There are many articles made out of sheet and plate metal that are either oval or elliptical in shape. Not that these two figures are identical, although they are often confused with each other. The ellipse is a figure in one quarter of which we may suppose every small part of the curve is of a different radius, the curvature of the end being most acute, and the curve becoming flatter as it approaches the middle point of the side of the ellipse. The oval, however, although somewhat similar in shape to the ellipse, is a figure which is built up entirely of arcs of circles. Equal-ended ovals can be drawn by using several arcs of differing radii that are a very good approximation to an ellipse. An oval, however, to the sheet and plate metal worker has distinct properties of its own that make it particularly suitable for use in those cases to which it can be applied. When an article is required to be elliptical in shape, the oval should not be used, as there are convenient methods for the development of this class of work. (Shown in Chapter XXI (Elliptical Work. Construction Of Ellipse).)
The most useful shape of oval is that which is made up of two different arcs of circles, the one with small radius forming the ends, and the flatter curve joining on to make the sides. This can be set out entirely by construction, or partly by calculation and construction. Both methods will be shown. First by construction: Draw a line A B
(Fig. 134) equal in length to the long diameter of the oval, and through the middle point O of this diameter draw a line at right angles. Make 0 C and O D each equal to half the small diameter of the oval. From A mark off A E equal in length to C D. Divide E B into three equal parts. Now set the compasses at a radius equal to two of the parts, and with O as centre, mark points Q, Q. Then with O again as centre, and the compasses set to length
Q Q, mark points P, P. It will be seen that O P is equal to four of the parts into which E B has been divided. The points Q and P will be the centres from which the arcs will be described. Join P to Q, and produce the lines through as shown. Now with centre Q and radius Q B describe the end arcs, and with centre P and radius P C describe the side arcs. If carefully and properly drawn, the arcs should meet and run into each other on the lines drawn through P and Q. The object, indeed, for which these lines are drawn is to determine the meeting points of the curves. They also serve another purpose, which we shall see when drawing out the pattern for an oval equal-tapering vessel.
It should be noticed that the points P may come either within or without the figure, according as the oval is broad or narrow.
The second method consists in calculating the radii for the arcs and then setting out the figure. The rules for finding the radii are as follows: -
To find radius for sides: "From eight times the long diameter deduct five times the small diameter, and divide the remainder by six." In Fig. 135, the long diameter
A B = 6 in., and the short diameter CD = 4 1/2 in., therefore the radius for the side is -
8 A B - 5 C D / 6 = 48 - 22 1/2 / 6 = 4 1/4 in.
To find radius for ends: " From four times the short diameter deduct the large diameter, and divide the remainder by six." The radius for the ends, therefore, in Fig. 135 will be -
4CD - AB / 6 = 18-6 / 6 = 2 in
After having marked the centres, it is generally a good plan to draw in the lines as before, so that the exact point of contact of the curves may be known, as these come in useful later.
The above methods can, of course, only be used in the case of ovals that are the same shape at each end, the egg-shaped oval demanding special treatment.