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Default 8 guns/ 4 guns Spitfire - don't get it

BBC News article claiming a 13 year olds intricate calculations
persuaded them to fit 8 browning guns rather than the four planned.
Obviously chances are improved of bringing down an enemy aircraft, the
more guns are being fired, but what is the intricate calculation needed
to prove that?

It seems the guns were aimed to coincide at a range of 250 yards. 250
yards seems awfully distant to me, what they show of the films of the
time, it seems much less than 250 yards, maybe as little as 50 yards,
unless the used telephoto lens?
 
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