ORIGINAL: AlaskanWarrior
From what I understand and have observed the flight time of a shell decreases faster the more verticle it goes. Just examine the max altitude a gun can fire as opposed to the max horizontal range. There are significant differences. I did not say that the ability to hit anything changed, just that for the 40mm example there was a max range you could expect to hit anything simply because of the fusing/auto detonate feature and that that max range was shorter in the verticle than in the horizontal. AAA fire in WWII was more about disrupting and damaging aircraft than actually shooting them down, thus soft kills over hard kills. Only until the advent of the late war guided missile (i.e. kamikaze) did it become important to actually hard kill the target far enough away that it would miss even if it went ballistic (read dead pilot). Indeed it took quite a few rounds to shoot down an aircraft from AAA guns.
For major caliber AA guns the timed fuzed shells did not have an impact detonator. The fuze could be set from .8 to 30 seconds on .2 second intervals. Thus at the very least there will be a min range and a max range that the gun/shell combo will be effective, somewhere between a little more than .8 to 30 seconds of flight time! Thus what I want to figure is the distance a shell can go at various angles during the time this time. this will be the absolute max and min an air target can be engaged. Thus for insatnce if an aa gun had an inital velocity of 3000fps then the round would be a little further than 2400 feet before it could explode.
Interesting discussion about flak. And in response to a thread started by Apollo11 several weeks back I did some digging into this area myself.
So several points in no particular order.
1. German ( 88mm ) had AA fuzes with 3 minimum settings, 1 second, 2 seconds and even 0. Of course the 0 minimum still had a minimum arming range, determined by a weighted rotating gyro that was activated by the round as in spun through and beyond the firing tube.
2. Regardless of the minimun range at which the round will be useful, heavy flak has another key issue with low altitude engagement and that is tracking. It is essentially impossible to track a low flying airplane across the engagement space for a heavy flak weapon. Thus to engage below a certain altitude, heavy flak has to switch from its designed directed engagement method, to the so-called barrage ( or barrier ) fire method. One description I have of German barrier fire technique for HAA, is that the barrels of the tubes are pre pointed at the sky in a pre-determined pattern. no attempt is made to "track" the target, merely to have the rounds explode in front of or in the middle of ... the attacking formation. It is stated that no enemy planes can be shot down by this type of fire, though it is hoped to "scare" them.
3. German first line AA units did not use barrage/barrier fire by doctrine, except during a few months in late 1940 overlapping into early 1941 ( I think you said you have Westermann - so you've got this info ) two reasons were, ammo was plentiful and directors were in short supply. Shootdown rates were however very low during this period, and first line HAA units were ordered to revert to directed fire only, in early 1941 and that remained the standing order for the rest of the war.
4. The Germans did have a fair number of ( seoncd line )HAA flak units which were manned by less trained crews and which used captured equipment, which for the most part did not have directors, hence these flak units did use barrage fire for the duration.
5. The primary success metric of the German flak was shoot downs of enemy planes. Both before and during the war. Yes they pointed out to themselves that causing the bombers to miss the target might be more or equally important, but the "enemy planes shot down" metric was never abandoned ( again per Westermann ).
So is there a "flak gap" ?? ... again sources are mixed on this .. Hogg clearly says yes and says this is what drove development of "medium flak" per war. USAAF late war training film says "flak gap is a myth" ... based on assimilation of what I've read to date ... my guess is that there is an altitude below which HAA falls off in effectiveness and this is probably somewhere between 5000-1000 feet ( at about the 2 second fuze point ) but fire is possible below that altitude though it is barrage fire and hence the accuracy is completely different than for directed fire above this point. The transition is not abrupt ( again Joe's guess ) but depends on many factors, including the crew itself. So if you really want to let HAA fire ( and this whole discussion is about land based flak firing at level bombers striking land targets ) barrage fire ( below say 5,000-8,000 feet ) then in the game, you may have to create separate device types ( like the german captured equipment ! ) which only fire barrage fire ... and maybe put them in separate units ( or not ). But I can't think of how you could model a flak unit switching back and forth between barrage fire and directed fire, in the game.
Oh and finally regarding ballistics ... going back a few years .. but my memory ( we had to learn this in non-linear ODE class ) is that ballistics curve is a parabola ( though purists will point out it is an ellipse though you only need to use elipse when you are leaving the atmosphere ) and can be modelled with a second order ODE. Note that with the simple model, terminal velocity ( the speed of the projectile when it again contacts the ground and the end of flight ) is equal to the initial velocity ... this is despite the fact that the velocity decreases to zero while on the upward path and then has to re-increase back to the initial velocity on the downward path. In the simple model the effects of gravity are reciprocal and equal(through reversed ) in either direction. Of course one can complpexify the model by tossing in air resistance and object shape and object rotation, air density etc., but if your purpose is to develop data for WITP these complexitites may not be worth the trouble.
Whereas if you're developing an ICBM guidance system then they absolutely are !!!
