The Nine Ball Flights

 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: Square to the target line, and 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 show this as between 80:20 and 70:30. That is, the ball is 80% of the way from the swing path to the clubface direction. 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 were well aligned to the swing path. But it's not; instead, the direction of the ball 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.

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).

1. 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 just arguing about how close the ball starts to the clubface angle. Which brings us to...
   
2. 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%.

Bibliography and acknowledgements

• 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.