Tennis results / Men

Written by: Staff on 14th August 2013

Tennis results / Men

epa03825027 Andy Murray ,of Britain, returns a volley to Mikhail Youzhny, of Russia, during the second round of ATP Masters in Mason, Ohio, USA, 14 August 2013. Murray won 6-2,6-3. EPA/Mark Lyons |

Singles – Second Round: (1) N Djokovic def. J Monaco 7-5 6-2

Juan Monaco loses his chance to return to the Top Thirty, but at least it appears he’ll be a U. S. Open seed.

Singles – Second Round: (2) A Murray def. M Youzhny 6-2 6-3

Mikhail Youzhny is in an interesting seeding situation: We show him at #24. But he could still be passed, so a Top 24 seed is by no means assured.

Singles – Second Round: (7) J Del Potro def. N Davydenko 7-5 7-5

Nikolay Davydenko loses his faint Open seeding chance — we show him at #40.

Singles – Second Round: J Isner def. (8) R Gasquet 7-6(8-6) 6-2

Apparently all it took to bring John Isner back to life was to raise the prospect of no American men in the Top Twenty. Isner isn’t back in, but he now needs only one more win. Richard Gasquet might possibly return to the Top Ten, but there will be no Top Eight seed for him in New York.

Singles – Second Round: (11) T Haas def. M Granollers 6-4 6-1

Scratch Marcel Granollers off the seed list, too; he will be a little below #40.

Singles – Second Round: (12) M Raonic def. J Tipsarevic 6-4 7-6(7-4)

Milos Raonic needs one more win to hold his Top Ten spot. At that, he’s doing better than Janko Tipsarevic, who could easily lose his Top Twenty spot to Isner or someone.

Singles – Second Round: D Goffin def. V Pospisil 7-5 1-6 7-6(8-6)

Vasek Pospisil is probably still tired after his incredible run. The good news is, he’s Top Forty; the bad is, he won’t be a U. S. Open seed.

Singles – Second Round: D Tursunov def. J Blake 6-4 6-4

Dmitry Tursunov will also be Top Forty. It has been quite a wait!

Singles – Second Round: F Lopez def. J Chardy 6-4 2-2, retired

A tough retirement for Jeremy Chardy. He was defending quarterfinal points, and will fall from #30 to no better than #35. Which means no seed at the U. S. Open….

Resistance Is Futile

Earlier this week, Ryan Harrison was credited with a 152 mile per hour serve. Another source calculated it at 138 miles per hour. We calculated it as, frankly, not possible. Unless Harrison was firing from a pogo stick, he isn’t that tall. And what does the disagreement tell you? It tells you that the whole radar gun question (and the semi-related shot-placement technologies) are a lot more complicated that they seem. We thought we’d resurrect one of our old features on the topic.

A curiosities of tennis is that one of its most-touted statistics isn’t even an official statistic. We’re referring, of course, to serve speeds as measured by radar guns. Tournaments love to offer this statistic, and it’s even included in the ATP and WTA media guides — but it doesn’t matter if you can serve the ball 600 miles per hour; if the other guy wins enough points, you’re going to lose the match.

And there is another reason not to trust service speeds too much. The reason is that they aren’t actually measured. Radar guns approximate service speeds, and they approximate them differently.

Let’s explain. This is going to get pretty complex before we’re through; we’re going to do our best, but it isn’t easy. We’ll try to use graphs to help you out.

The real problem is that tennis balls slow down a lot. And the faster they’re moving, the faster they’re slowing down. There is a nice hairy formula measuring this, calculating the force pushing against an object moving through the air.

C A p v

f = ———

a 2

Where fa is the force of air resistance, C is the drag coefficient, A is the cross-sectional area (in this case, of the ball), p(that’s actually a Greek rho, ρ) is the density of the air, and v is the velocity of the ball at the point we’re measuring. Which in turn means that the acceleration of the ball (from the above and Newton’s famous f=ma) is given by

C A p v

a = ———

Note that A and m are constant for all tennis balls of a particular model (and almost the same for all tennis balls), and C and p will be effectively constant for any given match. Which means, in a word, that for any given match, the rate at which the ball decelerates depends solely on how fast it’s moving — and the faster it’s moving, the more it slows down. And, because the velocity term is squared, that means that the ball slows down much, much more when it’s moving quickly than when it’s moving slowly. Hit a ball twice as hard and it will slow down four times as fast. Hit it three times as hard and it will slow down nine times as fast. The payoff for a few extra miles per hour on a serve is surprisingly small.

(This, incidentally, is why cars have poorer fuel efficiency when they are driven at high speeds. There are two forces which slow cars down once they’ve gotten moving: Road friction and air friction. Road friction is almost constant no matter how fast you drive — in fact, it decreases slightly at high speeds — but air friction increases according to that squaring rule. In a typical car, at speeds around 20 miles per hour/30 kilometers per hour, road friction is four times air friction. Get up to 60 mph/90 kph, and air friction is more than twice the road friction. It is, ironically, only the very inefficiency of automobile engines — which throw away two-thirds of the energy produced by the gasoline as heat — which makes high-speed cars economically viable; if engines were 100% efficient, a car driving 60 mph would get only a third the gas mileage of a car driving 20 mph, and we’d have everyone slowing down simply because driving fast costs so much!)

But if the ball is slowing down from the moment the serve is hit, just what are we measuring? It clearly isn’t the average speed of the ball — one of Ivo Karlovic’s balls, if it had an average velocity of 150 mph/240 kph, would be literally unreturnable; it would be in the stands on the far side of the court in half a second! No, the goal with radar guns, which are there mostly to supply inflated statistics, is to find the instantaneous velocity — how fast the ball is moving the moment it comes off the server’s racquet. This, we must note, is essentially impossible; we measure velocity by dividing distance covered by time. We have to project back from that to the initial velocity. And, for reasons which will eventually become apparent, we also want to find its velocity at every other point along its trajectory. This requires, formally, a bunch of calculus, integrating distance over time. We’ll spare you that, just constructing some numbers to cover the situation. We’ll start with a serve with an actual initial speed of 170 kilometers per hour (since that’s a speed that almost every man and very many women can hit, at least occasionally), which is the same as 47 meters per second. We assume the ball is hit from a moderate height. We assume a serve down the T. It turns out that it takes almost exactly 3/4 of a second for the ball to land, at point 18 meters from the point at which it’s hit.

We must note loudly that this is just a single “typical” serve; there are all sorts of variations on this theme, some faster, some slower. It may not even be a possible serve, at least for shorter players; we’re assuming they hit flat, and that may not be possible from some serving positions. We’re studying radar guns, not serves! But working out one serve based on the above data (starting speed of 170 kph, straight down the T, with an insignificant vertical component), we find the following “picture.” The table below shows the time in seconds, the approximate velocity of the ball at that time, and the distance travelled. We will examine things at .05 second intervals. Note that, at the beginning, the ball covers more than two meters in .05 seconds. By the end, it’s covering only a third of that distance in the same amount of time. The speed drops precipitously at the start (shedding almost a sixth of its velocity in that first twentieth of a second), much less at the end.

TIME….VELOCITY….DISTANCE

0.00……47.00…….0.00

0.05……39.93…… 2.23

0.10……34.83…… 4.14

0.15……30.95…… 5.82

0.20……27.88…… 7.32

0.25……25.39…… 8.67

0.30……23.33…… 9.90

0.35……21.59……11.04

0.40……20.10….. 12.10

0.45……18.81……13.08

0.50……17.67….. 14.00