Doorways should be kept well clear of landings both at top and bottom, and no intermediate landings should be separated by less than three steps. Odd steps in unexpected places are a source of danger. Where a landing is arranged between two flights in the same straight line its "going" must not be less than the width of the stairs.

Geometrical Stair 258

Fig. 170.

Hand-railing is the term applied to the work of forming and fitting hand-rails to stairs. In the case of Dog-leg and Open-newel stairs there is not much of a difficult nature to overcome, as the lengths are generally straight between the newels, any curves which occur being vertical and having their centre lines on plan coincident with the centre line of handrail. These curves are shown in Fig. 170, which illustrates a "Ramp" at A, and a "Knee" at B, a combination of these two being known as a "Swan-neck." Where the hand-rail is not fixed into the newel at the commencement of stairs, as shown in Fig. 166, it is usually carried over the top of the newel by means of a ramp, and finished with a cap, either plain or carved, or with a scroll. These various curves and parts may be easily set out and worked from the solid. It is when hand-rails have to be fitted to geometrical stairs that difficulties commence. There are several methods extant for obtaining the desired end, but space will only permit of a brief description of one, that known as the "Square cut and Tangent," as being perhaps the most general in use, and also the most easily grasped by the tyro. The name Square-cut applies mainly to the cutting of the wreath pieces "square" with the face of the plank, and also to forming square or butt joints. The term Tangent refers to the method of setting out and determining the plane in which the section of rail is contained, by means of lines drawn tangentially to the curve of the rail on plan. The simplest illustration which can be given of the curve required to form a wreath in a handrail is obtained by imagining a slice to be cut from a hollow cylinder, as shown in Fig. 171. The cylinder is cut diagonally by the lines AB and CD. These lines are parallel to each other, the distance between them being equal to the depth of the hand-rail in the square. The slice so cut is projected into elevation as shown, and cut through its axis by the line EF. By then eliminating half which is shown dotted, and assuming the hand-rails joined to the remainder as shown, the curve of wreath is complete. It will, of course, be understood that this would not do for a hand-rail, as it is all across the grain, but it serves as a model to illustrate the principle, the object now being to obtain a rail of similar form, but with the grain following the curve. The curve shown in Fig. 171 is for a half-turn wreath, and such must always be made in two pieces, jointed in the middle in order to avoid cross grain. Quarter-turn wreaths are worked from a single piece.

Geometrical Stair 259

Fig. 171.

Fig. 172 shows the various drawings necessary for setting out a wreath over quarter-space winders on the tangent system. The first step is to draw an exact plan of the winders, with two or three flyers above and below, as at (1), Fig. 172. On this plan the centre line of the rail is shown in a firm line, the width of the rail being indicated by dotted lines. The next step is to draw the "stretch-out " of the centre line of the rail as shown at (2). To do this, draw the two lines A'A' and C'C at a distance apart equal to the curved portion of the rail AC on plan, the curve being measured by taking a number of short steps with the dividers, this method being quite near enough for practical purposes. The points where the risers 11 and 12 occur are then measured off along the curved line AC on plan, and their position on the stretch-out is marked. The heights of the risers are then measured up either of the lines A'A' or C'C, and the stairs 10, 11, 12, and 13 are drawn upon the stretch-out. The stairs 8, 9, 14, and 15 are set out with the same going as is shown on plan. Now it is clear that the hand-rail should be the same height over each stair - that is to say, the hand-rail should be parallel with the nosing line. The nosing line is drawn, therefore, upon the stretch-out, and if it forms one continuous line, as in this case, it will be quite satisfactory. It sometimes occurs, especially when balanced winders are used, that the line connecting up the nosing line of the upper and lower straight portions of the hand-rail will fall above or below the nosing line of the winders, and either arrangement is a source of great danger to users of the stairs. In such a case there are two methods of overcoming this difficulty. If the stairs have not already been constructed, they should be again set out on the stretch-out, so as to give a more satisfactory falling line, as the centre line of the rail over the winders is called. If the stairs have already been constructed, then the falling line of the wreath must be adjusted so as to be as nearly as possible coincident with the nosing line of the winders, and where it joins the straight rails a slight curve or "easing" is employed, so that the slight difference in height of the rail above the stairs is less perceptible to those who have to use the stairs. The more gradual the easing, of course, the less perceptible is the variation in height, but the thicker will be the stuff from which the wreath piece is cut. The curved part of the hand-rail is now enclosed in a triangular prism ABC on plan, with the planes BA and BC tangential to the curve at the springings A and C, and a development, or stretch-out, is made of these tangent planes, as shown at (3), Fig. 172. To do this the prism is stretched out, the lines A"A", B"B", and C"C" corresponding with the edges A, B, and C on plan. The risers are then projected upon this development from the stretch-out of the central line of rail. The treads are measured off the plan, and in the case of stairs 10, 11, and 12 the treads are measured off along the tangent planes AB and BC on plan. The centre lines of the upper and lower straights are drawn in their position above the nosing lines, the upper line being produced to cut the line B"B" at b. The point a' on the stretch-out is then projected on to the point a in the line A"A" on the development of the tangents, and the points b and a are joined and produced to meet the centre line of the lower straight rail. The distance FG is measured off along the level line through a, equal to the distance AC on plan, and cG is joined. It should be noted that, if the drawing is correct, the point c on the development of the tangents will be level with the point c' on the stretch-out of the central line of the rail. The lines ab, bc, and cG are the true lengths of the sides of the section of the prism ABC, which contains the central line of the curved portion of the rail. To obtain the face mould, set down the line a"e" equal to Gc (as shown at (4)), and with centre a" and radius ab describe an arc, and with centre c" and radius cb describe another arc, cutting the former arc at b". Join d'b' and c"b". a"b"c" is the true shape of the section of the prism containing the centre line of the rail. From a" and c" draw the lines a"0 and c"O respectively, parallel to b"c" and a'b'. Then O is the centre of the elliptical curves bounding the face mould.