A New Twist on the Twistweight of a Tennis Racquet
By Howard Brody
One of the most important parameters of a tennis racquet, the “twistweight,” is rarely reported on. It is relatively easy to determine a racquet’s weight (all it takes is a scale) or a racquet’s balance point (a knife-edge and a ruler are needed). The swingweight of a racquet can be determined if you have a racquet diagnostic device, which is commercially available, but somewhat expensive. To the best of my knowledge, there is no commercially available instrument to determine twistweight, yet it is an important parameter that greatly affects how a racquet plays.
What is twistweight?
The twistweight (also known as the polar or roll moment of inertia) is a measure of the stability of the racquet to resist twisting around the racquet’s long axis. If you hit a ball dead smack in the center of the head, the racquet will recoil, but not twist around its long axis. If you hit a ball and inch or so away from the axis toward the 3 o’clock or 9 o’clock side of the strung area, in addition to recoiling, the racquet will twist around its long axis. The bigger the racquet’s twistweight, the less the racquet will twist when the ball impacts off-axis. In other words, it will be more stable against miss-hits.
In addition, because energy goes into a racquet’s spinning motion when there is an off-axis impact, the ball will rebound with less speed. The power you get out of a racquet degrades the further your impact is from the axis, but not as badly when the racquet has a large twistweight.
Because twistweight is a measure of the racquet’s stability against twisting and its uniformity of power, you might assume the bigger the twistweight, the better the racquet. This is not always the case. As the racquet’s twistweight increases, the racquet’s maneuverability decreases, so you must balance one against the other. Do you want a more stable racquet that has a more uniform response across its face or do you want maneuverability? A top-flight player with excellent eye-hand coordination, who rarely hits the ball off axis, will choose maneuverability. The recreational player, who tends to hit the ball over a larger area of the head, should go for stability and uniformity of response.
What determines the twistweight of a racquet?
The technical definition of twistweight is the sum of the square of the distance of every bit of mass in a racquet from the long axis. This definition does not directly help a player, because that sum is an impossible calculation. The wider the racquet’s head, the greater is the twistweight. Because twistweight goes as the square of the distance the mass is from the axis, if a racquet is 25 percent wider (10 inches versus 8 inches) it will have a 50 percent greater twistweight. Adding lead tape at 3 and 9 o’clock will increase the twistweight, but adding tape only at 12 and 6 o’clock will not increase the twistweight.
Measuring the twistweight of a racquet
In the laboratory, twistweight can be measured using a calibrated torsion pendulum. Because players and tennis technicians do not usually have a torsion pendulum handy, this is not a good solution for the average person.
There is a theorem in physics that says the twistweight (or polar moment) is the numerical difference between the swingweight (or moments of inertia) measured around the other two axes of the racquet. This is fine, if you can measure swingweight to an accuracy of a fraction of a percent. Because this accuracy is not readily achievable, this is also not a good method for determining twistweight.
There are several other possible solutions to the problem. The racquet manufacturer could list the twistweight of their racquet or the USRSA, which publishes the specifications of most racquets available on the market, could list twistweight in their annual Racquet Selection Map.
Another solution is that the twistweight of a racquet can be measured by using the procedure given on page 48 of the book The Physics and Technology of Tennis and using the following equation:
The method is shown on the USRSA on-line twistweight calculator, and it is relatively straightforward. You simply tap the racquet to set it in a pendulum motion, time how long it takes to make 10 swings, and you plug your numbers into the formula. A problem arises if the balance point is outside of the strung area of the head, which is true in many cases. Then the procedure is more complicated as shown in Figure 3 and described in the book of page 49. To get around this difficulty, you can shift the balance point well up into the strung area by adding weight to the tip and then use the method shown in Figures 1 and 2. Weight added at 12 o’clock will NOT change the twistweight, because it is on the axis of the racquet (it will greatly change the swingweight and balance, so remember to take the weights off after the measurement). To test this method, the twistweight of a racquet was measured with no extra weight on the tip, 50 grams added and then 100 grams added. The twistweight came out the same in each case, as long as the total mass (racquet plus addition) is used in equation at left.
There is, however, a simpler solution to the problem. Because it is only the relative value of the twistweight from one racquet to another that is of importance, not the actual value of the twistweight that is needed. The twistweight of a frame scales fairly well with the mass of the racquet multiplied by the square of the head diameter. This is fully explained in The Physics and Technology of Tennis and is presented here in Figure 4. A player can easily compare the relative twistweight of any two frames by just taking m (mass of the frame) and multiplying it by D² (the head diameter, D, squared). If all you want to do is compare two frames, it does not matter what units you use for m and D, (grams, ounces, inches, or centimeters) as long as you use the same units for both racquets. [USRSA’s on-line Twistweight Estimator makes this method even easier.] This method will not work well if the manufacturer has added extra weight at the side of the head as Wilson did in its PWS racquets or as Prince presently does in its Triple Threat frames.
In general, the value of the mass times the square of the diameter is about 16 to 18 times the measured twistweight. This means that using the mD² formula and dividing by 17 will usually get you within 10 percent of the correct twistweight value. For racquets such as the Prince Triple Threat series, the value is about 14.5, which means that those frames are somewhat more stable than a frame of comparable weight and size that does not have the extra mass added in the head.
Player sensitivity to twistweight
In a study of college varsity players, it was found that they could distinguish two racquets apart if the twistweights differed by more than 5 percent. In a related study, the same players required a difference in swingweight of at least 2.5 percent to distinguish two otherwise identical racquets (same balance, total weight and twistweight) from each another. Adding 5 grams to the racquet head at the 3 and the 9 o’clock locations increases the twistweight by about 10 percent, so a good player should be able to distinguish it from an unaltered frame.
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