View A shows the lateral, or curved, surface of a cylindrically shaped object, such as a tin can. It is developable since it has a single-curved surface of one constant radius. The width of the development is equal to the height of the cylinder, and the length of the development is equal to the circumference of the cylinder plus the seam allowance. View B shows the development of a cylinder with the top truncated at a 45-degree angle (one half of a two-piece 90-degree elbow). Points of intersection are established   to   give   the   curved   shape   on   the development.  These  points  are  derived  from  the intersection of a length location, representing a certain distance  around  the  circumference  from  a  starting  point, and the height location at that same point on the circumference. The closer the points of intersection are to  one  another,  the  greater  the  accuracy  of  the development. An irregular curve is used to connect the points  of  intersection. View C, shows the development of the surface of a cylinder with both the top and bottom truncated at an angle of 22.5° (the center part of a three-piece elbow). It is normal practice in sheet metal work to place   the   seam   on   the   shortest   side.   In   the development of elbows, however, the practice would result in considerable waste of material, as shown in view A. To avoid this waste and to simplify cutting the pieces, the seams are alternately placed 180° apart, as shown in figure 8-13, view B, for a two-piece elbow, and view C for a three-piece elbow. RADIAL-LINE DEVELOPMENT OF CONICAL   SURFACES The surface of a cone is developable because a thin sheet  of  flexible  material  can  be  wrapped  smoothly about it. The two dimensions necessary to make the development of the surface are the slant height of the cone and the circumference of its base. For a right circular cone (symmetrical about the vertical axis), the developed shape is a sector of a circle. The radius for this sector is the slant height of the cone, and the length around the perimeter of the sector is equal to the circumference of the base. The proportion of the height to the base diameter determines the size of the sector, as shown in figure 8-14, view A. The next three subjects deal with the development of a regular cone, a truncated cone, and an oblique cone. Regular  Cone In figure 8-14, view B, the top view is divided into an equal number of divisions, in this case 12. The chordal distance between these points is used to step off the length of arc on the development. The radius for the development is seen as the slant height in the front view. If a cone is truncated at an angle to the base, the inside shape  on  the  development  no  longer  has  a  constant radius; it is an ellipse that must be plotted by establishing points of intersection. The divisions made on the top view are projected down to the base of the cone in the front view. Element lines are drawn from these points to the apex of the cone. These element lines are seen in their true length only when the viewer is looking at right angles to them. Thus the points at which they cross the truncation line must be carried across, parallel to the base, to the outside element line, which is seen in its true length. The development is first made to represent the complete surface of the cone. Element lines are drawn from the step-off points about the circumference to the center point. True-length settings for each element line are taken for the front view and marked off on the corresponding element lines in the development. An irregular curve is used to connect these points of intersection,  giving  the  proper  inside  shape. Truncated  Cone The development of a frustum of a cone is the development of a full cone less the development of the part removed, as shown in figure 8-15. Note that, at all times, the radius setting, either R₁ or R₂, is a slant height, a distance taken on the surface of the cones. When the top of a cone is truncated at an angle to the base, the top surface will not be seen as a true circle. This  shape  must  be  plotted  by  established  points  of intersection. True radius settings for each element line are taken from the front view and marked off on the corresponding element line in the top view. These points are connected with an irregular curve to give the correct  oval  shape  for  the  top  surface.  If  the development of the sloping top surface is required, an auxiliary view of this surface shows its true shape. Oblique Cone An oblique cone is generally developed by the triangulation method. Look at figure 8-16 as you read this explanation. The base of the cone is divided into an equal number of divisions, and elements 0-1, 0-2, and so on are drawn in the top view, projected down, and drawn in the front view. The true lengths of the elements 8-11