An experiment in adding mass to the tip of a tennis racquet

In a recent discussion on a Tennis Warehouse message board discussion, a poster asked if anyone had analyzed the changes in weight, balance, and swingweight per inch of lead tape added at the tip of a racquet. Also, there was a question of how the racquet has to be oriented in the mount when measuring swingweight. I decided to provide answers to each of these inquiries.

My measuring device is a Prince PTC. I did not calibrate it prior to performing these measurements, because the measurements only have to relate to each other, not the outside world, and I'd just eaten a huge Kobe beef hamburger and had Vinnie Moore’s “Time Odyssey” blasting from the iPod Hi-Fi, so calibration was simply too much to ask. Note that the scale of the Prince PTC has a half-gram resolution.

I chose as my test racquet a Prince O3 Tour MS (internal ID #1), which was strung with Wilson Reaction 16. It had a replacement grip but no overgrip, a rubber grip band at the top of the replacement grip, and some built-up material in the handle between the end of the butt cap and 6.5 inches up. The racquet as tested was 26-15/16 inches in length. The other measurements appear in the table below.

I added ¼-inch lead tape in paired strips four inches long at the inside of the hoop at the tip (AKA the 12 o'clock position). Normally, I would not add lead to this racquet in this position because of the O Ports, and if I did, I would contour the tape into the O Ports. For this test, the tape lay more or less along the inner contour of the frame at this point. I used a lengthy strip of lead tape that I had just recycled from one of my Wilson Hyper Pro Staff ROKs, instead of using new tape that in all eventuality will be discarded shortly after this experiment.

I took the weight and balance measurements with the racquet in the same orientation each time. I took the swingweight measurements four times at each racquet weight, once on each of the four main “bevels” of the frame:

  1. Up signifying the “P” on the butt cap is right-side up;
  2. Right signifying that the “P” on the butt cap is lying down on its right side (a proper way to mount a frame);
  3. Down signifying that the “P” on the butt cap is up-side down; and
  4. Left signifying that the “P” on the butt cap is lying on its left side (a proper way to mount a frame).

During this experiment, the temperature was 75°F and the Relative Humidity was 44% (that is, a dewpoint of 40°F).

The center of the first strip of lead was 26.5 inches from the butt cap. However, the ends of this four-inch section were only 26 inches from the butt cap. When simply adding lead tape to a racquet to see what how it feels, this is not a problem. However, when adding lead tape in an attempt to duplicate the weight, balance, and/or swingweight of another racquet, typically the calculations call for adding X amount of lead tape at position Y on the frame. Due to the curvature of the frame, however, the exact centerpoint can be difficult to determine with accuracy. Because of the thickness of the strips of lead tape, the center of the eighth and final layer of lead tape was 26-7/16 inches from the butt cap, and the ends were 25-7/8 inches from the butt cap. This would further compound accurate calculation of during racquet matching.

As a check against heat-related error within the Prince PTC, after the final “weighted up” measurements I stripped the racquet back to its starting configuration and remeasured, achieving the same measurements as I did in establishing the baseline measurements.

Here, then, are the results, with the weight in grams, the balance in centimeters, and the swingweight in kg•cm² as it must be:

Measured changes
Configuration Weight Balance Up Right Down Left
Baseline 353.5 30.3 341 324 342 324
+8 inches 356.5 30.5 347 330 347 332
+16 inches 359 30.7 353 337 353 338
+24 inches 361 30.9 359 343 360 344
+32 inches 363 31.1 366 349 366 350
+40 inches 365 31.3 372 356 372 356
+48 inches 367 31.5 378 362 378 362
+56 inches 368.5 31.7 384 368 384 368
+64 inches 371 31.85 387 374 385 374
Baseline check 353.5 30.3 341 324 342 324

Not surprisingly, the edge-on swingweights (labelled “Up” and “Down” in the first table above) are way off from the properly-measured swingweights. I suppose that, to be rigorous, I should re-run this test with a racquet that does not have huge holes in the frame, to see what role aerodynamics play. I have no explanation or theory about the slight scatter in the Up/Down and Right/Left data, but I've seen it often enough that I expected it. You can only imagine what happens when you attempt to compare measurements of this sort taken from two different uncalibrated machines operated under different conditions, let alone if one of the operators doesn’t know the correct way to mount the racquet in the first place.

I took these figures and plugged them into a spreadsheet I use when matching and modifying racquets.

Because the measured figures did not agree with well-established formula for calculating the changes in racquet characteristics as a known mass is added to a known position on the frame, I took the two stacked strips of lead tape and weighed them on a beam balance. The lead tape that added 17.5 grams according to the Prince PTC actually weighed 14.744 grams, far short of the advertised one-quarter gram per inch. (This is just one reason why, when working on racquets where accuracy is important, I use 3M Model #420 Professional Lead Tape from Grand Slam Stringers instead of the bargain bulk-pack lead tape.)

I took the 14.744-gram figure, added it to the starting mass of the racquet, and ran the numbers again. This time, the agreement was much better between the measured results and the calculated results, as seen in the table below. It appears that I should have taken a few moments to calibrate the PTC before embarking on this adventure, and checked the calibration throughout the experiment.

Calculated changes
Configuration Weight Balance Swgwt
Baseline 353.24 30.3 324
+1.843 355.08 30.49 330
+3.686 356.93 30.68 336
+5.529 358.77 30.87 342
+7.372 360.61 31.05 348
+9.215 362.46 31.24 354
+11.058 364.30 31.42 360
+12.901 366.14 31.60 366
+14.744 367.98 31.78 372

I believe I've established that the formulas used for racquet matching and modification are correct — at least to the limits of my ability to cut lead tape accurately and apply it at the appropriate position on the frame. The problems seemed to arise from measuring the effects of the modifications once made. It appears that we need measuring equipment that is more accurate and with higher resolution than that currently available to the average racquet technician.

This is not a knock on the Prince PTC, as it is state of the art for professional equipment of this type. It some ways, it is better than the “industry standard” machine against which it competes.

For example, the next day I turned the PTC on again and re-ran the baseline and +64 tests. This time, I got 353 grams for the baseline mass, with a swingweight of 324 kg•cm². The two strips of lead tape showed as weighing 14.5 grams (which they would with a resolution of .5 grams), and the total mass of the racquet was 368.5 grams. Thus, the PTC was only one-half gram off at this point from the separate measurements, assuming that the measurement of 353 grams could have been as high as 353.24 grams.

After adding the lead strips back onto the racquet, the swingweight again measured 374 kg•cm². Given that the calibration method gets you within ±1, the measured swingweight is within the machine tolerance for theoretical swingweight. It’s just unfortunate that for those attempting to achieve perfection, these seemingly minute differences (including the differences between the advertised weight-per-inch of lead tape and the actual value*) can create major difficulties in measuring and applying lead tape, and checking the results of ones efforts.

Probably what we need is for racquet technicians around the world to get more involved with racquet matching and modification. The more demand there is for accurate measuring equipment, the better chance we'll have of actually seeing that equipment on the market.

* Keep in mind that under normal circumstances, racquet matching involves using strips of lead tape that still have the paper backing attached. The paper backing seems not to weigh much, and yet it is another potential source for error in the final product.