Indented Line. Siege of Charleston, South Carolina. 1780.

This tenaille line alternates obtuse and acute redans and is very similar to the alternating 60 and 120 degree tenaille line, but its trace is, as will be seen, arrived at through a somewhat more complicated process. This tracing abandons the requirement for 90 degree angles of defense and pays less attention to the measure of the acute and obtuse salient angles; it also reduces the depth of the line by intersecting acute and obtuse redan faces in front of (rather than on) the rear boundary line. In drawing this line it will first be necessary to establish the position and direction of the obtuse redan faces and then position redans with 60 degree salients between the obtuse redans.

Draw a right line of any length and mark points of division along the line that will represent the locations of the obtuse redans' capitals 200 yards apart. This is the front boundary line that will contain the vertices of both the obtuse and acute redan salient angles.

Bisect each 200 yard line segment on the front boundary line into two 100 yard line segments. These second points of division will mark the points on the rear boundary line (yet to be drawn) where the faces of the obtuse redans will intersect, and, therefore, will mark the position of the acute redans' capitals.

Drop perpendicular lines from each point of division on the front boundary line. The mathematics of this example (using 100 yard line segments) requires that the perpendiculars be extended a distance of 40 yards toward the interior (unengaged) side of the line. The interior extremities of the perpendiculars may then be connected with a right line that should be parallel to the front boundary line. This produces a series of rectangular boxes that are 100 yards long and 40 yards deep.

Starting from one or the other extremity of the front boundary line draw diagonal lines across each of the rectangular boxes produced in the previous step. The diagonals should be drawn to produce a flattened lateral zig-zag pattern, that is, by producing a diagonal starting from the front boundary line to the rear boundary and then from the rear boundary line to the front boundary line. These diagonal lines mark the positions of the faces and salient angles of the obtuse redans.

To produce the faces of the acute redans it will first be necessary to measure a distance equal to (approximately) 10% of the length of the distance between the capitals of the obtuse redans (200 yards in this case) along each diagonal starting from the extremities of the perpendicular lines that mark the capitals of the acute redans. In this case 10% of the distance between obtuse salients is 20 yards. Draw right lines from each point of division on the front boundary line that mark the locations of the acute redan salients to the measured points on the diagonal lines on either side of the acute capitals. These lines represent the faces of the acute redans. This, to sum it up, whacks 20 yards off the re-entering end of each line representing the the faces of the obtuse redans.

Erasing the rear 20 yards of each diagonal that represents an obtuse redan face gives the obtuse and acute redan tenaille line its basic trace.

This tracing, based on 200 and 100 yard long line segments on the front boundary, produces acute redan salients that are about 60 degrees and obtuse salients that are about 136 degrees. Acute redan faces will be about 37 yards long and obtuse redan faces will be about 88 yards long. Assuming a defense in two ranks with each file occupying one running yard of the interior crest a good defense of this trace would require 250 men for each 100 yards of lateral yards of front, or 30 men less than the alternating 60 and 120 degree redan salient tenaille line previously explained. But again, the angles of defense are not perpendicular and defense of collateral redan faces would be oblique to the point of allowing one troops on one redan face to fire into the sides and faces of troops lining the parapet of the next redan face.