While doing some research on string tension, I came across many papers published by Professor Cross of University of Sydney. He has done a ton of research on tennis physics and many deals with strings. If you care about strings (and why would you be here if you are not?), I think these papers are a must read:
Measurements of string tension in a tennis racket
Abstract
The pull tension in a tennis string is always monitored while a racket is being strung, but it is difficult to measure the string tension in a racket after it has been strung. In this paper, a simple technique is described based on measurements of the vibration frequency of the string plane. The key to this measurement is the fact that the vibration frequency depends primarily on the area of the string plane and not its shape. It is shown that there is a small loss in tension with time after a racket is strung but there is a large
decrease in tension during the stringing process. The tension immediately after stringing is typically about 30% lower than the pull tension. Additional experiments are described, showing that the large drop in tension is due to a combination of factors including stress relaxation, frame distortion and friction between the strings.
String tension effects on tennis ball rebound speed and accuracy during playing conditions
Abstract
The primary aim of this study was to determine whether variations in rebound speed and accuracy of a tennis ball could be detected during game-simulated conditions when using three rackets strung with three string tensions. Tennis balls were projected from a ball machine towards participants who attempted to stroke the ball cross-court into the opposing singles court. The rebound speed of each impact was measured using a radar gun located behind the baseline of the court. An observer also recorded the number of balls landing in, long, wide and in the net. It was found that rebound speeds for males
(110.1+10.2 km h71; mean+s) were slightly higher than those of females (103.6+8.6 km h71; P50.05) and that low string tensions (180 N) produced greater rebound speeds (108.1+9.9 km h71) than high string tensions (280 N, 105.3+9.6 km h71; P50.05). This finding is in line with laboratory results and theoretical predictions of other researchers. With respect to accuracy, the type of error made was significantly influenced by the string tension (P50.05). This was particularly evident when considering whether the ball travelled long or landed in the net. High string tension was more likely to result in a net error, whereas low string tension was more likely to result in the ball travelling long. It was concluded that both gender and the string tension influence the speed and accuracy of the tennis ball.
Laboratory testing of tennis strings
Abstract
Most tennis strings have a performance rating of almost 10 out of 10 if one can believe the manufacturers' claims. Laboratory tests of tennis strings provide a different picture. The test methods and the results of testing 90 different strings are described. This type of information is needed if players, coaches and stringers wish to make an informed comparison between different strings, and it is also needed if one wishes to model the interaction between a tennis racket and a tennis ball.
Flexible beam analysis of the effects of string tension and frame stiffness on racket performance
Abstract
It is generally accepted that a decrease in string tension leads to greater racket power and an increase in tension improves racket control. The increase in power at low string tension can be attributed partly to a decrease in energy loss in the ball and partly to a decrease in the vibrational energy transferred to the racket. Racket control is affected if the ball strikes the strings towards one edge of the frame, in which case the racket will rotate about the long axis through the handle. The angle of rotation is decreased when the string tension is increased. Quantitative estimates of the magnitude of these effects are presented, using a one dimensional ¯exible beam model to describe the racket and springs to model the ball and strings. For tensions in the range 50±60 lb (220±270 N), commonly used in tennis rackets, and for a ball incident at right angles to the string plane, changes in racket power and control are essentially negligible. However, a signi®cant increase in racket power can be achieved by increasing the stiffness of the racket frame.
Measuring String Tension
I am guessing the above paper is what those iPhone developers used to make the string tension tester app.
Effects of friction between the ball and strings in tennis
Abstract
When a tennis ball is incident at an oblique angle on a tennis racket, the ball slides or rolls along the strings before it rebounds. The dynamics of this interaction in a direction perpendicular to the string plane are determined by the coef®cient of restitution (COR). In a direction parallel to the string plane, the dynamics depend on the coef®cients of sliding (lS) and rolling (lR) friction, and also depend on the COR. For example, if lS 0, and if the ball impacts in the middle of the strings, then the ball will rebound with no change in its spin or parallel speed. Spaghetti strings, with a high value of lS, are
banned from competitive tennis since they can be used to impart excessive spin to the ball. It is shown that the most useful strings are those with lS > 0.3 and that the performance of the strings deteriorates sharply if lS drops below about 0.3.
And the holy grail of stringing...
Elite tennis player sensitivity to changes in string tension and the effect on resulting ball dynamics
Abstract
Eighteen elite male tennis players were tested to determine their ability to identify string tension differences between rackets strung from 210 N (47 lb) to 285 N (64 lb). Each player impacted four tennis balls projected from a ball machine before changing rackets and repeating the test. Eleven participants (61%) could not correctly detect a 75 N (17 lb) difference between rackets. Only two participants (11%) could correctly detect a 25 N (6 lb) difference. To establish whether varying string tensions affected ball rebound dynamics, the ball’s rebound speed and landing position were analysed. The mean rebound ball speed was 117 km h-1, with only the trials from the 210 N racket producing significantly lower (P\0.05) rebound speeds than the 235 N and 260 N rackets. This is contrary to previous laboratory-based tests where higher rebound speeds are typically associated with low-string tensions. The anomaly may be attributable to lower swing speeds from participants as they were not familiar with such a low string tension. Ball placement did not appear related to string tension, with the exception of more long errors for
the 235 N racket and fewer long errors for the 285 N racket. It was concluded that elite male tennis players display limited ability to detect changes in string tension, impact the ball approximately 6% faster than advanced recreational tennis players during a typical rallying stroke, and that ball placement is predominantly unrelated to string tension for elite performers.
Enjoy...
Measurements of string tension in a tennis racket
Abstract
The pull tension in a tennis string is always monitored while a racket is being strung, but it is difficult to measure the string tension in a racket after it has been strung. In this paper, a simple technique is described based on measurements of the vibration frequency of the string plane. The key to this measurement is the fact that the vibration frequency depends primarily on the area of the string plane and not its shape. It is shown that there is a small loss in tension with time after a racket is strung but there is a large
decrease in tension during the stringing process. The tension immediately after stringing is typically about 30% lower than the pull tension. Additional experiments are described, showing that the large drop in tension is due to a combination of factors including stress relaxation, frame distortion and friction between the strings.
String tension effects on tennis ball rebound speed and accuracy during playing conditions
Abstract
The primary aim of this study was to determine whether variations in rebound speed and accuracy of a tennis ball could be detected during game-simulated conditions when using three rackets strung with three string tensions. Tennis balls were projected from a ball machine towards participants who attempted to stroke the ball cross-court into the opposing singles court. The rebound speed of each impact was measured using a radar gun located behind the baseline of the court. An observer also recorded the number of balls landing in, long, wide and in the net. It was found that rebound speeds for males
(110.1+10.2 km h71; mean+s) were slightly higher than those of females (103.6+8.6 km h71; P50.05) and that low string tensions (180 N) produced greater rebound speeds (108.1+9.9 km h71) than high string tensions (280 N, 105.3+9.6 km h71; P50.05). This finding is in line with laboratory results and theoretical predictions of other researchers. With respect to accuracy, the type of error made was significantly influenced by the string tension (P50.05). This was particularly evident when considering whether the ball travelled long or landed in the net. High string tension was more likely to result in a net error, whereas low string tension was more likely to result in the ball travelling long. It was concluded that both gender and the string tension influence the speed and accuracy of the tennis ball.
Laboratory testing of tennis strings
Abstract
Most tennis strings have a performance rating of almost 10 out of 10 if one can believe the manufacturers' claims. Laboratory tests of tennis strings provide a different picture. The test methods and the results of testing 90 different strings are described. This type of information is needed if players, coaches and stringers wish to make an informed comparison between different strings, and it is also needed if one wishes to model the interaction between a tennis racket and a tennis ball.
Flexible beam analysis of the effects of string tension and frame stiffness on racket performance
Abstract
It is generally accepted that a decrease in string tension leads to greater racket power and an increase in tension improves racket control. The increase in power at low string tension can be attributed partly to a decrease in energy loss in the ball and partly to a decrease in the vibrational energy transferred to the racket. Racket control is affected if the ball strikes the strings towards one edge of the frame, in which case the racket will rotate about the long axis through the handle. The angle of rotation is decreased when the string tension is increased. Quantitative estimates of the magnitude of these effects are presented, using a one dimensional ¯exible beam model to describe the racket and springs to model the ball and strings. For tensions in the range 50±60 lb (220±270 N), commonly used in tennis rackets, and for a ball incident at right angles to the string plane, changes in racket power and control are essentially negligible. However, a signi®cant increase in racket power can be achieved by increasing the stiffness of the racket frame.
Measuring String Tension
I am guessing the above paper is what those iPhone developers used to make the string tension tester app.
Effects of friction between the ball and strings in tennis
Abstract
When a tennis ball is incident at an oblique angle on a tennis racket, the ball slides or rolls along the strings before it rebounds. The dynamics of this interaction in a direction perpendicular to the string plane are determined by the coef®cient of restitution (COR). In a direction parallel to the string plane, the dynamics depend on the coef®cients of sliding (lS) and rolling (lR) friction, and also depend on the COR. For example, if lS 0, and if the ball impacts in the middle of the strings, then the ball will rebound with no change in its spin or parallel speed. Spaghetti strings, with a high value of lS, are
banned from competitive tennis since they can be used to impart excessive spin to the ball. It is shown that the most useful strings are those with lS > 0.3 and that the performance of the strings deteriorates sharply if lS drops below about 0.3.
And the holy grail of stringing...
Elite tennis player sensitivity to changes in string tension and the effect on resulting ball dynamics
Abstract
Eighteen elite male tennis players were tested to determine their ability to identify string tension differences between rackets strung from 210 N (47 lb) to 285 N (64 lb). Each player impacted four tennis balls projected from a ball machine before changing rackets and repeating the test. Eleven participants (61%) could not correctly detect a 75 N (17 lb) difference between rackets. Only two participants (11%) could correctly detect a 25 N (6 lb) difference. To establish whether varying string tensions affected ball rebound dynamics, the ball’s rebound speed and landing position were analysed. The mean rebound ball speed was 117 km h-1, with only the trials from the 210 N racket producing significantly lower (P\0.05) rebound speeds than the 235 N and 260 N rackets. This is contrary to previous laboratory-based tests where higher rebound speeds are typically associated with low-string tensions. The anomaly may be attributable to lower swing speeds from participants as they were not familiar with such a low string tension. Ball placement did not appear related to string tension, with the exception of more long errors for
the 235 N racket and fewer long errors for the 285 N racket. It was concluded that elite male tennis players display limited ability to detect changes in string tension, impact the ball approximately 6% faster than advanced recreational tennis players during a typical rallying stroke, and that ball placement is predominantly unrelated to string tension for elite performers.
Enjoy...
