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Old 07-05-2011, 10:49 PM   #2
travlerajm
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Join Date: Mar 2006
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Default Analysis

Reserved for analysis of data:

The MgR/I value gives a measure of the racquet's natural swing frequency as it pivots about the wrist axis on a forehand.

A groundstroke can be simply modeled as a double pendulum, with the upper pendulum swinging from the shoulder, and the lower pendulum swinging from the wrist. The speed of the upper pendulum is mostly related to the length of the player's arm, while the speed of the lower pendulum is largely a function of the racquet's weight's distribution. The angular acceleration of a pendulum is proportional to MgR/I, where M is the mass of the pendulum (here in kg), g is the acceleration of gravity (here assumed 980.5 cm/s^2), R is the distance from the pivot point to the center of mass (here in cm), and I is the moment of inertia about the pivot point (here equal to Swingweight + 20MR - 100M). Thus, a racquet's MgR/I value gives a measure of its natural swing frequency.

If MgR/I is perfectly tuned to the optimum value, the racquetface angle will naturally stay constant through the hitting zone, greatly improving accuracy. If MgR/I is too low, the racquethead will lag behind the hand unless the player compensates by applying a force from the wrist, making control more difficult and the forehand stroke more sensitive to timing errors. And if the MgR/I value is too high, the racquethead will naturally move through the hitting zone faster than the hand, also making the stroke difficult to control.

The optimum MgR/I value is not the same for every player. It depends on the player's height because players with longer arms have naturally slower swings. For players about 6'2" in height, I believe that the optimum MgR/I value is about 20.8 (this is supported by the data above). For players about 5'11" tall, I believe the optimum MgR/I value is about 21.0 (this is further supported by my own personal experimentation, as I stand 5'11" tall). And for players about 5'8" tall, I believe the optimum MgR/I value is about 21.2 (this is supported by my analysis of WTA specs, which I plan to post soon).

The optimum MgR/I value is also likely dependent on the player's style of stroke or grip . For example, for players with full western grips, the importance of optimizing MgR/I may be lessened, or the stroke may be optimized with a lower MgR/I value than for an eastern grip. But for players with eastern or weak semi-western grips, I believe optimizing MgR/I is more crucial. Also, choking up the the handle will increase the effective MgR/I value.

It's my belief that the optimal MR^2 zone of ~385 arises due to circumstance, because those pros that have both high swingweight (>350) and optimized MgR/I value (~21.0) tend to have racquets with MR^2 of about 385.

There are many pros with high swingweight but suboptimal MgR/I value. And there are many pros with optimized MgR/I value but low (suboptimal) swingweight. In both cases, the MR^2 value tends be less than 380.

My opinion is that it is well worth it to tune your MgR/I value to your personal optimum for your body and your swing.

Steps for Tuning MgR/I to find your personal optimum for your swing, for maximum control.


Step 1: Get accurate measurements of racquet mass M (kg), balance R (cm), and swingweight about axis through butt end of racquet (I).

Step 2 is to calculate how much weight should be placed on the handle to move the MgR/I value to ~21.0 (to get it close).

Step 3 is to make the modification.

Step 4 is to remeasure the specs and verify that you are close to 21.0.

Caution: You're not done yet, as the most important step still remains!

Step 5: Tuning the racquet on the court:

I recommend that you grab some extra lead tape and find a wall or racquetball court. You cannot tune the MgR/I value by hitting balls that you drop -- you need the balls to be coming at you with decent velocity in order to tune the angular velocity of your stroke, so a wall is perfect for that.

The key to tuning your forehand is to unlearn your developed habit of compensating for racquet misalignment at impact by applying force with the wrist. You need to learn how to swing the racquet fluidly with a completely relaxed wrist.

A good analogy is when you go to the optometrist for the first time in your life to get glasses for near-sightedness. All of your life, you've been squinting in order to see the world. But when the optometrist is measuring the proper corrective power your eyes, it's important that you stop squinting for the first time in your life and let your eyes relax. Otherwise, you'll still need to squint even after you get your glasses or contacts.

So the same applies to tuning the MgR/I value of your racquet. You can't tell whether your MgR/I value is tuned properly if your wrist is not fully relaxed.

If your MgR/I value is slightly lower than your optimum, when you swing with a completely relaxed wrist, the racquethead will lag behind the hand at the moment of impact, causing you to naturally push your shots wide right (assuming you are righthanded). You need to resist the temptation to compensate by applying force from the wrist. It's kind of like when golfer has a slice swing and is less accurate because he has to always compensate for it.

Conversely, if the MgR/I value is slightly above your optimum, then when you swing with a completely relaxed wrist, the racquethead will get ahead of the hand, and you will tend to pull your shots to the left. The temptation here might be to convert the extra angular velocity into more topspin, but again you need to resist.

When your MgR/I value is perfectly tuned, you can simply fling your arm at the ball with a relaxed wrist, and the racquet will naturally stay perpendicular to your target all of the way through the hitting zone. This means that slight timing errors do not get punished. And you will notice that your targeting accuracy when hitting against the wall improves dramatically.

When my MgR/I value is tuned, I can hit a ball within a 1x1 foot square target almost every time. But if my racquet is slightly off, I can't hit as accurately. Compensating for the mistuned angular velocity might allow me to consistently hit the ball within a 3x3-ft square target, but why settle for that? That difference in accuracy is often the difference between winning a match and losing.

If MgR/I is too low, you can add a little more lead to the top of the handle. If it's too high, you can either remove some lead from that spot or add a dab to the tip. Don't settle for almost! Keep adjusting until you get that "in the zone" feeling.

When you are tuning for the first time, you might find it helpful to keep going beyond where it feels good until it's obvious that you've gone too far. You need to learn the difference in feel between MgR/I too low and too high.

Following all of these steps takes a lot of care and patience, but the end result is worth it.
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Last edited by travlerajm : 11-29-2013 at 09:15 AM.
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