This section is from the book "A Treatise On Architecture And Building Construction Vol2: Masonry. Carpentry. Joinery", by The Colliery Engineer Co. Also available from Amazon: A Treatise On Architecture And Building Construction.
Windows In Curved Walls. When the wall in which a window frame is to be built is not straight but curved, as would be the case in a circular tower or semicircular bay window, it is necessary to make a special form of frame laid out from a templet of the exact curve it is required to fit. And if, in addition to the wall being curved, the head of the window is semicircular or semielliptical, the problem is still further complicated by the necessary geometrical development of the details.
In Fig. 30 is shown the plan of a window opening and its frame built in the curved wall of a tower. The pulley stiles a, a are set parallel to the axial line n f of the opening, so that the sash may be easily removed and replaced from the inside of the structure, which could not be done if the stiles were set on radial lines from the center of the curve.
The back lining is set parallel to the pulley stile to form a proper weight box, and the other details of construction are precisely similar to those described in connection with Fig. 23, except that, owing to the curvature of the sill and head, the details of the framing do not join at right angles, and the semicircular shape of the window head demands special construction.
65. To unfold or develop this semicircular window head, we proceed as follows: Draw a line a a from the inside edges of the pulley stiles, and from each end of it erect the perpendiculars a b, which will be equivalent to the continuation of the inside faces of the pulley stiles. Above the plan, draw the line b b parallel to a a, and with the point where this line intersects the axial line n f at d as a center, and d b as radius, draw the semicircle b f b, which will be the elevation of the inside line of the window head. Now divide one-half of this semicircle b f b into any number of equal parts, by points u, v, w, x, etc., and from these points let fall perpendiculars to a a, as shown at x l, w j, v h, etc.
Somewhere below the plan, the line a' a' is then drawn, parallel to a a, from the center n' of which is laid off in each direction the lengths n' l', l' j' j' h', etc. each equal to the length of the curved lines fx, xw, wv, etc., and, from the points so established, perpendiculars to a' a', as n'p', l' q', j' r', h's', etc., are erected. On these perpendiculars are laid off n' o' and n'p' equal respectively to no and n p, l' m' and l' q' equal to l m and l q, j' k' and j' r' equal j k and j r, etc. These measurements are taken from the plan, where the perpendiculars from the subdivisions of the semicircle b f b intersect the curved lines a o a and t p t, shown in the plan of the sill. Curved lines drawn through the points p', q', r', s', g', t' and o', m', k', i', e', a' will describe the contour of the flat piece required to conform to the shape of the window head when bent around a semicircular form similar to b f b. The method of bending this semicircular head is described in subsequent articles.
66. The construction of a sash whose plan is the segment of a circle, and whose head is a semicircle, is shown in Fig. 31. It is designed to fit the curved window frame just described.
The most satisfactory way of constructing this sash head is to form it of two pieces, each piece being a quarter circle; and, as each of these quarter circles will have a compound curve, it will be necessary to prepare a face mold from which to mark out the curve. To do this, first draw the line a b, Fig. 31, on the concave side of the sash, from the outside edge to the center, and on the convex side draw the lines c d parallel to a b and tangent to the sash at u; also draw a c perpendicular to ab. The rectangle a b d c then represents the thickness and width of plank required to get out each piece of the top rail. Now divide the curved outside line of the elevation of one-half the window head a' b' into any number of equal parts by points g', g', and from each of these points draw lines parallel to the center line b' e, intersecting a b at r, t, etc.; and from these points of intersection draw the lines b g, r j, t l, etc., and the line d f, all perpendicular to a b. Lay off on these lines the distances b d', b g, r m, r j, t m', tI, etc., equal respectively to o'c', o'b', e'f', e'g', etc., and through the points thus established draw the curves a lg and nm' d'. Then the curved form a l g d' m' n will be the face mold which must be applied to and scribed on the stock, from which the half-sash head is to be sawed. The shaded portion at g f, shows the waste or surplus, which must be removed in order to permit the two quadrants to meet in a proper butt joint at b e. This surplus is removed on the bevel shown at d, which is the angle c d q, formed by the intersection of the tangent line c d with the prolongation of the perpendicular center line b' b.
The dotted curved line on the concave side of the face mold shows the amount of extra width required, owing to the fact that the head-piece is sawed squarely through the wood. The plank from which the sash head is to be cut, is first planed on its inside edge to conform with the bevel shown at d. The face mold is then set to the edge of this bevel on both sides of the plank and marked, and the surplus wood is then cut away to the lines as marked. The convex and concave edges of the circular head on the plan lines a c' e b and n p e b will then have the proper shape and angle.
67. Two patterns must now be made which may be applied to the finished convex and concave edges of the circular top rail, in order to mark the convex face line of the sash. To prepare these patterns, first draw a line a b, Fig. 32, on it lay off the distances a d, d g, etc. equal to the divisions a'g', g'g', etc. on the convex side of the sash head a'b' in Fig. 31, and from these points erect the perpendiculars a c, d f, g i, etc. equal respectively to q e, h s, k v, etc. of Fig. 31. Then through the points c, f, i, etc., draw a curved line, which will be the line required on the convex face of the sash head. Before applying this pattern to the sash head, it will be necessary to trace another curve l e h b, which will act as a guide in placing the pattern in position for scribing. To do this, a I, de, gh, etc. are laid off equal to q b, h r, k t, etc. of Fig. 31, and the curve b h e l is then drawn through the points so located. The pattern b h l c i k is then cut out and bent around the convex edge of the rough-sawed window head a b d c, Fig. 31, in such a position that b h e l corresponds with the inside line of the plank, as a t r b of Fig. 31. The outside curve k i f c is then scribed on the sash head, and will conform to the curve required.