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.
77. Window or door openings in a straight wall with splayed jambs and pointed soffits next demand attention. To unfold the length and shape of the soffit on the plan shown in Fig. 43, let r r' and p p' be the plan of the opening; let pr be the splay of the jambs; and let q x be a center line of the plan. Parallel to q f draw p g and p'g'; with r' as a center, describe the arcs g f and r x and divide them into any number of equal parts - as g f into five parts, and r x into seven. Draw r' y parallel to x q, and prolong r p to y. On y as a center, describe the arcs s s, r t, oo' and p s'; on the curve from p to s' set off the five divisions of the line g f; on r t, set off the seven divisions of the line r x, and connect s' t; then p s' t r is one side of the soffit, which will have to be bent over a suitable center by some of the methods hereafter explained. From p r the straight jamb will have to be spliced as the height may require.
78. The plan of a window or door opening in a circular wall, the jambs of which radiate to the center from which the circular wall is described, and the soffit of which is circular, is shown in Fig. 44. To unfold the shape and length of the soffit, let h be the center from which the circular wall j' g' t b g l' is described, and h f the center line of opening; draw b' b at right angles to h f, and equal to the required opening at the concave face of wall; from h, through b and b', draw h a and h a'; draw a a' at right angles to g' h, and tangent to the outer curve of the wall at g'; t b and t' b' are then the faces of the jambs. From g' as a center, describe the semicircle a' f a; divide the quarter circle fa into three or more equal parts, as at d and d'. From these points draw perpendiculars to a' a, as d r and d' z, and draw r h and z h. With h as a center, describe the arc a a" of indefinite length; on it, twice set off the number of divisions of a f as a z", z" r", etc.; from these points, draw lines to h. Next project g to g, and g' to a; then g, a is the true length of gg'. On h g", which is h g' in the development, lay off, from g", g" g"' equal to g,a. Again, from r, draw r r1; perpendicular to h r, and equal in length to r d. Draw h r1; also draw s s1 and y y1 perpendicular to h r; then y1s1 is the true length of y s. Mark it on the corresponding lines h r" and h r't by making r" s" and r' s' equal to rl s1; and .s" j" and s' y' equal to s1, y1. Similarly, find the true length of c x, and lay it off on h z' and h z". As at and t b are shown in their true length on the plan, a" t" and t" b" are laid off on h a" equal to the corresponding lengths on h a. Through all the points thus found, draw the outlines, and the Figure t bg" b" t" g" will be the required development of the soffit. From t b and t" b" the straight jambs will be spliced to the length required, a splicing portion to be left on at both sides. This soffit will also have to be bent over a suitable center in one of the ways hereafter described.
79. The plan of a window or door opening in a circular wall where the jambs and circular soffit splay equally, is shown in Fig. 45. Let A be the circular wall, and a b and a' b' the splayed jambs of the opening. Draw a' a equal to the width of the opening on the concave side of the wall, and b' b equal to the width of the opening on the convex side of the wall. Continue the sides of the jambs a b and a' b' till they intersect at e. Draw e f at right angles to a'a; with rasa center, describe the semicircle a' fa. Divide the quarter circle a f into three or more equal parts, as at k and k'; from these points draw k n and k'p, perpendicular to a'a; also, draw ep and en. With e as a center and ea as radius, draw the arc a a" of indefinite length, and lay off from a on it the distances an", n"'p"', etc., equal to a k, k k', etc., the number of divisions being twice those laid off on af; draw lines from e to n", p", etc. To find any developed length, u qp, for example, draw pp1 perpendicular to ep, and equal in length to pk' also draw ep1 Draw uut and qq1 parallel topp1; then p1ql and ql ul are the true lengths of pq and q u, and, laid off as shown on the proper lines, corresponding to ep, as ep' and ep", will give points on the development of the soffit. All other points being found in the same manner, the complete development is b d" b" a" r' a. The outer full line and the dotted line represent the beveled edges of the soffit.
80. The plan of a window or door opening in a straight wall with splayed jambs, and a semicircular soffit on one side of the wall, and a semielliptical one on the other side, so arranged as to preserve the crown of the soffit level, are shown in Fig. 46. Let A be the wall, and a a', o o' the opening and splay of the jambs; continue the splayed-face line of the jambs a' o' and ao to f; through the center of the opening, draw the center line fj; from k as center, and with a radius ko' draw the semicircle o'uo, which will be the interior elevation of the window head, and divide it into any number of equal parts - in this case six; through each of these parts, as r, t, etc., let fall a perpendicular to o' o, as re, td, etc. From f", through c and d, draw fz' and repeat the construction on the other side of the center; at right angles to a a' draw z' n', v n, Ij, etc.; make z' n' vn, Ij, equal to cr, dt, ku, etc., respectively, and through these points trace the semiellipse a n' nja', which will be the outline of the exterior of the opening. To find the length and shape of the soffit, draw fb at right angles to fa; make fx,fy, and fb equal to cr, dt, and ku, respectively; with fc as a radius, and with x as a center, describe an arc at z; then, with o; as a radius, and with o as center, describe another arc at z intersecting the first one. Through z draw the line xzz* indefinitely; with fd as a radius, and y as center, describe an arc, and with st as a radius, and z as center, describe a second arc intersecting the first at i; from y draw through i the indefinite line y i i". Next, with fk as a radius, and b as a center, describe an arc, and with tu as a radius, and i as a center, describe a second arc intersecting the first at m; through m then draw the line b m m" indefinitely. With b as center and bf as a radius, describe an axc fh g. Prolong mb to h; make the arc kg equal to the arc hf and connect bg; make bu'v' equal to by x. With b as a center, with any convenient radius, describe a measuring arc rw' from a", where the line h m" intersects this arc, lay off the spaces a" d", d" d", and d"' w equal to a" a", a" e, and er on the opposite side; through w draw gwp", and then through these points drawz v" l", u'v", etc. Make zz" equal to cz', ii" equal to dv, and mm" equal to kl, etc.; make wg and wp" equal respectively to r o and ra, d" k' and d" l" equal respectively to ez and ez", and d" f and d"v" equal respectively to a" i and a" i'"; a curve through ozimf k'g is the interior edge of the soffit; and one through a z" i" m" v" l"p" is the exterior edge. Sufficient overwood must be allowed beyond gp" and oa to bevel the edges of the soffit to attach to the straight jambs, p" g and ao, which are spliced on as required. The soffit must be bent over a suitable center.