Hi Beet1e,
>>Well, you're assuming that the bullets would spread out evenly over the entire area.
>Yes I was assuming that, for the purposes of my example.
The problem with that particular assumption is that it is not realistic, and that it has a major impact on the final result.
The Gaussian bell curve universially applies to all statistic events that are determined by a large number of independend random events, such as all the small effects we can't account for individually that contribute to moving the crosshairs off the aiming point.
Probably le statistician Straffo could explain it better than I can ;-) Anyway, the result of complex random events is not an even distribution as the one in your original example, but one with a noticable peak around the average value, which - due to the marksman's efforts - is the position in the centre of the sight.
>as 2bighorn has quoted from the US Navy manual, the .50 cal was effective to a maximum of 333 yards.
Well, the problem is that "effective range" is not a clearly defined terminus. I'd agree that with wing guns, divergence problems lead to a noticable drop in effectiveness somewhat beyond convergence range. So if the Navy was using a convergence range of 250 yards, 333 yards would be about the point where the effectiveness begins to drop off. It's not yet the point where it's zero, though. (If I remember correctly, the Navy was more into deflection shooting than the USAAF, too, so they might have had more complex situations in mind than the straight six shot our discussion started off with.)
>Gabreski claims to have got kills at 400yds, using the 8x.50cal wing mounted on his P47. But he also says in his book that getting in close made the guns much more effective.
I believe that's an accurate description of the drop in effectiveness resulting from divergence beyond the point of convergence, and well in line with the Navy observation.
Here's a quote from my original analysis near the beginning of this thread:
"At 200 to 300 m, most of the fire will strike the fuselage (with enough bullets missing to be helpful in a realistic situation where the aim is not perfect :-), and at 400 m, the tips of the horizontal stabilizer will be showered. At 500 m and beyond, the greatest share of the bullets will miss."
In my opinion, that agrees with the Navy advice and Gabreski's experience.
(If the target does not fly perfectly straight at 400 m, it can easily be hit in the fuselage by one wing's guns, so please don't focus on the small size of the tips of the horizontal stabilizer :-) But then the fire of the other wing's guns would miss almost completely, which explains the sharp drop in effectiveness compared to the convergence situation where both wings' guns can hit.)
>But... I don't think you've allowed for the fact the attacking pilot would not see the target as a circle, but as two wings and a fuselage in the middle.
You are right, I didn't account for that in my version of your example. In fact, I applied the "even distribution" logic I criticized, only divided in three uneven zones :-) I didn't mean to provide a final hit probability figure, just to illustrate the effect of the bell curve distribution.
>Some of you guys are expressing dispersion values as "mil". Can you indicate what this value would be expressed as degrees of variation from perfect centre?
1 mil = 0.057 degrees as it's defined as 1 unit of lateral displacement at 1000 units distances.
2bighorn seems to have found a different definition :-/ We had different definitions in some earlier thread, too, but the differences were small enough to be insignificant. However, if 2bighorn uses 0.09° and I use 0.057°, that's a bit of a problem.
The USAAF's K-14 LCOS (lead computing optical gunsight) as used for example in the P-51D had a 70 mil ring, by the way.
Regards,
Henning (HoHun)
