Club Path Math
Warning! High nerd factor in this post!
Even after 5 years of owning a Trackman, I continue to be intrigued by the correlations and relationships between the various data it provides. I’m certainly not a physicist, geometry expert or mathematician – in fact, I barely passed high school math – so I figure if I can get this stuff, anyone can. So let’s talk “club path math”.
Club path is resultant data derived from the relationship between swing direction, swing plane and attack angle. At a glance, swing direction and club path sound like very similar terms; in fact, they represent two distinct moments during the swing. Path is the direction the club head is travelling at that moment when the club strikes the ball, aka “impact”. Swing direction is the direction the club head is traveling at the moment when it reaches its lowest point on the swing arc.
Club Path = Moment of Impact | Swing Direction = Moment of Low Point
It seems intuitive to think that these two distinct moments would happen at exactly the same time, but in fact, this almost never happens. We have to consider how attack angle affects the relationship between swing direction and club path. With iron shots, a downward (negative) attack angle is mandatory – we aim to hit the ball first, then take a divot. In such cases, the moment of impact occurs before the moment of low point. If the moment of impact occurs after the moment of low point, then the attack angle will be upward (positive). Having a slightly upward attack angle is a key contributor to increased driver distance for golfers with lower swing speeds. The only time, then, that moment of impact and moment of low point will occur at the same time is when the attack angle is zero degrees. This is impractical with irons, but certainly a possibility with a driver.
Swing plane also has a part to play. The flatter the swing plane, the more attack angle affects club path. Note that swing plane and attack angle are often mistakenly interpreted as being one and the same. They are not; and it’s important to understand the difference between the two.
Swing plane is the angle made between the ground and the plane of club head trajectory, as viewed from a “down-the-line” perspective. Swing plane is generally described as “flat” (lower measured values) or “steep” (higher measured values).
Attack Angle: represents the vertical (up/down) angle at which the club head is moving in relation to the ground at impact, as viewed from a “face-on” perspective.
Thus, a steeper swing plane does not necessarily equate to a steeper attack angle; nor does a flatter swing plane equate to a shallower attack angle.
Effects of attack angle and swing plane on club path; and why the swing direction (aka “low point”) must be adjusted to create the desired path:
If a golfer had a perfectly vertical swing plane of 90 degrees, the angle of attack would have no effect on his aim. However, a 90 degree swing plane is a practical impossibility. A golf swing takes place on an inclined plane that ranges from about 45 degrees to about 65 degrees, depending on the club. Swing direction is essentially the horizontal orientation of the base of that plane. By default, golfers tend to aim their shots based on this low point. However, the ball does not respond to swing direction; it responds to the path. Although these points are often separated by only a few degrees, the effect on the resulting launch and curvature can be significant. For these reasons, “square” alignment is not necessarily “square” and aiming is not always a “what you see is what you get” proposition.
As we discussed earlier, in the presence of a downward (negative) attack angle, impact occurs before the club reaches its lowest point along the swing plane. In that case, the club head’s movement along the inclined plane is diagonal – both downward and outward at moment of impact. The swing direction must be adjusted to neutralize the outward club head movement that accompanies the downward movement along the plane. If the attack angle is upward (positive), impact occurs after the club has passed through the lowest point on the swing plane – thus, the swing direction would have to be adjusted to account for the inward movement that accompanies the upward. The flatter the swing plane, the greater the effect of attack angle on the club’s path; at a 45 degree swing plane (fairly typical/orthodox for a driver), the relationship is degree for degree. For example, given a right-handed golfer with a 45 degree swing plane, attack angle of negative 3 degrees and a desired swing path of zero degrees, the swing direction (aka low point, aim point) would need to be adjusted 3 degrees to the left to achieve the desired zero degree path.
Told you this one was high on the nerd factor! If you’re into geometry, you’ll surely have fun with this little calculator, which allows you to see what happens to club path when any or all of the variables of swing plane, swing direction or attack angle are changed!
Psst… here’s the formula: Club Path = (Swing Direction) – (Attack Angle / TAN Swing Plane) (where swing plane is converted from “degrees” to “radians”)