Sheet metal drafting/Chapter 9

by Ellsworth M. Longfield

CHAPTER IX
FRUSTUMS OF RECTANGULAR PYRAMIDS

Objectives of Problems on Frustums of Rectangular Pyramids.

Problem 32
DRIPPING OR ROASTING PAN

60. Dripping or Roasting Pan.—Figure 186 is a sectional view of a standard dripping or roasting pan. Since pans of this kind are subjected to temperatures above that at which solder melts, it is necessary to employ some means besides soldering to enable them to hold liquids. This is accomplished by folding the corners of the pattern so that they will lie flat against the ends.

Standards of Construction.—All dripping pans have a standard flare of three-eighths of an inch as shown in Fig. 186. They are wired with No. 8 tinned or coppered wire. The measurements for this type of pan are always understood to be measurements of the top of the pan outside of the wire. The dimensions of the bottom are always 1¼ in. less than the measurements of the top. Thus, a 12 in.×18 in. dripping pan measures 12 in.×18 in. outside the wire around the top, and the bottom measures 10¾ in.×16¾ in. The depth varies with the size of the pans.

Pattern of One Corner.—Figure 187 shows a full size development of one corner of a dripping pan, which is produced in the following manner:

Draw the lines ab and bc forming an angle of 90°, Fig. 187.
Continue these lines indefinitely (shown by dotted lines bd and be), and set off upon these lines the slant height of the pan, bd of Fig. 187.
Draw lines dH and ek parallel to lines ba and bc, respectively.
Make lines df and eg three-eighths of an inch long.
Prolong these lines until they meet at the point L.
Draw the diagonal Lb.
With point f as a center, and any radius, draw the arc mnp.
With n as a center, set off the distance mn on the other side of the point n so that arc np will exactly equal arc nm.
Draw the line fg, extending it until it intersects the diagonal at the point r.
Draw the line rg.
Draw the lines s–T and t–u parallel to f–r and r–g, and at a distance of ⅛ in.

This cutting away of the corner allows the wire around the top of the pan to lie flat against the ends and prevents thereby a "bunch" at each corner.

A wire edge of ⅜ in. should be added to each top edge as shown in Fig. 186.

Figs. 186-188.—Dripping or Roasting Pan.

First Operation.—The outline of the bottom of the pan is swaged on all sides by means of the "Square Pan Swage." The diagonals (line b. T. of Fig. 187) are next swaged in the same machine.

Second Operation.—The sides are "brought up" simultaneously over the hatchet stake, the corners taking the shape shown in the illustration. These corners are then closed down on the "square head."

Third Operation.—Each corner in turn is then placed in position on the "crooked square head" and the corner "brought around" as shown in the illustration.

Fourth Operation.—The wire edge is then "laid off" over the edge of the bench, the wire inserted, and finished in the wiring machine. The bottom edges are then straightened and the oval handles attached to the ends of the pan.

Laying out Directly upon the Metal.—Figure 188 shows the pattern of a dripping pan measuring 12⅜ in.×5⅜ in.×1 in. deep. The first step is to compute the size of the blank required. Since the bottom is 1¼ in. smaller than the top, the bottom measurements would be

${\begin{aligned}12{\frac {3}{8}}''-1{\frac {1}{4}}''&=11{\frac {1}{8}}''{\text{ (length)}}\\5{\frac {3}{8}}''-1{\frac {1}{4}}''&=~4{\frac {1}{8}}''{\text{ (width)}}\end{aligned}}$

To each dimension of the bottom must be added two slant heights and two wire edges. The slant height of a pan 1 in. deep and ⅜ in. flare is $\scriptstyle {1{\frac {1}{16}}}$ in.; therefore, the dimensions of the blank would be

${\begin{aligned}11{\frac {1}{8}}''+(1{\frac {1}{16}}\times 2)+({\frac {3}{8}}\times 2)&=14''{\text{ (length)}}\\4{\frac {1}{8}}''+1(1{\frac {1}{16}}\times 2)+({\frac {3}{8}}\times 2)&=~7''{\text{ (width)}}\end{aligned}}$

The workman cuts a rectangular piece of metal 7 in.×14 in. and lays off a ⅜-inch wire edge, Fig. 188. Inside of these lines he lays off a distance of $\scriptstyle {1{\frac {1}{16}}}$ in. to form the outline of the bottom. He then develops the pattern of one corner, according to the description given for Fig. 187. Having obtained the pattern for one corner, he transfers the measurements to the other three corners and the pattern is complete. The shaded portion of Fig. 188 denotes that part of the blank which is cut away.

61. Related Mathematics on Dripping Pans.—Dripping pans are made in a great variety of sizes, the more common of which are: 10″×15″×2¼″; 12″×17″×2¼″; 12″×19″×2½″; 14″×15″×2½″; and 18″×19″×2½″.

Problem 32A.—What will be the dimensions of the blanks required for each of the above sizes of pans?

Problem 32B.—What will be the weight of each of the above sizes of pans if made from No. 28 U. S. S. Gage black iron (.6375 lb. per sq. ft.) and "wired" with No. 8 gage wire weighing .07 lb. per running foot? (Do not deduct for the corners that are cut away.)

Problem 32C.—Using stock size sheets of 30″×96″ black iron, what would be the percentage of waste per pan for dripping pans measuring 12″×17″ and 2″ deep?

Problem 33
RECTANGULAR FLARING PANS

62. Rectangular Flaring Pans.—Frequently, the contour of the ash pit demands that a furnace or range ash pan be given unequal flares. Such a pan is shown in Figs. 189 and 190. It should be noted that the sides of the pan flare 2 in. as shown in Fig. 189, while the front end flares 5 in., and the back end flares 3 in. as shown in Fig. 190.

The Elevation.—A front and side elevation should be drawn, setting forth the exact dimensions of the pan. The pan is stiffened around the upper edge with a ¼-inch rod. When this rod is covered with the wire edge, not less than ⅜ in. should be allowed for clearance. Thus a pan measuring 34¾ in.×16¾ in. outside of the wire would measure 34 in.×16 in. inside of the wire. The pan has two profiles A,B, C, D of Fig. 190, and E, F, G, H of Fig. 189.

The Pattern.—Two lines of stretchout are drawn at right angles to each other as shown by the dotted lines of Fig. 191. The spacings of the profiles are set off upon these fines of stretchout, the spacings A,B,C, and D being taken from Fig. 190, and the spacings E, F, G, and H being taken from Fig. 189. Measuring lines are drawn at right angles to the line of stretchout through each of these points. The flares 5 in., 3 in., and 2 in. should now be set off at their respective corners as shown in Fig. 191. The inclined lines representing the meeting lines of each corner should be put in.

A ¾-inch lap is added to each corner of the sides of the pan, and a center line for the rivet holes drawn in. The centers for the rivet holes should also be located in the laps. With the corner of the bottom (point P) as a center, arcs intersecting a straight line drawn ⅜ in. in from the meeting line of the end should be drawn. Only one corner of Fig. 191 is treated for rivet holes, but it is required that the rivet holes for all corners be located. The ⅝-inch edge for covering the ¼-inch rod may now be added to complete the pattern.

The Bail—The bail is shown in Figs. 189 and 190 by dotted lines. Since the bail is below the top line of the pan, it must be drawn carefully in order to scale the dimensions accurately. It is generally placed so that the bail ear will be to the rear of the center. The ear is attached in such a manner that the "stop" will maintain the bail in an upright position. The center of gravity being in front of the bail allows the pan to be carried with one hand without danger of spilling the contents.

Figs. 189-192.—Rectangular Flaring Pan.

Figure 192 shows an elevation of the bail. The dimensions are all given for the center lines of the rod. In case the rod is bent to a "close angle" in the vise, these dimensions will answer. However, if a long radius bend is desired, the actual length of the center line must be computed, in order to obtain the length of the blank piece of rod required to make the bail.

63. Related Mathematics on Rectangular Flaring Pans.—

Problem 33A.—How much will the flaring pan of Fig. 191 weigh if made from No. 20 U. S. S. Gage black iron (1.53 lb. per sq. ft.)? The pattern is to be regarded as a rectangle.

Problem 33B.—How much will the rod around the top edge of the pan, Figs. 189 and 190, and the rod required to make the bail, Fig. 192, weigh if ¼″ rods weigh 0.1669 lb. per ft.

Problem 33C.—How much will the material required to make the complete pan cost at 7 cents per pound?

Problem 34
REGISTER BOXES

64. Register Boxes.—Register boxes are generally made from 1 C coke tin, commonly called by the trade "furnace pipe tin." The tin box must be made to fit the body size of the register. An allowance is generally made to assure an easy "fit" between the body of the register and the box. This allowance varies with the sizes of the registers as follows:

Size of Register Body.	Dimension of Box.	Depth of Box.
Not wider than  4 in., any length	Add ¼ in. to each dimension of body	4 in.
Not wider than  5 in., any length	Add $\scriptstyle {\frac {5}{16}}$ in. to each dimension of body	4 in.
Not wider than  7 in., any length	Add $\scriptstyle {\frac {9}{16}}$ in. to each dimension of body	4 in.
Not wider than  8 in., any length	Add ⅝ in. to each dimension of body	4 in.
Not wider than 11 in., any length	Add $\scriptstyle {\frac {11}{16}}$ in. to each dimension of body	5 in.
Not wider than 12 in., any length	Add ¾ in. to each dimension of body	5 in.
Not wider than 18 in., any length	Add ⅞ in. to each dimension of body	6 in.
Wider than 18 in., any length	Add $\scriptstyle {\frac {15}{16}}$ in. to each dimension of body	6 in to 8 in.

Figures 193 and 194 show end and side elevations of a register box for a 9 in.×12 in. register. According to the table, the dimensions of the top will be $\scriptstyle {9{\frac {11}{16}}}$ in.×$\scriptstyle {12{\frac {11}{16}}}$ in.

End Elevation.—The end elevation is drawn according to the dimensions given in Fig. 193. A half-profile of the "neck" is drawn and divided into equal spaces and each space numbered. The neck is joined to the box by a "bead and flange" joint. The corners of the elevation are numbered 1, A, 2, 3, B, and 4 as shown.

Side Elevation.—A side elevation should be drawn according to the dimensions given in Fig. 194. The points 5, C, 6, 7, D, and 8 are numbered as shown.

Pattern of Ends.—First, any horizontal straight line (line 2–3 of Fig. 195) is drawn equal in length to line 2–3 of Fig. 193. A perpendicular is erected at the point 2. The length of the slant height (line c–6 of Fig. 194) is set off from this perpendicular. The line

Figs. 193–198.—Register Boxes.

A B is drawn parallel to line 2-3. The point A is located ⅜ in. distance from the perpendicular. A ⅛-inch single edge is added to edges 4–2, 2–3, and 3–B, and a ½-inch flange is added to the top edge of the pattern, mitering the corners at an angle of 45°.

Pattern of Sides.—The pattern of the sides, Fig. 196, is produced in like manner. Instead of the single edge, however, a double edge is added to the edges that are to double seam onto the ends.

Pattern of Neck.—A line of stretchout, Fig. 197, is drawn and upon it is laid off twice as many spaces as there are in the half-profile of Fig. 193. Perpendiculars are erected at the points 9 and 9, Fig. 197. One-fourth inch edges are added to each end for the standard tin lock, and a $\scriptstyle {\frac {3}{16}}$-inch edge for the bead and flange joint notching as shown in Fig. 197.

Pattern of Bottom.—A rectangle. Fig. 198, whose dimensions are ¾ in. less than the top dimensions of the box, is drawn. The center is located by drawing the diagonals of this rectangle. From this center, a circle whose diameter is ⅛ in. less than the diameter of the neck, is drawn as shown in Fig. 198. This circle is cut out of the metal to provide an opening for the neck, and is always made smaller because the bead "draws in" when it is turned in the thick edge. A ¼-inch double edge is allowed on all sides to provide for double seaming the bottom to the body of the box. Over-all dimensions are placed on all views.

65. Related Mathematics on Register Boxes.—Problem 34A.— Furnace pipe tin is made in the sizes listed in the following table. Which size would you use in making the register box shown by Figs. 193 to 198 inclusive, in order to maintain as little waste as possible?

Coke Tin—Furnace Pipe Sizes

Size of Sheet.	Wt. Per Box No. Sheets.	Corresponding Pipe Size.
20″×23″	165 lb.	7″
20″×26½″	190 ''	8″
20″×29½″	211 ''	9″
20″×32½″	233 ''	10″
20″×36″	258 ''	11″
20″×39″	290 ''	12″

Problem 34B.—Any register has a series of holes cast in its face to correspond to some predetermined design. This design necessarily shuts off part of the opening, thereby retarding the flow of air through the register. Since most makers use nearly the same design, it has become the custom to deduct 33⅓ per cent of the area of the body size, in order to obtain the free area of the register. Fill in, in the following table, the free areas of the register sizes given.

Free Areas of Registers

Size of Body.	Free Area (66⅔ per cent of body area).	Size of Round Pipe Required (See Problem 34C).
6″×10″
8″×12″
9″×12″
9″×14″
10″×12″
12″×14″
12″×16″

Problem 34C.—Since a register cannot deliver more air than is conveyed to it, it is evident that the cross-sectional area of the round neck of the register box must equal the free area of the register. Using the formula, $\scriptstyle {D={\sqrt {{\text{Free area}}\div .7854}}}$, fill in the third column of the above table.