Hi Dan,
>Just a quick question to the experts and general groups out there. Our historical gaiming group is having a discussion about if centerline guns such as those in the P38 had an appreciable effect upon the damage delivered as opposed to wing and or/ combination mounted guns. Any comments or data would be useful.
The destructiveness of wing guns depends strongly on range, while the destructiveness of centreline guns is (in the first approximation) independend of range.
The reason is geometry - wing guns are way out of the centreline and fire inwards, with the two "beams" crossing at a certain distance (called "harmonization range"), and then diverging outwards.
Another factor in destructiveness is dispersion (the random deviation of the bullet from the average trajectory), which is usually greater with wing guns than with centreline guns simply because wings are inevitably somewhat flexible and will vibrate worse then the much more fuselage or the wing roots where centreline guns normally are mounted. In turns, the wings will additionally bend a bit and change the average aimpoint.
As a rule of thumb, the percentage of hits achieved is inversely proportional to the square of the range. That rule of thumb is mainly based on the aiming error of the shooting pilot. Weapon dispersion further decreases the percentage to hits achieved, though the larger the aiming error assumed for a specific attack, the less of a difference it makes.
The geometry of wing guns further decreases the percentage of hits, too: At ranges short of harmonization range, some bullets will tend to pass to the left or the right of the target, though at this short range the target silhouette is still quite big so the effect is not as bad as at long ranges. At harmonization range, the destructiveness of wing guns is exactly equal to that of an equal number of identical guns in a centreline mounting (ignoring the difference in dispersion for the moment), but beyond harmonization range, the destructiveness drops off pretty quickly.
(At very long range, the pilot has the theoretical chance of increasing destructiveness by not putting his aim point directly at the centre of the target, but a certain distance to the left or right of it so that the "beam" of fire from the guns on one side is exactly on target. If he makes a perfect guess of range and distance off centreline, that will give maximum hit percentage - but it will obviously be only 50% of the equivalent centreline battery because the beam from the other wing's guns will be pointing into empty airspace.)
I have attached two series of diagrams comparing wing gun patterns varying with range for the P-47 with wing guns and for the Me 109 with 30 mm cannon. I made it a while ago to contrast two extremes - maybe not perfect for your purposes as two very different gun types are used, but it gives the general idea. (Data was from P-47 and Me 109 harmonization instructions, with MK 108 trajectory data from the corresponding ballistic table. Dispersions are from different sources.)
The size of the yellow ring represents the size of the pattern in which 75% of the shots will land. Note that the target silhouette is roughly the size of a P-47 and is at a certain vertical position in the sight ring in every frame because I assumed the pilot to adjust his aim point perfectly to compensate for trajectory drop. The graduation of the scale is in mil. The ranges are 100 m in the lowest frame, increasing by 100 m with each frame as you go up.
The third diagram is a somewhat rough comparison I prepared from similar diagrams, assuming that the pilot made no correction for range but simply put his pipper right on the P-47-sized target. For the sake of the exercise, the target is considered to fly straight and without manoeuvring while the shooter is considered to make no aiming error (except for disregarding range).
The "hit power" figure on the vertical axis is the total energy of the projectiles impacting the target (kinetical energy plus chemical energy). Kinetical energy is based on muzzle velocity, not actual downrange velocity, because the impact on this comparison is minor. For your purposes, you could simply consider the maximum hit power "100%" to apply the results for identical batteries.
The three batteries have different dispersions - the MK 108 as a short-barrel, low-velocity, advanced primer ignition gun has a very low dispersion (but hit chances drop abruptly to zero at 600 m due to the curved trajectory) of 3 mil for the 100% circle. The Browning M2 as a long-barrel, high-velocity, short recoil weapon has a larger dispersion of about 8 mil for the 100% circle. In a wing mounting, the dispersion increases by about 50%, giving the wing-mounted M2 battery a 12 mil 100% dispersion circle. (There are different and sometimes contradictory figures to be found in the literature, I just decided on these because they looked best at the moment.)
Regarding the results:
The low-velocity, low-dispersion centreline cannon of the Me 108 is highly accurate at ranges out to 500 m. It shows a peculiar intermediate drop at 300 - 400 m though which is owed to the trajectory curving up so that some shells will be lobbed above the target (unless the pilots aims low). At 600 m, all shells will fall below the fighter-sized target. (The pilot might try to compensate, but with increasing range the drop becomes increasingly steeper so that any slight error in range estimation will cause a complete miss.)
The high-velocity, medium-dispersion centreline battery of the P-38 is highly accurate out to 1000 m, dropping in firepower only very gradually, because the target area becomes an increasingly small fraction of the pattern area and because the pattern drops below the target a bit. The pilot could even increase the destructiveness by aiming slightly high at 700 m and more.
The high-velocity, high-dispersion wing battery of the P-47 shows the disadvantage of the wing gun geometry - at most ranges, its destructiveness is less than the P-38's battery which has only half the number of barrels. P-47 destructiveness peaks very sharply at harmonization range, but is poor at shorter ranges and worse at longer ranges. In practice, this is somewhat compensated for by the the increased hit chances due to the larger size of the pattern at ranges near harmonization range, but at very short and very long range, the P-47 really has two separate patterns of which only one can be on target. It would be quite realistic to expect P-47 pilots to aim at the sky next to their target to consciously bring one of the two patterns on target (because that's better than missing with both), and this has been in fact anecdotally been reported for short-range combat. (Missing with both has also been reported by Luftwaffe pilots who found tracers overtaking them on both sides when they were jumped by a P-47.)
With regard to aiming errors, the optimum I found was a figure of just 1 mil for the continued tracking of a moving target with the help of a lead-computing optical gunsight by a very experienced USAAF pilot under test flight conditions in a non-hostile environment. Obviously, it would be worse in actual combat, though German reports on the experience with their version of a lead-computing gunsight shows good precision against USAAF heavy bombers, too.
Regards,
Henning (HoHun)
