What's New in this Update
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August 15, 2002
The 2002 Racquet Evaluations are now up. Calculations were done using a dwell time of 10 milliseconds, instead of the 4 ms previously assumed. Roland Sommer's lab results are convincing that the dwell time is much longer than previously thought. Changes in specs for 3 from Pro Kennex resulted in some shift in rankings. The changed specs were not the result of a design change, but of new measurements entered in the USRSA database, which were within the manufacturer's tolerances. PK, to its credit, insisted that the latest measurements be used, even though its rankings suffered somewhat. The PK 5g is still near the top of the rankings (4), but no longer best. That honor this year goes to the Prince Original Graphite OS. The Yonex Muscle Power 3i is a very impressive new introduction, ranked best for beginners and 2 for Experts. Bringing up the rear are the Wilson Triads and the Babolat Nanotubes.
August 17, 2001
The Pro Kennex Kinetic Pro 5g has not changed in its specs from last year, although the paint has changed. That means the Top Thirty table is inaccurate, in that it leaves out the PK 5g, which topped the survey last year and should again this year. The explanation for this mixup is this: PK sent a cosmetic sample to the USRSA for the purpose of taking a photograph. For some reason, this sample did not have the specs of the production model, but nevertheless its measurements replaced those of the old 5g in the new USRSA specs table for 2001. It was the only racquet that changed from 2000 to 2001, although now I am told by Slazenger/Dunlop that the Pro Braided has been changed too, and will have an even instead of head-light balance. Its cosmetic has also been changed from the old black and white. Doing the rankings is a big task, and to redo them now because of the error in the PK 5g specs is a daunting prospect. So please take note that the 5g is an outstanding racquet.
August 2, 2001
The balance specs in the Old Racquets table have been changed to show points head-light instead of points head-heavy, to be consistent with the table showing the specs of Current Racquets. Also, the confusing red lettering on some entries has been removed. The Dunlop/Slazenger rep says that the Slazenger Pro Braided has not only been given a new cosmetic but also an even balance, so the rankings are only for the old black and white model. The confusion about the USRSA measurements of the PK 5g has not yet been cleared up.
July 15, 2001
The Manufacturer Report Card updates are now up.
July 13, 2001
The new racquet evaluations are up. Manufacturer Report Card updates will follow later, but the Top/Bottom 30 racquets for experts and Top/Bottom 30 for beginners are now available, along with rankings under the evaluation criteria and all of the new specs. The separate rankings for skill/strength level have been added to aid consumer choice. Noteworthy is what happened to the ProKennex Kinetic Pro 5g: this top performer in last year's survey is now only a mediocre racquet, as the 2001 version has totally new specs. Beware. The Prince Triple Threat line made a very strong showing, and the new Dunlop Adrenaline line made an outstanding debut. See the 2001 portal page. Many thanks once again to our friends at USRSA for providing the database of racquet specs that was used in these calculations.
October 3, 2000
A Flex ranking table has been added.
July 1, 2000
Tables for Tip Speed and Sweet Spot were added. Tip Speed derivation has been added to the Derivations page. A page on how to use the rankings was added, as well as a page explaining the units of measurement used in physics, including conversion factors for English-metric units. Tip Speed is easy to find, and it may reveal why some racquets are reputed more accurate than others. I would appreciate some feedback on this before Tip Speed is included in the evaluation criteria. Thanks to all who have contributed their suggestions for improving the site, and for fixing missing links.
June 26, 2000
Manufacturer report cards and rankings under the performance criteria have been added to the June 2000 Rankings.
June 22, 2000
The June 2000 update, now with 187 currently available racquets, has been posted. The specs for the discontinued racquets are still available here, but no evaluations include them. The Introduction has been substantially revised. There are now five benchmark conditions, instead of only two: the first two that have been used previously (110 mph serve, 70 mph forehand received at 20 mph), plus three new ones: a 40 mph volley received at 40 mph, a 50 mph return received at 50 mph, and a 70 mph serve. The results from the five benchmark conditions were weighted according to the magnitude of the forces because some (particularly the Second, the 110 mph serve) were more severe than others. There are now five macro criteria: Efficiency, Elbow Safety, Shoulder Safety, Wrist Safety, and Dexterity. Efficiency is the measure of how much ball speed you get for your effort, and Dexterity is how easy the racquet is to wield, taking into account the weight, swingweight, and Moment. Flex has been incorporated in the rankings as one component of the macro criteria. There is now a formula for calculating the force from impact, and it turns out that the torque from that force is the same as Torque, which was independently derived, which proves that the Work derivation is OK. Wrist Crunch and Wrist Safety have been added as criteria because of the incidence of wrist injuries. The Racquet Specs now include head size, flex, and price. Thanks to Crawford Lindsey and the kind folks of the USRSA for providing these. There is now a customizing guide for matching the balance, weight, and swingweight of two racquets so you will have an identical spare in your bag.
January 13, 2000
Additional sections have been added to the Introduction: The Effect of Handle Size, The Effect of Heavy, Large Diameter, or Soft Balls, Impact Impulse, and Polar Moment. The discussion on using the Parallel Axis Theorem for finding racquet swingweight has been expanded to include a more complete formula derivation.
October 25, 1999
The derivation of the formula for new balance point resulting from adding weight has been added, and the formula added to the Formulas page. In the Idiot's Guide, two new tables have been added, showing the average weight and balance of the best and worst 50 out of 296 racquets under Elbow Crunch and Work. These tables prove that heavy and head-light is good, and light and head-heavy is bad, both for safety and performance, despite the hype you might hear from other sources.October 20, 1999
An additional 20 racquets, Fall 99 introductions, are in the Measurements page, which now includes how many points head-heavy (or head-light, minus) the balance of each is. There are some important new ones that have not yet been published, so the new rankings will wait on these. For customizers, a table has been added showing the effect of adding lead tape, with an easy formula to use for calculating the resulting balance point from any weighting modification. The Complete Idiot's Guide to Choosing a Tennis Racquet was in the October 15 update of TennisONE.September 23, 1999
A new performance criterion, Impact Impulse, has been added. This is the amount of momentum change of the racquet on impact with the ball. The derivation is included, and the Formulas Page has been revised.August 30, 1999
TennisONE now has a Racquet Research page, mirroring some of this site. If you haven't discovered TennisONE yet, check it out. Also recommended is the expertly moderated BBS on Racquets at Tennis Warehouse.
August 4, 1999
The discussion of tennis elbow has been collected all in one place in the Introduction. A new feature, a simplified summary entitled The Complete Idiot's Guide to Choosing a Tennis Racquet has been added. For the Top 30 in the June 1999 Evaluation, the results under the ten evaluation criteria have been added. Lots of recent interest in this site.
July 9, 1999
New discussion on the effect of frame stiffness and the effect of shoulder weighting has been added, as well as a re-examination of the effect of string tension in light of the fact that tight strings flatten the ball more so that topspin becomes easier to produce, thus giving greater control. Thanks to Ron Yepp for pointing this out. Thanks to all of the correspondents for their comments and suggestions.
July 4, 1999
Tailweighting, rather than counterweighting, is now the preferred term -- thanks to John Yandell. The links page now includes links to video clips of classic strokes at the marvellous TennisONE site.
June 14, 1999
The amazing effect of counterweighting is shown by the example of a Wilson Hammer 6.2 95 customized by the addition of a handle end weight, which added an inch to its length and 136 grams (that's right, about 5 ounces) to its weight. The radical balance point shift and big weight and swingweight boost raised the sweet spot way up and dramatically improved its performance under all evaluation criteria, so it became better than even the best racquets (!!). Measurements are included. Some additions to the June 1999 rankings were posted today. New pages show the best racquets under the particular evaluation criteria, plus the average and median values for the 276 racquets evaluated.
June 10, 1999
The June 1999 rankings of 276 racquets were posted today. The Introductory Discussion of the evaluation criteria has been revised yet again. New macro criteria (Elbow Safety, Shoulder Safety, Power, and Control) are explained, and used for the overall rankings. Rankings under the performance criteria are available through the rankings portal page.
June 3, 1999
The introductory discussion of the evaluation criteria, and the frequently asked questions, has been revised. Two additional evaluation criteria (Shoulder Crunch and Elbow Crunch) have been added. See also the changes in the derivations page. These two forces (in Newtons) result when the racquet mass center slows down in collision with the ball, resulting in a change in the centripetal force acting at the shoulder and at the elbow. For the shoulder, the change in centripetal force crunches the arm bone (humerus) into the shoulder as the muscles that were straining to resist the shoulder pull on the swing are released from their load but continue to contract. For the elbow, the crunch is on the extensor carpi radialis brevis (ECRB) muscle associated with tennis elbow, and it's greater than the Shoulder Crunch. The higher the Shock, the worse the Shoulder Crunch and Elbow Crunch, so Shock is an even more important criterion for safety. New evaluation tables and rankings will follow shortly. Thanks to all of the many correspondents who have made this work worthwhile.
February 6, 1999
There are new links to the surprising findings of John Yandell and his research group on typical ball speeds after bouncing. There is about a 50% loss in speed! Therefore, the assumed ball speeds in the First Benchmark Condition (70 mph before, 80 mph after impact) are somewhat heroic. To make the raw numbers of the performance criteria more intelligible, perhaps several indexes (e.g. Shoulder Safety), comprising the relevant performance criteria, should be added. I would appreciate some feedback on this.January 25, 1999
New evaluations and rankings have been posted, including the new Spring 99 offerings. There are now 228 premium racquets evaluated on this site, and ranked under the performance criteria. For the Second Benchmark Condition (110 mph serve) rankings under Impulse Reaction, I've decided not to exalt power (positive IR) over accuracy (close to zero IR), but to count positive differences from zero only half. Also, for the First Benchmark Condition, I've decided to use different ball speeds: 70 mph incoming and 80 mph outgoing. John Yandell's recent ball speed measurements show that by the time the receiver hits the ball, a serve has lost much of its speed. The old figure of 80 mph incoming was unrealistic. A correspondent pointed out an error in the calculations for Shock and Work: although the formulas were correct, spreadsheet typos caused an error. Thanks to Luigi Tonelli for checking the calculations. This error has now been corrected and all rankings and performance tables are completely redone to take into account the new First Benchmark Condition. For the rankings, I've decided to use the following criteria for the First Benchmark Condition, weighted equally: Moment, Torque, Impulse Reaction, and Shock. For the Second Benchmark Condition, the following criteria are used, weighted equally: Torque, Impulse Reaction, Shock, Work, and Shoulder Pull. Thanks to all of the correspondents for their support and suggestions, as well as their interesting questions and observations. This site is meant to be a collaborative effort to improve understanding of our sport.November 17, 1998
The discussion on the effect of string tension and on big head racquets has been expanded to include the downside for accuracy on off-center hits of a more deformable string plane. A transposition error in the Torque formula has been fixed (the derivation is correct).November 5, 1998
Rankings for 196 racquets have been added to the October 1998 evaluations. I'd like to do a section on racquetball racquets. What I need is: weight of a racquetball; ball speed before and after on a typical shot; ball dwell time; and typical coefficient of restitution (how high does the ball bounce off a racquetball racquet when it's dropped from a height of 1 meter?). Please help if you can.October 26, 1998
Added to the Introduction is a section on the pros and cons of large racquet heads.October 5, 1998
The last update was July 6, 1998. Since then, most of my time has been spent putting up another website, www.e-classics.com. This has an abridged and annotated version of Plutarch's Lives (15 biographies of heroes of Ancient Greece). It also has a vocabulary builder feature with a frame that displays definitions of words that you click in the text. It's meant for SAT verbal preparation and for foreign students who want to polish their English while reading the most famous classic of Western literature. Tennis players, who understand heroic exertion and sacrifice, should find this work of particular interest. Please check it out.In the September 9, 1998, issue of the San Francisco Examiner, there was a long front-page article on this site in the Business section. The reporter, Matt Beer, discovered that "pick up appeal" (how a racquet feels when you pick it up in the store) was the second most important factor in buying decisions, after cosmetics. This site has highlighted a raging debate in the industry over whether racquets are becoming too light for safe play.
Another criterion has been added to the previous seven. This is Longitudinal Torque, or Torsion, which is the twist about the racquet's centerline resulting from impact. We all know that there is Longitudinal Torque from off-center impacts, but what's new is that there will be Longitudinal Torque even for a dead-center hit, due to the interaction between Moment and Torque. Longitudinal Torque is the cross product (vector product) of Moment and Torque, and it produces a stress cycle of back and forth twists in the handle, which may have some effect on tennis elbow.
The two benchmark conditions have been changed to reflect the common experience of amateurs. Many more racquets have been evaluated. Instead of huge tables to download, I've opted for tables for each manufacturer.
Rankings will be done soon. In the rankings, I have tentatively decided to use the following formula:
For the First Benchmark Condition, a groundstroke, the most important criterion is Longitudinal Torque because of its relation to tennis elbow. This criterion comprises Torque and Moment, so it would be redundant to use all three, and so only Longitudinal Torque is used, and is weighted twice as much as the other two factors, Shock (which affects vibration), and Impulse Reaction (which affects accuracy). Work and Shoulder Pull are relatively insignificant on groundstrokes, so they have been omitted.
For the Second Benchmark Condition, the serve, Longitudinal Torque is immaterial because the racquet in the serve is practically pointing straight up, so the Moment is zero. Moment is disregarded, and so is Torque (which is a bending moment comprised in Shock). The four criteria used are Impulse Reaction, Shock, Work, and Shoulder Pull, and all are equally weighted for the overall rankings.
The October 1998 racquet evaluations were done using data from the US Racquet Stringers Association publication, Stringer's Assistant, June 1998 (pp. 12 et seq.), compiled by the tireless diligence of Crawford Lindsey. Several racquets have been omitted because of obviously erroneous data, such as a head-light balance given for the Wilson Hammer 6.2 and 5.0. Regrettably, I have no confidence in the rest. But, to my knowledge, this is the best available data because manufacturers are for some reason reluctant to publish the four vital statistics (weight, balance, swingweight, and length). Swingweight for strung and gripped racquets is the most difficult measurement to find, and when given you can't determine if it's for strung and gripped racquets, or where the axis of rotation was, so the swingweight measurement is useless. The industry standard measuring device, the Babolat RDC, is crude and appears to be subject to wide error unless Babolat can convince me otherwise. These data from Stringer's Assistant are for strung and gripped racquets, and appear at the right end of each table, highlighted in green.
Thanks to all of the correspondents and their suggestions. Together I hope we'll succeed in building a resource that will shine some light on the plague of tennis elbow.
Now, go to the revised Introduction where the new tennis elbow mechanism is described.