Last week we looked at faces, flanks, and curtains of a fortification. And with that discussion, we began to look at the geometry outside the fort which depicted the areas covered by the defenders. In particular, we saw how Mahan demonstrated the angle of the salient within the plan:
For any given salient angle, there is a line to depict the orientation of the salient. This line ran through the point where the faces intersected, and perfectly split the angle… or as Mahan described:
The line bisecting a salient angle is denominated the capital.
We see two capitals in Mahan’s textbook diagram:
The point at which the capital crossed the line of the fortification was an important feature. That intersection determined the forward-most defensive point on the salient. Taken in conjunction with the complementing salients (to the left and right), this set a forward-facing imaginary line (outside the physical lines of fortifications, that is). Mahan gave this a name and definition:
… the distance from a salient to its opposite flank is a line of defense.
Here is that line on the diagram:
Note that the line of defense is in this case parallel to the curtain. That was not always the case, as situations might demand asymmetrical salients. But going back to the nature of the layout with salients, angle of defense, and other components in order, the line of defense was in front of the curtain. In short, the line of defense depicted the line on which the defender hoped to resist the advance of the attacker. Consider how the two angles of defense served to provide a cross fire across that line:
Yes, a practical application of geometry there.
While that is fine to show where the defenders would shoot at the “bad guys.” There had to be a converse to that aspect of the defense – the places where the defenders could not engage the “bad guys.” In other words the natural defects of a defense:
The form of the parapet, and the direction in which a soldier naturally aims in firing over one, are the causes of two of the most important defects of intrenchments. Owing to the form of the parapet and its height, the fire can take effect only at some distance beyond it, so that when the enemy has approached very near the parapet, particularly when he is in the ditch, the fire will pass over his head, unless the flanks are so arranged that their fire will sweep every point of the ditch; an arrangement of which particular angular systems are alone susceptible. This space, where the enemy can find a shelter, is, generally, in the ditches at the re-entering angles. It is denominated a dead space, or dead angle.
We discussed one aspect of this in relation to the planing of the profile:
But now we are matching that in with the layout on the horizontal plane. Let me depict that on Mahan’s diagram:
Consider the play of the two causes cited by Mahan here. Because the defender on a given face cannot aim below the crest of the parapet, he cannot engage an enemy in the ditch to his front. And this space just happens to be outside of the area covered by the opposite face’s angle of defense. This meant the ditch directly in front of a face along with the ditch along a curtain were within the defined dead space. This is depicted with the red shaded line, in the figure above. To mitigate the dead space allowed by the works, the engineer had to carefully arrange the salients with respect to the curtain, thus minimizing the dead space encountered at the re-entering angles.
But that was not the only dead space to consider. Mahan noted another issue related to the orientation of the faces:
In delivering his fire a soldier usually aims directly to the front, so that the line of fire and the parapet make nearly a right angle with each other. In consequence of this the salients receive no protection from themselves, and there is angular space in front of each of them (which is equal to the supplement of the salient angle) that is defended only by the fire of flanks. This space is denominated a sector without fire.
Going again to the diagram, here are sectors without fire:
Note how the capital line also bisected the sector without fire. It’s a geometry thing again, and a good reference line. This flaw was not quite so bad as dead space, since the complementing salients had the area under the angle of defense… though at longer range.
What should be apparent in this discussion is how important the measure of those angles were for the arrangement of defense. If any of these angles were too extreme (too wide, or too narrow) that would introduce demands on the adjacent sectors of the defense. If those demands were not provided for – mitigating the natural flaws of the defense – then the works were compromised.
While it is easy to sit down with a blank sheet of paper and draw out a defensive arrangement which avoids those extremes, maps of the actual ground to be defended are not blank sheets. Variations in elevation, watercourses, foliage, buildings, and other features factored into the plan. You see, this was not a simple exercise in geometry. That’s why Mahan called the subject he taught “Military Science,” don’t you know!
(Citations from Dennis Hart Mahan, A Treatise on Field Fortifications, New York: John Wiley, 1852, pages 4-5.)