Volume, Displacement & Buoyancy
The Rules of Golf limit the volume of the head of a golf club to 460 cubic centimeters. To ensure that modern day clubs conform to this rule, the United States Golf Association relies on a 2,000 year old science principle discovered by Archimedes of Syracuse. "Science of Golf" is produced in partnership with the United States Golf Association and Chevron.
DAN HICKS reporting: Golf clubs are designed in many shapes and engineered from many materials, but when it comes to the head of a golf club, there are strict limits on its volume.
CARTER RICH (Equipment Standards, USGA): We decided, not based on performance at the time, but based on appearance that we needed to put a rule in place that would limit the size of a club head.
HICKS: Carter Rich is director of equipment rules and conformance at the United States Golf Association. He ensures that the design of the club head conforms to the Rules of Golf, which state that the maximum legal volume, or the amount of space it occupies, is 460 cubic centimeters, or 28.1 cubic inches.
JOHN SPITZER (Equipment Standards, USGA): The length and width and height and multiply those together and we’d get the volume. But it’s very difficult to do for a club head that’s got an odd shape to it.
HICKS: To measure the volume of an irregular shaped club head John Spitzer, managing director of equipment standards at the USGA, relies on an ancient concept discovered around 250 B.C. by the Greek physicist, mathematician and astronomer known as "Archimedes of Syracuse."
SPITZER: That’s basically, as you dip something, an object, into this bucket of water, it displaces the water.
HICKS: As the story goes Archimedes was asked to determine if a crown made for King Hiero the Second was made of solid gold without damaging it.
Because the crown was oddly shaped, Archimedes needed to devise a way to measure its volume.
Legend has it that as he was taking a bath he noticed the water levels rising when he got into the tub.
In a flash, the answer came to him, spurring him to run through the streets naked shouting "Eureka!"
SPITZER: That’s when he came up with a famous saying; ‘Eureka, I’ve found it!’
HICKS: What Archimedes discovered is that the volume of the displaced water is the same as the volume of the object submerged. This gave Archimedes the V for the equation D equals M divided by V.
The m in the equation stands for mass, or the amount of matter in an object. The d in the equation stands for density, or the amount of mass per unit volume.
Archimedes tested this principle by dipping the crown into a bowl of water and measuring the amount of water it displaced. Then, he compared the water displaced by a solid gold bar of equal mass.
When they didn't match, he knew the crown was a fake.
The Archimedes Principle would later be stated as: "any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object."
Buoyancy is the tendency of a liquid to keep something afloat.
By measuring the mass of a beaker of water before and after a club head is dipped into it, the USGA is able to determine the amount of buoyancy the club head produces, thus revealing its volume.
SPITZER: And that’s just clever because if you’re using water, water has a density of one gram per cubic centimeter.
HICKS: In this case, the change in mass on the scale is 360 grams, so the club head's volume is 360 cubic centimeters, or cc's. By setting limits on the volume of a golf club head the USGA is trying to prevent technology from giving players an unfair advantage due to the club head's moment of inertia.
SPITZER: What really makes a difference is how that volume is manifested into the distribution of weight and the moment of inertia that the club head possesses.
HICKS: The moment of inertia, sometimes called rotational inertia, is the measurement of the club head's resistance to twisting force.
SPITZER: So if you were to hit this ball, and I do this all the time, and you hit it off the toe, what’s going to happen is the club head is going to twist.
HICKS: Think of a tight rope walker holding a long pole as she walks across a rope. The pole increases her balance by increasing her rotational inertia, keeping her more stable.
SPITZER: Resistant to the twist that’s going to try to make them fall off the rope.
HICKS: Like the tight rope walker, the greater volume the club head has, the greater area over which the mass is distributed, making it easier to drive the golf ball farther and in a straighter line even with an off center shot. This is why the USGA sets limits.
RICH: So a club or invention that comes along that might make the game, you know, easier to play so to speak without the need for practice and skill, would be something that we would look at very closely from a rules standpoint.
HICKS: By relying on a 2,000 year old science principle to measure the volume of a club head, the USGA is preserving the challenge required to hit a good shot.