Controlling the Spin Axis of a Tennis Ball by Dr Paul Zarda

Dr. Paul Zarda of Sanford Florida has been working on a racquet that will increase rebound spin of a tennis ball. His patent can be found here:  https://www.google.com/patents/US20140274494 This patent offers an inner and outer frame that are tied together with isolators. 

 Figure 1 shows a basic depiction of the racquet with 4 isolators. A description of the tuning of the isolators to generate spin can be found in the patent. This article will talk about another important attribute of this racquet design.

Dr. Paul Zarda of Sanford also notes another important property of the spin control system invention is the ability to generate consistent and controllable spin, with properly designed isolators, for complex positions of the racquet as ball contact is made. 

Referring to Figure 3, if each discrete isolator has the same stiffness in the X and Y directions of coordinate system 305 (Kx and Ky of Figure 2), it can be mechanically shown that the global stiffness KGx and KGy of Figure 3 is the sum of the individually stiffnesses Kx and Ky of each isolator. Since KGx and KYy are the same value, it can be shown mathematically that the stiffness that the inner frame “sees” in any in-plane direction is exactly the same (the KGx = KGy value). This allows the tuned isolation system to respond exactly the same no matter the direction that in-plane load is applied. Figure 4 illustrates a tennis ball’s incoming projected trajectory onto the spaghetti racquet XR-YR plane is path 1501. While the spaghetti will offer some kick-back rotational spin increase for path 1501, path 1502 will improve ball spin; and path XR, the most effective re-bound energy direction, will offer the best opportunity to improve ball spin. 

The spaghetti racquet’s (and similarly open string pattern racquets’) ability to offer spin increase is directionally dependent on ball impact direction as implied in Figure 4.

Figure 5 illustrates the same condition just discussed for the proposed spin control system invention. For the condition of Kx and Ky equal and the same for all isolators, KGx and KGy are equal. Hence the in-plane stiffness that the inner frame ‘delivers’ to the ball, for any in-plane direction, including 1503, 1504, XR and YR (of Figure 5), is the same. The proposed spin control system invention can be designed to be a directionally independent system. Conversely a combination of isolators could be intentionally introduced to provide a different stiffness in the XY plane at varying angles as desired for a given player. 

Figure 6 illustrates a depiction of a racquet that is being swung and defines the court coordinate system and the racquet coordinate system. The global coordinate system 1508 is fixed on the tennis court 1509, and coordinate system 1510 is moving with the racquet. 

 Figure 7 illustrates a racquet being swung, as it goes from the open frame position 1505, to the position 1506 where it makes ball contact, to the closed face 1507 position after ball contact. At the moment of ball impact, the local racquet axes 1510 (see Figure 6 and position 1506 of Figure 104) are lined up with global axes 1508.  Hence at impact, the racquet is parallel to the ground (the YG-ZG plane). In this case the YR-axis does not intersect the ground (see Figure 7).

Figures 8 and 9 show contrasting racquet swings.  Ball impact occurs in position 1506 for Figure 8. A ball impact for this situation would get maximum spin effectiveness for a spaghetti or open string pattern (as well as the present invention). The resulting trajectory will occur in an XG-ZG coordinate plane.

Paul Zarda of Orlando and Sanford notes for a swing illustrated in Figure 9 for position 1506, the results are different. Position 1506 could occur when a player is striking a ball near the ground (not an un-common situation). Note that the XR axis intersects the ground for position 1506, and the swing would cause a ball impact similar to vector 1501 or 1502 of Figure 4 (for the spaghetti), or 1503/1504 of Figure 5 for the spin control system invention. Since the racquet swing motion is from minus XG to plus XG for top spin, while the racquet rotates about the YG axis, the spaghetti (or open string pattern) would cause a ball spin somewhat about YR and not YG. This would cause a reduced spin effectiveness of the racquet, as well as spin would occur about the YR axis. YR-axis spin would cause the ball aerodynamically to move out of an XG-ZG plane; this means a reduction in control/accuracy of the spaghetti or open string pattern system. In contrast, for this invention, there would no reduction in spin effectiveness of the racquet (see Figure 5 discussion), and the racquet system design, with the previously defined player’s swing motion 1506, would cause a ball rotation about YG and not YR. This would result in a pure XG-ZG plane trajectory, hence providing an effective increase in ball spin, with the corresponding control and accuracy.

A complete description can be found here:  https://www.google.com/patents/US20140274494