The Shape of Tennis

There are no straight lines in tennis. Importantly you are incapable of guiding the racket head along a straight line. It is not your fault you are just not built to do that. Try and draw a straight line with a ruler. No problemo. Now try with a compass; not possible. Your jointed limbs are more like a bunch of compasses than they are like rulers. What your body is designed to do is describe beautiful arcs and ellipses - so let us do that!

I was always told to move the racket along the desired flight of the ball in more or less a straight line. Since this is patently impossible, perhaps we can visualize our strokes as both more beautiful and more effective instead of struggling to hit "through-the-ball".

Universal Stroke Geometry

The fundamental shape of all tennis strokes is a conical helix or a "widening gyre" (apologies to W.B Yeats). A widening gyre is a three-dimensional geometric shape that has fascinated natural scientists, poets, and philosophers for millennia. Widening gyres are everywhere; the turns of a screw, seashells, tornadoes In tennis, they are important because they represent the secret of how A-players so easily develop pace, spin, and control, all with the same stroke at the same time with a minimum of muss and fuss. The conical helix is the ultimate source of beauty and elegance in any well-performed tennis stroke. In the illustration below, the racket head travels along the path of the helix (curved arrow) but the face points in the direction of the axis (straight arrow). If the racket face were pointing in the direction of the curved arrow, it would be rotating in space so fast that you could never control or even predict where it would be pointing at the moment of contact. Even finding the ball with the racket would be a challenge. Pointing along the stable straight axis means that whenever you happen to make contact with the ball, the racket is pointing in that unchanging direction, which is good for control and addressing the ball.. Since the racket is moving in one direction but pointing in another you get spin. The actual geometry of the individual strokes is way complicated, with expanding and contracting gyres with shifting centers of rotation. Every time I try to break it all down I end up with a splitting headache and the absolute conviction that I have no more talent for physics than I do for tennis.

Suffice it to say I get close enough to the solution to see clearly that knowledge of that solution, while perhaps elegant, is of no use to me or anyone else on a tennis court. One is way better off just recognizing that these shapes provide the raw material for sound stroke production and understand a few fairly simple codicils:

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Conical helix or "widening gyre": - the fundamental geometry of racket head motion found in all tennis strokes. Note that there are two distinct and independent directions or vectors of "flow"; straight through the center and around the outside. Although the motion is mostly circular, there is net forward motion through the center of the helix. The "looser" the turns of the helix, the greater the forward motion. The helix is the most reliable and consistent way to turn a rotational motion (of, say, your shoulder) into linear motion (of, say, the ball).
    Consequences of Helical Tennis
  • Every proper shot should be hit with some spin
    • otherwise it is a slap
    • or a spank
  • One must pull across the ball
    • dragging the racket by handle along its axis in orbit around a joint
  • Complex non-linear racket head path
    • reversal of rotation between backswing and forward swing
    • changing orbital center for leverage
      • from hips
      • to shoulders
      • to elbow
      • to wrist
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Conical helix in the Serve: The racket is orbiting around the shoulder in a helix and rotating around its axis due to pronation of the shoulder and forearm. The racket head brushes across the ball in the clockwise direction (left to right) even as pronation results in rotation around its axis in the counter-clockwise direction. The brushing introduces right+top spin and the rotation left+top spin. The left and right spin cancel and the net result is mostly topspin. Less pronation and you have mostly left+top spin - a slice serve.

An example of a conical helix is seen above. The foundation of the shape is a circle. If you start to draw a small circle (or gyre) on a surface, then move your pen off the surface as you are drawing you get a helix. If you widen the circle at the same time, then you get a conical helix. Now grab a racket and go through the motion of a topspin forehand in slow motion. After the unit turn, during the backswing proper, the racket describes a lazy circle in the clockwise direction. This move is the first conical helix. It begins as a wide circle that narrows as you bring the racket back. As your shoulders begin to rotate forward, the circle tightens up and disappears as you enter the lag phase of the stroke. Just before contact the arm and shoulder start to rotate in the counter-clockwise direction with the racket head describing a widening circle in a plane more-or-less parallel to the net as the racket moves through the ball. This rotation has been likened to a car's "windshield wiper" by teaching pros, but a windshield wiper stays on the windshield, while during a tennis stroke the racket head spirals across and towards the ball.

So in a full topspin forehand you describe two helices; first one in the backswing - a tightening gyre in the clockwise direction that then blends into a second, counter-clockwise, widening gyre as you address the ball and follow through. The purpose of the first helix is to "wind up" the shoulder and forearm using stretch-shortening to store spin and control forces. The second helix addresses the ball, injects pace and brushes across the back of the ball to add spin. The spin comes from the rotational velocity of the racket head (along the curved arrow), the pace from the forward velocity (along the straight arrow), control from the forward acceleration (along the straight arrow) and addressing the ball is simply a matter of arranging for the ball to meet the racket head somewhere along the course of the ellipse. Imagine trying to do all of this by moving the racket head along a single, straight trajectory, and you will see why adding spin to the ball is less about the spin itself than about everything else that makes a stroke successful. It is this process that I call "spindirection".

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The Moment of Contact in the ATP-style (Federer) Style Topspin Forehand: The backswing is a broad circle to the right and behind the player in a clockwise direction that contracts into a more linear lag phase then expands into a counter-clockwise ball-strike helix. The clockwise circle in the backswing "winds up" the muscles of the forearm and shoulder storing control and spin forces that unwind themselves after the ball has been struck. At the moment of contact those forces have no visible effect on the position, velocity or acceleration of the racket. The evidence that the forces exist is in the shape of the backswing and the follow through. strokelab

The Short Stroking Exception

No, no no! There are no exceptions! When I say that conical helices are fundamental to tennis stroking, I mean all stroking all the time. One of the keys to effective short stroking is spindirection - the application of the conical helix shape to even the shortest stroke. When you don't have time to swing at a stroke, as in hitting a volley, there is a terrible and tragic tendency to spank the ball flat to optimize pace and create the illusion of control. The pros hit all of their volleys with spin. They hit across the ball, not through it. Their volley strokes are real live strokes, with spin and snap and plenty of pace despite the lack of "swing".

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Ellipses and the Volley: Like all slice strokes, the shape of the volley is a counter-clockwise helix followed by a clockwise helix section. The shape is similar to a ski slope. The load is up, back and lay back the racket and the load is to pull down and forward from there. The feeling is one of pulling down and across the ball.