The frustum of an oblique cone can very conveniently be used to join together two circular pipes of unequal diameter, whose centre lines are parallel, and whose ends are cut square. A connecting pipe of this description, together with the pattern development, is illustrated in Fig. 143.
The elevation is first drawn by setting in the centre lines, the distance between the pipe ends and the pipe diameters. To complete the oblique cone, of which the tapered pipe is a part, the back and throat lines are produced until they meet at T. To obtain the pattern the surface of the whole cone is developed as in the last two examples, and the portion of the top of cone cut away, as will be explained. After swinging the points 1, 2, 3, etc., on to the base, they are joined up to the top of cone, and where these lines cross the joint line at the top of connecting pipe, will determine the lengths of lines required to mark along to obtain the shape of cut at small end of pattern. In the figure all the lines are shown swung around on to the pattern lines. The points so obtained are joined up with an even curve, and thus the net pattern is finished. No allowances are shown in Fig. 143; but these can be put on to the sides and ends of pattern to suit the method of jointing adopted.
Before passing from this it should be pointed out that whilst the ends of the connecting pipe in the above case are circular, a section of the tapered pipe taken perpendicular to its centre line will be elliptical, and consequently when the overhang is great the pipe will be very fiat, as in Fig. 142, and its area restricted. If it is required to have a tapered pipe of circular section, then the method shown in Chapter V (Tapered Pipe Elbows And Three-Way Pieces). will have to be followed.