Calculated my serve height margin...

[Nanshiki]

So, on a whim I decided to the exactly amount of margin I have on my serve, given my height, combined with the length of my racquet and the length of my arm... the height to the center of my racquet with my arm fully extended is 99 inches. The length from the baseline (assuming I served to a ball tossed exactly to the baseline) to the back of the service line is 504 inches. The height of the net at the center is 36 inches.

The hypotenuse of a serve hit perfectly flat (the absolute worst-case scenario as far as serve margin goes) is 513.63 inches.

Using this page http://www.csgnetwork.com/righttricalc.html I calculated the angle of my serve as 11.11 degrees below horizontal.

I put this angle back into the calculator, but reduced the distance from 504 inches to 252 inches (the length of the service box). This gave me a height of 49.47.

Subtract 36 and you've got 13.47 inches. Meaning, my serve margin over the middle of the court, to the T is a little over a foot. Now, if you add angles and wide serves into the mix it gets much more complicated, but if you want to serve at the wide of the net, you lose 6 inches, meaning my margin becomes 7.47 inches... much, much smaller. This isn't taking court position or the squareness of the net into account, though.

For Ivo Karlovic, the margin would be around 22.5 inches (almost two feet!), assuming his racquet height is about 1 1/2 feet higher than mine (I'm 5'11, he's 6'10). His wide-serve margin would be 14.5 inches. Which is ridiculously large!

Of course, your actual margin will be better if you serve from inside the court, if you jump into the air, and because spin and gravity will make the ball follow a ballistic trajectory, not a straight line.

But I for one hope that now I now how big my worst possible margin is, that I can improve my reliability somewhat now that I know where I can aim and have it go in.

[Nanshiki]

Did the math, and my serve margin from the center of the court to the sideline on the service line was 10.51 inches, over a net that's 39 inches high.

The length would be 720 inches, instead of 504... much longer. If you served from the wide part of the court, it would be an ever bigger distance and margin.


Oh yeah, you might point out that the ball is round (and about 2.6 inches wide), but any margin you lose on the side of the net (before you end up getting a let) is gained on the high side, due to the ball's width...

[Double bagel]

There isn't going to be a test is there?

[Nanshiki]

No... but I do expect you to know the Pythagorean theorem.

[chess9]

Over the length of a serve what is the maximum:

1. Drop of the ball due to gravity;
2. Maximum drop of the ball POSSIBLE due to spin (that's a hard one!);
3. Value, in inches, of leaping two inches off the ground on your serve? (that one should be easy)

:)

I suspect when you calculate the foregoing, and sum them to your previous numbers, you will about double your margin for error.

-Robert (44 years ago I knew some math and physics) :)

[J011yroger]

^^^ Elite servers don't hit the ball with the racquet extended as far up as it can reach though, the racquet is more paralell to the ground than perpendicular.

J

[WildVolley]

^^^ Elite servers don't hit the ball with the racquet extended as far up as it can reach though, the racquet is more parallel to the ground than perpendicular.

J

You're right that the racket isn't extended as high as you can reach, but I don't understand your point about parallel to the ground. When Roddick hits, his arm is almost pointing straight up, but the angle between his arm and racket is less than 180 degrees, I'd estimate it is closer to 135 degrees. Moving up towards the ball it is probably close to 90 degrees but then the angle widens just before contact.

[Nanshiki]

^^^ Elite servers don't hit the ball with the racquet extended as far up as it can reach though, the racquet is more paralell to the ground than perpendicular.

J

I know what you mean. I had considered the effect that the proper use of the continental grip and pronation plays, but I decided that it wasn't really that big of a factor (you might loose 3-4 inches of height on the serve side, which probably translates to at most 2 inches of height on the net...). I could have calculated how much height it would lose, except that it seemed like that wouldn't be very consistent because everyone serves a bit differently.

It took me long enough to even figure out how to calculate the height of the serve as it crosses the net... since I forgot most of my trigonometry. Don't even think about asking me to put spin, atmospheric conditions, ball condition, and gravity into the equation... lol

And fwiw, I actually miscalculated my serve height... it was 102 not 99.

[J011yroger]

You're right that the racket isn't extended as high as you can reach, but I don't understand your point about parallel to the ground. When Roddick hits, his arm is almost pointing straight up, but the angle between his arm and racket is less than 180 degrees, I'd estimate it is closer to 135 degrees. Moving up towards the ball it is probably close to 90 degrees but then the angle widens just before contact.

Yup, you're correct, it was a poor choice of words on my part. I was thinking of a few different things, torso angle, and racquet angle, and such, and it came out sounding wrong.

J

[Nanshiki]

It depends on the length of the racquet, how you hold the handle, and the strike zone on your racquet (some are lower and some are higher), but the difference would be a few inches... and I forgot how to calculate the sides of a non-right triangle. woops.

Also, I just noticed that my problem I was having with my serves (both kinds) wasn't the margin at the net... it was me not striking the ball high enough! Here I go calculating my serve height yet I end up not hitting it nearly that high. I started tossing and hitting the ball higher and my serves started going in more consistently, and with more pace... plus I had better reliability when going wide...all of this due to actually getting all the margin I've been talking about (I certainly didn't feel like I had over a foot of margin) ...sometimes I think I've forgotten more about serves than I've managed to remember...

What I want to do is find out whether the saying that one inch of net height equals seven inches of service box is anywhere near true... because wouldn't that all depend on your service height and the type of serve?

[Nanshiki]

According to my very basic knowledge of trigonometry, a serve struck from 100 inches (8'4" - Roddick supposedly strikes the ball at 9'6") right at a net (assumably so fast that the trajectory is virtually flat) that is 37 inches high will strike the ground 6.14 inches further back than a serve that is struck at right at a net that is 36 inches high... that's interesting.

[davidsmartin]

Gravity is surprisingly strong -- at 100 mph the ball will drop more than a foot because of gravity before it gets to the net then another foot and a half before it gets to the service line (assuming no spin).

Of course with slower serves gravity has a much larger effect which is why it is easier to hit slower serves without faulting.

So you have to go beyond trigonometry and remember your calculus and physics!

[mikeler]

It goes beyond calculus and physics into engineering dynamics. The hardest course I had in school...bad memories.

[LeeD]

Some of us are bad at math, dumbKiss, and non-intellectual...
If you ask any top player what his margin would be, he'd say... "flat serve, whatever goes fastest and goes in"....
Topspin serve, whatever has the most spin with consistent pace, goes deep, goes in is what counts"....
Nobody really cares to know exact centimenters you have to clear the net on each stroke.....
But if you did care, you'd know more than most of anyones.....

[Nanshiki]

I don't have access to the numbers involved that you need to calculate the exact trajectory of a ball... ie, air resistance (temperature, humidity, ball size, ball fuzz), gravity, downforce (ball weight versus lift generated at RPMS, and the rate at which downforce drops)...

[Mansewerz]

I was hoping I would not see words like "hypotenuse" and large math terms until september of this year.


Thanks Nan, thanks a lot! :twisted: