The Science of Bowling: How does ball weight affect rev rate?

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 I=MR^2

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:

KE_rotational=1/2 MR^2ω^2

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:

1/2 M_1 R_1^2 ω_1^2  = 1/2 M_2 R_2^2  ω_2^2
1/2*16*2.48^2 ω_1^2  = 1/2*15*2.46^2  ω_2^2
49.2032 ω_1^2  = 45.387 ω_2^2
1.084 ω_1^2  = ω_2^2
1.041 ω_1   = ω_2

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.

1.084*250^2  = ω_2^2
260.3 = ω_2

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

BowlSK

I’m proud to announce the start of my new bowling score/stat website, BowlSK. It’s still very much a work in progress, but please head over and check it out, sign up if you’d like, and make use of the feedback form!

‘nother update

Added even more video and pics to the Axis Rotation article.

Update

The Axis Rotation post has been updated with some video!

3 Basic Adjustments, Part 2: Axis Rotation

Welcome to part 2 of the “3 Basic Adjustments” series. Today, we are going to look at adjusting axis rotation. What is axis rotation? Axis rotation is the difference between the direction the ball is spinning and the direction that it is traveling down the lane, and is determined by how far around the side of the ball your fingers get during the release. During the skid phase, axis rotation remains relatively constant. As the ball enters the hook phase of its roll, the direction the ball is traveling starts to change as the ball grabs the lane – it moves left for a right-hander. At the same time, the friction causes the rotation of the ball to start moving to the right. Picture turning the steering wheel of your car, and then relaxing your hands. The car turns in the direction of your wheel, but your wheel also straightens out. Once the ball is traveling in the same direction it is rotating, it is in the roll phase, and its axis rotation is 0 degrees.

While the most versatile pros can change their axis rotation to virtually any angle between 0 and 90 degrees, we are going to work on learning 4 different release keys that will give us a pretty broad range of axis rotations to work with. What we are going to do to change our axis rotation is concentrate on driving towards the target with a certain finger. To give this the best chance to work, follow-through has to be long and low. You will need to reach out to the target, letting the ball roll off your hand. In addition to driving with a specific finger at the release point, I will provide different finger positions that can be used in the setup, which will help tweak some of these releases further.
Read the rest of this entry »

3 Basic Adjustments, Part 1: Speed

In a previous post, I mentioned that, according to Chris Barnes, there are 3 basic adjustments that every bowler should have – speed, axis rotation, and hand pressure. Today we’re going to look at ball speed as an adjustment.

As a pre-requisite for this adjustment (and also for getting to the next level in your game), your arm swing must be free. When gravity is controlling your swing, adjusting speed is a piece of cake. When you are controlling your swing, you will be hard pressed to keep a consistent ball speed to begin with, much less be able to alter your ball speed with any repeatability.

Ok, with that said, how do we change our speed? Throw harder! Just kidding. The answer lies in the setup.
Read the rest of this entry »

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