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.

The patterns for articles whose surfaces are of double curvature can be marked out very approximately by an adaption of the methods already explained. Before, however, the methods can be applied to this class of object, it will be necessary to give some preliminary explanation. Suppose it is required to get the size of a circular blank that will work up into a as shown by the section in Fig. 239. It should be remembered, as has already been stated, that the area of the pattern disc must be equal to the area of the bottom and body together of the vessel. The bottom being a circle, there will, of course, be no difficulty in finding its area. To calculate the area of the body-surface, however, is a more difficult task. We may consider the body as being a surface of revolution - that is, a surface swept out by the arc A D E moving at a constant distance from the centre line C F. It is manifest that if the arc revolves in this manner, the surface generated would be that as shown by the figure. Now, the area of a surface formed in this way is equal to the length of the generating curve - in this case the arc - multiplied by the distance that its centre of gravity would travel in one complete revolution. The centre of gravity, it may be explained, can be looked upon as an imaginary point upon which the section curve would balance in any position. For an arc of a circle, the position of its centre of gravity can be calculated by the following rule: "Multiply the radius by the length of the chord, and divide by the length of the arc; the result giving the distance of the centre of gravity from the centre about which the arc has been described."

Continue to: