Sea Skimmer wrote:It is a very complicated issue, made worse by the fact that the Germans did work on several different guidance systems.
The only guidance system that was practical for Wasserfall was manual command to line of sight (MCLOS). Essentially the operator held the target in view with a pair of binoculars and used a joystick to keep the missile in the line between those binoculars and the target. This has quite a few problems, not least of which is that the missile is on a very fuel-inefficient course. There's also a capture problem in that the operator has to get the missile within his binocular's field of vision very quickly after launch; if he fails to do so, then the missile goes ballistic and crashes.
I think a 25% hit rate is unlikely, even those anti ship glide bombs only managed a slightly higher success rate and that’s aiming for a much bigger target moving at 1/10th the speed in 2-D only. I like 5-10% is probably the best they would have managed, before jamming dropped this away to less then 1%.
25 percent is way out of the ballpark. To get an idea of the effectiveness of MCLOS, anti-tank missiles using this system got, at best, 10 percent accuracy (rarely they got 25 percent when fired against stationary targets) and a hit rate of 1 - 2 percent was more common. If we average that out, we can give MCLOS anti-tank missiles a pk of around 0.05. Your logic about target speed and the 3-D environment is spot-on; also the range factor is greater for aircraft and the missile speed is much greater for teh Wasserfall - this makes capture and control much harder (by the way, note that Wasserfall cannot be used at night or in bad weather). So, I would expect the pk of the missile against aircraft to be at least an order of magnitude less against aircraft - so we have a pk of 0.005 (a hit rate of 0.5 percent). That's very optimistic.
The radio link to Wasserfall is extremely susceptible to jamming. Just blasting out white noise across the whole frequency spectrum will do it. Other tricks applicable include dropping high-intensity magnesium flares to obscure the target and to blind the operators (think of looking at the sun through binoculurs. ) I'd say that countermeasures would cut the effectiveness of Wasserfall by at least another order of magnitude - and probably much more but let's stay with that.
So, the final Pk against aircraft equipped with defensive countermeasures would be 0.0005, a hit rate of 0.05 percent, one hit for every 2,000 missiles fired. The Germans could do maths, I'd guess that's why they cancelled the missile (they wouldn't have the anti-tank missile experience to darw on but they had been playing with teh guidance system so they knew it was a non-runner
However something to keep in mind is that the missile had a huge warhead, and if and when a missile did hit a bomber formation it would have the potential to damage or destroy multiple tightly packed aircraft. This might force the USAAF to simply abandon daylight raids over Germany until it could equip aircraft with jammers.
The warhead on Wasserfall was 306 kilograms, 684 pounds. Now remeber, destructive power is proportional to the cube root of explosive power (because the blast dissipates in three dimensions). The explosive weight of an 88mm shell was around 7 pounds (the whole shell weighed 20 - 23 pounds). So, allowing for the cube effect, the destructive radius of a Wasserfall is around 4.7 times greater that for an 88mm shell. That's bad but not critical. The destructive radius of an 88mm shell is (IIRC) around 20 feet max so that would give the Wasserfall a destructive radius of around 94 feet. B-17s even when boxed up had more than 100 feet between them so the prospect of multiple kills is remote.*****
By the way, the rate of fire of an 88 maxed out at around 20 rounds per minute. That means the shells it could put into the air in that time would have the following cumulative radii
One Wasserfall, radius of destruction = 27,763 square feet
20 88mm shells radius of destruction = 25,136 square feet
That gives a single Wasserfall a 10.5 percent edge over a single 88mm gun firing for one minute. Hardly an impressive performance edge and cost-efficiency is appalling (the 88mm can go on to fire 20 more rounds, the Wasserfall is GONE).
***** I checked the mathematics of this to confirm it.
The lethal blast radius of a 25 kiloton anti-aircraft warhead is 1,000 yards. 25 kilotons is the equivalent of 25 million kilograms of TNT. The explosive load of an 88mm shell is around 3 kilograms so the 25 kiloton warhead is 8.33 million times greater in explosive power than that of an 88 mm shell. the cube root of 8.33 million is around 204. The lethal radius of an 88mm is 20 feet so 20 x 204 = 4080 feet or 1,360 yards which is close enough for government work. Actually I suspect the lethal radius of an 88mm is closer to 15 feet than 20 which makes the maths work out almost perfectly.