Nate Clark's Musings

As some of you know, I used to be an above average tennis player. I still play once or twice a week and am very picky about my tennis racquets. If it doesn’t feel right it can throw your whole game off.

When you look at the specs for a racquet, two of the most important features are weight and swing-weight. Weight is pretty self-explanatory. Swing weight has to do with rotational inertia. If the weight is distributed more at the tip of the frame than the handle then the racquet will feel “heavier” because all that mass needs to move a farther distance.

Many people like myself like to add weight to their racquets, usually in the form of lead tape, to customize the weight and swing weight of their racquets, but I never knew how to directly measure swing weight. And while there are special machines that will tell you the swing weight, I wanted to figure out the swing weight of my racquet at home so that I can customize it without having to pay someone else to do it.

So without further ado, here’s how to do it yourself!

We’re calculating rotational inertia, so we need to swing the racquet about an axis. If you break out your old physics text book rotational inertia is…

Where M is the mass in kg, g is the gravitational constant 9.81, d is the distance from the center of mass to the pivot point in meters, and T is the amount of time it takes for the racquet to swing back-and-forth once, aka the period of oscillation. Calculating mass is pretty easy – break out a scale. My racquet is 336g strung.

Next we need to set up a way to swing the racquet. You want this to be as frictionless as possible. I found a dowel lying around and ended up taping it to my handle. With the dowel attached, hang the racquet between two objects and let it swing.

I counted the time to do sixty oscillations and computed the average time as 1.311 seconds. The dowel was taped at 9.2 cm from the butt of the racquet.

The last piece we need is the center of mass. You can compute this by using the dowel again and trying to balance your racquet so that neither side touches the ground. My racquet balanced when the dowel was 32.5 cm from the butt.

Putting this all together I get I = = 334.36 kg/cm^2 (the 10^4 is to convert m^2 into cm^2, which is how the racquet companies report their numbers). This is darn close to the company reported value of 334!

Now you can modify your racquet and confidently know what swing weight you’re getting.