Hi again,
>
The dispersion values I posted above are for 100% dispersion diameters. As a rule of thumb, wing mountings have about 1.5 times the dispersion indicated above.
After sorting it out, here my example:
With regard to long range fire, it's a combination of three factors:
- Trajectory
- Dispersion
- Divergence
(The latter simply describes what happens if you pass the convergence point - the lines of fire diverge.)
So let's have a look at three different batteries to estimate the long-range fire capabilities (against a fighter-sized target held perfectly stationary in the centre of the sight):
1.) 1 x MK108 engine cannon
2.) 8 x Browning M2, wing mounted
3.) 4 x Browning M2, nose mounted
The MK108 has low dispersion and no divergence problem. Out to 500 m, its fire will strike the target with hardly any misses (as long as the crosshairs are perfectly aligned with the target centre), but beyond that, the trajectory drops far below the sight line, so with our setup, the fire will miss completely.
The wing-mounted Brownings, set to 250 m convergence for our example, have a high dispersion, large convergence/divergence effects and a very flat trajectory. At 100 m, some of the fire will hit both wings of the target, 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, but you will still get strikes on the wings out to 900 m. (Realistically, you could deliberately aim at one wing tip to hit the fuselage, accepting that 50% of the fire will miss. In simulators, I do occasionally use this technique :-)
The nose-mounted Brownings combine low dispersion, centreline fire and flat trajectory. Out to 300 m, the fire will hit virtually without a miss, then the hit ratio will begin to drop very gradually, but even at 700 m about 80% of the fire will be on target. At 800 m, trajectory drop will become apparent, reducing target coverage to maybe 40%, and even less at 900 m. (Realistically, this drop is so slight that the pilot could probably compensate for it.)
So our three example batteries, modelled roughly after those of the Me 109, P-47 and P-38 (leaving out the 20 mm cannon of the latter) show rather different problems with long range fire.
The Me 109 enjoys great accuracy out to 500 m, but trajectory drop beyond that is very sharp, and it probably would not be worth trying to hit something at beyond 600 m.
The P-47 is limited in its range primarily by the divergence of its fire, and secondarily by the dispersion which means that even when hits are scored, a kill will not be guaranteed. Realistically, we can expect the pilot to be able to compensate a bit for the divergence problem, and while the fire won't be instantly lethal the dispersion means that he's still likely to hit and damage his target. (Note that barrel overheating limits firing duration, so he can't expect to use more than a fraction of his total ammunition load this way. Realistically, this is not really a limitation as the attacked pilot probably would see the tracers after a very few seconds and begin to evade.) An longer convergence range would improve long range firing capabilities, but historic combat experience obviously favoured short range fire.
The P-38 features a very accurate battery, and should be able to consistently score hits (admittedly on "sitting ducks", but these are a must for successful long-range attacks anyway :-) at up to 800 m, and with a bit of luck to 1000 m or more. Beyond 500 m, its fire will also be more effective than that of the P-47 due to the much higher density of the pattern. Add the Hispano, and you have a real long-range killer here :-)
Of course, pilot capabilities and "aim point wander" - the impossibility of keeping the crosshairs centered on the target - means that even in a situation where I have listed "100% hits" will not result in 100% hits. However, a tracking accuracy of 1 mil has been demonstrated by a highly trained fighter pilot during deflection gunnery tests, so the "ideal" situation above is not very far from the optimum human capabilities. Of course, a hastily trained wartime pilot might be very far from the expert I have just described :-)
Regards,
Henning (HoHun)
