Ballistics

What goes up....must come down. So much for gravity.

In tennis this passes for a deep concept. Many players still think that if you aim a hard-hit ball at a target that is one inch over the net strap, it will always end up somewhere in the opponent's court. This instinct is, of course, wrong. Most balls aimed at that point will fall short and end up in the net. If you are standing behind the baseline and hit a ball from waist high that barely passes over the net at the peak of its flight, it will be out over the baseline about four feet (neglecting air resistance). Most players don't know that if you hit a ball at knee height hard enough, it has no chance of finding the other court, but the same ball hit at waist height will be well in. Add aerodynamic considerations of drag and spin and whoah...you got some complex stuff going on. If you care about what happens to the ball after it bounces - and you really should - it is a bit too much for any of us.

The basics of projectile motion are summarized in Fig. 1. You make contact with the ball at some point in space - the origin. The key parameters of the origin are its height above the court surface and its distance from the net. The ball then sets out for a point some distance above the top of the net strap, but of course, gravity is pulling the ball down so it never actually reaches this point. That is a problem for a lot of people who think that aiming the ball at a point 3 feet over the net gives you three feet of clearance.

The actual clearance depends on all sorts of factors as anyone will tell you who has tried to hit an oh-so-safe high puffball and had it dribble into the net. It would help our feeble brains to estimate clearance if the ball reached maximum altitude - the summit - as it passes over the net, but it seldom does. The summit is important, however, because it is key to both clearing the net and hitting a certain area of the opponent's court, but more on that later. After it reaches the summit, the ball starts to come down, but seemingly faster and at a sharper angle than it went up. As a result, the "court distance" between the origin and the summit is sometimes greater than from the summit to the point where the ball reaches its starting height. The reason for this has to do with air resistance. This drag force pushes back on the ball as it flies through the air and it increases with speed so that at 20 mph the drag force is half the force of gravity and for a serve, at 125 mph it is seven times the force of gravity! Because the air drag slows the ball, it does not fly as far before gravity pulls it back to its starting height. That is why the ball appears to "crater" at the end of its path. Topspin increases this effect, and underspin decreases it. (Fig 2.)

Using Basic Projectile Motion

When picking a flight path for a tennis ball, focus on the position of the maximum height of the ball not the initial trajectory of the ball leaving the racket. Unless you have a protractor, you have no idea what angle the ball is coming off the racket face. More critical a tiny change in the initial angle makes a big difference in whether the ball is in or out; the "window of opportunity" for a topspin forehand is +/- 3.2 degrees and for a flat forehand +/- 2.0 degrees. Critical to where the ball lands are how high it is off the court and how far it is from the net at the point of contact. No amount of topspin will keep a ball in play if you intercept it at ankle height at the service line and hit it with pace. You can hit a shoulder high ball from the same position on the court as hard as you want with any brand of spin and it will easily land in. The implications of this realization are so enormous that it shocks me how many people ignore the ball's origin when planning a strike. Many players seem way more concerned with what their opponent is up to than where the ball is.

They make the good pickup of an ankle-high ball in no-mans-land and smack it with their best forehand drive and then wonder how they could hit such a routine shot long. Conversely, I see people struggling to put heavy topspin on balls above their shoulders and hitting weak balls. Now, I believe that you should hit every shot with some spin just for control and purposes of spindirection, but the amount of topspin one puts on a shoulder-high ball is irrelevant. Cut back on the spin and give that ball a ride! Or, better yet, hit high balls with underspin instead.

People also forget to account for the actual summit of a ball that they hit. A proper drop shot or lob never, I say never, peaks over the net. You should aim for a peak about halfway between yourself and the net. This rule only makes sense: Imagine you want to hit a drop shot from your service line. You wish the ball to land halfway between the net and your opponent's service. The ball is at waist height when you hit it. If you hit the ball so that it reaches its zenith directly over the net, the ball will still be in the air, waist high, when it reaches your opponent's baseline! You must hit a drop shot like a mini-lob so that it peaks halfway between you and the net and is heading down as it passes the net strap.