### The Blueprint Blog - The Latest in Blueprint News, Tutorials, and Technical Info

#### Axis Rotation and Axis Tilt Explained

Date Posted: December 16, 2011

Category: Bowling Technical Information

In this article, we will provide some information on axis rotation angle and axis tilt angle, the two parameters that describe the direction of the bowling ball’s rotation as it travels down the lane. Based on discussions with many bowlers and as evidenced by many bowling internet forum posts, we feel that these are often misunderstood (and sometimes incorrectly interchanged) parameters and we hope to clear up some of this confusion so bowlers can better understand their games and make better decisions, both on the lanes and in the pro shop.

##### Basic Definitions

Bowling balls are spheres (at least externally) and they rotate. A rotating sphere (and, in fact, any rotating object) can rotate about any axis passing through its center of gravity. This is where the parameters of axis rotation angle and axis tilt angle come in. They together uniquely describe which axis the ball is rotating about relative to both the lane and the ball’s direction of travel. We’ll explain why this is important in a future article. For now, let’s look at some images that will help us understand these two parameters a bit more clearly. (Note: All images shown in this article are for right-handed bowlers.)

Shown to the right is a top view of a bowling ball on a lane, just after the release (please note that this image is not to scale). In this image, the blue line denotes the ball's path and its direction of travel. The large blue arrow represents the ball's rotation. The black horizontal line is perpendicular to the ball's direction of travel. The dotted line represents the ball's axis of rotation (the axis about which the ball is rotating). The axis rotation angle is the angle between the horizontal line and the dotted axis of rotation line. So, in this example, the ball's axis rotation angle is somewhere in the vicinity of 30-40 degrees.

Axis rotation angle, quite simply, is a measure of the amount of "side roll" the ball has. A ball with no side roll has 0 degrees of axis rotation. A ball with maximum side roll has 90 degrees of axis rotation.

Now, let's consider axis tilt angle. To explain tilt, we'll use an image from a different angle: directly behind the ball, looking down the lane, and aligned with its direction of travel. This is shown below. In this view, the blue arrow again represents the ball's direction of rotation. The black horizontal line is parallel to the lane surface. The dotted line again represents the ball's axis of rotation. The axis tilt angle is the angle between the horizontal line and the dotted axis of rotation line. In this example, the axis tilt angle is approximately 20-30 degrees.

Axis tilt angle, then, is a measure of the degree to which a ball is spinning. A ball spinning like a top (and hence, rotating about a purely vertical axis of rotation) has 90 degrees of axis tilt. A ball with no spin whatsoever (having a purely horizontal axis of rotation) has 0 degrees of axis tilt.

##### How to Calculate Axis Rotation and Axis Tilt Graphically

With a properly-positioned video camera, it is possible to determine a ball's axis rotation and axis tilt angles from a single video shot. The first step of this process is to mark the ball's positive axis point (PAP). The PAP is the point on the ball intersecting its axis of rotation at release. When the PAP is marked properly on the ball (often with a small, white, round piece of tape), the mark will be completely stable as the ball is released (that is, the ball will be rotating about the mark). You can determine the approximate location of the PAP by tracing the ball's initial oil ring. We won't explain that process here, as there are already good online resources available describing this (for example, click here).

As a side note, you may have noticed that we used the term "approximate" above. Without getting too off-topic, it is important to remember that a high flaring bowling ball starts flaring immediately when it is released. Therefore, the first oil ring is not technically representative of the true PAP, as it instead gives you the average rotation axis for the first revolution in which the ball is in contact with the oiled lane. In most cases, this is close enough for practical purposes, but for better accuracy, you would need to manually adjust the originally-marked PAP location using slow-motion video until the marked position is perfectly stable just as the fingers are leaving the ball.

Getting back on topic, the next step of this process is to properly position the video camera so that errors are not introduced. To minimize perspective and alignment errors, the camera should be positioned behind the bowler, aligned with the ball's direction of travel, near lane level. (Note: A good bowling coach can be invaluable in helping a bowler capture correct video footage, so we highly recommend that you seek one out if you desire assistance with this process.)

Now, by capturing a video of the ball as it is thrown and extracting a frame from the video just as the fingers are leaving the ball, we can compute axis rotation and axis tilt angle graphically. This is done by utilizing an overlay graphic, as shown below: First, let's explain the overlay (containing all the black lines). The black lines represent a parameterization of the ball's surface using a spherical coordinate system. In a spherical coordinate system, any point on the surface of the sphere can be represented by two angles. In this bowling-specific representation, the two angles are axis rotation angle and axis tilt angle. Much like longitude and latitude describe a point on the earth's surface, axis rotation angle and axis tilt angle describe a point on the bowling ball's surface and that point represents its axis of rotation, measured with reference to its direction of travel.

In the above example, the PAP (marked with the white circle) tells us that the ball has about 45 degrees of axis rotation and about 20 degrees of axis tilt. One thing worth mentioning is that this overlay method utilizes a 2D projection of a 3D object. For this reason, the spacing between the lines is not equal. For example, the linear distance in the overlay between 10 degrees and 20 degrees is drastically different than the linear distance between 80 degrees and 90 degrees.  We mention this only as a caution and to remind you that half-way between 0 and 90 on the overlay is not 45.

Below is a slightly larger, less crowded version of the above overlay image, for reference: ##### Closing Thoughts

While the above-described graphical analysis process is extremely useful and we'd love to take the credit for devising it, we unfortunately cannot. Several versions of the rotation/tilt overlay graphic pre-date this article, including, for example, this one and this one. One reason we mention these alternate overlay images is that we are confident that astute readers will notice that the lines in our overlay graphic do not align perfectly with the lines in either of the previously referenced images (which, by the way, do not align perfectly with each other). Since we do not know the assumptions built into the other overlay images, we are not here to declare that ours is correct and the others are incorrect. We can instead only comment on ours, which is based on a mathematically-proper spherical coordinate system and which was generated using a 3D CAD modeling software tool. Additionally, our representation is consistent with the axis rotation and axis tilt definitions and conventions used in Powerhouse Blueprint, so we highly recommend that you use our overlay when calculating axis rotations and axis tilts for use in Blueprint.

Before closing this article, we'd like to take this as an opportunity to address a very relevant topic that is a potential source of confusion for Blueprint users. A popular statement in the bowling world today is that axis tilt angle cannot exceed axis rotation angle. Blueprint users, however, can clearly see that axis tilt angles can be input that do in fact exceed axis rotation angle. So, why the discrepancy? Again, since we don't know what assumptions and conventions are built into the "axis tilt angle cannot exceed axis rotation angle" statement, we're not interested in criticizing and refuting it definitively. Instead, we can only say that, based on the definitions of axis rotation angle and axis tilt angle used in this article, axis tilt angle can exceed axis rotation angle. To demonstrate this visually, we'll return to the top view of the bowling ball, this time with the rotation/tilt overlay, as shown to the right. The PAP mark on this ball represents an axis rotation angle of 10 degrees and an axis tilt angle of 50 degrees. Is this combination of rotation and tilt common? No, not really. Are these the rotation/tilt angles of an elite bowler? Probably not. But, is it possible for a bowling ball to rotate about this axis? Of course it is. A bowling ball can rotate about any axis. And, when representing axis rotation angle and axis tilt angle using the mathematically-proper spherical coordinate system used by Blueprint and presented here, the axis the ball rotates about can represent an axis rotation/tilt combination in which axis tilt angle exceeds axis rotation angle.

We hope that you've found this article to be both educational and beneficial to your bowling knowledge. Knowing the "what" and "how" of axis rotation angle and axis tilt angle are important prerequisites to knowing the "why" (as in, why should you care?). We'll explore the "why" in depth in a future article, but for now, we encourage everyone to make sure they have a good understanding of their own axis rotation and axis tilt by working with their coaches and pro shop operators in obtaining accurate measurements.