Rational Blog: Thoughts on Golf and the World
A drawing showing the forces acting on a golf club positioned in a Swingweight Scale is provided bellow. The three forces acting on the golf club are as follows:
The force F, acting downwards at the grip end of the club. This is the force measured by the Swingweight instrument.
The force G is the gravitational force acting on the golf club. It is simply the weight of the golf club acting at its center of gravity. The location of the center of gravity can be determined by balancing the club on a knife-edge. The center of gravity is located at distance BC from the fulcrum.
The third force is acting upward at the fulcrum. The fulcrum is located 356 mm (14 inches) from the grip end of the club. This force equals the sum of force G and force F, acting in the opposite direction.
From Newton´s Laws of Motion, it is established that the sum of all moments acting upon a body at rest is zero. By adding the moments acting on the golf club about the fulcrum in the Swingweight instrument, denoting clockwise as the positive direction:
Sum of all moments = ∑M = (G x AB) - (F x 356 mm) = 0
F = G x AB / 356 mm
The Swingweight of any golf club can thereby be calculated when the mass and center of gravity is known. Swingweight is purely a function of mass and center of gravity of the golf club. For example, a golf club is found to have a mass of 349.8 grams and a center of gravity located 824 mm from the grip end of the club. These measurements were carried out on an actual golf club using a scale, a knife-edge, and a measuring tape. From Newton´s second law of motion, the vector force G = 0.3498 Kg x 9.81 m/s^2 = 3.431 N. The distance AB = 824 mm – 356 mm = 468 mm = 0.468 m. Hence;
F = 3.431 N x 0.468 m / 0.356 m = 4.510 N
From a table that I will forward next, you can look up this number and see the Swingweight.
Swingweight Table From the table, the calculated force corresponds to a Swingweight of D7.8. Measuring the club in a Digital Swingweight Scale gives the same Swingweight of D7.8. The club used for this example is a TaylorMade 5 hybrid. The fact that a letter scale and a measuring tape can replace the Swingweight Scale, which has been utilized for almost a century, will come as a big surprise to the majority of golf club fitters. This ought to raise some concerns even for the die-hard Swingweight supporters. As the center of gravity does not enter any equations describing circular motion, the Swingweight of a body cannot be related to how a body acts under circular motion. Newton’s second law of circular motion states: Torque = Moment of Inertia x Angular Acceleration. There is, therefore, no relationship between Swingweight and how a golf club behaves when acted upon by a golfer. Ever since the Swingweight principle was developed in the 1920s, it has been the accepted method for matching clubs within a set, so they all feel alike when swung. In short, it is a measurement of the weight distribution of the club. And with the introduction of lighter shafts, grips, and club heads, the possibility of a wider range of Swingweights, and thus more inconsistency from club to club is greater. When Robert Adams was matching his set of golf clubs by waggling the golf clubs in a horizontal plane, he was in fact attempting to measure the moment of inertia of the club around the center of the grip. The moment of inertia around the center of the grip is henceforth referred to as MOIG. One can imagine how difficult it would be to adjust all 13 clubs until they all felt like having the same MOIG. There were no instruments available for measuring the moment of inertia at the time. Robert Adams made an instrument that would provide an indication of whether all the clubs in a set of golf clubs would have similar MOIG. The clubs used to develop the swingweight method all had similar wooden shafts. That is no longer the case. The Swingweight system is therefore even less useful today than it was 90 years ago.
Robert Adams of Waban, Massachusetts, made the first known system for matching golf clubs within a set in the early 1920s. His Swingweight Scale is called the Lorythmic Scale. It measures the upward force at the grip end of the club when balanced on a point 14 inches down the shaft. Robert Adams stated in his patent that approximately 14 inches is the preferred distance for golf clubs. No scientific reasoning for choosing 14 inches was offered. The Swingweight is measured in an arbitrary system of letters and numbers. The letters range from A to G, and the numbers range from 0 to 9. A0 being the lightest, and G9 the heaviest. Howe Scale Company in Massachusetts produced the scale. Kenneth Smith started to use this system for matching the golf clubs he was producing. Later his company was also producing such a scale. At some stage, Kenneth Smith recognized that there were some deficiencies in the Swingweight system. For all the clubs in the set to have the same feel, he realized that the woods had to be two Swingweight numbers higher than the irons. This was accepted amongst professional golfers at the time. To correct for this, Kenneth Smith introduced the Official Swingweight Scale in the late 1940s. The balance point of the new scale was set at 12 inches rather than 14 inches. The idea was that all the clubs, irons, and woods, should feel the same when they had the same Swingweight. The Official Swingweight Scale measures the Swingweight in ounces, indicating the load that has to be applied at the grip end to balance the golf club. The Official Swingweight Scale did however not catch on. The original Lorythmic Scale created by Robert Adams is still used by all the major golf club manufacturers.
If a set of clubs having the same grips and completely identical shafts trimmed incrementally are matched by Swingweight using only the club head for making adjustments, then the MOIG (Moment of Inertia around the center of the Grip) of each club will be reasonably matched. This was the original intent for the swing-weight process and worked reasonably well for the clubs of the time. However, because swing-weight is a static property of a club and moment of inertia is a dynamic property of a club, Swingweight matching is, at best, an approximation of the technically more useful MOIG matching.
With the more modern shafts, that have purposeful variation along their length, and the tendency to mix and match a variety of shafts and club heads within a single set, the less likely it is that a Swingweight matched set will resemble an MOIG matched set. Because the Swingweight Scale is not an MOIG measurement device, it does not produce a set of clubs with a matching moment of inertia.
Below is a graph showing that there is no relationship between Swingweight and MOIG. The graph was made by taking measurements of a random set of golf clubs. If swingweight had been related to the moment of inertia, the graph would have resembled a straight line.