What Causes Tennis Elbow?
Many professional researchers are still looking for an answer. Damage to the tendon attaching the extensor carpi radialis brevis (ECRB) muscle to the elbow is the cause of the pain, but the cause of this cause is a mystery. However, it is fairly certain that this type of damage is the result of repetitive stresses, such as hitting a tennis ball.
Producing causes of tennis elbow may include the following mechanisms, which are offered here for comment and further investigation:
(1) Elbow Crunch is a sudden shortening of the ECRB due to impact (explained at greater length above under Elbow Crunch). This effectively is a muscle spasm that stresses the tendons.
(2) On impact, the resultant Torque twists the racquet head back, while Moment is dragging the head down, and the hand is holding the racquet steady. The resultant twist of the handle (Torsion, or Longitudinal Torque) is clockwise for a right-handed forehand. This twist winds up a catapult. When the ball leaves the racquet, the catapulting force is counter clockwise for the right-handed forehand. The two opposite screwdriver twists in a short time give a severe stress cycle to the extensor carpi radialis brevis muscle that attaches the middle of the hand to the elbow, even for a dead-centre hit.
(3) The back-and-forth catapulting stress cycle of Torque from impact twisting the racquet back, followed by catapulting the racquet forward when the ball leaves, aggravates the handle twist cycle mechanism discussed above under (2). The extensor carpi radialis brevis muscle is anchored at the elbow and at the metacarpal (hand) bone of the middle finger, on the index finger side. The resultant Torque from impact is a twist backward that tends to yank this muscle as the middle finder is extended. On impact, this muscle is either straining (on the backhand) or slack (on the forehand). On the backhand, the first twist yanks this straining muscle, further stressing the tissues attaching it to the elbow. Then the muscle suddenly loses resistance but continues to work against the combined stress, so it suddenly shortens after impact, giving an even more severe yank to the elbow. For the forehand, the muscle is slack on impact, so the catapulting stress cycle cracks the muscle like a whip, stressing the points of attachment at the wrist and elbow. Elbow straps help because they damp the whip effect.
(4) Shock becomes internal energy, which expresses itself as frame vibration, and this vibration is transmitted to the arm holding on to the racquet unless it is damped somehow. (The correct term is damped, not “dampened.”) In the old wood racquets, vibration disappeared quickly because it was damped by the flex of the wood, but the new stiffer and lighter frames do a poor job of damping, so they efficiently transfer the subtle shaking to the arm. ‘Undamped’ high frequency frame vibration can stealthily sabotage the elbow, so the price of power may be pain. Vibration of the frame shakes the extensor carpi radialis brevis muscle that attaches the middle of the hand to the elbow. This causes cyclic stressing of the tendons at the lateral epicondyle, where the fat half of this long teardrop-shaped muscle attaches. Cyclic stressing is how you break a coat hanger by bending it back and forth. Eventually, with enough stress cycles, fatigue can cause tissues to snap, even without any tremendous force.
What you don’t want if you are concerned about the risk of tennis elbow is a stiff, high-Torque, high-Moment, high-Shock racquet. That means a light, head-heavy racquet.
Poor stroking technique is frequently accused, conveniently diverting scrutiny from racquet design, but, as the calculations prove, risk factors for tennis elbow include: (1) light racquet weight and (2) head-heavy balance. Stiff frames are also bad. What is good for minimizing elbow damage is low Shock, low Elbow Crunch, low Torque, and low Moment.
What Causes Wrist Problems?
See the foregoing discussion of tennis elbow. Wrist Crunch (the muscle spasm at the wrist resulting from impact) is even larger than Elbow Crunch, so it would be relatively more important than other risk factors. Again, light and head-heavy racquets should be avoided.
Is a Lightweight Racquet a Good Idea?
No, a lightweight racquet is not a good idea, as pro customisers attest. Weight is not bad. You need weight to return a “heavy” ball (lots of pace and spin). Lightweight racquets can’t put much pace on the ball if you don’t have time to develop a long stroke, such as when you are stretched wide. Pete Sampras used a racquet that is 14 oz. and evenly balanced, and when he was going for a ‘putaway’ he choked down so the swing-weight was even higher. Andre Agassi used a racquet that weighed 13.2 ounces and 5/8 inch (5 points) head-light. Mark Philippoussis uses one that is 13.5 ounces and is 3/4 inch head light. Lest you think that these heroic sticks are as unwieldy as the sword of Goliath, remember that the lightest wood racquet was 13 ounces. Ladies and children used them.
Maybe, in the short space that you have to execute your stroke, you might swing the lightweight racquet a little faster — but swing speed is not the key.
Momentum, not energy, and not force, is what counts in a collision, and in computing momentum the racquet’s mass is just as important as its velocity (momentum = mass times velocity). Readers with baseball experience know what happens when you try to hit a hardball home run with a softball (i.e. lightweight) bat. A softball bat cannot hit a hardball very far because it doesn’t bring enough mass to the collision, and therefore its momentum on impact is low.
High Tip Speed is bad for accuracy because it is harder to time a violent swing precisely. Even if you succeed in increasing the Tip Speed enough to offset the racquet’s lack of mass, the shot will be hard to place.
Aside from the foregoing performance considerations, there is the even more important question of safety. Light racquets are bad for tennis elbow.
Most racquet customers know little about the difference between weight, Moment, and swing-weight. “Pick up appeal” (how light the frame is when you pick it up in the pro shop) is the predominant criterion (after cosmetics) for the average player. An epidemic of elbow and other arm injuries has been the result.
The touring pros know better. They add weight when they customize their racquets. A more massive (heavier) racquet will crush majestically through the ball instead of bouncing off, which makes it more comfortable on impact and more accurate.
The Effect of the Sweet Spot
An interesting fact is that the higher the centre of percussion, the lower the force acting at the racquet’s mass centre upon impact. The “centre of percussion” is the real “sweet spot.” Proper weight distribution can raise the centre of percussion significantly, and the higher the Sweet Spot, the better.
But a racquet with a relatively high centre of percussion (such as the appropriately named Hammer) is not necessarily good. Even though the Impact Force will be less due to the high sweet spot, the resulting Torque will be higher because the mass centre where this force acts is far from the hand, giving the Impact Force a longer lever arm. Comparative calculations for the light and head-heavy racquets prove that their Torque and Shock will be high, even with a high sweet spot, and so will the Work, Shoulder Pull, Wrist Crunch, Shoulder Crunch, and Elbow Crunch. What you want is high sweet spot together with head-light balance and adequate mass. Such a combination can be achieved by means of a large tailweight.
The centre of percussion is a point along the racquet’s length; it is not a “spot” having an area. Do not be misled by deceptive advertising suggesting that some manufacturer has succeeded in expanding the sweet spot from a point to an area, so that you can get sweet spot performance nearly everywhere on the racquet face. Another misconception is that there is no shock if the impact is at the centre of percussion. One resultant force from impact (Impulse Reaction) is reduced to zero, but the other (Torque) still exists, and there is still some Shock, Work, Shoulder Pull, Shoulder Crunch, Wrist Crunch, and Elbow Crunch. Even when you hit the sweet spot dead on, you feel something.
The area concept of the sweet spot concerns mapping where the coefficient of restitution (a measure of the bounce, or elasticity, of the racquet) exceeds a certain arbitrary value. It is a plot of elasticity, with the more elastic region being inside the sweet area. Manufacturers who claim a large sweet area (they call it a sweet spot) are only claiming to have succeeded in making their racquets bouncier, or more elastic. A good string job (lower tensions, thinner gauge, springy string) can also increase bounce.
The upside of more elasticity (bounce) is less Shock, Work, Shoulder Crunch, Wrist Crunch, and Elbow Crunch. The downside — especially with a large head racquet — is that your shots are less accurate. Those who can’t aim their shots anyway won’t know the difference in accuracy, but experts prefer low power (less bouncy) racquets for cleaning the lines.
The Effect of String Tension
The variables affected in the formulas by string tension are dwell time and coefficient of restitution. Dwell time is the length of time the ball stays on the strings. Coefficient of restitution is the measure of the elasticity of the collision between the ball and the racquet (high means more elastic, i.e. a livelier bounce).
Longer dwell time means lower Torque and Impulse Reaction on impact, which means better accuracy. Dwell time decreases with increasing string tension, which is bad. And, after a point, as string tension increases, coefficient of restitution goes down. Lower coefficient of restitution means higher Shock, Work, Shoulder Pull, Elbow Crunch, and Shoulder Crunch.
The conventional thinking is that loose strings give more “power” and tight strings give better “control”.
Anecdotal evidence suggests that there is truth in the rule that tight strings give better control, but it isn’t for the reason that dwell time increases. With a loose racquet, especially a big head racquet, an off-centre hit will deform the string bed more severely than it would a tight, small-head racquet (like Pete Sampras uses), and therefore there will be less certainty as to the path of the rebounding ball. Ronald Yepp points out that with a tight racquet, the ball is flattened more, so topspin is easier to produce. This would be particularly true where the head is small. Pete Sampras is a case in point: he can generate amazing topspin on his second serve using his heavy, small-head, tightly strung (75 lb.) racquet. Bjorn Borg is another. Spin gives greater control, and greater spin is possible with tight strings.
Recommendation: for power, use a midsized racquet strung with natural gut at 60 pounds because this tension gives the maximum bounce. If control is your main concern, and your stroke puts a lot of top on the ball, string very tight and use small-head racquets. Restring often because string tension decreases quickly.
The Effect of Frame Stiffness
Flexible racquets (low flex number) absorb more of the Torque from impact, with the energy going into bending the material thus reducing the risk of injuries. Anecdotal evidence from expert players is that flexible racquets also perform better, possibly by increasing dwell time. It therefore appears that the present stampede to stiffer and stiffer frame materials is motivated not by safety or performance considerations, but by a desire for more “power.”
Frame stiffness is measured on the Babolat RDC as flex numbers, which represent deflection under a 25 kilogram load on the string bed. High flex numbers mean stiff frames. A stiff frame would have the effect of flattening the ball more (if used with tight strings and a small head), thus making topspin easier to impart, and it would allow the strings to do their job better because the frame would not be deformed so much on impact.
The downside of stiff frames, as many case histories suggest is that they feel bad and probably aggravate the risk of injuries. Stiff frames may result in shorter dwell time, thus higher Torque.
The Effect of Handle Size
Bigger is better for maintaining control. A large handle size gives more area to apply friction and a wider radius to apply the frictional force in order to resist racquet twisting about its longitudinal axis (Torsion, or Longitudinal Torque) on off-centre hits. Handle size is the circumference (distance around). It can be increased by adding an over-grip, or by building out the handle under the grip with tape or shims. Bigger handles should also be better for preventing blisters.
Big tennis servers, however, prefer smaller handles. The best thing would be a handle that for ground strokes had a large circumference at the forefinger, and for serves, a small circumference at the forefinger when you choke down: i.e. a coke-bottle-shaped grip, or rounding off the bevels about 4 cm up the handle to give a tapering smaller circumference at that spot. There is no reason but herd mentality why handles have remained uniformly octagonal for so long. This smaller circumference on the serve allows the racquet to cock back farther on the backswing.
The Effect of Heavier, Larger, or Softer Balls
To slow down the men’s game, and thus hopefully to increase its entertainment value for a high proportion of viewers, the rulers of tennis want to change the balls.
The ITF has authorized a ball with a 15% greater diameter to be used “on an experimental basis.” The intention is that the bigger ball will meet more air resistance, therefore play will be slower. Fluffing the nap (felt covering of the ball) will increase diameter and drag, but apparently the intention of the ITF is to require ball manufacturers to mould a larger rubber core.
The larger diameter of the rubber core, even if the weight of rubber remains the same, will result in a higher rotational inertia (swing weight) for the ball. That means a “heavy” ball because players will be able to impart a lot of angular momentum (spin). Angular momentum is the product of the rotational inertia and the rotation speed, and the higher rotational inertia permits a much “heavier” ball at the same spin rate. High angular momentum of the ball on impact will aggravate Torsion (screwdriver twist on the handle), causing more stress on the arm of the receiver.
Another problem with bigger balls: if the same ball weight (57 grams) is to be maintained, the rubber of the bigger ball must be made thinner to stretch over the larger surface. Thinner rubber means that the air will leak out easier, and higher air pressure will be needed to maintain the same ball bounce. These balls will go flat faster. They will also be less bouncy in actual pro-level play because of higher hysteresis loss from more air being compressed. These will be soft balls.
Presently, for professional tournament play, a ball must bounce more than 53 inches and less than 58 inches when released from a height of 100 in. Using softer balls, having a bounce at the low end of this range, means higher Shock, Shoulder Pull, Work, Shoulder Crunch, Wrist Crunch, and Elbow Crunch for the players.
As can seen ‘heavier balls’ means both higher resultant forces from impact (Torque and Impulse Reaction), and higher Shock, Shoulder Pull, Work, Shoulder Crunch, and Elbow Crunch, thus with heavy balls, the game becomes more painful and less accurate.
Club players can take a lesson here, especially those who play on clay, where the balls get heavier as play goes on. Change balls often to protect your arm. Tennis balls are a bargain, so leave them on the court.
Should Your Racquet Be Head-Heavy or Head-Light?
Head-light is better, no question. A head-light racquet (balance point closer to the hand than the midpoint of the racquet’s length), has significantly lower Moment, resultant forces from impact (Torque and Impulse Reaction), Shock, Work, Shoulder Pull, Shoulder Crunch, Wrist Crunch, and Elbow Crunch. That is good.
Head-light racquets with a high sweet spot is the really smart choice for reducing the risk of tennis elbow. That means a racquet with a large handle end weight produces significant improvement.
An important additional benefit of head-light balance is that Moment is less, so the racquet is easier to position for volleys and returns, and is not so heavy to hold up all afternoon. Moreover, with a low Moment, the Torsion from impact will be small, so the racquet will be easy on the elbow. Head-heavy racquets, on the other hand, increase the risk of tennis elbow because of their high Moment and high Torque (therefore high Torsion), their high Elbow Crunch, and their high Shock.
The Effect of Mass and Swing-weight
More mass is definitely better. More swing-weight (moment of inertia) is also definitely better. The touring pros, in customizing their racquets, add mass and increase swing-weight, because they know from personal experience what really works. Their customized racquets bite on the ball more, so they are able to generate heavy spin on their forehands and serves. Pete Sampras’ heavily customized Wilson Pro Staff 85 weighs 14 ounces, about the same as the ‘old woodies’, but much heavier than the heaviest racquets marketed to the public these days.
Many customers (including those who buy at pro shops) demand lighter racquets — completely the opposite of the pros! A candid observer must find it somewhat incredible that even though the racquet makers pay the pros lots of money to display what appears to be the same racquet they are selling to consumers, in reality the racquet is not at all the same in weight or swing-weight. Players with light racquets are increasing their risk of disabling injury if they insist on banging away with a these racquets. The heavier, the better. If 14 ounces sounds big to you, consider that even ladies and juniors used to play with wooden racquets that weighed that much.
Mass is a measure of the racquet’s “inertia,” a word that means essentially its resistance to change. The change resisted by mass is change in linear (straight-line) velocity. More mass means that the racquet will not slow down so much on impact. A short, controlled swing of a heavyweight racquet can hit the ball harder than a frantic flail of a featherweight. You want a racquet that will hit through the ball, instead of bouncing off. Pete Sampras’ second serve has an incredible amount of spin on it because his racquet can bite on the ball due to its high inertia on contact.
Swing-weight is another measure of the racquet’s inertia, but it is a different kind — rotational inertia, or a resistance to change in a racquet’s angular velocity about an axis of rotation. A useful way to understand swing-weight is as the energy storage potential of a racquet. Just like flywheels, racquets store up the player’s effort. A racquet with a high swing-weight requires more effort to swing, but will not lose much angular velocity on impact, and will snap through the ball more, biting for more spin, especially if the strings are tight and the head is small.
On the forehand, the axis of rotation is 7 cm from the handle end, which is between the ring and middle fingers. Hold a racquet and waggle it to see that this is true. On the serve, where most top players use a choked-down grip over the butt cap, the swing-weight will be higher because the axis of rotation has moved to 5 cm from the handle end. In other words, swing-weight will change depending on how low you grip the racquet. Notice when Pete Sampras is going for a forehand ‘putaway’, he chokes way down over the end cap to increase the swing-weight.
Other scientific names for swing-weight are moment of inertia, rotational inertia, and Second Moment. More swing-weight is good for accuracy and comfort (low Torque, Shock, Shoulder Crunch, and Elbow Crunch).
A racquet with a high swing-weight takes more effort to whip around the axis of rotation, but on impact that investment pays off in better speed and accuracy. “Manoeuvrable” is a term loosely used to describe a racquet with a low swing-weight (although there seems to be some confusion between swing-weight and Moment as this term is used). Manoeuvrability in a racquet, under this definition, is not good, because high swing-weight is good.
Two racquets that weigh the same (have the same mass) may have very different swing-weights because of the way this mass is distributed. More mass to the head of the racquet, such as by adding lead tape, will increase swing-weight. Although more swing-weight is good, head-heavy balance is bad for your arm, so lead head tape fixes one problem but aggravates another (increasing means a higher Shock, Torque, Moment, Work, Shoulder Pull, Shoulder Crunch, Wrist Crunch, and Elbow Crunch). Lead tape to the head should be counterbalanced somehow with a tail-weight. The tail-weight will not affect the swing-weight materially because it will be close to the axis of rotation.
The Effect of Shoulder Weighting
Adding weight to the 9 and 3 o’clock positions of the head (shoulder weighting) adds swing-weight, but not as much as adding the same amount of weight to the tip. Shoulder weighting also increases the Polar Moment of the racquet, which may be necessary to counter the “heavy ball” encountered in top echelon tennis when the opponent hits with a lot of pace and topspin. The heavy ball tends to rotate the racquet, even when the impact is dead centre, thus making it more difficult to put your own top on the ball and giving an uncomfortable screwdriver twist (Torsion). A racquet with a lot of rotational inertia about its longitudinal axis will not be pushed around so much by the impact and will be more dominant in play. Shoulder weighting should be offset by a tail-weight at the handle end, so the balance is head-light.
Are Big Head Racquets Better?
No. The increased length of string to be stretched in a large racquet head gives a more pronounced ‘give’ to the string bed, and therefore presumably a longer dwell time and a more pronounced trampoline effect (higher coefficient of restitution), both of which are good. But the trade-off is that accuracy on off-centre hits may be worse because the string bed is more deformable, and therefore the path of the rebounding ball is less certain. Also, the ball is not flattened against the strings as much, so it tends to just roll down the face when you stroke for topspin. Pete Sampras plays with an extremely small head racquet (85 square inches in area). The wood racquets were even smaller (65 sq in), and the tubular metal racquets that Jimmy Connors used were smaller still, and had a head size like a squash racquet. These world number ones are persuasive authority against big heads.
Another downside of big heads is that, due to their large width, there is a bigger chance for a badly off-centre impact. With the ball so far from the centreline, the shot is a loser anyway, so better to let it miss than to have it hit way off to the side and cause a severe jolt.
If there is a weighting system at 9 and 3 o’clock, such as shoulder weighting by lead tape, this jolt can be minimized, but better not to let it occur in the first place. Accept that you will have to learn to hit the ball better, and don’t rely on “forgiveness” to improve your game!
The consensus among physical therapists seems to be that big heads are a risk factor for tennis elbow. The pros who make their living winning tournaments do not favour them. The conclusion must be that big head racquets are not better.
Are Extra-Long Racquets Better?
Sometimes. If the impact point is at its standard distance from the hand (i.e. where it would be using a 27-inch long racquet), extra-long performance is worse on ground-strokes but better on the serve. Moment is increased by the extra length, which is bad for the reasons discussed above. There is no need to adjust your striking point on the serve because you do better with the impact point at the usual distance from the hand, even though that moves the impact point lower on the face than the centre of the strings. Two-handers should definitely consider an upgrade to an extra-long.
Does a Two-Handed Shot Have Any Advantages?
Yes. The axis of rotation on the two-handed shot is between the hands, which is higher up the handle than the axis on the one-handed shot. That’s good, because decreasing r and d (please see below) improves performance under all criteria, and you get those desired decreases by shifting the axis of rotation up the handle. Many players use a two-handed backhand with good results, but few use the cross-handed forehand of Seles and Gambill. A two-handed shot has the additional advantage of allowing a much heavier racquet to be used.
r = the mass centre radius, which is the distance from the axis of rotation to the mass centre (balance point).
d = distance, in cm, from axis of rotation to point of impact.
The Effect of String Damping Gadgets
Damping gadgets on the strings damp only residual string bed vibration, and do not really protect the arm by damping frame vibration. Adding more mass to the head in the form of a damping gadget is a bad idea because it increases r in the formulas and therefore worsens performance, so the damper should be light. Pete Sampras’ string damper is just a cable grommet, and Andre Agassi uses a rubber band.
The Coefficient of Restitution
The coefficient of restitution is a measure of the elasticity of the collision between ball and racquet. Elasticity is a measure of how much bounce there is, or in other words, how much of the kinetic energy of the colliding objects before the collision remains as kinetic energy of the objects after the collision. With an inelastic collision, some kinetic energy is transformed into deformation of the material, heat, sound, and other forms of energy, and is therefore unavailable for use in moving.
A perfectly elastic collision has a coefficient of restitution of 1. Example: two diamonds bouncing off each other. A perfectly plastic, or inelastic, collision has c = 0. Example: two lumps of clay that don’t bounce at all, but stick together. So the coefficient of restitution will always be between zero and one.
Impact Impulse is simply the change in racquet momentum upon the strike
Swing-weight, also known as moment of inertia and rotational inertia, is the resistance to change in the speed of the rotation about the axis of rotation. High swing-weight means that the racquet is hard to get rotating, but once it gets going it will not be pushed around so much on impact with the ball and will tend to produce better pace and spin. Swing-weight is the infinite sum of all infinitely small mass elements times the square of their distance from the axis of rotation.