Detail From M. d. Martemont. Instructions for Officers of Infantry. (1804) Columns of Fire Produced By A Tenaille Line.

This variation of a continuous tenaille line alternates acute and obtuse redan salient angles to maintain 90 degree angles of defense and reduce by half the number of faces that are vulnerable to enfilade by attacking batteries established in positions at a distance from the line. It may also be noted that this tracing increases the length of the faces of the obtuse redans to 87 yards, meaning that more troops can line the interior crest and increase the depth of the defenders' fire across the capitals of the acute redans.

Draw a right line of any length and mark points of division that locate the position of redan capitals along the line. In this example a distance of 100 yards will be maintained between the capitals.

Drop perpendicular lines from each point of division toward the interior (unengaged) side of the line. In this case the mathematics of the line require perpendiculars that are about 44 yards long to produce 90 degree re-entering angles where the faces of the acute and obtuse redans intersect. Connect the interior extremities of the perpendiculars with a right line to establish an interior or rear boundary line. This interior boundary will contain the vertices of the re-entering angles.

Taking up the protractor and placing its central point at each of the points of division on the front boundary line produce alternating 60 and 120 degree angles from collateral points of division. Each line representing the faces of the redans should e produced to its intersection with the rear boundary line, which should also be the point where the collateral redan faces intersect.

This tracing based on front boundary segments that are 100 yards apart produces obtuse redans with faces that are 87 yards long and acute redan faces that are approximately 53 yards long. Assuming the absence of an artillery armament and a defense in two ranks with each file covering one running yard of the interior crest 100 lateral yards of front would require 280 men for an adequate defense of the line and all points salient points of the line would be well within range of small arms fire.