How fast is too fast?

Serves have a ways to go before they become unreturnable

By Howard Brody, Special to SI.com

In the June 30 issue of Sports Illustrated, Jon Wertheim wrote a very nice article about Andy Roddick's 149-mph serve and the recent history of fast serves. The article also mentioned that Andre Agassi safely returned the 149-mph bomb, which also should be considered a record of some sort. This note focuses on the problem the receiver has when cannonball serves are being hit at him.

It is obvious that the harder the serve is hit, the less time the receiver has to return it. Is there some limit on serve speed, beyond which the receiver has no chance to return the ball in play? This depends on the reflexes and reaction time of the receiver, but there is some data on this, thanks to an experiment done in the middle 1970s by Sports Illustrated. SI measured the reaction time of several National Hockey League goalies when required to make a save by moving their hand, their stick, their leg or their whole body. Let us assume that tennis players do not have better reflexes than a top-notch goalie, and let's use the stick-save time as a guide for a racket-move-only shot. SI's recorded times ran between 0.26 and 0.29 seconds. If the entire body has to be moved (as is often the case in getting to and returning a serve), the measured goalie times ran between 0.56 seconds and 0.63 seconds.

Given the times it takes for serves of varying speeds to travel from the racket to the receiver's baseline, it is clear that a good tennis player (i.e., one with good reaction time) will be able to return any serve as long as that player does not have to move his body to get to the ball. Since the racket (or hockey stick) moving time is under 0.30 seconds, even for a 149-mph serve (time = 0.47 seconds), there is enough time to return the ball.

If the serve is not within the immediate reach of the receiver and he has to "go" for the ball by moving his body, then above 120 mph he will not be able to get there in time. This is because the time for a 120-mph serve is 0.60 seconds, which is the time it takes a hockey goalie to move his body. For serve speeds less than 120 mph, a good tennis player has a reasonable chance to get to the ball and return it.

If the ball takes a "bad" bounce, all bets are off. Acrylic-surfaced courts (such as those used at the U.S. Open) rarely produce a bad bounce since they are smooth and uniform. Grass courts, on the other hand, often give an erratic rebound, which leads to a mis-hit by the receiver, since the time between the ball bounce and the baseline is about 0.20 seconds.

In summary, it seems that in the foreseeable future, it is unlikely that serves will be hit hard enough (over 165 mph) to make it impossible to return them, if they are within arm's reach of the receiver. On the other hand, if the receiver has to move his body (a serve down the middle or out wide), then 120 mph is fast enough to be unreturnable.

Howard Brody is an emeritus professor of physics at the University of Pennsylvania and co-author of the book The Physics and Technology of Tennis.