The equipment and clothing of tennis players has evolved immensely from the 1970‘s when Jimmy Connors wore white short shorts and used a perfectly round metal tennis racquet with 70 square inches of string bed compared to the longer multi-colored Bermuda shorts worn by Roger Federer today who uses a tennis racquet with 104 square inches of string bed, made from karophite, a type of graphite. Today, technology and engineering, based on physics, has produced tennis racquets specifically designed to increase power and control, with a significant sweet spot.
The physics behind the design of a tennis racquet begins with understanding where the long axis of the racquet is located. If you put the tip of the racquet on the ground and spin it, the long axis is the line around which the racquet rotates. The long axis of the racquet is an imaginary line from the tip of the frame to the end of the grip. The goal is to hit the ball at a point or sweet spot along the long axis of the racquet so that maximum ball speed is produced with minimal shock, vibration and twisting of the racquet handle.
Just like a baseball bat, a tennis racquet has a sweet spot. In fact, tennis racquets have 3 different sweet spots. In general, the sweet spot is the point on the string bed that produces the best combination of power and feel, with the least amount of effort. The greatest coefficient of restitution (COR) point of the string bed produces the most power. The coefficient of restitution sweet spot is the point where the ball will rebound from the string bed with the most speed. A second sweet spot is called the node of the first harmonic (Node) and is the point on the string bed that produces the least vibration of the racquet on impact with the ball. A third sweet spot is called the center of percussion (CAP) point and it produces the least shock to the player‘s hand.
The greatest coefficient of restitution sweet spot on the racquet is where the impact of the ball produces the most power and speed and is located near the throat of the racquet. It is here at the point of impact that the racquet and the tennis ball deform and return to their original form. The energy transferred to the racquet‘s deformation is not returned to the tennis ball because it leaves the string bed before the racquet returns to its original form. It is in this area that the racquet is the stiffest and the string bed is tighter.
The node sweet spot is the point on the racquet where the ball impacts the string bed with minimal vibration and is located in the center of the racquet and the string bed. The farther a ball hits to either side of the node, the frame will not vibrate but will actually twist in the player‘s hand.
The center of percussion is located very close to the node and between the coefficient of restitution. A tennis ball can actually hit the center of percussion and the node simultaneously. The center of percussion produces the least shock to the player‘s hand and it will not cause any motion on the grip either forward or backward. Shock is the initial force transmitted to the hand from the ball‘s impact with the string bed. Repetitive shock ultimately leads to injury so lowering the tension of the strings, using a stiffer frame and increasing the weight of the racquet can reduce shock.
Over time, engineers have designed and developed three types of racquet heads that vary in shape and size given the physics behind the impact of the ball and the ability to control its flight and add power. They have produced an over-sized racquet head that has between 100 and 140 square inches of strung surface. This type frame provides a larger sweet spot because the hitting surface is bigger and the player can hit the ball farther from the heart of the sweet spot and still make a shot. This is an ideal racquet for a beginner. The downside of an over-sized racquet is that it creates air resistance and cuts down on the racquet speed which produces less power and they are harder to control as well.
A mid-size racquet head has between 85 and 100 square inches of strung surface. This size racquet is what most professional tennis players use but with a strung surface between 85 and 95 square inches of string bed. Recreational players typically use a mid-sized racquet with a string bed of 95 to 100 square inches. Mid-size racquets provide a happy median between an over-sized racquet head with a larger string bed and sweet spot and a comfortable frame that produces good racquet speed when swinging the racquet.
A standard-sized racquet head like the one Jimmy Connors used in the 1970‘s ranged from 70 to 85 square inches of string bed and are no longer produced. They provided a much reduced strung surface and sweet spot which meant less opportunity for power and control if you were not a professional player.
There is also the whole world of racquets that have produced for the juniors and small children. The same design and engineering principles, from a physics standpoint, have been applied to insure success.
Technology and design of racquets today is geared to maximize the potential so that when a ball impacts at a sweet spot, the force transmitted to the hand in the form of shock and vibration is minimal and the tennis player is virtually unaware that impact has happened.
Understanding the basic physics behind the design of a tennis racquet allows anyone to purchase a racquet that will provide them the utmost power and control for their ability.
Brody, H.,”How Would a Physicist Design a Tennis Racket?“ Physics Today, 48, No. 3, 26-31 (March 1995)
This journal article is very similar to how the information is formatted in the book that Brody co-authored with Cross and Lindsey. It is very science oriented and most claims are supported by the principles of physics. Brody suggests that if he were able to design a racket it would be light with minimal air resistance and could be swung comfortably with little transfer of shock or vibration to the player‘s wrist, forearm and elbow. He looks at the composition of the strings and notes that kinetic energy transfers from the strings to the ball so the string composition needs to provide for the most energy. The strings also have to have elasticity to help store and return energy. To minimize shock transfer to the player, the ball needs to hit the center of percussion, the sweet spot. He notes that the bottom line is for the player to be able to obtain optimal power and control from a tennis racquet. Brody points out that practice should not be understated. Although this is a dated article and a lot has changed it is credible and resourceful as it uses the principles of physics to understand the mechanics of an optimal performing tennis racquet.
Tennis for Dummies, by Patrick McEnroe with Peter Bodo, Published by Wiley Publishing, Inc., Hoboken, New Jersey, 1998 Chapter 3: The Well-Equipped Tennis Player, page 27 – 45, ISBN 10:0-7645-5087-X
This entire book is like the ”Cliff Notes“ for the game of tennis. It is very simplistic and geared for the beginning tennis player. The book is written by Patrick McEnroe, the younger brother of John McEnroe. Patrick played collegiate as well as professional tennis and knows what he is talking about. In Chapter 3 of the book, the information about the tennis racket and the sweet spot is presented very much like the information about the same topics in the book The Physics and Technology of Tennis without the scientific, physics-based reference. The most information about the sweet spot is actually contained on page 107 and it is a very simplistic. Essentially, he states that when the ball hits the sweet spot, the ball will stay on the strings longer which gives the ball more energy for the return. He also explains in simple terms that the further the ball hits from the sweet spot which is closer to the rim of the racket, there is less control and power. The book, albeit simplistic, is credible because of the tennis experience of the author but from a non-scientific perspective. The graphics and diagrams are useful.
Tennishead—The World‘s Best Tennis Magazine, September 2011 Published by Advantage Publishing,k (UK) Ltd, London, England, Volume 2 Issue 4 Article – Rackets: Junior Frames Explained, page 97 – 100
This article reviews the types of rackets available for junior players. It looks at the size, shape, weight and composition of the rackets that appropriate for players by age and ability. The article also promotes being mindful of price when looking for a racket for a junior player. The article stresses the importance of choosing the right racket so that the player can control the ball and be successful in obtaining strong tennis skills. After reading this article it is clear that many of the same principles behind choosing a racket for an adult are carried over to choosing a racket for a junior. The article is well written and very easy to understand and is credible because manufacturer specifications are used which otherwise wouldn‘t be used if there wasn‘t reasonable research done on the matter.
The Physics and Technology of Tennis–437 pages, published in Vista, California, published first in 2002 second printing 2007 By: Howard Brody, Rod Cross and Crawford Lindsey Published by Racquet Tech ISBN 978-0-9722759-0-3
This book, written by two physicists and a tennis professional, is the essential tool and reference for all tennis players but most specifically for competitive players trying to gain every edge to their game. The book is a compilation of credible articles that cover the entire spectrum of the game of tennis from a scientific, physics-based, yet relatively easy to read, perspective. The book provides scientific information about the racket construction, string materials, balls, and court surface. There are plenty of charts and diagrams that back-up the scientific statements. It also looks at the mechanics of the swing, serve and the ball bounce. It begins with detailed information about the racquet, specifically the sweet spots, with the ultimate goal to help a player find a racquet that provides power and control.
A tennis racquet has a sweet spot. If a ball impacts at the sweet spot, the player is unaware of the impact because of minimal transmission of the force. Conversely, if the ball impacts at a point away from the sweet spot, shock and vibration is felt by the player. Force on the hand is felt due to the motion on the handle through rotation translation, and vibration. This book is incredibly useful and is a credible source since the authors are physicists who like the game of tennis and a tennis professional that understands the game.
Racquetresearch.com, Wilmot McCutchen, 1998.
This website is designed to provide a ranking of tennis racquets from a scientific basis. It provides a section or summary of the main points titled ” The Complete Idiot‘s Guide to Choosing a Tennis Racquet.“ That section is authored by Wilmot McCutchen and covered the time span of 1999 – 2002. The section is infused with some science but the remainder of the site which includes a synopsis of racquet science is intended to have the reader understand how science relates to tennis racquets. Much of the information is identical to other articles and books that look at the size of the racquet head, strings and composition of the frame. It reviews the conservation of angular momentum and linear momentum. It defines the sweet spot as the ” center of percussion.“ The information was much harder to digest than the other references used for this project. Not knowing the background of McCutchen, it gives rise to the credibility or lack of credibility of the website and it is clearly dated, yet functional.