Problem 47
OVAL TO ROUND TRANSITION
85. Oval to Round Transition.—The oval to round transition is extensively used in hot air furnace heating. In Fig. 275 the oval and the circle have the same center, but often the job demands that the center of the circle be placed to one side of the oval. However, the method of developing the pattern is the same in all cases, as long as the planes of the top and the bottom are parallel.
The Plan (Fig. 275).—The profiles of the upper and lower bases should be drawn in their proper positions with a horizontal center line for each. Since these profiles have the same center, the line AJ divides the figure into two equal parts and, therefore, but one-half need be treated.
Both half-profiles are now divided into equal spaces and each division numbered or lettered as shown. The order of development, as explained in Problem 46, should now be determined.
The Diagram of Triangles (Fig. 276).—Having determined the order in which the base lines are to be taken from Fig. 275, short horizontal lines equal to each base line are drawn. These are shown in Fig. 276, and the order should be carefully studied. Perpendicular lines equal in length to the altitude of the fitting, as shown in Fig. 276, are erected at one end of each of these lines. The hypotenuses of the several triangles are then drawn in.
The Pattern (Fig. 277).—A distance equal to the hypotenuse of triangle AD is set off upon any vertical line. These points are lettered A and 1. With point 1 as a center and a radius equal to the hypotenuse of triangle 1–B, an arc is drawn bearing away from point A. This is intersected by an arc drawn from point A, whose radius is equal to line AB of Fig. 275, thereby locating point B.
With B as a center and a radius equal to the hypotenuse of triangle B–2, an arc is drawn bearing away from point 1. This is intersected by an arc drawn from point 1, whose radius is equal to the line 1–2 of Fig. 275, thereby locating point 2.
In like manner all points of the pattern may be located. Attention is called to the space between letters E and F of Fig. 275. Since this is a straight line it is not divided and, therefore, the space EF is greater than any of the others.
Curved lines passing through the points thus obtained give the
