Technical Info

Did you know that professional tennis players heavily customize their racquets to add mass and swing weight, even though the ceramics would lead you to believe that they are playing with the same racquet you can buy? Why is this?

It has been estimated that half of all racquet players over 30 suffer from tennis elbow. So it is important to have good information as the consequences of a bad racquet choice are worse than the waste of your money. But how can a player make an informed choice? Racquet ads are not very informative, and often deliberately mislead. You can’t rely on what the professionals pretend to use. ‘Playtests’ depend on the personal opinion of the testers, and like all subjective tests are suspect for obvious reasons.

What’s needed is a set objective performance criteria, some quantifiable and meaningful terms instead of ad hype and subjective playtests. Here are some scientific concepts and real performance criteria for (mainly) tennis racquets:

  • Sweet Spot 
  • Moment 
  • Torque 
  • Torsion 
  • Polar Moment 
  • Impulse Reaction 
  • Shock 
  • Work 
  • Shoulder Pull 
  • Shoulder Crunch 
  • Elbow Crunch 
  • Wrist Crunch 
  • Impact Force 

 

 

 

Other commonly used criteria:

 

  • Power
  • Manoeuvrability
  • Control

 

Evaluation Criteria for Racquet Performance

1. The Sweet Spot is known as the “centre of percussion.” It is dependent on the location of the axis of rotation at the hand in the stroke. A high sweet spot, i.e. a centre of percussion close to the tip of the racquet is good because it means low Impact Force.

The sweet spot is a point, not an area, although some refer to the “sweet spot” on the racquet being “large.” Another alias for the centre of percussion is “centre of oscillation.” The “sweet” area on the string bed is where the racquet’s bounce is maximized, and this has nothing to do with the centre of percussion.

The sweet spot is determinative of the force from impact: the higher the sweet spot, the lower the Impact Force acting at the racquet’s mass centre, and the more positive the Impulse Reaction at the hand. If the balance is close to the hand, this will also mean low Torque and therefore less stress on the arm.

Generally speaking, the higher the sweet spot on the racquet face (i.e. the longer the distance from the hand to the sweet spot) the better.

2. Moment is the turning force pivoting the racquet head down when you hold the racquet parallel to the ground. Moment is a measure of how heavy the racquet feels to hold up parallel to the ground (not merely the weight of the racquet, but this weight multiplied by its lever arm).

Moment should be especially important for juniors and ladies. A light racquet having a balance point far from the hand may have a larger Moment than a heavy racquet with a head-light balance, so merely knowing the weight of a racquet is not enough, and may be misleading.

When assessing the racquet weight – What counts is Moment, not weight.

Moment is the racquet’s weight times its lever arm, which is the distance to the balance point from the axis of rotation.   The lower the Moment, the better.

Moment is key for two reasons: (1) a racquet with a high Moment is bad because it is hard to hold up and to position for volleys and returns, especially for juniors and ladies; and (2) Moment multiplied by Torque gives the Torsion, which is the screwdriver twist about the racquet’s handle centerline resulting from impacts, even impacts on the centerline. High Torsion is bad for tennis elbow.

 

Torque and Impulse Reaction are the two “resultant forces” from an “eccentric impact,” such as the impact of a racquet with a ball. This is called an “eccentric impact” because the two mass centres (ball centre and racquet balance point) do not move along the same line to a point of collision. When you hit the Sweet Spot, Impulse Reaction is zero, but there is still some Torque.

3. Torque is a bending force resulting from impact, that causes the hand to bend back and then catapult forward. Note that Torque is not the screwdriver twist of the handle (which will be called Torsion, or Longitudinal Torque), but the bending back of the racquet. Torque winds up a catapult in the wrist, which flings the racquet forward after the ball has gone. The stronger this catapulting force, the worse the whipsawing stress cycle resulting from the stroke, and thus the worse for tennis elbow — so high Torque is bad.

Some loss of energy could be expected from the conversion of Torque into the subsequent forward catapulting force, due to absorption of Torque in the bending of the racquet frame and stretching of the muscles, so it will be difficult to quantify the catapult effect. Note, however, that a stiff racquet (high Flex number) will not absorb as much of this bending force, and therefore a stiff racquet is a risk factor for tennis elbow.

Expert players tend to prefer the slim, more flexible racquets, which absorb Torque in frame bending and thereby reduce the catapulting force that flings the racquet forward after impact. The “widebody revolution” (of the late 80′s) never caught on among the pros, for good reason. Stiff racquets may be good for power, but they are bad for tennis elbow. Note that Torque depends on dwell time, and the shorter the dwell time the worse the Torque. Flexible racquets may have the advantage of increasing dwell time, although no proof of this is presently available.

 

4. Torsion or Longitudinal Torque is the screwdriver twisting force around an axis running up the handle. Such a force arises even from impacts on the centreline. This criterion is the cross product of Moment and Torque. Torsion from a centreline hit is simply the cross product (vector product) of Moment and Torque.

Both high Moment and high Torque contribute to high Torsion. For a right-handed forehand, Torsion would be a twist in the clockwise direction. This twist winds up the racquet to release in a sudden handle twist in the opposite direction (counter clockwise) once the ball leaves. The magnitude of this second twist depends on racquet stiffness (stiff is bad).

 

5. Impulse Reaction is a push (positive Impulse Reaction) or pull (negative) on the axis of rotation (the hand) resulting from impact. Impacts above the Sweet Spot result in a pull on the hand; below is a push. A positive Impulse Reaction is better because it means less Impact Force

Impulse Reaction is measured in units of force, because it is a translational force (straight ahead push or pull) on the hand. For impacts above the Sweet Spot (center of percussion), Impulse Reaction is a pull from the player to counter the yank on the hand (negative value). For impacts below the centre of percussion, Impulse Reaction is a push against the hand (positive value). Right on the centre of percussion (sweet spot), there is no Impulse Reaction at all (zero value).

Our directional convention is that positive is toward the net, so a pull is a negative Impulse Reaction. Positive is better than negative because positive Impulse Reaction adds more speed to the racquet during the impact, while negative Impulse Reaction tends to bring the head under the ball as it yanks the arm forward.

The higher the sweet spot, the more positive (less negative) the Impulse Reaction, and the lower the Impact Force.

 

6. Shock loading of the racquet results from a sudden change in the racquet’s kinetic energy on impact, which produces an internal energy load on the racquet, which is expressed as frame vibration

Kinetic energy is the energy due to motion. When an object is moving, it has a kinetic energy measured in joules by the formula KE = 1/2 Mv2. (KE is kinetic energy, M is the mass of the object in kilograms, and v is the velocity of the object in meters per second, m/s).

When a moving object collides with something stationary, like a ball hitting a racquet for example, it loses kinetic energy.

 

 

Shock also determines Shoulder Crunch , Elbow Crunch, and Wrist Crunch (See Below).  This change in kinetic energy is how much the racquet slows down when it slams into the ball, while kinetic energy is converted into internal or potential energy. Shock is measured in joules (the same metric unit as work, heat and energy). Although the term “shock” has no generally accepted definition in engineering, for our purposes we will call Shock the difference between the initial and final kinetic energy of the racquet.

 

Before impact, you put energy into the racquet to get it up to speed for the collision, and during the impact you put in a little more energy to aim the shot. After the ball leaves, the racquet mass centre (balance point) moves at a slower speed, and this means a loss of its kinetic energy (kinetic energy = 1/2 mass times velocity squared). The ball gets some of this lost energy (the same for all racquets under all benchmark conditions), and the rest becomes internal energy, wasted in bending the frame.

If the frame is stiff and light, the frame bending energy will not be absorbed by the material of the frame but will but will have to be dumped into the arm holding on to the racquet. Don’t place any reliance on string buttons to save your arm. Damping gadgets on the strings are too small in mass to do much besides reduce residual string vibration, which is a minor annoyance, and damping gadgets in the frame must be expected to handle an energy load of the magnitude determined by the design of the racquet.

The most effective vibration damper is a large particulate handle end weight (e.g. a bag of shot or sand), which serves to divert and dissipate the energy. Also effective at vibration damping is the Pro Kennex Kinetic system, which has particulate weights in the racquet head, and the Wilson Triad system, which absorbs the energy in special frame joints.

Better than damping is prevention of Shock by proper weight distribution in the racquet (head-light and heavy overall).

 

7. Work is the energy required to produce a certain ball speed with the racquet. Work measures the energy efficiency of the racquet, so low Work is good &  High Work is bad because the player has to swing harder to get the same result. Work quantifies a racquet’s power: the less work the player has to put in to get the required ball speed in the allotted time for the stroke, the more powerful the racquet. Of course, a player may put in lots of effort and get lots of ball speed, especially with high swing weight racquets, but the power comes from the player, not the racquet.

In the evaluations, head size, flex, string tension, and ball bounce are comprised in a standard bounce or elasticity) of the racquet/ball system (0.85), so Flex and Head Size — which are said to affect bounce, and therefore “power” according to the popular understanding — are not used independently for Work or “power” evaluations. We assume that all racquets are strung such that they have the same bounce.

It turns out that head-heavy racquets require a lot more Work to hit the ball fast, which is bad. They are also hard on the wrist, elbow, and shoulder, which is worse. Head-light and heavy racquets with substantial swing weight are the most efficient and therefore most powerful according to most recent studies.

 

8. Shoulder Pull is the force exerted by the shoulder muscles in opposing the centrifugal force acting on the racquet as it moves around the shoulder in the swing resulting from the player’s Work. This opposing force is called a “centripetal” force because it acts toward the axis of rotation (here the shoulder socket); Shoulder Pull is equal and opposite to the centrifugal force while the racquet is getting up to speed for the impact, and reaches its maximum the instant before impact, which is where we measure it. After impact, this centripetal force continues, but the offsetting centrifugal force is reduced because the racquet has slowed down. The excess centripetal force becomes a radial compressive force known as Shoulder Crunch.

A light racquet having a head-heavy balance (See Moment above) may  still have a large Shoulder Pull, despite its light weight, due to its distant mass centre and consequent high mass centre velocity in rotation. That is bad.

9. Shoulder Crunch is the change in the centrifugal force acting on the racquet, a change that occurs due to the impact slowing the racquet down, thus creating a sudden excess in centripetal force at the shoulder. Before, the centripetal force and centrifugal force were in equilibrium, but suddenly there is an excess centripetal force. This is effectively a muscle spasm in the shoulder muscles.

 

10. Elbow Crunch is the excess centripetal force acting at the elbow, an excess that occurs because on impact the racquet slows down, so its centrifugal force drops. The centripetal force of the muscles attaching to the elbow and the centrifugal force of the racquet in its swing had been balanced before the impact, but the sudden slowdown creates what is effectively a muscle spasm. The muscle continues to contract as if it still had a full load, so it suddenly shortens and yanks on the tendons that attach it to the elbow. This yank (Elbow Crunch) is a cyclic stress which, repeated over time, may be a contributing cause to tissue failure. Elbow Crunch is larger than Shoulder Crunch because the elbow is closer than the shoulder to the mass centre of the racquet.

Evidence now supports the conclusion that stiff racquets are a risk factor for tennis elbow. Moment is not as severe a force, but it is present for longer during play and stresses the elbow as the arm holds up the racquet.

 

11. Wrist Crunch is derived the same as Elbow Crunch, only the new distance is measured from the mass centre to the wrist, not the elbow.

 

12. Impact Force is the change in the racquet’s momentum on impact, divided by the time it occurs (the dwell time) – it is the force appearing at the mass centre (balance point) upon impact with the ball. For a smooth follow through, and for low resultant stresses on the arm, the Impact Force should be low. The higher the sweet spot, the lower the Impact Force.

 

13. Tip Speed is the velocity of the racquet tip just before impact. A low tip speed means that the swing need not be as violent to achieve the same ball speed, and therefore easier to control and more accurate.

 

14. Polar Moment is the racquet’s rotational inertia about its longitudinal axis: its resistance to a screwdriver twist. This should be high. Shoulder weighting, such as by Wilson’s Perimeter Weighting System, or by lead tape at 9 and 3 on the racquet head, increases Polar Moment, so does larger racquet head size.

 

Non-Scientific Evaluation Criteria

There is another vocabulary that one frequently encounters in discussions of racquets:

Manoeuvrability is vague jumble of Moment and swing weight, with a meaning varying from player to player. Some understand manoeuvrability to be another name for swing weight, so for them a manoeuvrable racquet is easy to slap at tough gets. Others understand it to be Moment, and a manoeuvrable racquet is one that is easy to get in position for quick reaction strokes like volleys and returns. There is a difference between Moment and swing weight, despite the common misunderstanding that high swing weight necessarily implies a head-heavy balance and therefore high Moment. It is possible to have a racquet that has a low Moment and a high swing weight. The confusion with regard to the term “manoeuvrability” has resulted in the unjust charge that high swing weight is bad, when the problem is actually high Moment.

 

Power. The weaker the player, the stronger his lust for a racquet (at any price) that promises to improve his “power.” No term features so prominently in racquet ads, yet has so little clarity of meaning. It could mean:

(1) racquet bounce (i.e. high coefficient of restitution);

(2) high swing weight (a racquet which allows you to load up a lot of angular momentum so that it will not bounce off the ball); or

(3) low Work (an efficient racquet, which requires the least player effort to achieve a given ball speed, or, which produces the greatest ball speed with a given player effort).

It appears that the common understanding of “power” is (1), high coefficient of restitution -

The coefficient of restitution is the ratio of the differences in velocities before and after the collision. In other words, the difference in the velocities of the two colliding objects after the collision, divided by the difference in their velocities before the collision.

 

Proponents of stiff materials make the claim that their racquets are “powerful” because the stiff frame recovers in time to catapult the ball forward. There is little evidence to confirm this claim – the strings are the major component in racquet bounce. Maybe the advantage of the stiff frame is that it does not flex as much initially, thus requiring the strings to stretch more on impact. Anecdotally, stiff frames with large heads are known to be bouncy, with a pronounced trampoline effect. Control, however, suffers as bounce increases, particularly with large heads. Expert players tend to prefer low “power” racquets because they don’t need any help putting pace on the ball, and they have learned the value of accurate placement.

The player/racquet system has power, with the player providing the effort and the racquet providing the interface with the ball to deliver that player effort. So, if consistent with this scientific meaning, we consider a powerful racquet to be one can achieve a certain ball speed with the least player effort per unit time, and we limit the time of the stroke, what power then becomes is the inverse of Work: low Work means high power. In the June 1999 Racquet Evaluations, Power was thus defined, but the reaction has been unfavorable because this is not the popular understanding of the term “power.” Instead, the new term will be “Efficiency.”

 

Control — everybody wants it, but nobody knows how to measure it. Just what is “control,” exactly? Power and control are generally at two ends of a continuum, so high power is low control, and vice versa.

Another meaning of “control” might be how easy the racquet is to wield, but now we have some confusion with “manoeuvrability” and all of its uncertainties. “Stability” is another vague term often heard.  The idea of controlling the shot by your effort during the impact is generally accepted by most players and coaches alike.

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