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Science & Mathematics How many square metres in an AFL 50 metre arc?

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Teffy

Norm Smith Medallist
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May 6, 2011
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Any takers?
 
I did a VERY rough calculation on the MCG. The 50m arc isn't a perfect circle, so i basically took the length (50m) and the height (which i worked out to be about 87.5), split the difference (68.75), and then used my old mate Pi to get 3712m².

No idea if that's in the ballpark, or if i'm even on the right track. But it's as good as it gets from me.
 

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Yes, some pretty horrible integration that I probably could've done when I was at uni 7 years ago but have long since forgotten.

It's the area between a 50m radius circle centred on the goalline centre and an ellipse with an equation that varies depending on the ground. Horrible.
 
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I did a VERY rough calculation on the MCG. The 50m arc isn't a perfect circle, so i basically took the length (50m) and the height (which i worked out to be about 87.5), split the difference (68.75), and then used my old mate Pi to get 3712m².

No idea if that's in the ballpark, or if i'm even on the right track. But it's as good as it gets from me.

Props for at least having a crack.:thumbsu:
 
Yes, some pretty horrible integration that I probably could've done when I was at uni 7 years ago but have long since forgotten.

It's the area between a 50m radius circle centred on the goalline centre and an ellipse with an equation that varies depending on the ground. Horrible.
I've always wondered if the 50 metre line is straight when parallel to the goal line?
 
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I've always wondered if the 50 metre line is straight when parallel to the goal line?

:confused:

Is that a trick question?

It is supposed to be a 50 metre arc from the centre of the goal line.
 
:confused:

Is that a trick question?

It is supposed to be a 50 metre arc from the centre of the goal line.
Ok, I didn't know whether it was from the centre of the goal line or to the closest part of the goal line.

Thanks.
 
Ok, I didn't know whether it was from the centre of the goal line or to the closest part of the goal line.

Thanks.

No worries, it's a good question.

Technically, I imagine that very few points in the arc are actually a true 50 metres from the goals.

The laws of the game don't actually make a specific reference, but I have seen local grounds marked out in this fashion.

Rule 3.3 (f) states:

The following areas shall be marked on the Playing Surface:

(f) "a Fifty-Metre Arc at each end of the Playing Surface."
It doesn't really go in to specifics, so your assumption may hold true at times. However, this would make the drawing of an arc a much more complex exercise when instituting a sliding point across a 19.2 metre goal line.
 

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If you download the exe you should be able to run it.

For the MCG with dimensions 171 x 146 (wiki) it comes to 3538. That does come closer to 3700 if you widen the arc, use 160 for "Arc Ellipse Width" say. SugarCane had it about right, though I'm not sure how he did it!
 
Amazing that even in the age of billion-dollar broadcast rights and professional footballers, the vast majority of fans still don't even know such rudimentary things as how the 50-metre arc is actually marked.

Not that I'm trying to pretend I am clever, either. I certainly don't know how they do the arc at the professional venues. At the local clubs I've played for, I've seen two basic methods for marking the arc: by sight, and by rope tethered in the middle of the goal. I reckon the latter is probably the wiser option, but I digress.

Perhaps one day our broadcasters will smarten up and use the dead-time before/during games to educate the punters about things like these.

:thumbsu:
 
Also complicated by the fact that the straight line which connects the boundary to the goal line acutally extends straight a little bit past the point posts. so it's more then 19.2m (probably 20m)
 

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Except the goal line isnt curved, its straight.

AFL-Ground.gif

Try looking at a real one!

http://maps.google.com.au/maps?q=ge...076&sspn=44.915189,86.572266&vpsrc=6&t=h&z=19

http://maps.google.com.au/maps?q=do...83654&sspn=0.002343,0.005284&vpsrc=6&t=h&z=19

http://maps.google.com.au/maps?q=MC...54435&sspn=0.001166,0.002642&vpsrc=6&t=h&z=19

2uivq8o.png


I should have used a circle though instead of an ellipse, or if anything have turned a slight ellipse the other way to account for the flat goal face.

The parameters are tailorable.

Edit: Scratch, yes, "goal line". The diagram posted shows an almost straight 50m line, I was looking at that.
 

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Science & Mathematics How many square metres in an AFL 50 metre arc?


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