Sheet metal drafting/Chapter 1

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Sheet metal drafting
by Ellsworth M. Longfield

Chapter I: Rectilinear Figures

Chapter II: Wired Cylinders

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1870378Sheet metal drafting — Chapter I: Rectilinear FiguresEllsworth M. Longfield

SHEET METAL DRAFTING

CHAPTER 1
RECTILINEAR FIGURES

1. Sheet Metal Drafting.—Sheet metal drafting is merely the application of the principles of ordinary mechanical drawing to objects which, for the purposes of drawing, lack thickness. By this is meant that the materials dealt with are usually in the form

Fig. 1.Pictorial Representation of Anvil.

of thin sheets and that their thickness is so slight that it may be represented by a line rather than by four lines and an included surface. The ordinary rules and conventions in use in mechanical drawing apply in general to sheet metal drafting. A knowledge of elementary arithmetic is also essential.

2. Orthographic Projection.—Before attempting to make any drawings, one must first get a clear idea of the way in which objects are represented in mechanical or orthographic drawings. If a person is going to make a photograph of an object, he nearly always makes a view taken from one corner so as to show as many sides as possible in order to give a complete idea of the object in one picture. For example, Fig. 1 shows how an anvil would be represented in a single view or picture so as to give a complete idea of its shape. Such a drawing of most objects would be very

Fig. 2.Mechanical Drawing of Anvil.

complicated or difficult to make, and even then in many cases it would not give the complete idea. Instead of making a pictorial drawing, the draftsman makes two or more views as if he were looking straight at the different sides of the object as in Fig. 2.

At A is shown what would be called a "front elevation," meaning a view of one side taken from the front with the anvil set up in its natural position. At D is shown the "plan" or top view. This shows what would be seen by looking down on the anvil from above along the direction of the arrow Y. At B and C are shown the views of the ends as seen by looking along the arrows, W and X. These views are called the "right end elevation" and "left end elevation," depending upon whether the view is that of the right end or the left end. At E is shown the bottom view, which would be that obtained by looking up from beneath in the direction of the arrow, Z. These views are not all needed to show the complete shape of the anvil. They are, however, all the different views that might be used by the draftsman. These "views" are also called the "projections" of the object, and this method of showing it is called "projection."

Drawings are made in the drafting room and are then sent to the shop so that the object shown can be made. Consequently, all drawings must have complete information on them so that no questions need be asked. Besides showing the shape and size of

Fig. 3.Drawing Board.	Fig. 5.Testing Straightness of Working Edges.
Fig. 4.T-Square.

the parts, the drawings must have full information as to the material to be used, its gage, number wanted, etc.

3. Drawing Instruments.—The Drawing Board and T-Square.—The drawing board. Fig. 3, is for the purpose of holding the paper while the drawing is being made. It is usually made of some soft wood, free from knots and cracks and provided with cleats across the back or ends.

The T-square, Fig. 4, consists of a head and blade fastened together at right angles. The upper or working edge of the blade is used for drawing all horizontal lines (lines running the long way of the board) and must be straight.

The left end of the drawing board must also be straight. The working edge of the T-square and the working edge of the drawing board may be tested for straightness by holding them as shown in Fig. 5. They should be in contact along their entire length. If they are not, one or the other is not straight.

The working position of the drawing board and T-square is illustrated in Fig. 6. In this position the blade of the T-square can be moved up and down over the surface of the board with the left hand while holding the head firmly against the working edge

Fig. 6.Working Position of Drawing Board and T-Square.

of the board. For a left-handed man, the working edge of the board will be at the right, with the head of the T-square held firmly in place with the right hand.

All horizontal lines should be drawn with the T-square, drawing from left to right, meanwhile holding the head of the T-square firmly against the working edge of the hoard with the left hand.

The Triangles.—The triangles are used for drawing lines other than horizontal. They are made of hard rubber, celluloid, wood,

Fig. 7.

Fig. 8.

or steel. There are two common shapes, called the 45° triangle and the 30°×60° triangle. These are illustrated in Figs. 7 and 8. The 45° triangle, shown in Fig 7, has one angle (the one marked 90°), a right angle. There are 90° in a right angle. The other angles are 45° each (just half of a right angle). One angle of the 30°×60° triangle is a right angle; another angle is 60° (just ⅔ of a right angle); and the other is 30° (just ⅓ of a right angle).

For drawing vertical hues (lines at right angles to the horizontal lines which have already been explained), the T-square should be placed in its working position and one of the triangles placed against its working edge. In Fig. 9 is shown the correct position

Fig. 9.Drawing Vertical Lines by the Use of T-Square and Triangle.

Fig. 10.Method of Drawing Various Angles by Use of Triangles.

of the hands and the method of holding the pencil for drawing these lines.

Figure 10 illustrates the method of getting various angles by means of the triangles separately and in combination. These angles, of course, can be drawn in the opposite slant by reversing the triangles.

Always keep the working edge of the triangle toward the head of the T-square and draw from the bottom up, or away from the body.

The Pencil.—The pencil must be properly sharpened and kept sharp. Good, clean-cut lines cannot be made with a dull pencil.

Fig. 11.Pencil Sharpened in the Proper Way.

A pencil sharpened in the proper way is shown in Fig. 11. The end "a" shows the chisel point which is used for drawing lines; the end "b" shows the round point used for marking off distances and for putting in dimensions, lettering, etc. About ⅜ in. of lead should be exposed in making the end "a." Then it should be sharpened flat on two sides by rubbing it on a file or piece of sandpaper.

The Scale.—A scale is used in making a drawing on an ordinary-sized sheet of paper, so that the drawing is of the same size as the object, or some number of times larger or smaller than the object.

Fig. 12.Triangular Scale.

The triangular scale illustrated in Fig. 12 has six different scales, two on each side.

The ordinary architect's triangular scale of Fig. 12 has eleven scales. On the scale of three inches equals one foot, a space that is three inches long is divided into twelve equal parts, each of which represents an inch on the reduced scale and is itself sub-divided into two, four, eight, or sixteen equal parts, corresponding to halves, quarters, eighths, or sixteenths of an inch. The other scales are constructed in the same way. A little study of the scale with the above description of its construction will make its use clear.

4. Lines.—In Fig. 13 the names and uses of various kinds of lines which are used in making a drawing are shown. This figure also shows a table of the relative weights of these lines.

Border Lines.—The border line needs no detailed explanation.

Object or Projection Lines.—The visible object line is a line that represents any definite edge that may be seen from the position that the observer assumes in obtaining the given view. The invisible object or projection line represents a line or edge of an object that cannot be seen from the observer's point of view but which actually exists and may be seen from some other position or point of view. For instance, the drawing board cleats on the bottom

Fig. 13.Lines used in Drawing.

could not be seen from above, but could be seen from the sides or when the board was held above the eye. For the sake of determining the relation of such cleats to some other member that might be required on the top of the board, the cleats would be shown by invisible or broken lines on the top view.

Bending Lines.—The lines that are drawn on a layout or pattern of an object to indicate the location of an edge in the completed object are called bending lines, since they locate on the layout or pattern the line along which a bend must be made. These lines differ from the regular object or projection lines only by having at each end a small free-hand circle drawn upon them. Bending lines are drawn differently by different authors and in some shops, but as long as a definite logical system is followed it does not make much difference what system it is.

Center Lines.—Center lines are, in general, lines of symmetry; that is, they usually divide the views of an object into two equal though not exactly similar parts, since one is right-handed and the other left-handed. In some cases, however, the two parts are sometimes unequal, as well as dissimilar.

Center lines are used to aid in dimensioning; to line up two or more related views; and to fix definitely the centers of circles. All circles have two center lines at right angles to one another, usually a vertical and a horizontal center line.

Extension Lines.—Extension lines are used to extend object or projection lines in order to line up related views and to insert dimensions without placing them on the object itself, causing

Fig. 14.Simple Title for Drawing.

a confusion of lines. They should fail to touch the object by about $\scriptstyle {\frac {1}{16}}$ in.

Dimension Lines.—Dimension lines are used with arrowheads at each end to show the limits of a given dimension. The lines are broken at some point, usually near the center, in order to insert the figures.

5. Dimensions.—Dimensions up to 24 inches are, in general, given in inches, as 16½". Above 24 inches, practice varies, but, in general, feet and inches are used as 3'-2½", for 3 feet 2½ inches.

Vertical figures about ⅛ in. high are usually used for dimensions. Fractions should be as large as whole numbers and care should be taken to see that the figures do not touch the dividing line. The dividing line of a fraction should be on a level with the dimension line as in Fig. 14.

Horizontal dimensions should be read from the bottom of the sheet, and vertical dimensions from the right-hand side of the sheet as in Fig. 16.

Fig. 15.Satisfactory Style of Lettering for Sheet Metal Drawings.

6. Lettering.—Lettering is very important for the draftsman, and ability to make good letters is a good asset for anyone. Figure 15 shows the type of lettering that is very frequently used and that is probably most easily made. The strokes for forming the letters are shown by the arrows.

Fig. 16.Detailed Title Corner.

7. Titles.—No drawing is complete without a title which gives such information as the drawing itself fails to impart. Figures 14 and 16 illustrate two different titles, of which the former is the simpler. Figure 16 represents a title such as would appear on an up-to-date shop drawing made in a large office where it would have to be traced, checked, and approved before being blue printed.

8. Filing Circles.—In all well-regulated manufacturing establishments some system of filing away the drawings is used so that they may be easily found when needed.

In one such system, filing circles are placed, one at the lower left-hand corner of the sheet and another, upside down, at the upper right-hand corner, so that no matter how the drawing is placed in the drawer, a filing circle will always appear at the lower left-hand corner.

Figure 14 shows the size of the circle to be used, its location on the sheet, and three different numbers. The first number on the upper line represents the number of the general order; the second number is the number of the detail sheet under this general order; and the bottom number is the number of the section or drawer in the filing case in which this sheet is to be found. A card index is used in connection with this filing system to facilitate the location and the handling of the drawings.

Objectives of problems on Rectilinear Figures

Problem 1
LAYING OUT A METAL CLEAT

9. The Sheet Metal Cleat.—The work of this problem will consist in laying out, to full size, the views and pattern for a galvanized sheet metal cleat. In making the layout for this cleat, the following points must be kept in mind:

The proper relation of views in a drawing.
How to dimension a drawing.
Accuracy in the use of the scale rule.

This cleat is to be formed from a flat piece of No. 16 galvanized iron; all the bends to be made to an angle of 90°. Figure 17 represents the cleat as it would appear on a photograph.

Before starting the layout, it must first be determined how many faces the cleat has. By holding the cleat with the largest surface directly in front of the eyes, three of these faces can be seen. A drawing should be made of what is actually seen. This drawing would appear as shown in Fig. 18. This view is called the front elevation and from it the exact sizes of the three faces or surfaces shown can be determined.

If the cleat is turned so that the eyes see the thin edge of the metal, the view will be as shown in Fig. 19. This view is called the profile because it is the exact shape or outline to which the cleat must be formed in the shop.

In drawing the profile, it can be located directly under the front elevation by using extension lines such as shown. In addition to showing the exact outline of the cleat, the profile also shows the dimensions necessary for laying out the pattern. In order to transfer these dimensions to the line of stretchout on the pattern, the profile should be numbered as indicated.

The front elevation and profile furnish all the information required to lay out the pattern. Consequently, there is no need to draw other views.

The line of stretchout is always drawn at right angles to the side of the view from which the pattern is to be taken. Upon this line of stretchout, all of the distances (called the spacing of the profile) of the profile should be placed and numbered to correspond. This has been done in Fig. 20. Perpendicular lines are then drawn through these numbered points. These are called the

Fig. 17–20.Sheet Metal Cleat.

measuring lines of the stretchout. Extension lines carried over from the elevation locate the top and bottom lines of the pattern. The side lines of the pattern are formed by measuring lines No. 1 and No. 6. Small free-hand circles should be placed as shown to indicate to the workman where the bends are to be made. The views and the pattern must be fully dimensioned.

10. Related Mathematics on Sheet Metal Cleat.—If the drawing is correct, the sum of all the lines in the profile will be equal to the length of the line of stretchout.

Problem 1A.—Compute the sum of all the lines in the profile from the dimensions given in Fig. 17. Measure the length of the line of stretchout in Fig. 20 and compare with the sum of the profile lines. If the answers do not agree, either the drawing or the arithmetic is incorrect. They should be made to agree.

Problem 2
GALVANIZED MATCH BOX

11. The Galvanized Match Box.—In laying out the views and the pattern for the galvanized match box, special attention should be directed to the following:

Locating holes accurately.
Showing hidden hems and surfaces.
Showing lapped and soldered joints.

Figure 21 shows a rectangular match box having the back raised above the other upright surfaces. There are two screw holes drilled or punched in the back.

The top edges of the back, the ends, and the front side are provided with a $\scriptstyle {\frac {3}{16}}$ -inch hem so that the edge will be smooth. The hems on the top of the back and on the right end can be seen in Fig. 21, but the hems on the top of the front and the left end cannot be seen from the outside because they are hidden from view. These hems are shown by dotted lines. The dotted line is always used to show the position of a line which cannot be seen. All dotted lines in this view represent lines or edges which cannot be seen.

This box has five surfaces, a back, a front, two ends, and a bottom. A full size elevation of the end surface will appear as in Fig. 22. The hem on the top edge of the end surface is shown by a dotted line and the lap by a solid line. This end elevation is also a profile view, and dimensions taken from it can be used in laying out the line of stretchout for the pattern. The end elevation is, therefore, numbered in a way similar to that in Fig. 19 of Problem 1.

The front elevation is constructed by using the extension lines from the end elevation. This front elevation shows the length of the box, together with the location of the two holes in the back.

As in Fig. 20 of Problem 1, the line of stretchout is drawn at right angles to the view from which the pattern is to be taken. The line of stretchout should be numbered to correspond to the profile numbering in the end elevation. Extension fines dropped from the front elevation determine the outside edges of the box on the pattern. The

\scriptstyle {\frac {3}{16}}

-inch hems must be added at the top and the bottom of the stretchout line. The ¼-inch laps must also be added

Figs. 21–25.Galvanized Match Box.

to the remaining edges of the pattern. Free-hand circles must be placed to indicate where the bends are to be made. Suitable notches are provided at the laps so that they will fit together at an angle of 90° at the bottom corners of the box.

A separate pattern must be drawn for the two ends of the box, as these are not included in the main pattern. Extension lines dropped from the end elevation will determine the length of the end pieces. The height of the end pieces can be taken either from the pictorial view in Fig. 21, or from the end elevation. A $\scriptstyle {\frac {3}{16}}$ -inch hem must be added to the top of the end pattern as shown. The ends of the hem are notched slightly as indicated.

The over-all dimensions of the patterns should be put in as indicated by the question marks on the drawing. The end and front elevations are to be dimensioned as indicated in Figs. 22 and 23.

12. Related Mathematics on Galvanized Match Box.—Girth and Cut.—The "Girth" is the distance around the profile view. The "Cut" is the distance around the profile plus the laps or locks necessary to join the pieces of metal together.

Over-all Dimensions.—Dimensions showing the sizes of the blank pieces of metal required to "get out" the job should be placed upon every pattern. These are known as "over-all" dimensions, as they include both the pattern and the edges allowed. Dimension lines for this purpose are indicated on Fig. 24 by question marks.

Rectangle.—A rectangle is a flat surface bounded by four straight lines forming right angles at their points of meeting. Figures 20 and 24 are examples of rectangles. The area of a rectangle is equal to the length multiplied by the width.

Problem 2A.—Compute the over-all dimensions from Fig. 22. Check these answers by measuring the drawing, and place the correct figures on the over-all dimension lines of Figs. 24 and 25.

Problem 2B.—Find the area of Fig. 24 and also the area of Fig. 25. (Use over-all dimensions.)

Problem 2C.—Find the total area of the metal required to construct the box. (One body and two end pieces.)

Problem 3
CANDY PAN

13. The Candy Pan.—As already pointed out in the previous problem, the elevation view of an object may sometimes be used as a profile for laying out the pattern. This is the case with the layout of the tin candy pan considered in this problem. Particular attention should be given to the methods of wiring the top of this pan.

The pan shown in Fig. 26 is known to the sheet metal trade as a rectangular flaring pan. Flaring is another word for tapering. Since the sides flare or taper, the bottom of the pan must be smaller than the top. This pan has an equal flare on all sides. Some pans have an unequal flare; that is, some of the sides taper more than others. This candy pan is to be made of sheet tin, wired with No. 12 wire, the corners to be lapped and soldered.

A full size elevation, as in Fig. 27, showing one corner broken away to reveal the wire, is to be drawn. Care should be taken that the flare is equal on both sides. As stated before, this elevation also serves as a profile and is numbered 1, 2, 3, and 4. It should be noticed, in numbering the profile, that the metal necessary to cover the wire is not included. This is on account of the fact that there is a standard allowance for covering wire. For covering a wire with metal, add an edge to the top of the pattern equal to $\scriptstyle {2{\frac {1}{2}}}$ times the diameter of the wire. This allowance, however, must be increased for metal heavier than No. 23 gage.

The plan view is drawn below the elevation as shown in Fig. 28. The line of stretchout is laid out at right angles to the long side of the plan. The spacing of the profile is laid off on the stretchout and is numbered to correspond. The allowance for covering the wire must be computed according to the rule given above. Number 12 wire has a diameter of approximately

\scriptstyle {\frac {7}{64}}

in. This allowance for wiring is set off to the right of No. 4 and to the left of No. 1 on the line of stretchout. The measuring lines of the stretchout are then drawn. The extension lines from the plan are carried over to the stretchout view and the pattern of one of the flaring sides constructed as shown in Fig. 29. Since the flare is equal on all sides of the pan the other three sides can be laid out

Figs. 26–29.Candy Pan.

from the side already drawn. A ¼-inch lap is added to the long sides of the pattern at each corner.

All necessary dimensions should be placed on the plan and elevation, and all over-all dimensions on the pattern.

14. Related Mathematics on Candy Pan.—Problem 3A.—The candy pan shown in Fig. 26 is to be made of IXX Charcoal Tin. (Read two cross charcoal tin.) This tin is generally carried in stock in two sizes of sheets, 14″×20″ and 20″×28″. Calculate the area in square inches of a sheet 20″×28″.

Problem 3B.—What is the area of Fig. 29? Use over-all dimensions.

Problem 3C.—What is the largest number of blanks (Fig. 29) that could be cut from a sheet of 20″×28″ tin?

Problem 3D.—What are the dimensions of the pieces of tin left after cutting the blanks from the sheet?

Problem 3E.—What is the total area of the pieces of tin left?

Problem 3F.—Divide the total area of tin wasted (Problem 3E) by the total area of the sheet (Problem 3A). The result will be the percentage of the 20″×28″ that is wasted.

Problem 3G.–Divide the total area of tin wasted (Problem 3E) by the number of blanks obtainable (Problem 3C). This will give the amount of tin wasted per blank. Divide this result by the total area of one blank (Problem 3B) to get the percentage of waste per blank or per pan.

Illustrative Examples

Tin blanks 6″×8″ are to be cut from a sheet of 14″×20″ tin plate. The problem is to find the maximum number of blanks obtainable and the percentage of waste.

Example of Problem 3A.
width	14″
×
length	20″
	280 sq. in., area.	Ans. 280 sq. in., area.
Example of Problem 3B.
width	6″
×
length	8″
	48 sq. in., area.	Ans. 48 sq. in., area.
Example of Problem 3C.
(See Fig. 30.)		Ans. 4 blanks.

Example of Problem 3D.

Fig. 30.

Example of Problem 3E

			Ans. 2"×16" and 4"×14"
1=2"×16"=	32		or
1=4"×14"=	56		2"×20" and 4" × 12"
Total	88	sq. in.	Ans. 88 sq. in., total waste.

Example of Problem, 3F.

(Area of sheet) 280	88. 000 (area of waste)	.314
	84.0
	04.00
	02.80
	01.200
	01.120
	0.080	Ans 31.4%, waste per sheet.

Example of Problem 3G.

88÷4=22 sq. in., waste per blank.

(Area of blank)	48	22.00	(waste)	.46	(approx.)
		19.2
		02.80
		02.88		Ans.	46%	waste per blank.

Problem 4

BREAD PAN

15. The Iron Bread Pan.—The particular feature of the construction of this bread pan is the method of joining the body to the end by double seams.

The bread pan, Fig. 31, is to be made of No. 28 black iron. It is to be wired with No. 8 wire and the ends are to be double seamed in. Figure 36 shows that this double seaming is accomplished by turning a hook on the body and a right-angled bend on the end. After being slipped together, these edges are hammered down to form the double seam. The Double Edge is the trade name for the hook that is turned on the body. The Single Edge is the trade name given to the right-angled bend on the end. Allowance must be made for the metal necessary to make these bends. This allowance is called the "Take-up" and is indicated in Fig. 36.

The end elevation is drawn first and the points of the profile numbered 1, 2, 3, and 4 as shown in Fig. 32. The front elevation can be located by using the extension lines from the end elevation. The line of stretchout is drawn at right angles to the bottom of the pan. The spacing of the profile and the corresponding numbers are then transferred to the line of stretchout. This pan is to be wired around the top with a No. 8 wire which is $\scriptstyle {\frac {5}{32}}$ in. in diameter. After this allowance for wiring is computed, this distance must be added to the line of stretchout outside of points 1 and 4. After the measuring lines are drawn on the pattern, extension lines are dropped from the front elevation into the stretchout. These will locate the extreme points of the top and the bottom and permit the drawing of the outline of the body pattern as shown in Fig. 34. Three-eighths inch double edges are added as shown. The bending lines of the double edges are drawn ⅛ in. in from the outside edge. This allows $\scriptstyle {\frac {1}{16}}$ in. for take-up.

The pattern of the end is constructed by dropping extension lines from the end elevation and by carrying extension lines over from the upper surface of the body pattern. The intersections of these extension lines will locate the corners of the end pattern as in Fig. 35. Three-sixteenths inch edges are added on the three

Figs. 31–36.Iron Bread Pan.

sides as indicated. The bottom corners of the end pattern are notched straight across. The single and double edge notches should be dropped below the bending line at the top of the pan a distance equal to the diameter of the wire. This will allow the wire to lay against the pan instead of riding over the double seams.

All necessary dimensions should be placed on the front and end elevations and the over-all dimensions on the pattern.

16. Related Mathematics on Iron Bread Pan.—Trapezoid.—A trapezoid is a flat surface bounded by four straight lines only two of which are parallel. The parallel sides are known as the upper and lower bases of the trapezoid.

The area of a trapezoid is equal to one-half the sum of the bases multiplied by the altitude. The altitude of any surface is always the shortest distance between its upper and lower parts. The altitude must always be measured at right angles to the lower base.

Problem 4A.—How many body blanks, Fig. 34, can be cut from a sheet of black iron 30" wide and 96" long? Treat the pattern as a rectangle using the over-all dimensions.

Problem 4B.—Could any of the pieces left from the body blanks be used for end blanks? If so, how many end blanks could be obtained from these?

Problem 4C.—What is the total area of the waste pieces?

Problem 4D.—What is the percentage of waste for one body blank?

Problem 4E.—By reversing the end pattern when laying out on the sheets some material may be saved. Show by a sketch how to effect this saving of material from a 30"×96" sheet. How many end blanks can be obtained from one of these sheets?

Problem 4F.—What is the total area of the waste pieces from one of the above sheets?

Problem 4G.—What is the area of one end blank? What is the percentage of waste?

Problem 4H.—The bread pans are to be made of No. 28 black iron weighing .625 lb. per sq. ft. How much will 1000 body patterns weigh after corrections are made for waste? How much will 2000 end patterns weigh after corrections are made for waste? What will be the correct weight of 1000 of these pans?

Illustrative Examples

1000 bread pans 4"×8"×2" deep with ½" flare on all sides are to be made. The size of the body pattern is 7½" by 8½". The size of the end pattern is: top 4½", bottom 3½", depth 2½".

Example of Problem 4A.

Fig. 37.

Ans. (a) 36 blanks for body.
(b) 38 blanks for ends.

Example of Problem 4C.

1 piece 1½"×25½" =	38.25	sq. in.
1 piece 4½"×1"=	04.50	sq. in.
Total	42.75	sq. in.	Ans. 42.75 sq. in., waste from bodies.

Example of Problem 4D.

length	08.5"
×			Total waste 42.75÷36=1.18 sq.
width	07.875"		in., waste per blank.
	66.93	sq. in., area of body

(Area) 66.93	1.11800	(waste)	.017
	0.6693
	0.51070
	0.46851
		Ans.	1.7%	, waste per body blank.

Example of Problem 4E.

Fig. 38.

Ans.							266	end blanks.
Number	of	blanks	from	width	of	sheet	7
"	"	"	"	length	"	"	38
Total number of blanks 38×7=							266

Example of Problem 4F.

One	piece	95"×1½"=	142½	sq.	in.
"	"	30"×1"	030	"	"
Total waste			172½	sq.	in.	Ans. 172½ sq. in., waste from end.

Example of Problem 4G.

The end blank is in the form of a trapezoid, the area of which is equal to one-half the sum of the upper and lower bases multiplied by the altitude. In this example the lower base is 4½", the upper base 3½", and the altitude 2½".

4½"	+3½"=	8"	, sum of lower and upper bases;
8"	÷2=	4"	, half of the sum of the bases;
4"	×2½"=	10	sq. in., area of trapezoid.

(No. of end blanks)	266	172.50	(area of waste)	.64 sq. in., waste per blank.
		159.6}
		012.90
		010.64

(No. of blanks)	266	640	(waste per blank)	.002
		532
				Ans.	(a)	10 sq. in.
					(b)	$\scriptstyle {\frac {2}{10}}\%$ waste.

Example of Problem 4H.

Area of one body blank 66.93 sq. in.

Area of 1000 body blanks 66930 sq. in.

	464.8	area in sq. ft. (approx.)
Sq. in. in one sq. ft. 144	66930
	576
	933
	864
	690
	576
	1140
	1152

464.8	area in sq. ft.
1.017	correction for 1.7% waste.
32536
4648
46480
472.7016	corrected area.

472.70	area in sq. ft.
000006.25	wt. per sq. ft.
236350
94540
273620
285.43750	lb. wt. of 1000 body blanks.

Area of one end blank			10 sq. in.
Area of 2000 end blanks			20,000 sq. in.
	138.88	area in sq. ft. (approx.)
144	20000.00
	144
	560
	432
	1280
	1152
	1280
	1152
	1280		Ans	(a)	285.43 pounds.
	1152			(b)	086.96 pounds.
				(c)	372.39 pounds.

138.88	area
01.002	correction for $\scriptscriptstyle {\frac {2}{10}}$ % waste.
00027776
1388800
139.15776	sq. ft. corrected area.

139.15	area
00.625		285.43	corrected	wt.	of 1000 bodies
00069375		86.96	"	"	of 2000 ends
0027830		372.39	weight of 1000 pans.
083490
86.96875	lb., wt. of 2000 end blanks