Most articles that are circular, equal-tapering in shape, do not take the form of a complete cone, but come out as a frustum of a cone - that is, the shape that is obtained when the top of a cone is cut off parallel to the base. The bodies of the bulk of tapering articles such as buckets, funnels, coffee-pots, wash-ups, and a host of others are of this character, and their patterns are obtained by considering the surface to be that of a frustum of a cone, or a truncated
Fig. 86, cone, as it is sometimes called. The shape referred to is that shown by Fig. 87.
To obtain a pattern for this class of vessel is, generally, a very simple matter. The method adopted is to draw a half-elevation to the given dimensions, t h c n produce the slant height until it meets the centre line, and thus obtain the slant height of the cone of which it forms a portion. Having done this, the pattern for the complete cone is set out, and the part cut away that belongs to the top portion of the cone. Thus in Fig. 88, the half-diameter of wide end A B is set along, and the vertical depth A E drawn down square from it. The half-diameter of narrow end E D is marked from E square to A E, or parallel to A B. The slant line B D is produced until it meets the centre line of cone in C. This will, of course, give the top or apex of complete cone. To mark out the pattern the compasses are fixed on C as centre and C B as radius, and the outer curve drawn as shown, the inner curve being drawn with C D as radius. To mark the length along the outer curve a quarter-circle is set on A B and divided into three equal parts, one of these parts being marked along six times (the body t of article being made in two pieces). The first and last points are joined up to centre C, and thus the net pattern is determined. It will be noticed that no length is measured along the inner curve, this being cut off proportionately by the end lines. In some cases it is most convenient to mark the length along the inner curve (which, in the above example, would be equal to half the circumference of small end of vessel), join the points so found to the centre, and produce the lines out to cut the outside curve. If measured out accurately the resulting pattern should be the same in both cases; but generally, in practice, it is the best plan to mark the length along the outer curve.
The number of pieces in which the body of any article is made will depend upon its size and shape, the considerations being the economical cutting up of the sheet or plate, and the work on bending or conveniently shaping the plates into their proper form. On the other hand, some thought must be bestowed on the number of joints, or else the extra work on the joints will more than balance the saving in material. No particular rules can be given, as each job must be decided upon its own merits.
The laps for grooving or riveting should be added on to the net pattern, the lap lines being drawn parallel to the end lines. Allowances for wiring, knocking-up, or other form of joint, as required, can be added on, as mentioned in other chapters.
The position of a joint in an article is of some importance. In circular objects the joint is usually the weakest part: hence it is nearly always arranged so that it shall be covered by an ear, lug, or handle, to give it additional strength. In some articles it is arranged for the joint to be at the back, so that, for the sake of appearance, when the article is standing in its position the joint will be hidden.