Redan and Curtain lines were a rather common feature of the art of fortification during the late seventeenth and early eighteenth centuries in Western Europe; this type of line was taken as the archetypical trace for lines of circumvallation and countervallation used to cover armies conducting attack against fortified places. This trace was also commonly used to fortify the extremely over-extended fortified positions intended to defend large chunks of territory and block heavily traveled invasion routes that were considered so essential to the defense of states in the early eighteenth century. Since this type of line was described and used by the famous Vauban it became an essential element in the education and engineering repertoire of military engineers through the eighteenth to the latter half of the nineteenth century.

This method produces a series of regular redans joined by curtains. Redans in Vauban's Method will have gorges that are 60 yards long, capitals 44 yards long, and faces that are about 53 yards long. Each redan forms an isosceles triangle that can be divided into two similar scalene right triangles.

Produce a base boundary line of any length. This line will contain the re-entrant angles of the redans where their faces join the lines of the curtains and, consequently, mark the lines of the gorges of the redans.

Mark points of division on the boundary line that indicate the position of the curtain angles vertices and capitals of the redans,or, the demi-gorges of the redans. In Vauban's method the demi-gorges are 30 yards long and the distance between collateral redans (length of the line of the curtain between two redans) is about 100 yards. This distance is variable and can be increased or decreased within certain limits: fire from the salient of one redan must cross the capitals of collateral redans and must not strike the faces of collateral redans. It should probably be noted that Vauban's method actually placed capitals of redans at 240 yard (120 toises) intervals.

From the points of division on the boundary line that mark the location of redan capitals produce perpendicular lines equal to 44 yards toward the engaged side of the line. Taking the curtains at 100 yards and the demi-gorges of the redans at 30 yards, the distance between capitals will be 160 yards.

Produce the faces of the redans by connecting the exterior extremities of the capitals to the points of division on the boundary line that mark the location of the curtain angle vertices. This produces faces that are approximately 53 yards long and salient angles that are approximately 70 degrees and curtain angles that are approximately 125 degrees.

Variation

A common variation in producing a redan and curtain line involved altering the size and shape of the redans, which would, necessarily, alter the distance between the capitals of the redans. In this variation the redans have been constructed as equilateral and equiangular triangles. This requires redan capitals that are about 52 yards long; the faces and gorge of each redan is 60 yards; maintaining a curtain 100 yards long produces a line of defense from the curtain angles to the salient of the collateral redan that is approximately 140 yards long.