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I offer some assorted thoughts regarding taking oblique shots below:

If you stand in front of a tank, directly on the centerline, 100 percent of the exposed silhouette is frontal surface of the tank. As you move such that you are 5, 10, 15 degrees offset from the centerline, the exposed silhouette of the tank changes such that the portions of the angle of the field view occupied by the tank change.

For example, at 1500 meters range, the tank may occupy a 2 degree field of view. As you rotate around the tank, at 20 degree offset from centerline, the front portion of the silhouette may consist of 1.7 degrees of the field of view, and the side may occupy .3 degrees of the field of view. If you continue around to maybe 40 degrees, the side portion of the exposed silhouette will take up about half or 1 degree of that field of view. At 45 degrees, the side, being longer, will take up more than half of the exposed silhouette, as the tank is longer than it is wide, thus the side is more likely to be hit than the front, through random distribution of the shot. the point at which this occurs will vary depending on the proportions of the tank, but will always be true at 45 degrees, assuming the gunner is not leading a moving target.

At long range, the tank silhouette fits in a smaller portion of the field of view , a smaller angle of the total degrees of field of view. At close range, the tank is appears wider, as does the angle of its silhouette in the field of view.

At longer ranges, aiming at a narrow slut of exposed side could be quite challenging, especially if the target is moving.

Consider also , that at the extreme oblique angles the trig functions on the armor are the same as if the armor was sloped from vertical, and is compounded with any effect from slope of the armor. Thus, shooting at a side plate, while standing 30 degrees off set of the tank’s centerline, is more or less like shooting at a plate sloped at 60 degrees from vertical.

There are a lot of things to consider with these oblique shots. For example, penetration is lost as the round slides along the side armor plate, the more efficient the ballistic coefficient of the penetrator, generally the less likely that the penetrator is to initiate penetration at extreme oblique angles. The rate at which the penetrator loses effectiveness will increase as the length of the penetrator increases relative to its length.

If the penetrator is a HEAT round, at such oblique angles, the formation of the cone will be severely deformed, radically reducing the effectiveness of the round.

In the end, while I would support the 45 degree approach to locating the shot, though other mechanisms could be practical. Maybe from a about 30-35 degrees offset from the front corners of the target, roll a 50/50 randomizer to locate the shot. Or just give the armor a 30-50 percent increase in effectiveness, maybe except on rounded surfaces. And, though I don’t really support Tim’s 30 degree argument , I would have no problem playing with it.

I think that in reality, shooting at the slit of side armor at a sharply oblique angle would be less likely to have effect, than say aiming at the target’s gun barrel, sights, or commanders cupola.