Just as we may have a circular cone, either right or oblique, so in the same way we may have an elliptical cone. A sketch of a cone whose base is an ellipse, and whose axis is perpendicular, is shown in Fig. 167. A cap may be of this shape, or an object may be formed by some part of an elliptical cone surface. We shall now give a few examples of pattern-marking for this class of work.
In Fig. 168 the method employed to set out the pattern for a complete and also for a frustum of an elliptical cone is shown. A half-elevation of the cone c 0 t is drawn, and also a quarter of the base ellipse. This latter is divided into four equal parts, and taking c as centre, the points 1, 2, etc., are swung on to the base line c 0. The points 1' 2', etc., are then joined to the apex t. To mark the pattern out the compasses are set respectively to t 0, t1', t 2', etc., and the arcs of circles, as shown, described from the point T. Then, fixing the compasses to the length of one of the parts on the quarter-ellipse, and commencing at 4 on the pattern, the points 3, 2, 1, and 0 are stepped from one arc to the other, the points then being joined to form an even curve. To form a complete cone, two parts like 0 T 0 would have to be cut out.
For an article made up like the shape of a frustum of a cone, the inner portion of the cone pattern would have to be cut away. Thus, suppose a b represents the half top of the article, then the lengths of lines from t down to where they cross a b will give the lengths of lines to mark the points to form the curve B D B. Thus, T B equals t b, and T D equals t d, and so on for the other lines.
It should be noted in setting out the shapes of tapered elliptical articles that only three dimensions for top and bottom can be worked to. In the present case we have the length and breadth of the bottom and the length of the top only. If required for shaping, or other purposes, the width of the top can be measured from a d, the length of this line giving half the width of the top. It should also be remembered that articles of the above description are not equal tapering, the ends having a greater overhang than the sides.