# What is meant by the 'speed' of a tennis serve?

## Not all 130mph serves are the same

In the Wimbledon semifinal against Roger Federer, the Canadian Milos Raonic produced some fearsome serves.  Some of them were measured at over 140 mph.  Yet at other times, his first serve was recorded as being slower than 105 mph.

Strangely, his fastest serves were all ones that were directed down the centre of the court, while his angled serves that pushed Federer wide tended to be much slower.

Now it's possible that Raonic simply serves slower when he serves at an angle - by putting more slice on the ball, for example.  But maybe the speed gun isn't measuring the speed at which the ball is passing through the air.  Some claim that it is measuring the speed at which the ball is heading towards the line of the net - what would technically be described as the component of the velocity vector that is perpendicular to the base line.

If this is true, then if Raonic were to turn 90 degrees and serve the ball full pelt at the crowd at the side, the IBM speedo would declare that the serve was travelling at 0mph, while the poor spectator that it hit would be carted off to A&E.

In any case, the speed of a travelling tennis ball is a much fuzzier concept than the speed gun would have us believe.  Air friction means that the ball slows down rapidly as it flies through the air.  From the receiver's point of view, what really matters is not how fast the ball is travelling when it leaves the racket, but how long it takes to get from the racket to the receiver.  This will depend on the average speed of the ball through the air, and also the distance between server and receiver.  A receiver who stands back has more reaction time than one who aggressively stands in front of the baseline.

All this means that when you hear that Raonic served at 140mph, you should take that figure with a small pinch of salt.

POST SCRIPT

Back of envelope calculations by Colin Beveridge indicate that serving to the corner rather than straight down the middle would 'slow' the forward component of a 140mph serve to 135mph, which suggests that the angle only accounts for some of the discrepancy.

[If anyone reading this is able to confirm that the speed gun measures the speed of the ball travelling perpendicular to the baseline as it leaves the racket, please let me know.  If I'm wrong, I'll edit the blog]