Analysis of tennis string tension

[kayan]

I have a decent background in physics, but something that has always confused me is how to think about how the tension of the string in a tennis racquet affects how the ball leaves the strings. For example, the traditional lore in tennis is that tauter strings will give more control, whereas looser strings will give the player more power (strings are more 'springy'). However, I struggle to find a clear explanation for this common statement.

For example, if I think about conservation of momentum, I have a tennis racquet with a certain mass that is moving (sure, rotating to be accurate) and it contacts the tennis ball. One part of me thinks that the tension of the strings should have absolutely no effect on the speed of the ball after you hit it b/c since momentum is conserved, if you hit the ball with the same racquet speed, then the same momentum will be transferred. However, I also feel like this may not be true. Can someone talk with me about this?

Is it the case that at a certain string tension, the ball hits the strings in a more harmonic manner so the ball isn't dampened as much?

 

[PeroK]

I have a decent background in physics, but something that has always confused me is how to think about how the tension of the string in a tennis racquet affects how the ball leaves the strings. For example, the traditional lore in tennis is that tauter strings will give more control, whereas looser strings will give the player more power (strings are more 'springy'). However, I struggle to find a clear explanation for this common statement.

For example, if I think about conservation of momentum, I have a tennis racquet with a certain mass that is moving (sure, rotating to be accurate) and it contacts the tennis ball. One part of me thinks that the tension of the strings should have absolutely no effect on the speed of the ball after you hit it b/c since momentum is conserved, if you hit the ball with the same racquet speed, then the same momentum will be transferred. However, I also feel like this may not be true. Can someone talk with me about this?

Is it the case that at a certain string tension, the ball hits the strings in a more harmonic manner so the ball isn't dampened as much?

You could try playing tennis with some loose fishing net instead of strings.

It's strange how many people think it's the momentum of the tennis racquet! What would happen if you threw the racket at the ball (or at least let go of it just before impact)?

 

[kayan]

You're reply only confuses me. Assuming that the loose fishing net is elastic, then in my conceptual model, it wouldn't change how fast the ball leaves the racquet. No energy is lost, therefore, it all ends up back in the ball as kinetic energy. Right? Also not sure what you're talking about concerning the racquet momentum...if it's not momentum in the racquet that you are holding, what is it that gives the ball speed?

 

[PeroK]

You're reply only confuses me. Assuming that the loose fishing net is elastic, then in my conceptual model, it wouldn't change how fast the ball leaves the racquet. No energy is lost, therefore, it all ends up back in the ball as kinetic energy. Right? Also not sure what you're talking about concerning the racquet momentum...if it's not momentum in the racquet that you are holding, what is it that gives the ball speed?

Maybe the person swinging the racket has something to do with it?

 

[kayan]

This isn't really answering my question of whether or not there is any truth to the "loose strings give power, tight strings give control" claim. I'm looking for a scientific explanation of why looser strings would generate more power in a shot. If it helps, take the person swinging the racquet out of the situation. Let's talk about just a racquet fixed in mid-air and a ball at a certain height is dropped on the strings. Does the height that this ball reaches after bouncing depend on the tension in the strings?

 

[rcgldr]

http://livehealthy.chron.com/tighter-vs-loose-strings-tennis-5204.html

I'm also wondering about the effects of tennis ball deformation versus string tightness. Maybe it's a minor or negligible effect, but it seems the ball would deform more with tighter strings due to the higher rate of acceleration during the "collision" time.

 

[kayan]

I'm also wondering about the effects of tennis ball deformation versus string tightness.

I don't like the link you posted b/c it's just rehashing the same old information I've always heard in the tennis community without explanation.

However, the 2nd point you bring up about ball deformation is actually something that I have wondered about. Could it be that since tighter strings are certainly going to deform the tennis ball more when it strikes, that that deformation is simply converted into heat/friction, hence the ball has less kinetic energy on the rebound? Whereas if a ball hits strings that are loose, it will decelerate slower, deform less, and hence retain more energy to use as speed?

This explanation might explain the phenomenon from an energy standpoint, but what about a conservation of momentum analysis? I'm not sure how tension plays into that side of things.

 

[rcgldr]

ball deformation

Ball deformation is an issue. In reading more articles the difference in tension is small, 6 pounds or less on 55 to 60 pounds of tension, so only a 10% difference.

I assume that string deformation retains more energy than ball deformation.

I'm wondering about another issue, string deformation time versus ball deformation time, a timing issue. I'm wondering if tight strings result in "out sync" deformations that result less energy retention.

What I do know about other sports. In the case of a trampoline, the energy retention is nearly independent of how tight the springs / surface is. With tighter springs, you bounce just as high, but "dwell" time is lower. There's a compromise in that lower tension and longer dwell time means less chance of injury on a bad landing, but the tension needs to be high enough that the trampoline doesn't collide with the ground.

In the case of table tennis, thicker sponge means more dwell time and more energy retention, both in rebound speed and rebound spin, but similar to tennis it's harder to control. Different types of rubber and sponge provide a different range of speed and spin energy retention. Good table tennis rubber is very elastic and quite sticky (coefficient of friction over 5.0). Unlike tennis strings, the sponge can get compressed beyond it's elastic range (in which case the "wood" in the paddle becomes a dominant factor). I don't think that tight tennis strings are so tight that they go beyond their elastic range during collisions, but it might be possible.

 

[256bits]

Here's an angular deflection analysis and deflection equation.
http://web.mit.edu/3.082/www/team1_f02/angerrderiv.html

 

[PeroK]

This isn't really answering my question of whether or not there is any truth to the "loose strings give power, tight strings give control" claim. I'm looking for a scientific explanation of why looser strings would generate more power in a shot. If it helps, take the person swinging the racquet out of the situation. Let's talk about just a racquet fixed in mid-air and a ball at a certain height is dropped on the strings. Does the height that this ball reaches after bouncing depend on the tension in the strings?

If you take the person swinging the racket out of the equation, then it's just not tennis!

Analysing a free collision between a bat and a ball is hardly a model for any sport. Much of the energy for a tennis shot comes from the player's muscles during the collision: looser strings will increase the amount of time and distance that the player has to impact the ball. This is essentially external energy/momentum being added to the system of bat and ball during the collision.

Without the player, analysis of momentum would give you a very different picture.

 

[kayan]

Analysing a free collision between a bat and a ball is hardly a model for any sport.
Without the player, analysis of momentum would give you a very different picture.

Obviously, it's not tennis without the player. But your answers were far off-topic, so I wanted to get you to think about it in a physics sort of way. Simplifying the situation to just a fixed racquet and a dropped ball is still helpful. This is what much of physics is about, simplifying nature and breaking it down until you can think of laws that govern behavior. Hence, if we determine that without the player the tension makes no difference, then we have learned something: we have learned that the players movement during the swing is what causes the difference in ball speed, and not the string tension. Not sure how much clearer I can be about my confusion and explanations I'm looking for.

 

[rcgldr]

Scroll down to page 7/11 (shows as page 698), section IX - tennis rackets:

http://www.physics.usyd.edu.au/~cross/PUBLICATIONS/9. ImpactofBall.pdf

A tennis ball bouncing off a solid surface loses about 45% of it's energy, while the bounce height off the strings is about 70% to 80% of original height depending on conditions (including string tension). Since height is a parameter of gravitation potential energy, then collision with the strings loses about 20% to 30% of energy. So tension in strings would affect the amount of ball deformation (more energy loss) versus string deformation (less energy loss).

Much of the energy for a tennis shot comes from the player's muscles during the collision: looser strings will increase the amount of time and distance that the player has to impact the ball.

The duration of the collision is probably in the tenths of a second or less, and the peak force during the collision is probably quite high and beyond what a players muscles could respond to in such a short time. It's the players muscle inputs before the collision that matters the most, the muscle inputs during the collision probably makes little difference, and many players whip a tennis racket just before impact with a lot of wrist flex, so there's not much leverage to apply muscle force during the actual collision.

 

[kayan]

Scroll down to page 7/11 (shows as page 698), section IX - tennis rackets:
http://www.physics.usyd.edu.au/~cross/PUBLICATIONS/9. ImpactofBall.pdf
A tennis ball bouncing off a solid surface loses about 45% of it's energy, while the bounce height off the strings is about 70% to 80% of original height depending on conditions (including string tension). Since height is a parameter of gravitation potential energy, then collision with the strings loses about 20% to 30% of energy. So tension in strings would affect the amount of ball deformation (more energy loss) versus string deformation (less energy loss).

Awesome find. This is what I've been looking for. I'm glad it somewhat validates mine/your thoughts about ball deformation causing more energy loss. However, the thing that I still cannot wrap my mind around is using conservation of momentum to view this situation. Momentum is always conserved, unlike energy, whether it is elastic or inelastic collision, so how do we justify the slower ball speed from tight strings here? Why should the string tension affect the speed of the ball if the momentum transfer is the same?

 

[rcgldr]

Why should the string tension affect the speed of the ball if the momentum transfer is the same?

You're assuming momentum transfer is the same. If the ball retains more energy, then it's higher rebound speed means the racket is slowed down more, so more momentum transfer. If the ball retains less energy, then there is less momentum transfer.

 

[Mausam]

First of all if you are talking about real life experiences then you can't apply conservation of momentum(because of the external forces).And as far as speed of the ball after the impact is concerned it depends on many factors such as
1)if the strings have more elasticity it would have a more linear part in stress- strain curve and hence less heat loss.
2)Same applies for the material of ball.
3)And the Tension in the strings which would determine the coefficient of restitution.
Hope this helps,[emoji5]

 

[olivermsun]

Scroll down to page 7/11 (shows as page 698), section IX - tennis rackets:

http://www.physics.usyd.edu.au/~cross/PUBLICATIONS/9. ImpactofBall.pdf

A tennis ball bouncing off a solid surface loses about 45% of it's energy, while the bounce height off the strings is about 70% to 80% of original height depending on conditions (including string tension). Since height is a parameter of gravitation potential energy, then collision with the strings loses about 20% to 30% of energy. So tension in strings would affect the amount of ball deformation (more energy loss) versus string deformation (less energy loss).

In addition, tennis players don't usually hit the ball straight on -- instead they brush across the ball (motion in the plane of the racquet) to produce spin. The strings slide on one another and "snap back" to varying degrees, which affects both the rebound angle of the ball and the amount of spin imparted on the ball.

The perception of the "power" of the racquet has to do with some combination of the rebound, the in-plane snap-back + spin, and the launch angle of the ball, all of which change the trajectory of the shot.

The duration of the collision is probably in the tenths of a second or less, and the peak force during the collision is probably quite high and beyond what a players muscles could respond to in such a short time. t's the players muscle inputs before the collision that matters the most, the muscle inputs during the collision probably makes little difference, and many players whip a tennis racket just before impact with a lot of wrist flex, so there's not much leverage to apply muscle force during the actual collision.

IIRC, Cross, Brody and others (e.g., some of their other works also available at the website you linked) estimate the contact time at around 5 ms, so it should be as you say — the muscles are doing very little during the actual collision. It's all the momentum that goes into the racquet and the hand/forearm attached to the handle at impact that should be important.

 

[Unholy Racketeer]

This is an old thread now, but I've just come across it. Kayan's question is a very valid one: the standard stuff you read is largely repetition of conventional wisdom (lower tension for power, higher tension for control etc) with very little examination of the physics.

I think the various replies here do just about get to what I think is the answer to Kayan's question, but I'd like to have a try at explaining it. The issue with trying to apply the "law" of conservation of momentum is that it holds for a "closed system" in which there is no input or output to or from the system. In the case of the racket and ball there is, during the impact, some loss of energy as the strings are stretched and the ball is deformed.

So consider the energy in this situation: we'll say there are only two forms in which energy may be possessed by a racket and a ball; kinetic energy (to do with velocity) and thermal energy (to do with temperature). Before impact we'll say that the racket had a certain amount of kinetic energy and zero thermal energy, and the ball zero of both. In other words, the racket had all the energy, and it was kinetic energy due to its velocity. After impact both have kinetic energy (the racket less than it had pre-impact and the ball much more) but the ball and the racket strings also have thermal energy because they have heated up very slightly. (Momentarily, as the racket string stretched and the ball was compressed, there was elastic potential energy but this was quickly converted to thermal potential energy).

So the combined kinetic energy of racket and ball after impact is a bit less than the pre-impact total: some of the kinetic energy of the pre-impact racket has been lost (converted) to thermal energy in the form of heat. Because kinetic energy is the product of mass and velocity-squared, the more heat generated by the impact the less the velocity of the racket and ball afterwards.

So, moving to momentum: the momentum of the racket and ball system after the impact is less than the pre-impact momentum because the system has lost energy as heat. Now to the effect of string tension: simply put, compression of the ball "consumes" more energy than does stretching of the racket strings. The more energy "consumed" in that way, the less energy there is for kinetic energy: as the mass of racket and ball don't change, the reduced energy is seen as a reduced velocity. And the tighter the strings, the less they (efficiently) stretch and the more the ball (wastefully) compresses. Incidentally,

I don't know why pro tennis players always choose the least-used ball to serve with - the one played with in the previous rally will be warmer and therefore will compress more "efficiently" and, all other things being equal, will come off their strings at a higher velocity.

[Thread edited by a Mentor]