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if you are still puzzled and until a ballistics expert appears you might try the high school physics i used to check this. Starting 6 or 7metres call it 20ft short of the middle of the target calculate how far any fragment travelling at 2200 ft per second radially would get before impact (2200 was a figure i got from online source so a low credibility but it 'sounds right'). Result is about 40 or 50ft right? The area goes up by the square of the distance from target. And that is a 100% swept area as far as the aircraft skin is concerned until the pattern of fragments loses cohesion. Because the fragments take some time to acceelerate to 2200 ftpsec the real radius would be much less - as far as i can tell the 'delayed fragment' diameter of effect would be about - 88 to 100mm for a 88mm shell. Thats why 70 ft distance of detonation is much better than 6 meters or 7 metres
or you may want to remember the effect of 'grape shot' (smooth bore cannon stuffed with bent nails, bits of chain, fragments) in the days of wooden ships at very close quarters.
Germany was only still developing the proximity fuse at wars end after its development had been interrupted by a Hitler order around 1941. The proximity fuse was used with great effect by the Allies, most notably against the V1 flying bombs against which it was highly successful. The Americans were very mindful of the Germans reverse engineering proximity fuses and would at first not allow their use over enemy held territory through fear of a dud being captured. Proximity fuses were later used against ground targets with devastating effect and are generally considered to be one of the major inventions to come out of World War Two.
German anti aircraft batteries concentrated their fire into a box and relied on timed fuses which were timed to exploded at a pre-determined altitude with the hope and expectation that shell splinters would destroy the oncoming enemy aircraft. If the Germans had of had proximity fuses fitted to their anti-aircraft shells then presumably this would have made them far more effective as the fuse itself would have exploded the shell upon detecting the presence of a bomber.
Obviously the Allies had seen for themselves just how effective proximity fused shells were against the fast moving flying bombs and they would have been more than a bit concerned about the safety of their slow moving four engine bombers should the Germans had developed their own.
Reading this forum is very entertaining. So many experts, each one proving the impossibility of ever building a proximity fuse. They must all have gone to public schools and attended college recently. The snowflake generation and it's knowledge level impresses me less every day.
Oh, I almost forgot, try reading Tuxedo Park. It's an actual book and it explains in some detail the work of Alfred Lee, Loomis. Or, if you're a snowflake, watch this video. It's on the web so it must be true. Now we can move on to other ridiculous opinions they learned in school.
I was not meaning to be derogatory just stating a fact. German technology was good but to affect the war air defense needed huge numbers of fuzed munitions in late 1943. Ammunition that explodes in transit or being handled is not a minor issue, it is solving these issues that takes the time. The allied (American) use against the V1, the Battle of the bulge and against kamikazi were very limited compared to the task of defending the whole of Europe from high altitude air attack.I do not disagree. What I do object, however, are the generalisations found in wikipedia that Germany did not had the technology to develop or produce proximity fuzes.
MT fuzed shells striking an A/C would have rendered the fuze unservicable, causing duds and low order detonations. D.Z. fuzed AAA shells would be able to explode always high order on predefined time or impact, depending on which circuit was closed first. Rate of fire very significantly improved with D.Z. shells (similar to AAA firing VT-fuzed shells enjoying this nice side effect).