In recent years, the concept of a putter's face balance point as a technical specification has increased in perceived importance for fitting a particular type of putter to a particular golfer. Terms like "face-balanced", "toe hang", and "toe flow" are becoming more and more commonplace when discussing putters. Yet what causes a putter head to balance a certain way is still a mystery to many.
However, if we simply look at the two key factors, the shaft axis and putter head's center of gravity, and examine how they relate to each other, it's not only easy to understand why a putter balances a certain way, but it's also easy to calculate what the exact face balance point will be.
In its simplest terms, the face balance point is a reflection of how the head of a putter will situate itself if the head were allowed to freely rotate about its shaft axis when the axis is oriented horizontally with respect to the ground (i.e. perpendicular to the direction of gravity). In this equilibrium position, the center of gravity of the putter head aligns itself directly below the shaft axis as in the picture below. Note that the image below is from the perspective of looking straight down the shaft axis. The purple "triad" indicates the location of the putter head's center of gravity.
From this equilibrium position, the angle that the face forms with respect to the horizontal axis (i.e. the horizon) is termed the "toe hang". In order to calculate what this angle is in degrees, we need to determine the distance of the shaft axis and center of gravity of the head (CG) to the intersection of their orthogonal projections along the target line axis and the heel-toe axis, respectively. The image below illustrates these two distances (X and Y).
More simply put, the distance X is the shaft axis offset from the targetline axis and the distance Y is the CG setback from the heel-toe axis. In order to determine the amount of toe hang, we need to apply a little trigonometry. The tangent function gives us the ratio between X and Y based on a given angle formed by the hypotenuse of a right triangle with sides of distance X and Y. In order to calculate this angle based on the ratio between the lengths of sides of the right triangle, we apply the arc-tangent (or inverse tangent) function. In the picture above, the angle formed by the line between the shaft axis and the CG with respect to the heel-toe axis is:
A
cg = arctan(Y/X)
However, this angle is not the same as the angle of toe hang when the head is allowed to rotate. The angle is actually 90 - A
cg. More simply the angle of the toe hang can be calculated by transposing X and Y in the equation above. The equation to calculate toe hang is thus:
A
th = arctan(X/Y)
On an Anser-style putter X and Y are generally equal. Therefore, the toe hang angle is calculated as:
Given: Y > 0
A
th = arctan(X/Y) = arctan(1) = 45 degrees
On a face-balanced putter, X is generally 0 (i.e. the shaft axis is inline with the head's CG along the targetline axis). Therefore, the toe hang is calculated as:
A
th = arctan(X/Y) = arctan(0) = 0 degrees
On a severely toe-heavy putter, Y is generally small and X is generally much larger. Therefore, the toe hang is calculated as:
Given: X >> Y
A
th = arctan(X/Y) = arctan(
) = 90 degrees
What this tells us is that the amount of toe hang that a putter exhibits is simply a reflection of the ratio between the shaft axis offset distance and the CG setback distance. This is why lie angle adjustments to putters, in general, will affect the face balance point of a putter. When a putter's shaft (or neck) is bent more upright, the distance X is increased. Therefore, the toe hang will also increase. When a putter is adjusted for a flatter lie angle, the distance X is decreased as is the amount of toe hang.
The type of neck (or lack thereof) that a putter has only matters to balance insofar as the neck positions the shaft axis in a particular position with respect to the head and its CG. For instance, as mentioned above, a standard plumber's neck positions the shaft axis such that the offset is nearly equal to the setback of the CG. This results in a 45 degree toe hang. However, there are also "long neck" versions of the plumber's neck. Since the neck is higher, the shaft axis intersects the head at a position that is closer to the center of the head (i.e. distance X is decreased). Therefore, the toe hang is also decreased--on some putters to the point of creating a neutral face-balance (i.e. 0 degree toe hang).
