at six degrees from the 17.5 board back toward the bowler (see Figure 2).

The line that connects the two X's is the basis for the equation. A triangle can be formed (as shown) to help us derive the equation.

Theoretically, this is the line you want your ball to roll on from its breakpoint all the way into the pocket. We must realize, however, that the ball won't roll straight into th epocket from the breakpoint. We will look a the real world aspects of this line (arc) and the ball's actual entry angle into the pocket in an uplcoming article. For now, let's focus on this line and its associated "bowling equation." So, from the above line, we can now draw a triangle and then derive the following equation:

tan(angle) = (opposite / adjacent) => tan(entry / angle) = (board / distance)

This equation needs work. It must be changed into user-friendly, common sense bowling terms. Let's look at it one section / term at a time.

"Tangent" (Tan) of the entry angle needs no adjustment. You might want to look up the background of this equation in a geometry book. Additionally, you will ned a scientific calculator to perform the calculation. One can be found online, for example, at http://www.creativearts.com/scientificcalculator/. "Board" is a board on the lane. But as the triangle is drawn, it would be the board (in inches) to the right of the 17.5 board (where the perfect strike occurs), not the actual board on the lane as we typically refer to it. This should be adjusted. "Distance" also is accurate, but it is the distance (in feet) from the headpin back to the breakpoint, not the breakpoint distance as we all know it. This also should be adjusted.

In an effort to adjust the above enginnering-type equation into bowling-type terminology to make sure we obtain information from the equation that makes sense, we need to change it to the following:

tan(entry angle) = ((17.5 - board) / ((80 - pattern length) * 12))

or

Entry Angle = Tan^{-1} * ((17.5 - board) / ((80 - pattern length) * 12))

Okay, now let's look at this equation more closely. "Entry Angle" is the ball's angle into the pocket as we have discussed before. "Board" is now the board on the lane as we normally refer to it (where the ball comes off the end of the oil pattern as it enters its roll phase). "Pattern Length" is the distance the lane is oiled. Tangent and inverse tangent (Tan^{-1}) are geometric terms and require a scientific calculator to compute. "Pattern Length" values and "Board" values are a good place to start for creating this triangle, but ultimately we will need to look at actual break point values.

For now, assumptions will need to be made. In an upcoming article, we will look at typical skid length past the end of the pattern to the breakpoint. We also will discuss how skid length is dependent on speed, revolutions and coverstocks and how this equation is most accurate on USBC Sport Bowling-type patterns.

Now that we have an equation, let's use our scientific calculator to plug in some numbers and see what we get:

17.5

Pattern Distance / Entry Angle | 6" | 5" | 4" |
---|---|---|---|

60 Feet | 17.5 | 17.5 | |

59 | 16.2 | 16.5 | 16.7 |

58 | 15.0 | 15.4 | 15.8 |

57 | 13.7 | 14.4 | 15.0 |

56 | 12.5 | 13.3 | 14.1 |

55 | 11.2 | 12.3 | 13.3 |

54 | 9.9 | 11.2 | 12.5 |

53 | 8.7 | 10.2 | 11.6 |

52 | 7.4 | 9.1 | 10.8 |

51 | 6.1 | 8.1 | 9.9 |

50 | 4.9 | 7.0 | 9.1 |

49 | 3.6 | 6.0 | 8.3 |

48 | 2.4 | 4.9 | 7.4 |

47 | 1.1 | 3.9 | 6.6 |

46 | -0.2 | 2.8 | 5.8 |

45 | -1.4 | 1.8 | 4.9 |

44 | -2.7 | 0.7 | 4.1 |

43 | -3.9 | -0.3 | 3.2 |

42 | -5.2 | -1.4 | 2.4 |

41 | -6.5 | -2.4 | 1.6 |

40 | -7.7 | -3.5 | 0.7 |

39 | -9.0 | -4.5 | -0.1 |

38 | -10.2 | -5.6 | -1.0 |

37 | -11.5 | -6.6 | -1.8 |

36 | -12.8 | -7.7 | -2.6 |

35 | -14.0 | -8.7 | -3.5 |

This chart shows board positions of each "Line" (refer to Figure 3) at a given pattern distance and entry angle.

First, we must realize that the negative numbers mean the line is off the lane and into the channel (See Figure 4).

This is a graphical representation of the chart in Figure 3. Now that we can see where the lines are, the next objective is to figure out how to get our ball on that line and into the pocket. Another advantage of the chart is that it can help us determine what our entry angle is based on and where our breakpoint is (based on a known oil pattern length).

The third and final article of this series will tie this information together to help you become a better bowler. We will do that by using these lines as a starting point and determine the arcing path a ball takes as it rolls into the pocket. Using Computerized Aided Tracking System (CATS) data, we will look at the "offset" different types of bowlers have while trying to get to six (or four) degrees of entry angle.

Finally, we should be able to develop a chart that will show you where you want the ball to be at its breakpoint based on the length of the pattern. How you get there and what angle you can achieve will be up to you.