Hi everyone,
by coincidence, I just today received a copy of "Rohrwaffen in Flugzeugen der Luftwaffe bis 1945 - Waffenstände" ('Barrel Armament in Aircraft of the Luftwaffe until 1934 - defensive gun positions').
It seems that the Luftwaffe had two reasons to adopt larger calibres: One was the extended range 20 mm guns gave them, the other was the greater effectiveness against heavy fighters.
Since bullets fired rearwards from a moving platform have a slower "airspeed" than those fired forward, a bomber's defensive guns tended to out-range the attacking fighters' weaponry. As protection against frontal attacks however, the Luftwaffe relied on 20 mm cannon with relatively little ammunition: They'd have little time to fire, but the attacker had to be engaged at long range to deter him. The 20 mm nose guns preferably should have a wide downward field of fire, too, to enable them to double as ground attack weapons.
With regard to the weapons: As early as 1938 work had begun on providing 20 mm defensive guns with the explicit goal of increasing the firing range. However, against the fighters of the Battle of Britain era, the Luftwaffe considered 7.92 mm and 13 mm machine guns effective, though apparently they weren't happy about the limited field of fire of their positions. (I'd say that was partly due to the lack of tail turrets, and partly due to the limitations of hand-operated weapon mountings.)
Against heavy fighters (Beaufighter, Mosquito etc.), even a 4 x 13 mm battery was considered inadequate, and 2 x 20 mm were demanded for heavy bombers. The Heinkel He 177 nevertheless had to make do with a single hand-operated gun due to the lack of space in the aircraft's tail.
Coming back to the B-17, I think the reason that they weren't converted to 20 mm armament simply was the lack of time for that. The USAAF had been firmly convinced that the "Flying Fortress" would be able to defend itself against any fighter attack, and had the B-17F flown as Luftwaffe bomber in the Battle of Britain, the result would undoubtly have proved them right. The problem was that by 1943, the fighters had improved firepower and protection, too, and the destroyers made it even worse for the USAAF.
As it was, the first Schweinfurth raid of August 1943 shook the USAAF's confidence for the first time, and the second probably shattered it in October of the same year. Only now the USAAF had reason to think about substantially increased armament, but the time needed to get a new weapon into mass production (or erect a new plant for an existing weapon) and for broad-scale introduction of this new weapon probably would have been at least 12 months. The USAAF didn't have this time, and the obvious solution was to provide long range fighter escort, for which in October 1943 there were two promising candidates: the P-38 and the P-51.
What would the USAAF have done without the long-range fighter option? I think they'd most probably have found it easier to mount more 0.50" gun positions instead of going to a larger calibre. The YB-40 had an additional dorsal durret and twin guns in each waist position, and perhaps this would have been copied for the B-17 bomber squadrons, which of course would have suffered from an impact on payload and range.
Regards,
Henning (HoHun)