This section is from the book "Practical Sheet And Plate Metal Work", by Evan A. Atkins. Also available from Amazon: Practical Sheet And Plate Metal Work.

This is shown in Fig. 104, the base of the complete cone being marked 0 6, and the apex C. The part of the cone for which a pattern is required is shown by the thick outline 0 A B D. It is best to imagine the base circle of the cone divided into twelve equal parts, and lines drawn to the apex from each of the division points. The cone being cut away at both ends will limit the surface lines to a definite length, and these we can obtain the true length

Fig. 104.

Careful observation should be taken of this method for obtaining the true lengths of lines, as it is applicable to all cases in which the surface of the article comes out as any portion of a cone.

In setting out the pattern, the development of the complete cone is first drawn (Fig. 104), the girth of the cone-base circle either being calculated or marked along by using one of the parts of the semicircle twelve times. Whilst there will be only twelve lines on the surface of the cone, it will be seen that there are thirteen on the pattern, the two outside lines coinciding to form the seam when the sheet or plate is bent into shape. After the radial lines are drawn, their required lengths can be marked off by taking the distances already projected on to the side of cone. Thus, to follow one point only, the line which is brought from 4 on the semicircle down to the cut on cone and then run to the outside will, when swung on to the pattern, cut off points on line 4. So with all the other lines. When the points are joined with a free curve, the net pattern is complete.

For purposes of shaping, it should be noted that the slant ends of the conical pipe are elliptical in form, their respective long diameters being 0 A and D B. To obtain the short diameter of the large ellipse 0 A will be bisected in E, and a line drawn through the point square to the centre line of the cone. On this line a quarter circle is described, then the line E F which is drawn parallel to the axis of cone will give half the short diameter of the ellipse. This method for obtaining the width of the cone at any part should be taken particular notice of, as it very often comes in useful in getting out shapes of holes in the flat.

Continue to: