# Hawk-Eye computer system used in sports to track ball trajectory

1. Jan 12, 2008

### _Mayday_

Hey, today while watching the cricket I was fascinated by "Hawkeye" and how it predicted the ball trajectory, from the bowlers hand to a few metres past the batsmen.

"Hawk-Eye is a computer system used in cricket, tennis and other sports to track the path of the ball."

http://en.wikipedia.org/wiki/Hawk-Eye" [Broken]

Now I've looked around the net, to find some explanation of how it works, but have failed. I can only think of two things that it would rely on, either there are many cameras that follow the ball, and then create a model for the trajectory, or there is some equations(s) that are used aswell. Does anybody have any knowledge of this subject, or possibly an explanation of how it works?

What type of equations would you use to calculate the trajectory? I am an AS Student studying physics so my knowledge on equations of motion is fairly limited.

Though this thread is specifically about cricket ball trajectory, I would also be interested in the ball trajectory of other sports such as golf or even tennis.

Thanks. :shy:

EDIT: I changed the first post, because the original post was poorly written.

Last edited by a moderator: May 3, 2017
2. Jan 12, 2008

### Danger

Sorry, but I just can't understand the question (especially the part about cameras). Cricket, like most other sports, is entirely based upon hand-eye co-ordination. You'd need a super-computer to model the variables.

3. Jan 12, 2008

### _Mayday_

First post edited, sorry

4. Jan 12, 2008

### _Mayday_

Ok I've found some more information on Hawkeye for anyone interested, it's a bit waffly but it's ok.

"It uses six specially placed cameras around the ground to track the path of the ball, from when it was released from the bowler's hand right up until when it's dead.

The images captured by the camera are then turned into a 3D image by a special computer to show how the ball will travel on an imaginary cricket pitch.

It's so good it can track any types of bounce, spin, swing and seam. And it's about 99.99% accurate too.

So you can see on the TV whether the ball would have gone on to hit or miss the stumps on an lbw decision.

But while the viewers get to see the replay of an lbw decision several times, the umpires only get to see it once - and they have to make their minds up instantly. "

I think, my interest lies more in the mathematical side of this, can anyone direct me to some equations on ball trajectory etc.?

Oh and I see alot of people writing equations out, and it looks as if they have used a program? May I ask the name of that programme? A free one preferably. Thanks.

5. Jan 12, 2008

### Loren Booda

99.99% accurate over a path of about 22 yards gives an error of about a millimeter. Much better than the accuracy of a "baseball umpire miscreant" (B. U. M.) Why not replace the players with robots?

6. Jan 12, 2008

### Danger

The edit was very helpful, Crawford. Unfortunately, I can't help you. As I am not a sports fan whatsoever, the only time that I ever saw anything about 'Hawkeye' was during a TV news sports segment last year. At that time, it was used only to determine in or out for a tennis shot.

7. Jan 12, 2008

### mda

I know nothing about the actual workings of the system but I'm going to make some educated guesses.

First there's two parts to the system: tracking the actual path of the ball and then predicting the path of the ball, and I am not sure which the OP wants to know about.

The first part is all that is required for tennis, and once the image positions of the ball have been registered by detection processes the remainder is a case of simple triangulation.

The lbw type prediction is more difficult. Ignoring fluid effects (spin/swing/drag) the ball will follow a parabolic path as per Newton's laws of motion and gravitation. I doubt they can truly predict the result of fluid effects and at least some fudge factors would come into play. They probably just fit higher order terms to the path to do the extrapolation. If there's the possibility of a bounce in the extrapolated path that will surely make prediction even less accurate.

Just my two cents, and if someone out there worked on this project I'd love to hear about it also.

8. Jan 12, 2008

### _Mayday_

^ mda, I think you are correct, as when a spinner is bowling, Hawkeye cannot predict the spin before the ball has actually made contact with the floor and has reacted. So I think you are right in saying that the ball follows a parabolic path.

I think that in the case of Hawkeye that it is very much to do with the actual cameras, though I was more interested in the actual equations of finding the ball path.

Thanks for the input though.

Loren, there has been much discussion in using such technology in cricket, and allowing umpires to refer to them but people don't seem to keen on the idea. =]

9. Feb 3, 2008

### rakshak

The Complete Knowledge

hello friends...
i am an engineering student..even i was fascinated with the concept of hawkeye...
i would like you all to know that i have created a computer program in C++ programming language that actually tracks the trajectory of a cricket ball from the baller's end to the batsmen's end...
the program asks the user to choose the type of bowler(leg or off spinner), the bowling speed as well as the spin angle with which it is released.. hence to develop this program i have applied some very easy to understand physics equations that involve all of the above related data...if anyone is interested please let me know..i shall post the c++ program or the physics equations involved as required

10. Feb 3, 2008

### rakshak

to ^mayday and ^mda
the hawkeye not only uses the cameras to track the trajectory but also takes into account greatly the fluids involved,the spin swing and drag all have respected equations, which i would like to share with you.. the extrapolation of the cricket ball is done by taking into account all the minutest of detail..for example if the ball released by a spinner onto a grassy patch ..the ball would not bounce much and would rather spin more..as a result the cameras are instantly able to grab hold of the new projected velocity ,release angle and the spin angle of the new trajectory of the ball after bounce which is all that is required to trace it to the stumps at least!!!!!!!!!!!
hence my friends please do not underestimate the power of this program ..after all Hawkeye has been developed by a cricketer who also happens to have a phd in artificial intelligence..

11. Feb 3, 2008

### klystronman

very old technology here.
if you pass an object over a matrix that has light polarized reaching the matrix you see the angle and speed. a cpu runs at a certain speed so time becomes a constant and is counted in steps in the equation . knowing the mass of the objects and how they react to each other is the only equation. so the only question is where will it stop based on where it started from.

Last edited: Feb 3, 2008
12. Feb 3, 2008

### Claude Bile

Hawkeye's predictive powers are somewhat limited. It can predict where a ball will go, by extrapolating the existing trajectory of the ball, but that is about it.

The impressive engineering behind Hawkeye is the ability to make the measurement non-intrusively from long distances and at speed (cricket balls and tennis balls travel can travel upwards of 150 km/h). Not so much its predictive power. That is why Hawkeye has recently been adopted in Tennis majors (which don't require a prediction), but has yet to be adopted in cricket (which do require a prediction).

Claude.

13. Sep 14, 2008

### Wrishi

Re: The Complete Knowledge

Hie rakshak

I am heading our group in software and AI. The program on ball prediction developed by you is of intrest to me. Pls. give details of the same or call me on 98300 83044/94317 91981.

14. Feb 24, 2010

### Rohsik

Re: Hawkeye

@Rakshak
I am also interested in the hawk eye system and would love to see your program. Could you possibly give me the details
Thanking you