# I Analysis of tennis string tension

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1. Feb 23, 2017

### 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?

2. Feb 23, 2017

### PeroK

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)?

3. Feb 23, 2017

### 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?

4. Feb 23, 2017

### PeroK

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

5. Feb 23, 2017

### 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. Lets 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?

6. Feb 23, 2017

### rcgldr

7. Feb 23, 2017

### kayan

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.

8. Feb 23, 2017

### rcgldr

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.

9. Feb 23, 2017

### 256bits

10. Feb 24, 2017

### PeroK

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.

11. Feb 24, 2017

### kayan

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.

12. Feb 24, 2017

### 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).

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.

13. Feb 24, 2017

### kayan

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?

14. Feb 24, 2017

### rcgldr

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.

15. Feb 25, 2017

### 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,

16. Feb 25, 2017

### olivermsun

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.

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.

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