Redans are protruding angles of a fortification, the rays of which are connected by straight lines are their ends, as shown in fig. 79.
Formerly, redans were used in extensive lines of fortification by constructing fleches at 300 paces from each other, and connecting them by a curtain, fig. 57. Furthermore, to give the faces of the fleches and redans a perpendicular defence, the curtain was broken again, as in fig. 53. However, all of these entrenchments are of no use for long lines, because they are usually lost if the enemy surmounts the parapet at any one point. Instead, separate closed redoubts are now used, conforming to the terrain, and placed such that one defends the other, and they sweep the entire area between them by fire.
Source: Rumpf, H. F.: Allgemeine Real-Encyclopädie der gesammten Kriegskunst (Berl. 1827)
Redan (French), in fortresses, an angle protruding from a straight line in order to flank it.
Source: Meyers Großes Konversations-Lexikon, 6. Auflage 1905–1909
Construction of the Line with Redans
To trace a line with redans, upon the straight line t i, (fig. 6) representing the direction of the gorge of the entrenchment, take the parts e p, p m, etc. 540 in length,* at the points of division e, p, m, etc. raise the perpendiculars, e f, p c, m c, of 130 feet, which are the capitals of the redans, set off then 90 feet from e to a, from p to b, and d to e, and so on for the demi-gorges. Draw the faces f a, b e, c d, and there will remain the curtains a b, d b. The faces will be about 160 feet, and the flanked angle 68½ degrees, or thereabouts.✝
It will be remarked, that (drawing the lines of fire b m, a r, f q, (fig. 10) through the extremities of the faces a f, b c, and of the curtain a b,) the salients are without protection for an extend of about 120 feet upon each capital, and for the space f x m to the right and left of each capital, that the ditch receives no fire, and is without defence, and that the interior of the redans is not spacious.
The weakness of the salient may be remedied by cutting off the angle, or rounding the termination, which will afford some fire in the direction of the capital, that is naturally regarded by the enemy as the weakest point.
This system of redans may be improved by making the demi-gorge 120 feet instead of 90, and the capital 170 feet instead of 130; (fig. 10) the faces f a and c b are prolonged, and the straight lines c h, f i, drawn through the summit of the salients, making the angles f h c, c i f, each of 100 degrees; or else perpendicular lines are drawn through the capitals c f, upon the prolongation of the faces f a, c b; the faces thus prolonged will give fires i m upon the approaches of the ditch of the capital, which was before deprived of them. The interior of these redans is more spacious and more favourable for manœuvres; but the faces of the redans, as well as the ditches, are still without defence; these two faults may be diminished by breaking the curtain k i outwards, and substituting in its place the redan h o i, whose fires will take the approaches of the faces in flank, and plunge into the advanced part of the ditches. The system thus amended, adds considerably to the labour of erection, and cannot be employed in all cases.
* Formerly 720 feet was taken from salient to salient, but the angle of defence was too open, and the part of the capital left without defence, very great in consequence.
✝ The measures used are the usual ones of the United States.
Source: Lallemand, Henri Dominique: A Treatise on Artillery (New York 1820)