Lousitania is actually correct. Running away TECHNICALLY does not increase your range.
Your shells still travel just as far. But due to the hang-time of the shells and the
movement of your ship, if you are running from the enemy, you are moving away from the
point of impact, while your target moves towards it, which effectively gives you a range
boost. And the higher the angle of the gun, the longer the shells stay in the air, the
more pronounced the difference is.
Your opponent, by the same principle, also gets an effective decrease in range due to how
he is travelling towards the point of impact for his shells, while you head away from it.
He has to aim ahead of you in order to hit you, which is much more difficult to do if
you're moving away from him. If the two ships have the same or very similar range, he will
not be able to hit you.
I am going to borrow a couple of diagrams from LordKelvin's "Basic Battleship Tactics"
guide, which is stickied up at the top of this forum:
You are the running ship, and the red lines indicate the trajectory of your shells,
beginning with the instant you fire them at the target.
Now you are the chasing ship, but the red lines still indicate the trajectory of your shells.
The pictures basically sum it up. If you need a full written explanation, check out LK's
guide, here:
http://tinyurl.com/48l4g7
But the answer to the original question, from a practical standpoint, is yes. Running
gives you "more range."
--Helms