Although I've only been playing a short time, I've yet to see the flak cannons on my ships activate. I know they have an incredibly short range, but there are times I've had a corvette hovering right above me (and killing my ship in 5 seconds, but that peeve is another matter) and been practically nose to nose with another ship and I haven't seen the flak cannons fire at all. Am I missing something here?
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Flak Cannons
You have to press Q to switch weapons to the flak cannons and fire them yourselves. If you're looking for an automated proximity defense system, look into autocannon modules.