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The British Medium Capacity bomb body shape was inspired by the Luftwaffe SC (Sprengbombe Cylindrisch) but the tail design remained much the same as the older GP bombs. The GP bomb shape was very good aerodynamically and when Jets came along the bomb shapes reverted to the GP style though with much thinner higher quality steel walls to keep explosive capacity high
With the accuracy of bomb aiming from 25,000 feet I think most of the aerodynamics was concerned with making sure the bomb exploded when it hit.
Some of the German bombs were stored in the bomb bay vertically (H-111, maybe others too), fins down, so that fact might have had something to do with the size of the fins on German bombs.
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The other part of answer is fact that German bombers could receive more bombs in there bomb bays vertically than horizontally.
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British MC design was inspired by both German SC and US GP design. Actually, British GP design was among the poorest bomb designs at the beginning of the WWII. Quality of British steel prior to WWII was lower than US and German forcing British bomb designers to increase bomb casing thickness and decrease charge weight. That is why British bombs performed worse than German. That was the reason for the development of MC series which corresponds with SC and US GP designs.
British forging technology prior to WW2 could not produce casing strong enough so they were forced to produce casings by casting and make them thick. Later that technology improved due to some American "know how"
Britain did make significant advances in explosives, in particular their development of RDX.The British after WWI ended reduced investment into the explosive ordnance development. Due to such policy at some point during late 1930s they just could not keep up with Germans which ordnance designs at the time were among the best globally. Fortunately on some other fields British were in front of Germans significantly.
So the box-fins came out of this period of time?"In 1921 the War Department convened a Bomb Board to conduct an extensive program for testing bombs against various kinds of structures and surfaces. The tests, running over a period of two years, provided data that guided the Ordnance Department and the Air Corps through the 1930s, Ordnance engineers strengthened demolition bomb cases by forging them as nearly as possible in one piece, with a minimum of welding, and substituted for the long fins of World War I short box fins that gave greater stability in flight"