This section is from the book "The New Metal Worker Pattern Book", by George Watson Kittredge. Also available from Amazon: The new metal worker pattern book.

Fig. 400. - Ptan and Elevations of a Cold Air Box in Which the Inclined Pertion Joins the Level Portion Obliquely in Plan. - First Solution,

Now drop lines from all the points of the plan at right angles to A' E', intersecting each with its corresponding line of the new elevation, thus locating each point of the miter in that view As points D' and C are upon the floor, their position will be found at D2 and C2 Likewise lines from A' and B' will locate those points in the upper surface of the horizontal pipe, as shown at A2 and B2, where they are also shown to be in the side elevation. A line dropped from E' will also locate that point at its proper hight, as shown at E2. A line connecting A2 and E2 will then be the hypothenuse above alluded to and be the correct length sought. As all edges or corners of the pipe are necessarily parallel, lines drawn from B2 C2 and D2 parallel to A2 E2 will complete this part of the elevation as far as necessary. In these, as in all geometrical drawings, lines showing parts concealed from view by other parts are always shown dotted. Lines from X and Y locate those points in the new elevation and show that, while a correct elevation of the inclined arm of the pipe has been obtained, the view of the horizontal portion is oblique, the space between X2 and Y2 showing the open end to fit against the furnace body.

Having now obtained a correct oblique elevation, the next step is to obtain a correct profile upon any line, as F H, drawn at right angles across the pipe, which may be accomplished in the following manner: From each point upon the line of the section F, G, J and H project lines parallel with the direction of the pipe to a convenient point outside the elevation, as shown at the left, across which draw a line, x y, at right angles to them as a base from which to measure distances from front to back.

Assuming its crossing with the line from G (point 1) to represent the near angle of the pipe, set off from x on the line from F the horizontal breadth of the pipe b, thus locating point 4, which corresponds to the point F in the elevation. In like manner on the line from H set off from y the distance o of the plan, locating the point 2, which corresponds to point II of elevation, and draw the lines 1 4 and 1 2. The distance of point 3 from line x y is equal to distance b plus the distance o, or in other words, draw the line 2 3 parallel to 1 4 and the line 4 3 parallel to 1 2, thus locating the point 3.

Having now a profile and a correct elevation of the miter, nothing remains but to lay off a stretchout, as shown, upon the line H K and drop the points in the usual manner from the profile to the miter line A2 B2 C2 D2, thence into the measuring lines of the stretchout, all as clearly shown in the drawing.

As the plan shows all the dimensions of the horizontal arm of the pipe, the pattern for that can be developed in the usual manner. To avoid confusion a duplicate of that part of the plan has been transferred to Fig. 401, where a stretchout of the normal profile is laid off at right angles to the lines of the pipe, into which the points are dropped from the miter line A B C D. In the normal profile of course the distances 1 4 and 2 3 are equal to b and the distances 1 2 and 4 3 equal to a of Fig. 400.

Fig. 401 - Plan and Pattern of Level Arm of Cold Air Box.

It may be noted here that, as is the case in all raked profiles, the dimensions and shape of the profile obtained from the oblique elevation differ somewhat from those of the normal profile shown in Fig. 401, and that their stretchouts are therefore necessarily different.

Second Solution. - It may be asked naturally, is there no way of producing a miter without a change of profile, just as a carpenter would saw off the ends of two square sticks of timber of the same section and produce a perfect miter at an oblique angle? There is, but the method of doing it is not so apparent as the one just described. To accomplish this a drawing or view must be obtained, in which the surface of the paper represents a plane common to both arms of the pipe. As three points determine the position of a plane, it will be seen at once that such a plane passes through the points Z, A and E of the side elevation, Fig. 400. The best means of obtaining this view is shown in Fig. 402, in which the plan shown in Fig. 400 has been reproduced, but turned around in such a manner as to facilitate the projection from it of an end elevation, all of which is clearly shown in the drawing. This view shows the offset e and the rise c of the oblique portion of the pipe. The new view, which will give the required conditions, is obtained by looking at the pipe in a direction at right angles to A E of the end elevation, and is obtained as follows: Parallel to A E at any convenient distance away draw A' E', which make equal to A E by means of the lines drawn at right angles to A E, as shown. Upon the line E' E set off from E' the slant d as given in the side elevation and plan, Fig. 400, locating the point E2, and draw the line E2 A'. From all points of the profile or end view of the horizontal pipe, 1, 2, 3 and 4, project lines also at right angles to A E, continuing them across the line A' E', and make A' Y2 equal to A Y of the plan. Then A' Y2 will be the length of the horizontal arm in the new view and A' E2 will be the length of the inclined arm, both lying in the same plane, and the angle E2 A' Y2 will be the angle at which the two arms meet. Under the above conditions, then, a line which bisects that angle, as A' C, will be the miter line between the two arms. As the two arms of the miter are symmetrical, the view can be completed, if desired, by drawing lines parallel with A' E2 from the points of intersection with the lines from the end view with the miter line A' C. As 1 2 3 4 is the profile from which the short arm was projected in the new view, a stretchout may now be taken from it and laid off on any line at right angles to C W and the point-dropped in the usual manner, all as shown. If desired, the stretchout may also be laid off at right angles to the inclined arm and the pattern for this piece thus developed from the same miter line, although the miter cut A B C D A is the same in both pieces, one simply being the reverse of the other.

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