## Could you return Andy Murray’s serve?

January 29, 2015

Mathspig is, like, soooooo excited. Tonight I’m gong to watch

TOMAS BERDYCH

Tomas Berdych (CZE) [7] play Andy Murray (GBR) [6] in the Semi-finals at the Australian Tennis Open.

Andy Murray

Some quick maths.

Tomas Berdych is 1.96 METRES (6 FT. 5 IN.)

While Andy Murray is 1.91 METRES (6 FT. 3 IN.)

But, but, but …. Andy Murray, who is 26 years old and is 2 years younger than Berdych.

# Would you be able to return the serve of a top tennis player?

Here is the serve speed of the of the fastest recorded tennis serves in the world:

How long would it take a tennis ball traveling at these speeds to reach the service line on the other side of the court?

# BUT … BUT … BUT …

The tennis ball leaves the servers racket approx 3m above the baseline and travels along the hypotenuse to the service line. We must call in Pythagorus Theorem!!!!

You can calculate the time it takes a tennis ball to reach the service line for each player in the Top 10 Service Speeds List by using the simple v = x/t equation.

The big question is this:

# How fast is YOUR reaction time?

You have to be able to move your racket before the ball arrives.

Can you do it mathspiggies?

You can calculate your reaction time by two methods:

# 1. The meter rule Method:

See details at Top End Sports Website.

# 2. Online Reaction Time Test

This is the best reaction time clock I’ve seen because it uses a traffic light system. Here is Mathspig’s reaction time:

Mathspigs reaction time was : 0.33 secs (see above)

So Mathspig would probably be hit on the head by a serve by Samuel Groth.

# Could you return Andy Murray’s serve?

According to Wikipedia fastest service speed times for these two players are:

Andy Murray = 233 km/h (145 mph)

Tomas Berdych = 226.0 km/h (140.4 mph)

Tomas Berdych service speed just beats the fastest female tennis serve by Barbora Záhlavová-Strýcová at 225 km/h (140 mph).

Could Mathspig react in time to return Andy Murray’s server? Could you react in time?

Tomas Berdych’s serve would hit the line after 0.29 secs. Once again, I’d still be hit on the head. Ditto the top female tennis players.

Mathspig might lose if she played in the Aussie Tennis Open, but I’m a pig. I’d win serve GRUNT of the match. Ha!

1. Fantastic post! I run a tennis group in Los Angeles and am going to share it with them 😀

2. Very interesting! I’m doing my dissertation on tennis (I’m a psychologist, no clue of math/physics) and I stumble upon your article. Are you taking in consideration the loss of speed generated by the bounce? Thanks!

• Helloooo Camilio, well, I have just used maximum recorded speeds of serves for tennis players. I didn’t include the influence of spin, impact, wind or court surface(grass would slow serve speed). But these calculations are a reasonable approximation. Cheerio Mathspig

3. Just a quick note that the tennis serve does not travel along the path of a hypotenuse. It goes up and then down (and often sideways), in an arc. The (partial) objective of a good serve is to add spin to the ball by brushing on various parts of the ball of the ball so that it curves into the court using Magnus force (uneven air pressure due to ball rotation during ball flight). You have to include spin, because even a “flat” serve has a lot of spin. No one hits the serve flat into the box in the pro game, except perhaps Ivo Karlovic. For slower serves, gravitational pull also ads significant arc to the ball.

A better use of geometry and much more useful is to calculate how high you can make the ball bounce off a kick serve. If you see the ball bounce just above the back fence, and you know how high your eyes are, and how far the fence is behind the bounce point, and how tall the fence is, how high did the ball bounce? If you can make it bounce 1 foot about the opponents head, you’ll probably win the point no matter how fast the serve is.

• Hello P Jakobsen, What you say about the curved path and spin is entirely true clever mathpig. But all equations are approximations of the real world. You aren’t including a wind factor, for instance. And, surprisingly, using a triangle for the ball path is a reasonable approximation at those speeds. This would not work for a loopy lob shot.

As for your spin strategy. That’s more about tennis than maths. But worth a thought. Cheerio Mathspig

4. Most players will stand behind the baseline to give themselves more time to return the serve. Therefore they would have the full length of the court (24 metres) to react. Meaning with your reaction time you would have a chance of being able to stick your racquet in the way of the ball. Alternatively go into the stand to give yourself more time!

5. […] Could you return Andy Murray’s serve? […]

6. […] here to see why this simplified calculation […]

7. […] here to see why this simplified calculation […]

8. […] Go here to see why this simplified calculation works!  […]