Axis Rotation and Tilt

Almost every day, I feel like I see or hear something that is completely incorrect about axis rotation or axis tilt. Sometimes, people just mix up the two terms and say “tilt” when they should have said “rotation.” Other times, I see people completely misunderstand the effect that axis rotation and axis tilt have on the bowling ball. And, other times yet, I see people very inaccurately describe why axis rotation and axis tilt affect the ball the way they do.

To be fair, I should say that this can be a difficult topic. I remember spending many, many years being confused myself about the mysteries of ball roll, and I never could find answers that satisfied me. As I look back, it’s easy to see why: vague definitions, misinformation, and completely invalid explanations—even though always very well-intentioned—are unfortunately the norm when it comes to this topic.

The goal of this article is to clear up whatever confusions you might have related to axis rotation and axis tilt. We’ll start by defining what axis rotation and axis tilt are, in hopes that you will never mix them up again. We’ll then cover how you can measure your own axis rotation and axis tilt angles. This can be an important first step in knowing whether or not you have a problem that deserves some attention. And, finally, we’ll go in-depth on how and why axis rotation and axis tilt affect the bowling ball as it travels down the lane, hopefully clearing up some serious misconceptions along the way.

What are axis rotation angle and axis tilt angle?

When a bowling ball is released, a certain type of “rotation” is created: as the ball leaves the bowler’s hand, it rotates about a specific axis, and it rotates about that axis at a specific speed. The speed of the ball’s rotation is its rev rate. The axis the ball is rotating about is set by the bowler’s axis rotation angle and axis tilt angle.

Axis rotation angle

In very simple terms, axis rotation angle can be thought of as a measure of how much “side roll” a bowling ball has. Slightly more technically, axis rotation angle is a measure of how the ball’s axis of rotation is oriented relative to its direction of travel, when viewed from the top looking down:

In the above image, the ball’s axis of rotation is represented by a red arrow, and its direction of travel is represented by a black arrow. Note that the angle between the two arrows is 90 degrees. This corresponds to 0 degrees of axis rotation. This is what you would get, for example, if you pushed a ball down a ramp onto the lane, or if you came straight up the back of the ball with your fingers during the release.

In the real world, bowlers typically throw their strike shots with at least some amount of “side roll” applied to the ball. When “side roll” is applied, the ball’s axis of rotation forms an angle with the ball’s direction of travel that is greater than 90 degrees:

In the example shown above, the angle between the ball’s direction of travel and axis of rotation is 135 degrees. This corresponds to an axis rotation angle of 45 degrees.

In practice, axis rotation angle varies from bowler to bowler, and from delivery to delivery. A bowler who throws a straight ball at his spares might employ an axis rotation angle of close to 0 degrees, while a bowler who really gets around the side of the ball—think Pete Weber—might have an axis rotation angle of close to 90 degrees.

Axis tilt angle

The simplest way to grasp axis tilt angle is to think of it as a measure of how much “spin” the bowling ball has. A slightly more technical definition is that axis tilt is a measure of the vertical inclination of the ball’s axis of rotation relative to the plane of the lane. This is most easily visualized from a vantage point directly behind the ball:

In the above example, the ball’s axis of rotation is purely horizontal, parallel to the lane surface. This corresponds to an axis tilt of 0 degrees. A ball rolled down a ramp onto the lane, for example, would have 0 degrees of axis tilt.

At the complete other end of the spectrum, consider a ball that is placed onto the approach and spun like a top by the bowler’s hands. You sometimes see this sort of thing when the pros do trick shots, for example. In this case, the axis of rotation of the ball is pointed straight up in the vertical direction, toward the ceiling. A ball with a purely vertical axis of rotation has 90 degrees of axis tilt:

Most bowlers have non-zero axis tilt. The actual amount of tilt a bowler has is largely a function of the finger and wrist positions throughout the release. Most bowlers tend to have somewhere between 0 degrees and 30 degrees of tilt. And, in recent years, it has become somewhat common to see bowlers—usually two-handed bowlers—who have a small amount of axis tilt in the negative direction (meaning that their ball’s axis of rotation is oriented below parallel with the lane surface).

Putting the two angles together

So far, our examples have only looked at rotation and tilt in isolation. But, of course, in the real world, bowling balls generally have some amount of both axis rotation angle and axis tilt angle simultaneously. It can be a bit more difficult to think about rotation and tilt at the same time, but it’s really just a matter of remembering the basics from above.

When we view a bowling ball from behind, its axis rotation angle is basically a function of how much its rotation axis “points” back toward us. In the above image, for example, the ball on the left has 80 degrees of axis rotation; note how its rotation axis is pointed back toward us. The middle ball has much less axis rotation—45 degrees—and you can see that its rotation axis is pointed less toward us than the 90 degree example, and more toward the left side of the ball. And, the ball on the right, whose rotation axis is pointed even more toward the left side of the ball, has just 30 degrees of axis rotation.

What about tilt in these examples? Recall from above that axis tilt is just the vertical angle that the rotation axis makes with the plane of the lane: the more the ball’s rotation axis points up toward the ceiling, the more tilt the ball has. Referring back to the above image, the ball on the left has 5 degrees of tilt, the ball in the middle has 20 degrees of tilt, and the ball on the right has 40 degrees of tilt.

Now that we’ve given basic, high-level definitions for what axis rotation and axis tilt are, let’s talk about how they can be measured. As I mentioned in the introduction, it’s important to know your numbers, and the first step in knowing your numbers is to learn how to measure them.

How to measure axis rotation angle and axis tilt angle

One of the very popular ways of determining both axis rotation angle and axis tilt angle is through video analysis. This process has been described elsewhere hundreds of times before, but the basics are as follows:

Step 1: Place a small piece of tape (usually white tape) on the bowling ball at the bowler’s positive axis point (PAP).

How do you do this, you might ask? Well, first you have to find the PAP. The PAP is the point on the bowling ball that intersects the ball’s rotation axis, and it will look “stable” just as the ball is released. This point can be determined via trial and error with video (place the tape on the ball, record the shot, adjust the tape as needed, and then repeat until the tape is stable), or with the help of a reliable friend.

Step 2: Place a video camera behind the approach, at ball-center height, oriented along the initial target line.

Note here that camera position matters. If your camera is off to the side of the initial trajectory of the ball, you’ll introduce error into your axis rotation angle measurement. And, similarly, if your camera is higher than ball-center, you’ll introduce error into your axis tilt angle measurement. Your best bet is to place the camera behind the approach (this puts it at least 15 feet from the ball at the point of release, which helps to minimize perspective error), as close as possible to ball-center height, and positioned/oriented as close as possible to the intended ball path.

Step 3: Record a shot, with the camera zoomed in as much as possible on the ball during the release.

This step is pretty straightforward: capture as clear a shot as you can of the ball being released.

Step 4: Extract a frame of the video just as the fingers are leaving the ball and place this image beneath a transparent rotation/tilt overlay, using an image editing software tool (such as Photoshop or GIMP). Use the overlay to determine the axis rotation and axis tilt angles based on the location of the PAP.

A rotation/tilt overlay is a reference graphic that helps you correspond a given PAP position with an axis rotation angle and axis tilt angle combination. To use it, you simply need to scale and move the image of the ball so that it is properly aligned with the overlay and then read off the axis rotation and axis tilt values that correspond to the PAP’s position.

Here’s an example of what this method ends up looking like when done properly:

From the overlay, we can see that for this example, the position of the PAP indicates an axis rotation angle of about 67 degrees and an axis tilt angle of about 13 degrees.

Before moving on, I should mention that there is an alternate method of determining axis tilt that doesn’t require video analysis. It turns out that axis tilt is related to the size of the ball track, so tilt can be determined by measuring the distance across the initial oil ring along the surface of the ball. This is typically done in the pro shop using a Pro Sect or quarter scale tool, but it can also be done using a flexible tape measure.

I’ll spare you the math, but axis tilt angle ends up being inversely proportional to the measured distance along the ball surface from one side of the ball track to the other. A ball with no axis tilt will have a track that measures 13.5 inches across, and every 10 degrees of axis tilt will reduce this measurement by 1.5 inches.

Assuming you’re careful with your measurements, this can be a good way of determining tilt. But, unfortunately, there is no equivalent method of measuring something about the ball track to determine axis rotation angle. So, assuming you’re trying to measure both rotation and tilt, the video analysis method is usually required anyway.

The effect of axis rotation and axis tilt on ball motion

Thus far, we’ve defined what axis rotation and axis tilt are, and we’ve shown how you can determine your own numbers. Now, let’s switch gears and talk about how rotation and tilt affect the bowling ball’s motion as it goes down the lane.

This section could be its own article, and perhaps someday it will be. But, my intent for now is to keep this somewhat non-technical. In truth, though, to really examine this topic properly, we’d need to use a fair amount of math that would probably not be of interest to many of you.

Specifically, the thing that really helps when analyzing rotation and tilt is to analyze the slip vector between the ball and the lane. The force of friction acts on the ball in the direction of the slip vector, and the direction of the slip vector is set by the bowler’s delivery parameters, which of course include axis rotation angle and axis tilt angle. I discussed this to some extent in a prior article, but for now I’m going to mostly omit that type of analysis and try to stick to somewhat non-technical descriptions.

The effect of axis rotation angle on bowling ball motion

Axis rotation angle affects two things about how the ball hooks:

• It affects the rate of the ball’s hook: When I say “rate” in this context, I’m referring to the amount of hook the ball experiences per unit of time. You might also think of this as the “aggressiveness” of the ball’s hook. The rate of the ball’s hook is literally how much its direction of travel changes (in degrees) per unit of time (in seconds).
• It affects the duration of the ball’s hook: This refers to how long (in time) the ball hooks before it rolls out and goes (mostly) straight.

So, I’ve stated that axis rotation angle affects these two things, but I haven’t yet covered “how” specifically it affects these two things. For that, let’s turn to some examples. Consider a bowler with fairly normal delivery specs: 18 mph ball speed, 400 RPM rev rate, and 10 degrees of axis tilt. Let’s say this bowler throws a shot with an axis rotation angle of 20 degrees. Here’s a short video (shown at 25% speed) showing what that might look like:

Now, let’s get to the question we’re interested in answering: what will happen if this bowler increases his axis rotation angle, while leaving everything else unchanged? Let’s take a look. Here is the same shot, but this time thrown with 40 degrees of axis rotation instead of 20:

As you can see, this shot hooks more. But, let’s talk about why it hooks more. In this case, going from 20 degrees of rotation to 40 degrees of rotation causes an increase in the rate of the ball’s hook, as well as an increase in the duration of the ball’s hook. In other words, it hooks harder (meaning more aggressively) and for a longer amount of time (meaning it rolled out later).

OK, that’s great, but what happens if we further increase the axis rotation angle to 60 degrees? Let’s take a look:

Again, this increase in axis rotation angle causes more hook—not as much more as the difference between 20 degrees and 40 degrees, but slightly more. And, again, the reasons are the same: the ball hooks harder, and it rolls out later.

Finally, let’s increase the axis rotation angle one more time, up to 80 degrees:

What happens here? Well, as you can probably see, the ball actually hooks slightly less. How can that be?

Well, this is a bit tough to explain, but at 80 degrees of axis rotation for this bowler’s style, we’ve crossed a line: specifically, we’ve reached a range at which an increase in axis rotation angle results in a decrease in the aggressiveness of the ball’s hook. Let me say that another way, in hopes of being a bit more clear: at 80 degrees of rotation, this ball hooks less aggressively (with less change of direction per unit of time) than it did when it was thrown at 60 degrees of rotation.

So, we’ve established that the aggressiveness of this ball’s hook was reduced due to the increase in axis rotation angle from 60 degrees to 80 degrees, but what about the duration of its hook? Well, we’ve actually also increased the hook’s duration, but in this case it didn’t really matter, as even the 60 degree shot in this case didn’t roll out until just after it hit the pins. The 80 degree shot would have rolled out later and eventually changed direction even more than the 60 degree shot, but it was already hitting the pins and going off the back of the pin deck before any of that happened. The net result? The 80 degree delivery hooks less than the 60 degree delivery.

This example illustrates one of the really confusing things about axis rotation angle: changing it in a given direction doesn’t always create the same effect on the ball’s motion. This makes it different from ball speed, rev rate, and axis tilt (which we’ll talk about very shortly). For example, if you increase your ball speed, you can always count on that resulting in a decrease in your ball’s hook. Similarly, if you increase your rev rate, you can always count on that resulting in an increase in your ball’s hook. This is not the case with axis rotation angle: increasing it might make your ball hook more, but it also might make it hook less!

So, let’s recap what we’ve learned. At the beginning of the section, I stated that axis rotation angle affects two things: the aggressiveness of the ball’s hook, and the duration of the ball’s hook. Here is a brief summary of how axis rotation angle affects those two things:

• From 0 degrees of rotation up to some “transition” amount of rotation, an increase in axis rotation angle will result in an increase in the aggressiveness of the ball’s hook. Beyond that “transition” rotation amount, further increases in axis rotation angle will result in a decrease in the aggressiveness of the ball’s hook.
• An increase in axis rotation angle always results in an increase in the duration of the ball’s hook. In other words, if you increase your axis rotation angle, your ball will have the potential to roll out later and change direction by a larger overall amount than it did prior to the increase. Whether it actually does this or not before it hits the pins depends upon how early on the lane the ball rolls out.

The obvious question in everyone’s mind must be the same: at what amount of axis rotation angle does this “transition” occur? In our example above, this transition actually occurs at an axis rotation angle of 56 degrees. But, this isn’t a universal number that applies to everyone: it turns out that it actually varies as a function of the bowler’s ball speed, rev rate, and axis tilt angle. A formula can be derived to precisely define this transition angle for all bowler styles, but to keep things simple, here are some generalizations:

• A typical speed-dominant bowler (someone with a low rev rate relative to ball speed) will have a transition angle of around 70 degrees or so.
• A typical rev-dominant bowler will have a transition angle of around 50 degrees or so.
• Bowlers who are closer to being speed/rev balanced will have a transition angle in the ballpark of 60 to 65 degrees, give or take.

A lot more could be said on axis rotation, but let’s stop right there for now and move on to axis tilt.

The effect of axis tilt angle on bowling ball motion

Luckily, it is much easier to explain the effect of axis tilt on ball motion. In short, an increase in axis tilt angle—assuming all other things stay equal—will result in less hook.

Since tilt is so much simpler to understand than axis rotation angle—and since it requires pretty much no further explanation along the way—I’ll combine our axis tilt examples into one video. Shown below are four shots where everything other than axis tilt is held constant, starting with 0 degrees of tilt, then 10 degrees, then 20 degrees, and then 30 degrees.

As I hope you can see, these examples show exactly what I described above: each increase in axis tilt resulted in less hook.

There really isn’t much more that needs to be said about this, but you may be wondering why the ball hooks less when tilt is added. Well, just as in the case of explaining the effect of axis rotation angle, it all comes down to the direction of the slip vector between the lane and the ball as it travels down the lane. All other things equal, a larger tilt angle creates less slip in the lateral direction, which causes less friction force in the lateral direction, which causes less hook.

Now, this explanation should not be confused with what I’ve often read about this topic, which is that axis tilt causes the ball track to be smaller, which causes the ball to experience less friction. This is completely untrue. Until you get to the far extreme of very, very high amounts of axis tilt, the magnitude of the friction force acting on the ball is essentially unchanged as tilt changes. What does change is the direction at which that friction force acts, and this is actually why the ball’s motion changes as a result of different amounts of axis tilt. Any explanation of axis tilt that attempts to relate the reduction in the size of the ball track to a reduction in the amount of friction the ball experiences is simply incorrect.

Closing thoughts

Well, we’ve covered quite a bit of ground thus far, and I hope you’ve found this to be informative. I personally think that it is worthwhile to try to understand things like axis rotation and axis tilt. It’s certainly true that not all great bowlers do understand these things, but being knowledgeable about this topic certainly can’t hurt. And, in a lot of cases, I believe it can actually help, because knowledge of this type can guide you toward making better decisions, both when it comes to figuring out what you need to work on as a bowler, as well as when it comes to making the correct adjustments during competition.

Let’s close by discussing a few key ideas you might take away from this article:

• I encourage you all to measure your axis rotation and axis tilt angles. Knowing what they are is an important first step in figuring out whether you should focus effort on changing one or both of them.
• A bowler who has an extremely low axis rotation angle would most likely benefit from working on increasing it. If your axis rotation is down in the 10 to 30 degree range (roughly speaking), you’d probably benefit from having more axis rotation. A release of this type just can’t create enough change of direction to be competitive—at least in most cases. And, we didn’t discuss this directly in this article, but extremely low axis rotation angles are very unforgiving and very sensitive to the small variations that occur in the release from one shot to the next. Now, some people might argue that having a very low rotation release can provide an advantage in certain situations. That might well be true for certain styles, on certain conditions. But, a low rotation release as your “A-game” release, or as your only release, isn’t likely to be a winning strategy these days in high-level competition.
• Bowlers who want to be competitive across a wide variety of lane conditions should definitely focus on developing axis rotation angle versatility. Even with just two different axis rotation angles available, a bowler can drastically change the shape of their ball’s hook on the back end. If your current “A-game” release has about 40 degrees of rotation, for example, try to develop a “B-game” with around 70 degrees of rotation (or vice versa).
• In most cases, I don’t believe there is much benefit to learning how to change your axis tilt. Most of us are perfectly fine with whatever axis tilt we have. That said, there are some exceptions, of course. If you have extremely low tilt, you might find that you struggle to keep your ball from tracking over the gripping holes. That’s not good, and you might benefit from increasing your tilt a bit, just to avoid this situation. And, if you have extremely high tilt, you might find that you just can’t develop a very powerful hook. That’s also not good, and you might benefit from working on decreasing your tilt. The rest of us can probably find better things to focus our efforts on.
• I often see high-level bowlers or their coaches talking about a player’s “high tilt” release versus their “low tilt” release. A lot of the time, these labels are quite misleading. In some of these cases, the person talking just has their terminology mixed up and they might have actually meant “high rotation” and “low rotation.” But, other times, it’s not necessarily that they have the terminology confused; instead, it’s that they fail to notice or mention that the bowler’s “high tilt” release is different in some way from their “low tilt” release above and beyond the change in tilt. If a bowler goes from his “low tilt” release to his “high tilt” release and the result is that the ball hooks more, you can be pretty sure that the “high tilt” release also had some combination of more axis rotation, more rev rate, or less ball speed. This is obviously a bit of a pet peeve of mine, but I guess my point is that tilt is rarely changed in isolation, so try not to get fooled into thinking that more tilt (by itself) means more hook.

Finally, as a side note, I just wanted to share a quick observation. In writing this article, I came to notice over and over again that we still have serious terminology problems in our industry when it comes to accurately describing ball motion. As I tried to explain what really are fairly simple concepts in this article, I repeatedly found myself trying to avoid certain words that are ambiguous or otherwise inaccurate, while struggling to find suitable replacements.

For example, when we talk about a bowling ball as being “more angular” than another bowling ball, I think most of us can generally picture in our minds what that means. But, if we try to use that same type of terminology to compare one axis rotation to another, things get a bit less clear. In this article, I eventually settled on using terms like “rate of hook” (or “aggressiveness of hook,” both of which refer to change in the ball’s direction of travel per unit of time) and “duration of hook” (which refers to how long the ball hooks before rolling out). Both of these things can change drastically as a result of different amounts of axis rotation, and they both affect the shape of the ball’s path down the lane. The more generic terms that we all know and use like “length,” “angularity,” and “hook” just don’t cut it in this context, as they really don’t give us the ability to accurately describe what is going on.