# The General Description of the Tennis Strokes. For math oriented players only!

Discussion in 'Tennis Tips/Instruction' started by toly, Aug 14, 2012.

1. ### sureshsBionic Poster

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There is nothing wrong, but there is nothing useful either. If you remember all the collision problems you have solved, do you ever recall any mention of acceleration? No, it was always, u1, v1, u2, v2 etc. Why? Because no force was acting on those objects. When a racket head hits a ball, it is accelerating just prior to impact. So, conservation of momentum cannot be applied.

2. ### bhupaesProfessional

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Going directly to your post #32...

This is a different problem, isn't it? The original problem assumed an elastic collision to simplify the calculation, which would be true if the energy lost in the collision is small (as I think it is). But in any case, even with totally inelastic collision, the relative speed between the two masses after the collision is zero in both of the cases you have mentioned. Not sure what I am missing...

3. ### bhupaesProfessional

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I understand, and you are right in the large picture. But we are applying the rules differentially, as when solving a problem in numerical analysis, by dividing time into very small segments.

4. ### sureshsBionic Poster

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I am asking why the difference in speeds if analyzed with one at rest, then with the other at rest. If m is moving to the right with v towards M, isn't it the same as M moving to the left with v towards m? Then why is there a difference in the speed of the combined mass after the collision? (direction will of course be different).

5. ### sureshsBionic Poster

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Then you are saying the velocity is constant almost at collision, even if the racket was accelerating before? Then toly's point would be that the person applies no force, and of course he doesn't, because we just made the acceleration 0. That would be true for anything! If we say we will go by a boxer's hand's final speed only, we can claim that the boxer did not do anything at the instant of impact!

What use is that?

6. ### bhupaesProfessional

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In a given coordinate system or frame of reference, of course there is a difference between a small mass and a big mass moving with a given velocity. I don't think anybody is disputing that. As I recall, this argument started because someone wanted to measure the angle of reflection of a ball when it hits a racquet, and that is a relative entity which only depends on the relative movement between the racquet face and the ball.

7. ### bhupaesProfessional

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The racquet could be accelerating all the way to impact. But the actual impact lasts only a few milliseconds. As toly pointed out, how much energy could the force have contributed in that time? IMO, negligible for the purposes of this calculation. If someone can prove this to be wrong, I will accept it - I don't have any means other than the above logic to prove my assertion.

8. ### tolyHall of Fame

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I analyzed Federer inside out hard FH on the APAS System http://www.youtube.com/watch?v=pPLmCqGIotM

There are data about his arm speed and acceleration around the wrist during forward swing.

The picture demonstrates that Federer is able to increase acceleration/force of the arm from frame #1 to #9. The magnitude of the force declined after frame #9. Around impact, frame #24, acceleration decreased more than 70%.

So, he is not able to accelerate the arm significantly near impact. But, this is very hard FH and without doubt he is trying to produce maximum acceleration/force.

Question: What is wrong with Federer?
The answer will be tomorrow.

9. ### tolyHall of Fame

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IMO you are right. Thanks for clarification!!!

10. ### tolyHall of Fame

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1. In first case momentum before collision was mv. After collision momentum is

(M+m)(mv/(m+M))=mv. So, mv=mv and everything is fine with law of conservation of momentum.

2. In second case momentum before collision was Mv. After collision momentum is

(M+m)(Mv/(m+M))=Mv. Again everything is fine and Mv=Mv.

Last edited: Dec 5, 2012
11. ### sureshsBionic Poster

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The force has already driven the acceleration of the racket, that is why it has reached that velocity! Moreover, the force that acts during collision is huge and when multiplied by the small time is called the impulse. The force is called the impulsive force. See the example of the magnitude of the force below. toly is saying that the force is negligible!!!!

http://www.acs.psu.edu/drussell/bats/impulse.htm

The impact between bat and ball is an extremely violent one, in which the bat imparts a huge force on the ball thereby causing it to change directions and gain speed. Consider a baseball weighing 5.125oz (mass = 0.145kg) which approaches the bat at a speed of 90mph (40.2m/s). After the collision with the bat, with a contact time of 0.7milliseconds (0.0007s)[1,2] the bat has a speed of 110mph (49.1m/s) in the opposite direction. Using Newton's second law we can estimate the average force acting on the ball during the hit:

Plugging in the numbers we find the average force to be Favg=18,436 N, which is equivalent to 4124 lbs of force.

12. ### sureshsBionic Poster

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Circular argument since I derived the speed using the conservation of momentum and you used that expression.

I am asking why the system behavior is different in the two cases. I know I am wrong, but I want to know why.

13. ### sureshsBionic Poster

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Acceleration will obviously decrease as he is swinging up into the ball, compared to swinging down with gravity. So what? Whatever force he is exerting needs to counteract gravity, so he cannot keep on increasing the force. What counts is the momentum already built up leading to collision.

14. ### BreakPointBionic Poster

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Without nerds, you wouldn't be able to post on a message board on this thing called "the Internet".

15. ### Swissv2Hall of Fame

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Indeed!

Nerds created the "precious" iPhone, i-This, i-That, that most everyone cannot live without.

16. ### bhupaesProfessional

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Suresh, the force we need to worry about is the external one being applied by the player wielding the racquet. That is a component that could skew the otherwise perfect equations of momentum and energy conservation, should it be significant enough.

Of course, the racquet and ball exert huge forces on each other. The equation for conservation of momentum will apply if that is the only force we need to worry about. The equation for energy conservation will also apply if the collision is perfectly elastic. However, an external force like the player can skew things, but in this case, as pointed out earlier, its contribution in terms of energy during the collision period can be ignored for the purposes of getting an approximate result.

17. ### r2473G.O.A.T.

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I believe it's called "The Internets"

I hear there's rumors on the Internets that we're going to have a draft. I don't know how many of these Internets are carrying these rumors, but they're just wrong. I think the problem here may be more of a question of getting rid of the bad Internets and keeping the good Internets. You know, 'cause I think we can all agree... there're just too many Internets

http://new.hulu.com/watch/1623

Last edited: Aug 24, 2012
18. ### sureshsBionic Poster

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The impulsive force is the force of collision and the equation for it is just the 2nd law. It applies whether or not momentum is conserved. The calculation uses the observed speed of the ball before and after to determine the change of momentum, and some other technique to determine the contact time.

From the racket point of view, the same force would be calculated it its initial and final speeds were recorded. We are interested in the initial speed because that is the independent variable.

This speed (at contact) is due to the acceleration of the racket till impact. For this acceleration, the force applied is difficult to calculate - it is the integral of m*a as a itself changes. The player then must exert this force plus the component of gravity force which is pulling down on the upward swing.

As I said before, toly can suspend a ball and a racket and swing the racket back and see if the ball shoots off at 80 mph. That will settle once for all whether gravity is the main force. I suspect strongly it is not. It is better to do this than claim stuff based on some math.

Last edited: Aug 24, 2012
19. ### tolyHall of Fame

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There is figure from http://sanderroosendaal.wordpress.com/2010/07/26/muscle-power-vs-contraction-speed/

Figure 1. Muscle force versus muscle contraction speed

Figure 1 shows the muscle force versus muscle contraction speed. Itâ€™s a very important graph because it marks where classical mechanics stops and exercise physiology starts. Note that the graph is idealized, with no absolute values on the axis. Each athlete will have a slightly different graph, which will probably also change as a result of training.

This fundamental property of muscle has numerous biomechanical consequences, including limiting racquet speed and force around impact.

So, there's nothing wrong with Federer. It's just a biomechanical law that he must unquestioningly obey!:shock:

20. ### pushing_winsHall of Fame

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what is the question?

21. ### tolyHall of Fame

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The question is - after reading this thread can you clearly explain:

1. How carpenter hit a nail without spin component of the hammer velocity?

2. What exactly you should do to hit pure flat serve, FH, and so on?

Last edited: Aug 27, 2012
22. ### pushing_winsHall of Fame

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inside out swing path. for power, you want draw spin not slice spin.

23. ### mntlblokProfessional

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The only good stuff I've ever seen on this issue is in the book _Technical Tennis_ on pages 108 to 117, at the end of Chapter 3. It's not easy stuff, and will likely take several readings by most of us to make sense of it. It certainly did with me. It didn't help that (I *think*) the angles given in Figure 3.15 are not measured in the same manner as in the other Figures in that section.

The concept is "relative path". And, while maybe difficult to grasp, it is *very* worthwhile. I don't think most of us take into account how important the incoming angle of the ball nor the pace of the incoming ball are for determining the angle at which the ball wants to leave the racket face. This chapter doesn't even take into account the incoming *spin* of the ball, which also has a major (predictable) effect on how the ball leaves your strings (that's in Chapter 4). A hint about understanding "relative path" - which I tended to discount the first couple of times through - is to look hard at the *length* of the "arrows" in the diagrams, as they are proportional to the speeds of the incoming ball and the speed of the racket head.

Yes, I understand that this stuff causes the eyes to glaze over, but measure that against the steam that comes out of your ears when that "pusher's" soft shot gets sent into the fence or the bottom of the net. That slow, steeply dropping ball is not going to come off your racket face the at the same angle as a nice, low, hard drive. The answers (mostly) lie in those pages.

As I am wont to point out, all this stuff can be tested via the fine,free app here on the site - The Shot Maker Tool. It works and it works in the real world, too.

Would love to hear from the "Professor" about my suspicion about the way the angles are measured in Figure 3.15. . .

kb

24. ### SystemicAnomalyG.O.A.T.

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Sadly, The Professor passed away early in 2014:

Not heard from @toly since Spring of 2015 either.

25. ### mntlblokProfessional

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Please don't make me have to learn how to make those cool "spoiler" thingies. Prior to clicking, I had assumed you were talking about Professor Brody. And, yes, I miss Toly's cool composite pics.