The shapes of some unequal tapering articles may be made up wholly or partly of the surface, or some portion of the surface, of an oblique cylinder; by which is meant a pipe whose ends are circular and inclined to its centre line. Such a cylinder is shown as an in Fig. 158. It should be remembered, in dealing with this, that although the ends of the oblique pipe are circular, a cross-section of the pipe will be elliptical in shape; hence the more inclined the pipe becomes the flatter it will be, and the smaller its passage area. For this kind of connecting pipe it will be observed (Fig. 158) that the straight pipes are the same size, and also that their ends are cut square.
We shall first set out the pattern for a pipe of this description, and afterwards give a couple of examples illustrating its application to irregular tapering objects.
The elevation of the connecting pipe only is shown in Fig. 159, that being all that is necessary to obtain the development. A semicircle is described on one end of the pipe as in the figure, this being divided up into, say, six equal parts, and perpendiculars drawn to the end line 0 6, as seen. Through each of the last found points lines are run along parallel to the centre line of the pipe. Now to sweep out the pattern. Run lines down through points, 0, 1', 2', etc., square to the pipe, and then carefully setting the compasses at a distance equal to the length of one of the six parts of the semicircle, step distances 0 to 1, 1 to 2, etc., from one line to the other on the pattern. The curve on the pattern for the other end of the pipe can be set out in the same way, or lines run down and points from the first curve projected across. The better plan in the workshop is to mark one curve out carefully (or one quarter of it will do, as shown by the shaded part in Fig. 159), cut out in sheet metal, and use this as a template for the other end. The pattern, too, should be set out quite distinct from the elevation, as methods of projection are useless in workshop practice, and are only used in this descriptive way to better explain the connection between the elevation and the pattern. Allowances for jointing are put on as shown by the dotted lines. M u1t i p le-w a y pieces having portions of an oblique cylinder for the branch pipe connecting tubes can be set out in a somewhat similar manner to those shown in the last chapter.