I happen to have in front of me the official Air Ministry report on Operational Research in the RAF. There is a paragraph on "Research into expenditure of ammunition by air gunners." It includes the following:
1. The Lancaster could hold up to 18,000 rounds of .303 ammo, of which the stowage capacity for the rear quad turret was 10,000 rounds.
2. An analysis of actual use showed that 1,000 rounds for the mid-upper turret were adequate for 99% of missions (the average expenditure was 235 rounds) and for the rear turret, 2,000 rounds. It was suggested that ammo for the rear turret should be restricted to 3,000 rounds to save weight.
Incidentally, there is no doubt that two .5" completely outclassed four .303" in range and hitting power. However, about 10% of Lancasters were engaged by night fighters on each mission, and half of them were shot down. The best chance of escape was violent manouevring in the hope of losing the night fighter and the value of the gunner was in warning the pilot of impending attack rather than shooting at the fighter.
Studies at the time showed that the Lanc would go 50mph faster, as well as fly higher, if the turrets were removed, and this would greatly improve their chances of avoiding interception. However, it was considered bad pyschology to send the planes out with no means to defend themselves.
Tony Williams
Author: Rapid Fire - The Development of Automatic Cannon, Heavy Machine Guns and their Ammunition for Armies, Navies and Air Forces.
Details on my military gun and ammunition website:
http://www.users.globalnet.co.uk/~autogun/