# The Nine Ball Flights

Dave Tutelman  -  June 3, 2006

On May 25, 2006, Ed Johnson posted on Spinetalk (Ed is the owner/moderator of the Spinetalk forum):
I know there are 9 basic ball flights in golf shots. Straight with square face, open face, and closed face, Right with square face, open face, and closed face, and Left with square face, open face, and closed face.

I've seen graphics depicting these ball flights in many places but now that I need one, I can't find one!

Anybody have a link to a graphic described above?

A link was posted to the "standard" diagram (see picture at left), and Ed was satisfied. But this standard picture does not show the nine trajectories that Ed asked for. Ed asked for:
 Straight with: square face open face closed face Right with: square face open face closed face Left with: square face open face closed face

Giving the  graphic its due, the flight patterns are correctly named, and the influences on ball flight are correctly described. But unfortunately, the names are not related to cause and effect, and there is no correspondence to the nine trajectories that Ed asked for.

In fact, Ed's question is ambiguous. In order to understand why, we need to ask, "What does 'square' mean?" There are two equally valid answers:
1. Square to the target line, and
2. Square to the clubhead path (the direction the clubhead is traveling).
Unless we're talking about a straight down-the-line clubhead path, these two definitions of "square" give very different clubface positions. And the ball flights will reflect these differences. By the way, the nine trajectories shown above do not answer Ed's question for either definition of "square".

So let's go back to basics, and get a set of ball flights that correspond to Ed's question. Actually, we'll need two sets of ball flights: one for each interpretation of what "square" means.

The diagram at the right shows how the ball comes off the clubface if the clubhead is not moving in the same direction that it is facing. Here are the basics of what happens:
• The ball will take a direction (red arrow) somewhere between the direction the clubface is pointing and the direction the clubhead is moving.
• The ball's path will be closer to the clubface direction than to the swing path.
• Most references cite a ratio of clubface influence to path influence between 80:20 and 70:30. That is, the ball is 80% of the way from the swing path to the clubface direction. (The most convincing data, to me at least, suggests a function that varies from nearly 100% at very small angles -- incorporating the loft angle as well -- to 60:40 for short irons.)
The other obvious consequence of the clubface direction being different from the swing path is spin. The conditions in the diagram will result in clockwise spin on the ball, resulting in a fade or slice.

How does this relate to the "usual" diagram shown above. Well, it would relate very well -- if only the direction of the ball in real life were well aligned to the swing path. But it's not; instead, the direction the ball actually takes is closely aligned to the clubface direction. This fact is not reflected in the "usual" diagram.

When we take this inconvenient fact into account, we get a somewhat different set of ball flights on our diagram. Below are two diagrams. Each has nine trajectories on it, corresponding to the nine ballflights that Ed asked about. In the diagrams:
• Red arrows correspond to an outside-to-in swing for a right-handed golfer -- that is, a swing path to the left.
• Green arrows correspond to a down-the-line swingpath, straight at the target.
• Blue arrows correspond to an inside-to-out swing for a right-handed golfer -- that is, a swing path to the right.

 This graphic shows ball flights where the clubface direction is referenced to the target line. That is, instead of using the ambiguous term "open", we say the clubface points right of the target line. The different kinds of arrows mean: Solid arrow: clubface points at the target. Dashed arrow: clubface points right of the target. Dotted arrow: clubface points left of the target. This graphic shows ball flights where the clubface direction is referenced to the swing path. That is, instead of using the ambiguous term "open", we say the clubface points right of the swing path. The different kinds of arrows mean: Solid arrow: clubface points the same direction as the clubhead travels. Dashed arrow: clubface points right of the swing path. Dotted arrow: clubface points left of the swing path.

A few notes about the graphics:
1. If you click on the pictures above, you will get a larger-size stand-alone picture suitable for printing.
2. The angles for both the swing path and clubface directions are the same. That is, the swing path is 19º right or left, and the clubface is facing the same 19º right or left (of the target or the path). The curvature of the extreme slices and hooks are not quite to scale; there wasn't room on the page.
3. A consequence of this is that there are actually a lot more possible ball flights than can be shown here. For instance, the usual diagram's trajectory #3 is a pull-slice that starts out hard left and slices back to the middle or even the right of the fairway. This -- frankly very common -- ball flight comes from:
• A clubface pointing well left of the target (causing the ball to start to the left), and
• A swing path even further to the left (because it has to be even further left to put a slice spin on the ball).
A discussion on the Wishon Golf web forum criticized these findings. In particular, Bill (a professional clubfitter from Santa Barbara) argued that "ball flight rules" said that the ball started in the direction of the swing path and curved toward the direction of the clubface. Simple -- but wrong. (H.L. Mencken once said, "For every problem, there is a solution that is simple, neat, and wrong.") Here are my responses to his arguments:
 As a rebuttal to Bill's version of the "ball flight rules", I pointed out that, whatever they are, they must work in the vertical direction as well as horizontal. If they were as Bill proposes, a wedge shot should start out horizontal and climb in trajectory only due to spin. But we have all seen personally that wedge shots take off on a rather high trajectory, closer to the loft angle than to horizontal. So it is just wrong to say the ball starts off in the direction of the clubhead path; we're only arguing about how close the ball starts to the clubface angle. Which brings us to... Bill pointed out that 19º is a huge amount to be off, either clubface angle or swing path. And so it is for "misses"; it might not be for a deliberate hook or slice. But sorry, Bill; for smaller angles, the results are pretty similar -- but more so. That is, instead of the direction of the ball being 70-80% in the direction of the clubface, it will be more like 90%. If you are still unconvinced, here are some slow-motion videos of impact. The clubhead path and clubface angle were deliberately chosen to show the true ball flight rules. (And the side comments about the old rules are downright sarcastic. Sorta' what I'd like to say, but I'm too polite.)
Bottom line: I stand by what I say here.

## Application: Diagnose a Slice

This is not just an academic exercise. I find it shocking how many instructors -- even the supposed swing "experts" on TV -- give lip service to the new rules but don't have a clue about their implications for debugging a swing. The most common example of this is the misinformation around about the cause of a slice. Sure, there is general agreement on the indisputable facts that:
1. A slice is caused by the clubface being pointed to the right of the clubhead path (for a right-handed golfer), creating spin to curve the ball to the right.
2. It can be due to two kinds of swing flaws: an open clubface or an outside-to-inside swing path.
But, when it comes down to the nitty gritty of diagnosing a particular slice, most of the golf books and instructors ignore the ball flight rules and go by old wives tales. Here are the two most common slices:

• The straight slice starts out straight at the target, then curves disappointingly to the right.
• The pull fade starts out at the left rough, and curves back to the target line. (Ever note how a good result gets called a "fade" and a bad result gets called a "slice"? No, I'm not going to comment on that.)
Let's see if we can diagnose the cause of these two slices. Most of the literature around gets it wrong, as do a lot of instructors.

### Diagnosing the straight slice

Here we have a shot that starts out at the target and curves well to the right. Most teaching says, "Oh, you have an open clubface at impact. If you can square up the clubface, you'll be fine." Let's see what the ball flight laws would say.

Remember that the ball starts out very close to the direction the clubface is pointing. If the ball starts out at the target, then that is where the clubface was pointing. No, you do not have a problem squaring up the clubface. In order to generate slice spin with a square clubface, the clubhead path must be to the left, an out-to-in swing. This is going to be harder to fix than originally thought, because a square clubface is generally easier to achieve than a square swing plane.

The trajectories for this section were generated using the computer program TrajectoWare Drive. The specifics for this straight slice were:
Clubface to target = 0º
Resulting angle clubface to path = 3º right
The ball starts 1yd left of the target line (essentially on target), and finishes 18yd right.

Most instructors look at a pull fade like this one and say, "You're coming over the top, but your clubface is pointing nicely to the target." Closer than before, but still no cigar.

If the ball starts left, then the clubface must have been pointing left. If it then curves right, the clubhead path has to be even more to the left. So you have a shut face but an even more severe out-to-in swing path.

This consists of two errors that need correction, including a severely over-the-top move. And you need to fix both! If you fix either one by itself, the golf results will get much worse. (A pull hook if you get the swing plane fixed, and a really big slice if you get the clubface pointing at the target.) My recommendation (unless the golfer wants to spend a lot of time with lessons and practice) is to live with the good result and not worry how the ball got there. Bruce Lietzke made a fine career on the PGA Tour by not messing with this, his well-grooved swing. And, as they say, "There's no room on the scorecard for pictures."

The computer specifics were:
Clubface to target = 5º left
Resulting angle clubface to path = 3º right
The ball starts 19yd left of the target line, finishes 1yd right

### Diagnosing the push slice

Let's look at one more scenario, the push slice. This one starts somewhat right and curves much righter, often eliciting an "Omigod!" from the golfer. It's so horrible you imagine it is the result of lots of very wrong things, and would be hard to fix if chronic. Nothing could be further from the truth; in fact, it's so easy to fix that it can be done during a round of golf. (There are very few things I would advise a golfer to mess with during a round without practicing it first, but this is one of them.)

Of course, before we fix it we must diagnose the cause. And this one is easy. It's a wide-open clubface, pure and simple. The ball starts right because that's the way the face points. If the swing path is down-the-line, then that adds slicing curve. And there you have it: a good swing path and an open clubface.

I have often helped golfers fix this on the course. When I see them push-slicing routinely, I have them address the ball and ask them, "How many knuckles do you see on your left hand?" I have them strengthen their grip so they can see more knuckles. It's a quick fix that requires no swing change and works every time. It pays to know the ball flight laws!

The computer specifics were:
Clubface to target = 3º right
Resulting angle clubface to path = 3º right
The ball starts 9yd right, finishes 30yd right

Note that all three examples had the same curvature to the shot; the difference was where the shot started out. That's because, for all three examples, the clubface was pointed 3º to the right of the clubhead path. I generated the examples by picking a starting direction, aiming the clubface there, then picking a swing path 3º to the left of the clubface direction. Works every time.

### Bibliography and acknowledgements

Where does my information come from? Here are a few reference materials that collectively add up to the story as I tell it above:
• Theodore Jorgensen, "The Physics of Golf", American Institute of Physics Press, 1996. Jorgensen, a Professor Emeritus of Physics at the University of Nebraska, undertook several studies -- experimental and analytical -- to decipher the mysteries of golf mechanics. One chapter is devoted to the direction the ball leaves the clubface.
• Cochran & Stobbs, "The Search for the Perfect Swing", The Golf Society of Great Britain, 1968 (reprinted many times since; my copy is the 1994 printing). This is the best beginner's book on golf physics. Chapter 23 is entitled "The Ballistics of Golf: How Spin and Flight Begin".
• Tom Wishon's "Trajectory Profiler" program (version 2.0, 2005) incorporates the latest thinking on golf ball ballistics and aerodynamics. Since physics works vertically as well as horizontally, you can use loft to simulate an open or closed clubface and determine the resulting initial ball direction and spin.

I'd like to thank Ed Reeder for a few suggestions that made the graphic better.