This article is the first in a series of articles that will investigate the physics of bowling and bowling ball motion. While there are many bowlers that rely on feel and instinct, there are those that are intrigued by the science behind bowling, and this series intends to help those people learn the whys and hows of this sport.
The first topic we will cover is the effect of ball weight on rev rate. Recently, many (if not most) bowlers have switched to 15 pound equipment. Many of the touted benefits are decreased fatigue, increased revolutions, and for some, increased deflection. It is hard to argue about the fatigue factor – even using a free arm swing, there are points in a swing where the weight of the ball is supported by the body, and a lower weight ball will lessen the strain. But, just how much can the change in ball weight affect the bowler’s rev rate?
The Setup
- The bowler will put the same amount of energy into his release with each ball. With a heavier ball, it is possible that the bowler would eventually fatigue, causing him to put less energy into the release, but we aren’t going to take that into consideration this time around. We will assume that the bowler has trained sufficiently for the amount of bowling they will perform, so fatigue will not be a factor.
- We will examine 3 ball scenarios – a low RG core and a high RG core, whose RGs change as weight changes, and a medium RG core whose RG is constant. MoRich changes the density of the core in their different weight balls, so that the core dynamics are the same for all weights.
- We will look at the effect of dropping from 16 lbs to 15, 15 lbs to 14, and 16 lbs to 14.
- When calculating rpm differences, we’ll use a bowler with a rev rate of 250 rpm with a 16 lb ball, no matter which ball that is. A bowler that put 250 rpms on one ball would not necessarily put 250 rpms on another ball of the same weight, but with a different RG.
The Science
The technical specs for the balls we will be analyzing are as follows:
| Ball | 16 pound RG | 15 pound RG | 14 pound RG |
|---|---|---|---|
| Ebonite’s NVD | 2.48 | 2.46 | 2.46 |
| Storm’s Rapid Fire | 2.53 | 2.57 | 2.62 |
| MoRich’s Solid LevRG | 2.53 | 2.53 | 2.53 |
Now, we need our formulas. There are 2 formulas that we will need to look at. The first relates the rotational energy of an object to its angular momentum (rev rate) and Moment of Inertia (MoI). The second equation gives us the MoI for the ball. The MoI is where the ball’s weight and RG come into play. What is RG in scientific terms? The value is an expression of an object’s resistance to change in angular velocity. A bowling ball’s RG represents the radius (in inches) of a hollow cylinder that would have the same MoI as the ball. So, a higher RG equates to a larger cylinder. The formulas are:
and 
Where:
- KE = The kinetic energy of the ball
- I = The moment of inertia of the ball
- M = The mass of the ball
- R = The RG of the ball
- ω = The angular momentum of the ball
Next, we combine the 2 equations:
Since we are assuming that the bowler will apply the same amount of energy into rotating the ball, we know that the KE side of the equation will be the same for both balls. So, we have the following equation, where the variables with a subscript of 1 are the values of the first ball, and the variables with a subscript 2 are the values of the second ball. Let’s start with the first case, the 16lb NVD vs. the 15lb NVD. We will fill in the mass and RG, leaving the angular velocity to be calculated:
This means that the 15 lb ball will see about a 4.1% increase in revs, over the 16 lb ball. Substituting 250rpm at 16 lbs, we see that the 15 lb ball will have around 260 rpms.
Calculating the rest of the values in the same manner, we see:
| Ball | 16 to 15 | 15 to 14 | 16 to 14 |
|---|---|---|---|
| Ebonite’s NVD | 4.1% gain | 3.5% gain | 7.7% gain |
| Storm’s Rapid Fire | 1.7% gain | 1.5% gain | 3.2% gain |
| MoRich’s Solid LevRG | 3.3% gain | 3.5% gain | 6.9% gain |
| Ball | 16 lb rev rate | 15 lb rev rate | 14 lb rev rate |
|---|---|---|---|
| Ebonite’s NVD | 250 | 260.3 | 269.3 |
| Storm’s Rapid Fire | 250 | 254.3 | 258 |
| MoRich’s Solid LevRG | 250 | 258.3 | 267.3 |
Conclusion
What can we take away from this? One thing that stands out is that the difference is not very significant – dropping from 16 to 15 gave, at most, a 4% gain, which is not a great deal. Another thing that stands out is that if the RG of the ball goes up as the weight goes down, the gain is much smaller. When the RG dropped, the gain in rev rate was magnified. Analyzing the equations, we can see that when the RG remains constant, the percentage difference in rev rate will be the percentage difference in the square root of the weight of the ball. If the core changes in dynamics, that difference can be exaggerated or reduced. My conclusion? A higher rev rate is not a great reason to drop in weight.
References
The following were used as sources/inspiration:
http://hyperphysics.phy-astr.gsu.edu/Hbase/rke.html
http://www.bowlingcommunity.com/b/ubbthreads.php/topics/72012/Re_Best_ball_for_pin_axis_dril.html#Post72012
CMG's Bowling Blog 