To wrap things up there will be a Part 3 to this series in the near future. We'll take a break from tennis elbow and next month talk with Crawford Lindsay of the United States Racquet Stringers Association.

Physics of Tennis Racquets

A number of papers have addressed mechanical aspects of tennis -- notably the racquet-ball interaction. Professor Howard Brody, a physics professor from the University of Pennsylvania, is clearly one of the most respected researchers in this field.

With the appearance of the then new 'oversized' racquet, Brody wrote the first of many influential papers. Titled Physics of the tennis racquet (1979), the work primarily discussed the center of percussion, the coefficient of restitution of the ball, and the oscillations or vibrations of the racquet. A second paper, Physics of the tennis racquet II: the 'sweet spot' (1981), noted three definitions of the sweet spot on the stings of the racquet: the point giving a maximum in the coefficient of restitution (i.e., where the ball is returned fastest); the center of percussion (the point at which the impact gives no reaction impulse at the racquet handle); and the node, the point at which being struck by the ball results in minimal vibrations in the racquet. A third paper, Physics of the tennis racquet III: the ball-racquet interaction (1997) defined a simple, rigid model of a racquet, with strings, interacting with a ball which is applicable to the newer, rigid, composite racquets.

Biomechanics of the ball-racquet-arm system

A great deal of research has been carried out on the forces transmitted from the racquet to the arm during and immediately following the ball impact. In 1976, Professor Herbert Hatze from the University of Vienna, Austria published the equations of motion of the racquet during the ball impact, allowing for both the string deflection and bending of the racquet. (The wooden racquets of the time bent significantly; of course modern composite racquets bend much less and can be reasonably modeled with the simpler Brody approach we discussed above.) He also performed experiments on a wooden racquet instrumented with strain gauges and optical sensors sensitive to bending of and vibration of the racquet. Experiments were performed with balls striking the racquet while it was clamped, held by a player and swung by a player.

His main (and very important) conclusion was that the impulses at the racquet handle were strong enough that the player could not significantly counteract them. Why is this important? It means that the reaction on the hand and wrist from the ball's impact can be treated as a physical displacement (jerk) and twist. For a particular stroke, Hatze showed the racquet handle might jerk about 1 mm regardless of how strong or light the player grip is. Although the reaction in the arm (the forces in any given muscle) may depend on how tightly the handle is gripped, the grip strength will have minimal influence on the distance the handle jerks.

Another interesting result Hatze showed was that although the time the ball is in contact with the racquet's strings is in the 3-7 millisecond (ms) range, the vibration of the racquet continues for typically another 40 ms afterwards.

Dr. Duane V. Knudson has conducted a great deal of research into forces induced in the arm by the tennis racquet. Knudson and White (1989) reported on experiments using "pressure pad" type sensors on the grip of a tennis racquet to measure the forces between the hand and the racquet during a stroke, and vibration sensors on the racquet. The racquet was used by seven expert players on forehand drives from balls fired from a machine.

Using the same instrumentation as above, including three-dimensional cinematography, Knudson (1991a) investigated the variability of the hand forces. He found that the hand forces were somewhat correlated with both pre-impact grip tightness and off-center impacts; and recommended that tennis elbow sufferers grip the racquet lightly, and use a racquet with high polar moment of inertia (more on this next month).

Knudson (1991b) then evaluated the Forces on the hand in the tennis one-handed backhand, considered to be the key stroke for tennis elbow. Using two pressure pad type sensors in the grip he noted there was less variation between players and strokes than for the forehand case, and also higher forces at one point on the grip.

Tomosue et al (1991) measured vibrations in the racquet handle and in the player's wrist during forehand drives. No significant differences between 7 Dunlop racquets were found. They also found that off-center ball impacts gave 1.9-3.1 times greater vibrations in the wrist -- and that the wrist vibrations were about one tenth of the racquet handle vibrations.

Hatze (1991) investigated The effectiveness of grip bands in reducing racquet vibration transfer and slipping. Tennis balls were fired at a racquet gripped in an artificial arm. The 'arm' was fitted with a range of pressure and acceleration sensors. He tested 26 band grips (commercially available damping material designed to be wrapped around the racquet grip in order to reduce slippage and vibration transfer). Only small vibration reductions were found (maximum vibration reduction of 5% compared with a control leather grip) which suggested that relaxing the grip is much more effective than using these bands.

Hennig et al. (1992) performed experiments to address the Transfer of tennis racquet vibrations onto the human forearm Using accelerometers at the wrist and elbow on 24 players vibrations induced in the arm during simulated backhand strokes were measured. Each player tested 23 different racquets. They found (in contrast to Tomosue et al. 1991) some difference between racquets. In agreement with Tomosue et al. they observed greater vibrations, by a factor of 3, when the ball strikes the racquet off- center. They also find vibration levels at the elbow to be approximately a third those at the wrist.

Roetert et al. (1995) reviewed some previous work on muscular activity during tennis strokes in The biomechanics of tennis elbow, an integrated approach and in particular electromyographic (EMG) analysis. (EMG is a method of determining muscle activation.) Using indwelling wire electrodes (which penetrate the skin and actually go into the muscles), Morris et al. (1989) observed high levels of wrist extensor muscle activity (especially the extensor carpi radialis brevis -- diagram available in last months column) during the acceleration and follow-through phases of the backhand and the cocking phase of the serve and suggested that this may be one reason for the predisposition of these muscles to injury. Giangarra et al. (1993) also using indwelling wire electrodes to obtain EMG data from five forehand muscles presented evidence explaining why a two-handed backhand was much safer. Adelsburg (1986) using surface electrodes (a noninvasive method, doesn't penetrate the skin) tried to relate forces in the muscles to changes in grip size and although they found some significant differences between different sized grips, they did not find differences during backhand strokes.

Yet with all of this research one key question still hasn't been answered: how the injury arises physically; what combination of mechanical stresses causes the inflammation, strain, or tears to the tendon at its attachment to the bone.

We'll conclude this segment at this point. As I mentioned there will be a third article on this subject to tie things all together.

Again I'd like to thank my good friend Dr. Alison Cooke for her assistance in preparing this column.

Until Next Month ... Jani

References:

Adelsberg, S., "The tennis stroke: an EMG of selected muscles with rackets of increasing grip size", American Journal of Sports Medicine vol. 14 (2), 139-142, 1986.

Brody, H., "Physics of the tennis racket", American Journal of Physics vol. 47 (6), 482-487, 1979.

Brody, H., "Physics of tennis II: the 'sweet spot'", American Journal of Physics vol. 49 (9), 816-891, 1981.

Brody, H, "The physics of tennis III: the ball-racket interaction", American Journal of Physics vol. 65 (10), 981-987, 1997.

Cooke, A.J., Roussopoulos, K., Pallis, J. M., Haake, S., "Correlation between racquet design and arm injuries," 4th International Conference of the Engineering of Sport, September, 2002.

Giangarra, C.E. et al., "Electromyagraphic and cinematographic analysis of elbow function in tennis players using single- and double-handed backhand drives", American Journal of Sports Medicine vol. 21, 394-399, 1993.

Hatze, H., "The effectiveness of grip bands in reducing racquet vibration transfer and slipping", Medicine and Science in Sports and Exercise vol. 24 (2), 226-230, 1991.

Hatze, H., "Forces and duration of impact, and grip tightness during the tennis stroke", Medicine and Science in Sports vol. 8 (2), 88-95, 1976.

Hennig, E.M., Rosenbaum, D. and Milani, T.L., "Transfer of tennis racket vibrations onto the human forearm", Medicine and Science in Sports and Exercise vol. 24 (10), 1134-1140, 1992.

Knudson, D.V. and White, S.C., "Forces on the hand in the tennis forehand drive: application of force sensing resistors", International Journal of Sport Biomechanics vol. 5, 324-331, 1989.

Knudson, D.V., "Hand forces and impact effectiveness in the tennis backhand", Journal of Human Movement Studies vol. 17, 1-7, 1989.

Knudson, D.V., "Forces on the hand in the tennis one-handed backhand", International Journal of Sports Biomechanics vol. 7, 282-292, 1991.

Knudson, D.V., "Factors affecting force loading on the hand in the tennis forehand", vol. 31 (4), 527-531, 1991.

Morris, M. et al., "Electromyographic analysis of elbow function in tennis players", American Journal of Sports Medicine vol. 17, 241-247, 1989.

Roetert, E.P., Brody, H., Dillman, C.J., Groppel, J.L., and Schultheis, J.M., "The biomechanics of tennis elbow: an integrated approach," Clinics in Sports Medicine vol. 14 (1), 47-57, 1995.

Roussopoulos, K., and Cooke, A.J., "Correlation between racket design and arm injuries: A feasibility study report," Technical report prepared for the International Tennis Federation, 2000.

Tomosue, R., Mutoh, Y., Yoshinari, K., and Kawazoe, Y., "Measuring the vibrations of a racket handle and the wrist joint in the tennis forearm drive", Abstracts from International Society of Biomechanics XIII, 1991.