Concave vs. Convex Loop (Which is which/better?)

zeio wrote: And for that to happen the best path to follow during a swing is a curve that most closely resembles the brachistochrone.

The brachistochrone works because the brachistochrone allows the ball to drop or accelerate faster initially.  This isn't the case with a swing that opposes gravity.

I know where you are going with this.  You are thinking of the brachistochone with a upwards swing where the swing starts out shallow to get moving and then starts in the upwards direction.  Good one, but if the paddle attitude is always changing the resulting timing errors will result in poor control.  However, if the paddle attitude can be kept constant during the up swing it may work.   The big question is will this make any practical difference?   Most of us can swing far faster than what is necessary anyway.

mikepong wrote: can someone correlate these math equations or whatever it is to TT?

What amazes me is those mathematicians from the past didn't have Mathematica.   How did they know there was a symbolic solution?   It is amazing what people can do when their mind is "stupidfied" with TV.  I would imagine this is common knowledge for those that design roller coasters. Zeio, where else would you apply this?   I don't see what this has to do with TT.

V-Griper wrote: zeio wrote: For those who have chosen to jump to conclusions, I invite them to answer the following question. Given two balls released from the top at the same time, which one reaches the bottom in the shortest time, Red or Green? Why? Sliding or rolling? Friction? Off the cuff I would say green(if they are rolling, or sliding with no friction). Larger initial acceleration(linear and rotational) in the beginning and greater momentum and inertia at the end to maintain velocity. The green ball is accelerating/moving/rolling a lot faster. You will have to explain the relevance. I don't get it.

Doesn't matter whether there is friction or not.  The end result is the same.

You are correct in picking the green, but you may be surprised to know that the acceleration of the ball down the path is actually constant.  The mass and thus inertia of the ball also does not have any effect on its speed, as evidenced by the conservation of energy.  It just so happens that the curve produces the best speed from the acceleration due to gravity.

The curve seen in the image is referred as the Brachistochrone curve, which is Greek for "the shortest time."  The brachistochrone curve happens to be a segment of an inverted cycloid.  Before the brachistochrone was solved, the closely related Tautochrone curve, meaning "same time," was found to be part of a cycloid also. 









For those who are still reading:

The brachistochrone problem was first posed by Johann Bernoulli, in which a point is to start from rest at point a and, solely under the effect of gravity, follow down to point b along a curve that is to be covered in the least time.

The brachistochrone problem was posed by Johann Bernoulli in Acta Eruditorum in June 1696. He introduced the problem as follows:-     I, Johann Bernoulli, address the most brilliant mathematicians in the world. Nothing is more attractive to intelligent people than an honest, challenging problem, whose possible solution will bestow fame and remain as a lasting monument. Following the example set by Pascal, Fermat, etc., I hope to gain the gratitude of the whole scientific community by placing before the finest mathematicians of our time a problem which will test their methods and the strength of their intellect. If someone communicates to me the solution of the proposed problem, I shall publicly declare him worthy of praise. The problem he posed was the following:-     Given two points A and B in a vertical plane, what is the curve traced out by a point acted on only by gravity, which starts at A and reaches B in the shortest time. ... Johann Bernoulli was not the first to consider the brachistochrone problem. Galileo in 1638 had studied the problem in his famous work Discourse on two new sciences. His version of the problem was first to find the straight line from a point A to the point on a vertical line which it would reach the quickest. He correctly calculated that such a line from A to the vertical line would be at an angle of 45 reaching the required vertical line at B say. He calculated the time taken for the point to move from A to B in a straight line, then he showed that the point would reach B more quickly if it travelled along the two line segments AC followed by CB where C is a point on an arc of a circle. Although Galileo was perfectly correct in this, he then made an error when he next argued that the path of quickest descent from A to B would be an arc of a circle - an incorrect deduction.

The brachistochrone problem was one of the earliest problems posed in the calculus of variations. Newton was challenged to solve the problem in 1696, and did so the very next day (Boyer and Merzbach 1991, p. 405). In fact, the solution, which is a segment of a cycloid, was found by Leibniz, L'Hospital, Newton, and the two Bernoullis. Johann Bernoulli solved the problem using the analogous one of considering the path of light refracted by transparent layers of varying density (Mach 1893, Gardner 1984, Courant and Robbins 1996). Actually, Johann Bernoulli had originally found an incorrect proof that the curve is a cycloid, and challenged his brother Jakob to find the required curve. When Jakob correctly did so, Johann tried to substitute the proof for his own (Boyer and Merzbach 1991, p. 417).

Follow the second quoted passage to see the maths behind it.  Equations (16) and beyond consider the condition where friction is present.  The curve is slightly different as a result of that.


Edited by zeio - 06/24/2012 at 7:01am

@Zeio

Edited by hobbes203 - 06/24/2012 at 6:03am

I've had a few different coaches that span many different points in my life.  PRC coaches teaches the basic FH that way.  Mostly, shoulder movement.  They don't say lock the elbow, but it just happens, to give more control over the ball, if you pivot with mostly shoulder movement.

Edited by power7 - 06/24/2012 at 2:59am

Because ML elbows are at a fixed angle when he is loop driving.  So the forward rotation is done with the shoulders.  They are taught to use the shoulder as major pivot point of their swing, not the elbow.

icontek wrote: pnachtwey wrote: I also know that the ball doesn't care about the stroke leading up to and after impact.  Only the attitude and rate of change in attitude of the paddle make a difference as well as the stoke and rate of change in the stroke directions DURING the stroke make a difference.   I understand what you are saying, I think... But why then does followthrough make so much difference in consistency, power and placement of a stroke?

pnachtwey wrote: I also know that the ball doesn't care about the stroke leading up to and after impact.  Only the attitude and rate of change in attitude of the paddle make a difference as well as the stoke and rate of change in the stroke directions DURING the stroke make a difference.

I understand what you are saying, I think...

But why then does followthrough make so much difference in consistency, power and placement of a stroke?

For example:
Takie a mid distance BH topspin, with the backswing from the hip, rotation from the leading shoulder, and uncoiling of the core while contacting the ball in front into a big followthrough that ends with the arm high, out to the right (assuming right handed)...

Why does the larger arc (relative to a smaller backswing and smaller followthrough) require less adjustment against incoming spin?

In other words, why do bigger mechanics seem to ignore incoming spin more than smaller mechanics?

Is it because there is a larger section of the arc where a "reasonably good shot" is possible?

bluebucket wrote: There is no such thing as a convex or concave loop, if you have the spare time and muscles to make that shape movement when looping you are simply doing it wrong.

A famous English dude figured this out in 1696 :-)

V-Griper wrote: I may be wrong but it seems to me that the the curve of the stroke, and the relatively closed or open paddle condition, is largely determined by where the ball is taken off the bounce.  If you take the ball early, anywhere up to, and including, slightly after TOB (top of bounce) and the ball is above net height, I think it would be preferable to have "positive" arc loop stroke and emphasize a relatively closed paddle face. It also facilitates over the table looping.  If the ball is taken much after TOB and below net height it would then be preferable to use the "negative" arc loop stroke with a more open paddle face. The arc of the ball as it descends requires a more vertical "lifting" action. Also, of course, when you are stroking underspin. Of course each individuals adjustment is different. Examples- Positive arc Negative arc

racquetsforsale wrote: This is what I'm referring to: Wu Jing Ping on the FH; at the end of the article, he mentions that Chinese players tend to brush more because they use tacky rubbers, as opposed to their European counterparts who drive more with their grippy and elastic rubbers. http://www.mytabletennis.net/forum/forum_posts.asp?TID=33003&PN=1&title=national-coach-wu-jingping-on-chinese-fh

Wu Jingping's article, at the time of writing(2005 as indicated by one source), did point out that the forehand loop of Chinese penholders lacked power, a trait common among players owing to the short-pips hitter style.  And so he had made it a first priority and had forced Wang Hao and Ma Lin to practice hitting harder.

The notion that the Chinese hit harder probably first took root a decade ago along with Wang Liqin's first claim of the WTTC title.  Duan Xiang(段翔), deputy director of R&D of the CTTA, uses the term "扭轉爆發鞭沖技術(Rotation-induced Explosion Whip-like [Forward"> Loop Technique, literally)" to separate Wang Liqin's forehand loop from the rest whom he describes as "加速制動擺沖技術(Acceleration-Braking Pendulum-like [Forward] Loop Technique)".  The latter is likely an extension to the term "加速制動(Acceleration-Braking)", first coined by Zhuang Zedong, who takes a minimalistic approach to stroke mechanics where great emphasis is placed on maximizing acceleration before contact and brakes to a halt as soon as the ball takes off to reduce the time of recovery.  According to Duan's words, what sets Wang Liqin apart is the unique[at that time] kinetic chain he uses to harness the rotational kinetic energy by coupling the arm, waist, crotch and so on.


Edited by zeio - 06/23/2012 at 8:48am

I may be wrong but it seems to me that the the curve of the stroke, and the relatively closed or open paddle condition, is largely determined by where the ball is taken off the bounce. 

Edited by V-Griper - 06/22/2012 at 2:16pm

king_pong wrote: racquetsforsale wrote: zeio wrote: It is claimed that the grazing loop stroke is more suited for tacky rubbers, whereas the hitting loop stroke is suitable for high tension or tensor rubbers.    This seems to go against the perception that most Chinese players drive or hit through the ball more than their European counterparts when looping. Even a famous Chinese coach has stated the same thing. I think the statement is correct -- that it is easier to get a blistering brush-loop with tacky rubber, while bouncy-grippy rubber more easily facilitates a loop-drive -- but since it is possible to do either with either rubber, the CNT has discovered that driving with their harder-tackier rubber is, for some reason, better than the traditional brush-looping.  Perhaps it is the arc that it produces, outlined in the article that Lexsha posted above -- http://protabletennis.net/content/mechanics-table-tennis.

I can understand where racquetsforsale is coming from.  Liu Guozheng has been quoted for commenting on Chen Qi having more of a wrapping motion than other players, yet he happens to generate more power than would have been thought possible.


Edited by zeio - 06/22/2012 at 12:47pm