Fig. 516. - Plam and Elevation of Cone Interserted by a Cylinder at Right Angles to its Base.
In Fig. 516, let B A C represent the elevation of the cone, D E G H the elevation of the cylinder, which joins the cone at right angles to the base BC. J K L M N O P Q is the plan of the articles, which is to be drawn in line and under the elevation, making like points correspond in the two views, as shown. Draw a section of the cylinder in line with the elevation, as shown by E F G R. Divide the section of the cylinder into any convenient number of equal parts, as shown by the small figures. From the apex A drop a line through the plan, as shown by A M. Through the center of the section of the pipe, as shown in plan, draw a straight line to the center of plan of cone, as shown by J P. This line will also be at right angles to K M. From each of the points in the section of the pipe in elevation drop lines parallel to the sides of the pipe cutting the side of the cone, extending them to the line J P in plan, as shown by N a b c, etc. Through each of these points, from Pas center, describe circles.
As shown, cutting the sides of the plan of cylinder. From each of the points of intersection with the side of the cone (A B) draw lines parallel with the base, and extend them inward. If it is desired to show the miter line in elevation formed by the junction of pipe and cone, from the points d ef in the plan of cylinder carry lines vertically to the elevation, producing them until they meet the horizontal lines having similar letters drawn through the side of the cone A B, giving the points g h j. A line traced through these points, as shown by D g hj H, will be the miter line.
Fig. 517. - Half Pattern of Cone Shown in Fig 516.
Fig. 5 18. - Perspective View of Cone and Cylinder Shown in Fig. 516.
The half pattern of the cone, with the opening to lit the cylinder, is shown in Fig. 517, to describe which proceed as follows: From any convenient point, as A in Fig. 517, with A B of Fig. 516 as radius, strike an are indefinitely, as shown. From B of pattern set off each way the stretchout of J M and J K of plan and connect K and M with A. Then KAMB is the half pattern of the cone, or as much as shown on plan by K J M. To obtain the shape of opening to be cut in cone to correspond with the shape of pipe, on A B, the center line of pattern, set off points corresponding to
H fe d D of elevation, as shown by H c b a D. From the center A of pattern describe ares catting the points
H c b a D.
It is only necessary now to make each of these arcs equal in length to the one to which' it corresponds in the plan by any method most convenient. Thus make ad and a d1 equal to a d of the plan, b e and b e1 equal to b e of the plan and c f and cf equal to c f of the plan. A line traced through these points, as shown by H Q DO, will be the shape of the opening. Another method of making the measurements of the arcs is shown by the radial dotted lines of the plan and pattern in the manner explained in the problem immediately preceding.
The pattern for the cylinder is obtained in the manner usual with all parallel forms, its only peculiarity in this case being that its stretchout is taken from the irregular spaces upon the profile N O P Q of the plan, which are transferred to the line P' P", as shown.
A pictorial representation of the finished article is shown in Pig. 518, upon which some of the lines of measurement shown in Fig. 510 have been traced.