Chapter Two. Layouts and Lettering


Objectives

After studying the material in this chapter, you should be able to:

1. Identify six types of technical drawings based on the projection system they use.

2. Identify the line patterns used in technical drawings and describe how they are used.

3. Identify standard drawing media and sheet sizes.

4. Label drawing scale information.

5. Add lettering to a sketch.

6. Fill in a standard title block with the appropriate information.

7. Lay out a drawing sheet.



Refer to the following standards:

• ANSI/ASME Y14.100 Engineering Drawing Practices

• ANSI/ASME Y14.2M Line Conventions and Lettering

• ANSI/ASME Y14.1 Decimal Inch Drawing Sheet Size and Format

• ANSI/ASME Y14.1M Metric Drawing Sheet Size and Format


Illustration shows the dimensions of a 3-D object.

Layout with Title Block of a Small Part at Scale 1:1 (Courtesy Dynojet Research, Inc.)


Overview

Two-dimensional technical drawings, whether they are sketched by hand, drawn using instruments, drawn using a CAD program, or generated from 3D solid models, follow certain rules so that they can be correctly interpreted. Unlike artistic drawings, which communicate self-expression and emotional content, technical drawings communicate size, shape, and feature information about a product, system, or device. To clearly describe this information, technical drawings adhere closely to formal standards.

These formal standards include systems of projection for developing and understanding drawing views. They also include an “alphabet of lines,” in which each line of the drawing represents certain information. Lettering is also standardized, to make drawings quick to create and easy to read and reproduce. Standard sheet sizes for drawings include a title block that provides important information such as the drawing name, company information, scale, revision numbers, and approvals for release of the drawing.


Understanding Projections

Behind every 2D drawing of an object is a space relationship involving the object and three “imagined” things:

1. The observer’s eye, or station point

2. The plane of projection

3. The projectors (also called visual rays or lines of sight).

Figure 2.1 shows two drawings of a shape projected onto a plane as viewed by an observer, whose eye represents the station point. The lines projecting from the corners (or vertices) of the object are the imagined lines, called projectors.

Illustration shows perspective and parallel projections.

2.1 The Concept of Projection

To understand projection, imagine that the drawing is produced by points, called piercing points, where the projectors would pierce the projection plane. The drawing may be a two-dimensional representation on a sheet of paper, or it may be a two-dimensional representation shown on your computer screen, as shown in Figure 2.2, but the basic principles are the same. One reason 2D projection skills remain relevant, even with the advent of 3D modeling, is that computer monitors still display a 2D view on their flat screens.

Figure shows a three dimensional block on a computer screen.

2.2 A View of a 3D Object “Projected” onto a Computer Monitor

Types of Projections

There are two main types of projection: perspective and parallel. These are broken down into subtypes, as shown in Figure 2.3.

Figure shows the classification of projections.

2.3 Classification of Projections

In perspective projections, the projectors come together at the station point to form a cone, as in Figure 2.1a. Perspective drawings represent objects as we see them or as they would appear in a photograph.

In parallel projections, the projectors are parallel, as shown in Figure 2.1b.

Orthographic projections are one type of parallel projection. In orthographic (meaning right-angle) projections, the parallel projectors are perpendicular to the plane of projection. Because orthographic projections show objects in a way that their features can be represented at true size or scaled at a proportion of true size, they are especially useful in specifying the dimensions needed in technical applications.

If the projectors are parallel to each other, but are at an angle other than 90° to the plane of projection, the result is called an oblique projection.

Technical drawings of 3D objects usually use one of four standard types of projection, shown in Figure 2.3:

• Multiview

• Axonometric (includes isometric)

• Oblique

• Perspective

Multiview projection shows one or more necessary views. Either of two systems is used to arrange the views in a multiview drawing: third-angle or first-angle. You will learn about multiview projection in Chapter 6.

Axonometric, oblique, and perspective sketches are methods of showing the object pictorially in a single view. They will be discussed in Chapter 3.

The main types of projection are listed in Table 2.1.

Table 2.1 Classification by Projectors

Class of Projection

Distance from Observer to Plane of Projection

Direction of Projectors

Perspective

Finite

Radiating from station point

Parallel

Infinite

Parallel to each other

Oblique

Infinite

Parallel to each other and oblique to plane of projection

Orthographic

Infinite

Perpendicular to plane of projection

Axonometric

Infinite

Perpendicular to plane of projection

Multiview

Infinite

Perpendicular to plane of projection

Drawing Vocabulary

Drawing lines, lettering, measurement systems, scale, sheet sizes, and title blocks are presented in this chapter.

Drawing Lines Projected drawing views use specific line patterns to represent object features. For example, when showing a 3D object, some lines represent the edges of surfaces that are hidden from that viewing direction. These hidden lines have a dashed line pattern to help the reader understand the drawing. Another type of line indicates the location of the center of a symmetrical feature, such as a hole. Familiarity with the types of lines used in technical drawings helps you read drawings and create drawings that others can easily understand.

Lettering The shapes of letters that are easy to read and write are described as part of drawing standards. Often, freehand sketching is used early in the design process to present ideas. Showing notes and information legibly helps present your ideas to others clearly. Good lettering often makes or breaks a sketch.

Measurement Systems Two measurements systems are used for technical drawings: the metric system and U.S. customary units. It is important to be familiar with both measurement systems to create and read drawings that are used worldwide.

Scale Obviously, a large item (a house or bridge for example) cannot be shown full size on a paper sheet. To clearly convey important information about particularly large or small objects, you need to select an appropriate sheet size and show drawings to scale (proportionately smaller or larger than the actual size). Standard lettering sizes for drawings depend on the sheet size.

Title Blocks Company information, the drawing scale, sheet size, and other information is included in a standard title block located in the lower right corner of the drawing to make it easy to locate these important details on every drawing layout.

2.1 Alphabet of Lines

The meaning of each line on a technical drawing is indicated by its width (thick or thin) and its particular line style. The person who reads the drawing will depend on these line styles to know if a line is visible or hidden, if it represents a center axis, or if it conveys dimension information.

To make your drawings easy to read, make the contrast between thick and thin lines distinct. Thick lines (0.6 mm) should be twice the width of thin lines (0.3 mm), as shown in Figure 2.4. The line gage in Figure 2.5 shows various widths.

A thick line is shown as a solid line of thickness 0.60 millimeters, while a thin line is shown as a narrow line of thickness 0.30 millimeters.

2.4 Thick and Thin Drawing Lines

Figure shows several lines of varying thickness.

2.5 Line Gage

Figure 2.6 shows freehand line technique. You may find it helpful to use 1/8″ graph paper at first to get a feel for the length of dashes used in hidden lines and centerlines. Soon you will be able to estimate the lengths by eye.

Figure shows good and poor freehand line techniques.

2.6 Good and Poor Freehand Line Technique

Figure 2.7 illustrates line styles for technical drawings. All lines (except construction lines) must be sharp and dark. For visible, cutting-plane, and short-break lines use thick lines. Thin drawing lines should be just as sharp and black, but only half the thickness of thick lines. Construction lines and lettering guidelines should be thin and light so that they can barely be seen at arm’s length and need not be erased. All lines should be uniform in width and darkness. Ideal lengths of the dashes used to form the line patterns are also shown in Figure 2.7.

Figure shows the various types of lines used in a drawing.

2.7 Alphabet of Lines (Full Size)

2.2 Freehand Lines

The main difference between an instrument or CAD drawing and a freehand sketch is in the appearance of the lines. A good freehand line is not expected to be precisely straight or exactly uniform, as is a CAD or instrument-drawn line. Freehand lines show freedom and variety. Freehand construction lines are very light, rough lines. All other lines should be dark and clean.

2.3 Measurement Systems

When you create a technical drawing, the item you show will be manufactured or constructed using a particular system of measurement, which you indicate on the drawing. The metric system is the world standard used for measuring lengths.

U.S. Customary Units

U.S. customary units based on inch-foot and yard measurements (where there are 3 feet to the yard, and 12 inches to the foot; a yard equals exactly 0.9144 meter) continue to be used in the United States. Drawings may use either measurement system and still follow ANSI/ASME drawing standards as long as the system of measurement is stated clearly on the drawing. Figures 2.8 and 2.9 show the same part dimensioned with the two different measurement systems.

Figure shows a drawing dimensioned using metric units.

2.8 A Drawing Dimensioned Using Metric Units

Figure shows a drawing dimensioned using US customary units.

2.9 A Drawing Dimensioned Using U.S. Customary Units

The Metric System

Today’s metric system is the International System of Units, commonly referred to as SI (from the French name, le Système International d’Unités). It was established in 1960 by international agreement and is now the international standard of measurement, with all countries in the world adopting it, although some continue using traditional U.S. units to a greater or lesser degree.

The meter was established by the French in 1791 as the length of one ten-millionth of the distance from the Earth’s equator to the pole along the meridian that, coincidentally, passes through Paris. Since then the definition has been updated to be the distance that light travels in a vacuum in 1/299,792,458 of a second. A meter equals 39.37 inches or approximately 1.1 yards.

The metric system for linear measurement is a decimal system similar to the U.S. system of counting money. For example,

1 mm

= 1 millimeter (1{{#}}8729;1000 of a meter)

1 cm

= 1 centimeter (1{{#}}8729;100 of a meter)

 

= 10 mm

1 dm

= 1 decimeter (1{{#}}8729;10 of a meter)

 

= 10 cm = 100 mm

1 m

= 1 meter

 

= 100 cm = 1000 mm

1 km

= 1 kilometer = 1000 m

 

= 100,000 cm = 1,000,000 mm

The primary unit of measurement for engineering drawings and design in the mechanical industries is the millimeter (mm). Secondary units of measure are the meter (m) and the kilometer (km). The centimeter (cm) and the decimeter (dm) are rarely used on drawings.

Some industries have used a dual dimensioning system of millimeters and inches on drawings. However, this practice can be confusing because the sizes displayed in the two systems may contain rounding errors. If two systems are shown, the primary units are used for all manufacturing measurements, and the secondary system units (shown in parentheses or brackets) are for general information purposes only. Figure 2.10 shows a drawing using dual dimensioning. Most large manufacturers use all metric dimensions on the drawing for ease and consistency.

Figure shows a dual-dimensioned drawing using both metric and US customary units.

2.10 A Dual-Dimensioned Drawing Using U.S. Customary Units as the Primary Units

Dimensions that are given in U.S. customary units (inches and feet, either decimal or fractional) can be converted easily to metric values. In standard practice, the ratio 1 in. = 25.4 mm is used. Decimal-equivalents tables can be found inside the back cover, and conversion tables are also given in Appendix 30. Many handy unit conversion sites are also available on the Web at sites such as www.onlineconversion.com.

2.4 Drawing Scale

Unlike a computer drawing (where an object is drawn actual size so that the information stored in the computer file is accurate), a printed or paper drawing may represent the object at its actual size (full size) or may be larger or smaller than the object, depending on the size of sheet used. Drawing scale is the reduction or enlargement of the drawn object relative to the real object (Figure 2.11).

Figure shows a reduced scale and enlarged scale of a three dimensional object.

2.11 Reduced and Enlarged Scale. Many drawings must be shown at reduced scale for the object to fit on the paper.

Scale is stated as a ratio of the number of drawing units to the number of actual units. For example, a machine part may be shown on a sheet at half its actual size, a scale of 1:2; a building may be drawn 1/48 of its size, a scale of 1:48 (or in U.S. customary units, 1/4″ = 1′); a map may be drawn 1/1200 actual size, a scale of 1″ = 100′ or 1:1200; or a printed circuit board may be drawn four times its size, a scale of 4:1.

2.5 Specifying the Scale on a Drawing

There are several acceptable methods of noting scale on the drawing, but all of them show the relationship of the size of the object as drawn to the size of the actual object. For a part that is shown on the paper at half its actual size, the scale is listed in one of these three ways:

SCALE: 1:2

SCALE: 1/2

SCALE: .5

For machine drawings, the scale indicates the ratio of the size of the drawn object to its actual size, regardless of the unit of measurement used. Expansion or enlargement scales are given as 2:1, 4:1; 5:1, 10:1, and so on. Figure 2.11 illustrates how the actual object relates to a drawing at half size and how that might be noted in the title block of the drawing. Figure 2.12 shows the scale for a 1 to 24 reduction noted in a title block.

Figure shows a drawing with the logo "Dynojet" and several other details such as the Size, Part number, and so on displayed. In the title block at the bottom, the scale of the drawing reads "1 is to 24."

2.12 List the predominant drawing scale in the title block. (Courtesy of Dynojet Research, Inc.)

Architectural drawings in the United States typically list the scale based on the number of fractions of an inch on the drawing that represent one foot on the actual object. For example, SCALE: 1/8″ = 1′.

The various scale calibrations available on the metric scale and the engineers’ scale provide almost unlimited scale ratios. Preferred metric scale ratios are 1:1; 1:2; 1:5, 1:10, 1:20, 1:50, 1:100, and 1:200.

Map scales are indicated in terms of proportions such as Scale 1:62500, fractions such as Scale 1/62500, or graphically, such as:

Figure shows a graphical scale.

Step by Step: Using a Measuring Scale to Lay Out a One-Fiftieth Size Metric Drawing

Figure shows the dimensions labeled on an object.

Image Determine the full-size measurements of the object you will draw. This example will lay out a 3500 × 2500-mm flat plate with a rectangular slot in it. A picture of the part to be drawn with dimensions representing its actual size is shown above.

Image Many measuring scales are available that use standard drawing scales, like this 1:50 ratio metric one.

Figure shows a portion of a measuring scale with a "1 is to 50" ratio metric. The readings on the top portion are labeled in increments of 100 millimeters.

Image Starting from the 0 end of the 1:50 scale, use a sharp pencil to make a thin, light, short line to mark off the length of the 3500-mm line. To make accurate measurements, be sure to place the scale edge parallel to the line you are measuring on the drawing, and make your dashes at right angles to the scale, at the correct graduation mark, as shown.

Illustration shows a person using a pencil and a measuring scale to draw a line.

Image Check the length of your scaled line by calculating how many millimeters the length should be, then measuring the line you have drawn with a full-scale metric scale. In this case the 3500-mm length should be 70 mm when shown at 1:50 scale.

In the illustration, the drawn line is measured using a 1:50 scale. The 3500 millimeter length line measures 70 millimeters on the scale.

Image Continue to lay out the remaining lengths. Even slight errors in measurements when using a scale may accumulate to produce a significant error, so work carefully.

Illustration shows an outline drawn on a sheet of paper using a pencil and a measuring scale. Several distances are marked on this outline without repositioning the scale, for the purpose of accuracy.

To avoid cumulative errors, instead of setting off distances individually by moving the scale to a new position each time, position the scale once and mark all of the distances by adding each successive measurement to the preceding one.

This is useful in dimensioning drawings, too. Keep in mind that providing dimensions from one end to each successive location (say, in the case of building a wall) makes it easier for the worker to lay it out quickly and accurately.


For more about the use of measuring scales, see Appendix 51.




Step by Step: Measuring with with an Architects’ Scale

Figure shows the top view of an object labeled "Deck." At the bottom of the view, the scale reads "Three eighth of an inch equals one foot."

Image To make measurements with an architects’ scale, first determine which scale to use by reading the scale noted in the title block or noted below the view. In the example above, 3/8 inch = 1 foot.

Image Position the scale so that the 0 value is aligned with the left end of the line being measured and note the division mark nearest to the line’s right end (in this case, 2).

Figure shows a measuring scale of a 3 over 8 metric.

Image Slide the scale to the right so that the closest whole division you noted in Step 2 lines up with the right end of the line you are measuring.

A fractional portion of the line you are measuring now extends on the left, past the scale’s 0 mark.

Counting toward the left, note how many fractional division marks are between zero and the left end of the line. (In this example, there are two.)

Figure shows the measurement of an outline using an architects' scale.

Add the fractional value to the whole value that you noted in Step 2. In this example, you noted two whole division lines, plus two fractional division lines, so the length of the line is 2′–2″ at actual size.

Figure shows the completion of measurement of the outline portion using an architects' scale.

*On architects’ scales, there are 12 fractional divisions because there are 12 inches per foot.


For more about the use of measuring scales, see Appendix 51.



2.6 Lettering

Lettered text is often necessary to completely describe an object or to provide detailed specifications. Lettering should be legible, be easy to create, and use styles acceptable for traditional drawing and CAD drawing.

Engineering drawings use single-stroke sans serif letters because they are highly legible and quick to draw. (Sans serif means without serifs, or spurs.) The sans serif letters used for drawings are also referred to as Gothic. (Serif letters are sometimes called Roman, but today that term is commonly used for the upright form of the letters.) A font is the name for a set of letters with the same style. Figure 2.13 shows the distinctions among Roman, italic, serif, and sans serif fonts.

Figure distinguishes a few letter forms.

2.13 Distinctions Among Letter Forms

Lettering is a standard feature available in computer graphics programs. With CAD software, you can add titles, notes, and dimensioning information to a drawing. Several fonts and a variety of sizes may be selected. When modifications are required, it is easy to make lettering changes on the drawing by editing existing text.

Freehand lettering ability has little relationship to writing ability. You can learn to letter neatly even if you have terrible handwriting. There are three necessary aspects of learning to letter:

• Knowing the proportions and forms of the letters (to make good letters, you need to have a clear mental image of their correct shape)

• Spacing of letters and words for legibility

• Practice

2.7 Lettering Standards

Most hand-drawn notes use lettering about 3 mm (1/8″) high. Light horizontal guidelines are useful for producing consistent letter heights. CAD notes are set using the keyboard and sized to be in the range of 3 mm (1/8″) tall according to the plotted size of the drawing. Lettering heights vary with the size of the sheet and the intended use of the drawing.

CAD drawings typically use a Gothic (sans serif) lettering style but often use a Roman (serif) style for titles. When adding lettering to a CAD drawing, a good rule of thumb is not to use more than two fonts within the same drawing. See Figure 2.14 for a sample of the fonts available using CAD. You may want to use one font for the titles and a different font for notes and other text. Keep in mind that if you open a drawing created with software such as AutoCAD, you must have the fonts available that were used in the drawing, otherwise the software will have to substitute different fonts. This can be a problem because the horizontal spacing may be different and the text will no longer fit correctly. It may be tempting to use many different fonts in a drawing because of the wide variety available, but this tends to look distracting on the drawing. Drawings that use too many lettering styles and sizes have been jokingly referred to as having a “ransom note” lettering style.

A sample of eight different lettering styles available when using CAD are shown. They are: AutoCAD Txt Font, Roman Simplex, Roman Duplex, Baskerville, Times New Roman, Playbill, Arial, and Letter Gothic.

2.14 Examples of Lettering Using CAD

2.8 Using Guidelines for Hand Lettering

Use extremely light horizontal guidelines to keep letter height uniform, as shown in Figure 2.15. Capital letters are commonly made 3 mm (1/8″) high, with the space between rows of lettering being from three-fifths to full height of the letters. Do not use vertical guidelines to space the distance from one letter to the next within a word or sentence. This should be done by eye while lettering. If necessary, use a vertical guideline at the beginning of a column of hand-lettered text to help you line up the left edges of the following rows. Beginners can also use randomly spaced vertical guidelines to practice maintaining the correct slant.

Figure shows the use of guidelines for hand lettering.

2.15 Using Guidelines

2.9 Vertical and Inclined Letters and Numerals

The proportions of vertical capital letters and numbers are shown in Figure 2.16. The letter shapes are probably a little wider than your usual writing. Hand lettering and text added to engineering drawings is typically upper case. Lowercase letters are rarely used except for large volumes of notes or when there is some other particular need for it. Lowercase letters are shown in Figure 2.17. The lower part of the letter (or descender) is usually two thirds the height of the capital letter.

Figure shows the strokes of a few uppercase letters and numbers.

2.16 Vertical Capital Letters and Numerals

Figure shows the strokes of lowercase letters.

2.17 Vertical Lowercase Letters

Inclined (italic) capital letters and numerals are shown in Figure 2.18. They are similar to vertical lettering, except the slope is about 68° from the horizontal. Although you may practice hand lettering slanted at approximately this angle, it is important in CAD drawings to always set the amount of incline for the letters at the same value within a drawing so that the lettering is consistent. Inclined lowercase letters, shown in Figure 2.19, are rarely used.

Figure shows the strokes of inclined uppercase letters and numerals.

2.18 Inclined Capital Letters and Numerals

Figure shows the strokes of inclined lowercase letters.

2.19 Inclined Lowercase Letters

Keep in mind that only one style of lettering or font, either vertical or inclined, should be used throughout a drawing.


Tip: For Even Freehand Letters

• Use 1/8″ gridded paper for drawing to make lettering easy.

• Use a scale and set off a series of spaces, making both the letters and the spaces between lines of letters 1/8″ high.

• Use a guideline template like the Berol Rapidesign 925 shown in Figure 2.20.

Figure shows the Berol Rapidesign 925 template.

2.20 The Berol Rapidesign 925 template is used to create guidelines quickly for lettering.

• For whole numbers and fractions, draw five equally spaced guidelines.


2.10 Fractions

Fractions are shown twice the height of the corresponding whole numbers. Make the numerator and the denominator each about three-fourths as high as the whole number to allow enough space between them and the fraction bar. For dimensioning, the most commonly used height for whole numbers is 3 mm (1/8″), and for fractions 6 mm (1/4″), as shown in Figure 2.21.

Figure shows the right and wrong ways in lettering fractions.

2.21 Common Errors in Lettering Fractions

• Never let numerals touch the fraction bar.

• Center the denominator under the numerator.

• Avoid using an inclined fraction bar, except when lettering in a narrow space, as in a parts list.

• Make the fraction bar slightly longer than the widest part of the fraction.

Dimensioning in fractions is still used in the US, but even there it is less and less common. Calculating with fractions often takes manufacturing workers extra time and errors are common. Much of the numerically-controlled manufacturing for cabinets and countertops uses millimeters as the default units, even in the United States.

Figure shows the plan of a custom cabinet. The dimensions are predominantly labeled in mixed fractions.

2.22 Custom Cabinetry Dimensioned in Fractional Inches (Courtesy of Centermark Industries, Inc.)

2.11 Spacing of Letters and Words

Spacing between Letters

Uniform spacing between letters is done by eye. Contrary to what might seem logical, putting equal distances from letter to letter causes them to appear unequally spaced. The background areas between letters, not the distances between them, should be approximately equal to get results that appear balanced. Figure 2.23 illustrates how using equal spacing from one letter to the next does not actually appear equal. Space your lettering so that background areas appear equal, like the example shown in the bottom half of the figure.

Figure shows two instances of letter spacing based on visual balance.

2.23 Visually Balancing Letter Spacing

Some combinations, such as LT and VA, may have to be slightly closer than other letters to look correctly spaced. In some cases, the width of a letter may be decreased slightly. For example, the lower stroke of the L may be shortened when followed by A. In typesetting, pairs of letters that need to be spaced more closely to appear correctly are called kerned pairs.

Spacing between Words

Space letters closely within words to make each word a compact unit, but space words well enough apart to clearly separate them from adjacent words. For both uppercase and lowercase lettering, make spaces between words approximately equal to a capital O.

Spacing between Rows

Be sure to leave space between rows of lettering, usually equal to the letter height. Rows spaced too closely are hard to read. Rows spaced too far apart do not appear to be related.


Tip: Creating Letters that Appear Stable

Certain letters and numerals appear top-heavy when they are drawn with equal upper and lower portions as in the example below.

To correct this, reduce the size of the upper portion to give a balanced appearance, as in the example below.

If you put the central horizontal strokes of the letters B, E, F, and H at midheight, they will appear to be below center.

To overcome this optical illusion, draw the strokes for B, E, F, and H slightly above the center as you letter, keeping letters uniform, as in the second example below.

Figure shows two sets of strokes of the alphabets: C, G, B, E, K, S, X, and Z at the top and bottom.

The same practice applies to numerals. In the illustrations below, the example at left looks top-heavy. Note how the example at right looks more balanced.

Figure shows two sets of strokes of the numbers: 3, 8, 5, 2.
Figure shows a good example of uniform lettering. The word "relatively" is shown in upper case with uniform styling, size, and spacing.

These examples show what not to do

Figure shows few examples of nonuniform lettering.

2.12 Lettering for Titles

In most cases, the title and related information are lettered in title boxes or title strips as shown in Figure 2.24. The main drawing title is usually centered in a rectangular space, which is easy to do using CAD.

Figure shows the title and related information lettered in title strips.

2.24 Balanced Machine-Drawing Title

In any kind of title, give the most important words prominence by making the lettering larger, heavier, or both. Other data, such as scale and date, can be smaller. One technique for centering words in the title block when hand lettering is to roughly letter the words on a scrap of paper, slide it in the available space, and make a light mark to indicate where to begin lettering the title (Figure 2.25).

Figure shows centering a title in a title box.

2.25 Centering Title in Title Box

Figure 2.26 shows examples of freehand lettering at actual size.

Figure shows samples of good and bad pencil lettering.

2.26 Pencil Lettering (Full Size)


Tip: Lettering with a Pencil

• Because practically all pencil lettering will be reproduced, the letters should be dense black, not gray or blurred. Use a sharp, soft pencil, such as an F, H, or HB to make lettering dark and sharp.

• If you like using wooden pencils, sharpen them to a needle point, then dull the point very slightly.

• Don’t worry about making the exact letter strokes unless you find it difficult to make the letters look right, but do use them as a reference if you are having trouble drawing uniform, symmetrical letters.

• Use extremely light, 1/8” (3 mm) horizontal guidelines to regulate the height of letters. A few light vertical or inclined lines randomly placed help you visually keep the letters uniformly vertical or inclined.

• Draw vertical strokes downward with a finger movement.

• Draw horizontal strokes from left to right with a wrist movement and without turning the paper.

• Draw curved strokes and inclined strokes with a downward motion.

Left-handers: Traditional lettering strokes were designed for right-handed people. Experiment with each letter to develop a system of strokes that works best for you.

Figure shows the strokes drawn for the English alphabet E.
Figure shows two different stroke patterns that are vertical.
Figure shows two different stroke patterns that are inclined.

2.13 Drawing Pencils

High-quality drawing pencils help produce good-quality technical sketches and drawings. Use light lines for construction lines, lettering guidelines, and precise layout work. Use dark, dense black lines for the final lines, lettering, and arrowheads. Drawings are often reproduced, and the lines need to be dark for the copies to turn out well.

Drawing pencils are made of graphite with a polymer binder or clay binder. They are divided into 18 grades from 9H (the hardest) to 7B (the softest) as shown in Figure 2.27. Specially formulated leads of carbon black particles in a polymer binder are also available in several grades for use on polyester film (Mylar).

Figure shows 18 grades of drawing pencils.

2.27 Lead Grade Chart

Hard leads are used where accuracy is required, such as on graphical computations and charts and diagrams. For other uses, their lines are apt to be too light.

Medium leads are used for general-purpose technical drawing, such as sketching, lettering, arrowheads, and other freehand work on mechanical drawings.

Soft leads are not useful in technical drawing. They make smudged, rough lines that are hard to erase, and the lead dulls quickly. These grades are generally used for artistic drawing.

Which grade of pencil works best for you depends on your hand pressure, the humidity, and the type of paper you are using, among other things. For light lines, use a hard lead in the range of 4H to 6H. For dark lines, use a softer lead in the range of 2H to B.

Mechanical pencils are available with 0.3-, 0.5-, 0.7-, or 0.9-mm-diameter drafting leads in several grades (Figure 2.28). Their thin leads produce uniform-width lines without sharpening. The .5-mm lead is a good general size, or you can use a .7-mm lead for thick lines and .3 mm for thin lines.

Figure shows 3 types of drawing pencil.

2.28 Drawing Pencils


Tip

You might be surprised how much your drawings benefit from finding a style of pencil that suits your use. Soft pencils, such as HB or F, are mainly used in freehand sketching. Choose a pencil that:

• Is soft enough to produce clear black lines, but hard enough not to smudge too easily.

• Is not so soft that the point breaks easily.

• Feels comfortable in your hand.

• Grips the lead without slipping.

Be aware that some lead holders require special sharpeners.

You can sometimes tell the difference in hardness of a mechanical pencil lead just by looking at it. Smaller-diameter leads are used for the harder grades, and larger-diameter leads are used to give more strength to the softer grades.

Plain wooden pencils work great. They are inexpensive, and it is easy to produce thick or thin lines by varying the amount that you sharpen them. An old trick to keep the lead sharp longer is to turn the pencil frequently as you work to wear it down evenly.

Gum erasers and nylon erasers work well to pick up smudges without leaving much eraser dust.

Nylon eraser strips that come in refillable holders like mechanical pencils can be convenient for areas that require some precision. A trick for erasing fine details is to sharpen the end of the eraser strip in a small handheld pencil sharpener.


2.14 Templates

Templates are available for a great variety of specialized needs (Figure 2.29). Templates may be found for drawing almost any ordinary drafting symbol or repetitive feature.

Figure shows a few drawing templates. Various shapes such as a circle, triangle, hexagon, and so on are shown in different sizes.

2.29 Drawing Templates

2.15 CAD Tools

Most people who create technical drawings use CAD. Advantages include accuracy, speed, and the ability to present spatial and visual information in a variety of ways.

However, these advantages do not eliminate the need for drawings to be easily and accurately interpreted. CAD drawings use the same general concepts and follow the same drafting standards as drawings created by hand.

Most CAD drawings are plotted on standard sheet sizes and to similar scales as hand drawings. Both CAD and hand drawings should contrast thick lines for objects with thin lines for hidden, center, and dimension lines to make the printed drawing easy to read. CAD drawings should use correct line patterns. Likewise, lettering on CAD drawings should follow these same general guidelines as for hand drawings.

One benefit of CAD is the ability to draw perfectly straight uniform lines and other geometric elements. Another is the ability to quickly represent the various styles of lines (Figure 2.30). Making changes to a CAD drawing takes about a tenth the time that it takes to edit a drawing by hand. Using CAD, you can quickly plot drawings to different scales.

Figure shows a drawing created using CAD.

2.30 A Drawing Created Using CAD (Courtesy of Mark Perkins.)

Keeping CAD drawing files organized, backing up data regularly, and following conventions for naming files so that you can find them again are important considerations. Even skilled CAD users use freehand sketching, to quickly get ideas down on paper and to show their ideas on a whiteboard.


CAD at Work: Model Space and Paper Space in AutoCAD

Using CAD, you can make an accurate model of the device or structure. To do this, you create the object at the actual size that it exists in the real world, using whatever system of measurement that you would use when constructing it.

On paper it is a different matter. You would have to have some really large sheets to print your building full size. AutoCAD software uses the concept of two “spaces,” model space and paper space, to describe how to transform the full-size CAD model to proportionate views that fit your sheet of paper.

Understanding scale as it relates to paper drawings or as it relates to creating layouts from a CAD drawing is an important concept for technical drawing because the ultimate goal is for drawings to be interpreted and used in the real world. Therefore, they must be easy to print and read.

Figure shows the model space and paper space in AutoCAD.

(A) In AutoCAD, paper space allows you to see how various views of the full-size model can be shown on a sheet of paper.

Figure shows the Paper space and Model space windows.

(B) The window at left shows a paper space representation of the full-size CAD model in the smaller window at right. Note that AutoCAD uses icons to help users differentiate the two “spaces.” (Autodesk screen shots reprinted courtesy of Autodesk, Inc.)


2.16 Sketching and Drawing Media

Many choices of media (paper and other) are available for particular sketching or drawing purposes. Whether you are sketching or are plotting a drawing from a CAD workstation, choose the type of sheet and size that suits your needs.

Small notebooks or sketch pads are useful when working at a site or when it is necessary to quickly record information. Many companies require bound notebooks of graph paper for recording engineering design notes so they are preserved for patent and documentation purposes. Graph paper can be helpful in making neat sketches like the one in Figure 2.31. Paper with 4, 5, 8, or 10 squares per inch is convenient for maintaining proportions.

Figure shows a sketch drawn on a graph paper.

2.31 Sketch on Graph Paper

A sketch pad of plain paper with a master grid sheet showing through underneath works well as a substitute for grid paper. You can create your own master grid sheets using CAD. Specially ruled isometric paper is available for isometric sketching, or you can use CAD to create masters.

The best drawing papers have up to 100% pure rag stock. Their strong fibers hold up well to erasing and folding, and they will not discolor or grow brittle with age. Good drafting paper should have a fine grain (or tooth) to pick up the graphite and produce clean, dense black lines. Paper that is too rough produces ragged, grainy lines, is harder to erase, and wears down pencils quickly. Look for paper that has a hard surface that will not groove too easily under pencil pressure.

Polyester film is a high-quality drafting material available in rolls and standard sized sheets. It is made by bonding a matte surface to one or both sides of a clear polyester sheet. Its transparency and printing qualities are good and it provides an excellent matte drawing surface for pencil or ink, it is easy to erase without leaving ghost marks, and it has high dimensional stability. Its resistance to cracking, bending, and tearing makes it very durable. Many companies still plot their drawings in ink on polyester film for long-term storage and reproduction.

Even large coated sheets of aluminum (which provides a good dimensional stability) have been used in the aircraft and auto industry for full-scale layouts that were scribed into the coating with a steel point rather than a pencil.

2.17 Standard Sheets

There are ANSI/ASME standards for international and U.S. sheet sizes. Table 2.2 describes the height and width of these standard sheets, the letters used to refer to them, and their margins and zones. Note that drawing sheet size is given as height × width. Most standard sheets use what is called a “landscape” orientation.

Table 2.2 Sheet Sizes

Nearest
International
Size (mm)

International
Number
of Zones

International Margin

Standard U.S. Size (in.)

U.S. Number of
Zones (width)

U.S. Margin
(in.)

A4 210 × 297

6

10

A* 8.5 × 11.0

2 (optional)

.50

A3 297 × 420

6

10

B 11.0 × 17.0

2 (optional)

.50

A2 420 × 594

8

10

C 17.0 × 22.0

4

.50

A1 594 × 841

12

20

D 22.0 × 34.0

4

.50

A0 841 × 1189

16

20

E 34.0 × 44.0

8

.50

* May also be used as a vertical sheet size at 11″ tall by 8.5″ wide.

 

 

 

 

 

The use of the basic sheet size, 8.5″ × 11.0″ or 210 mm × 297 mm, and its multiples permits filing folded prints in standard files with or without correspondence. These sizes can be cut from standard rolls of media.

2.18 Standard Layout Elements

Margins and Borders

Each layout begins with a border drawn inside the sheet margin. Drawings in the U.S. use a .50″ margin. Refer to Table 2.2 for international sheet sizes and margins. Some companies use slightly larger sheets to allow drawings to be bound into a set. This extra allowance should be added on to the standard sheet size so that the drawing border meets the size standards (see Figure 2.32). Figure 2.33 shows the alternative orientation of an A size drawing.

Figure shows 4 sheet sizes and borders.

2.32 Typical Sheet Sizes and Borders (See Table 2.2 for E-size and international standard sizes.)

Figure shows the vertical orientation of "A size."

2.33 Vertical Orientation of A Size

Zones

You have probably seen zone numbers on maps, where the margin is subdivided by letters along one side and by numbers along the other. These are also used along the outer edges of technical drawings so that you can refer to items by the area on the sheet where they are located. This is particularly useful when a client calls with a question. You can use zone numbers to make sure you are talking about the same item. Zone numbers are also useful for locating revisions. You should provide zone numbers on all sheets larger than size B.

Typical Letter Sizes

Most lettering on drawings should be at least 3 mm or .12″ (about 1/8″) tall. Lettering is typically sized as follows:

Drawing Title, Drawing Size

6 mm (.24″)

DAI

6 mm (.24″)

Drawing Number, Revision Letter

6 mm (.24″)

Section and View Letters

6 mm (.24″)

Zone Letters and Numbers

6 mm (.24″)

Drawing Block Headings

2.5 mm (.10″)

All Others

3 mm (.12″)

Title Block

The title block is located in the lower right corner of the format. Refer to Figure 2.34 for dimensions for a typical title block for A-, B-, and C-size sheets.* Standard areas in the title block provide the following information.

Figure shows a typical title block for A size, B size, and C size sheets, with the dimensions labeled.

2.34 Title Block for A-, B-, and C-Size Sheets

Name Show the name of the originating company or business (and address if desired). Refer to Figure 2.35.

Figure shows a typical title block.

2.35 Company Name and Drawing Title

Drawing Title Briefly describe the item using a singular noun or noun phrase and modifiers if necessary to distinguish it from similar items. Do not use the terms “for” or “or” in the title. For example, “Dust Cap” would be preferred over “Cap or Cover for Dust Protection,” which is too wordy.

Drawing Number Give each drawing a unique number, using the company’s numbering system.

Sheet Revision Block Track the drawing version using the number of the revision. The original release of the drawing typically shows revision 0.

Approval Block List the name(s) of the person(s) approving the drawing and the date it was approved. Additional areas of this block can be used for various design activities, if separate approval is required. For example, a company may use separate areas for structural design or manufacturing engineering approvals (Figure 2.36).

Figure shows a typical title block.

2.36 Approval Block, Scale, Revision, and Drawing Size

Scale List the predominant scale for the drawing. Drawings may include details at other scales, which should be noted below the detail. If the drawing is not made to a particular scale, note NONE in the scale area.

Drawing Size List the sheet size used for the drawing. This helps track the original size when the drawing is reproduced at a smaller size.

Sheet Number List the number of the sheet in the set, using whole numbers starting at 1. A format that lists this sheet out of the total number helps keep track of the entire set, for example, 1 OF 2.

DAI List the Design Activity Identification in this area when it is required. This block may be left blank or the block removed if it is not needed. Examples of DAI include: design activity name, activity name and address, and Commercial and Government Entity (CAGE) codes if applicable. CAGE codes are numbers assigned to entities that manufacture items for the government, based on the DAI.

Weight List the actual or estimated weight of the part if required (Figure 2.37).

Figure shows a typical title block.

2.37 DAI and Weight May Be Listed

*For more formats, title blocks, revision blocks, and materials blocks, see inside the front cover of this book.

2.19 Layouts

A particular size sheet with a drawing border is called a layout. Using a CAD system, you may often be able to select from standard layouts or templates that set the sheet size limits, the border, and even the title block as the starting point for your drawing. Regardless of whether you draw by hand or use CAD or 3D modeling methods, you need to plan your sheet so that the information will fit and show clearly.

When you are sketching, your layout may be a simple border and title strip along the bottom of the sheet (or you may be using preprinted tablets that have space to record the sketch title, date, and other pertinent data).

When creating a 2D CAD drawing, you may use a drawing template showing the sheet and border and title block, perhaps using different templates or even software interface settings for different types of drawings, such as mechanical/manufacturing, architectural, or civil.

When creating a 2D drawing from a 3D solid model, you may use a layout space that contains different viewports that allow you to show different views of the same 3D model with a border and title block.

2.20 Planning your Drawing or Sketch

When laying out a drawing sheet, you will need to consider:

• the size and scale of the object you will show;

• the sheet size;

• the measurement system (units) for the drawing; and

• the space necessary for standard notes and title block.

The object you are drawing is the “star” of the sketch. Keep the object near the center of the sheet. It should be boldly drawn, using thick visible lines. Make it large enough to fill most of the sheet and so that details show clearly (Figure 2.38).

Figure shows the selection of appropriate scale and sheet size.

2.38 Show details clearly by selecting the appropriate scale and sheet size.

Show Details Clearly

Show small objects larger than their actual size to represent the details clearly. If the details are too small, switch to a larger sheet size and use a larger scale.

You can also add details at a larger scale if necessary to show features that are smaller than the typical features of the drawing. If you add details at a different scale, label the view, for example, DETAIL A, and note the scale for the detail below it.


Step by Step: Sheet Layout

Figure shows a drawing in the shape of a rectangle, with the top left corner chamfered. Inside the rectangle, a circular shape near the top left corner, and two smaller circles aligned one below the other are shown at the top right.

Image To draw the part shown in the given figure, select the sheet size, keeping in mind the size of the objects. Show the part large enough to represent features clearly. Use larger sheets for larger or more detailed objects. (8.5″ × 11″ will be large enough for the part shown.) Add the border and title block to the sheet using the margin sizes specified in the standards. Refer to Table 2.2.

Figure shows a sheet of paper mounted using tape.

Image Determine the units for the drawing. Will it be metric or U.S. Customary (inches, feet and inches)? What system will be used to construct, manufacture, and inspect the actual object? Use that system of measurement for the drawing. This part is in inches.

Figure shows a sheet of paper with a border drawn inside.

Before you begin drawing, determine the scale at which the object will best fit on the sheet.

First, figure the available space within the drawing border. For example, the horizontal 8.5″ × 11″ sheet with a .5″ margin leaves 7.5″ × 10″. If you subtract space for a .375″ title strip across the bottom, it leaves 7.125″ × 10″ for the drawing.

Now, consider the size of the object. Will it fit on the sheet at full size? Half size? Do you need to enlarge it to show small features larger than actual size? The 12″ gasket shown in the example will fit well at half size on the 8.5″ × 11″ sheet and still show the details clearly. Use typical scales when possible. Refer to Section 2.5.

Approximately center the object on the sheet. To do this, subtract the size of the scaled drawing from the available sheet space and use half of the difference on each side of the object.

Image One quick technique is to find the center of the available space and lay out the drawing on each side of that centerline. Using CAD, you can easily move the drawing to the center of the sheet visually.

Figure shows a border drawn on a sheet of paper.

Sketches do not have to be perfectly centered, but plan ahead so the drawing isn’t crammed in one corner of the sheet. Let your drawing be the “star” of the page. Remember to leave enough space around your drawing for notes and dimensions. If you don’t, you will run out of room and your layout will look crowded.

Image Lightly add details of the drawing.

Figure shows the addition of details to the drawing from earlier.

Image Darken final drawing lines.

Figure shows the darkening of final lines of the drawing and addition of title block.

Tip: Scale When Using CAD

Keep in mind that when using CAD you will create the object the size that it actually exists in real life. On the plotted sheet, when showing the drawing to scale, it is easy to try a few different scales and see which fits. You can always change the scale later if needed.




CAD at Work: Scaling Annotations Automatically Using AutoCAD

You might think that displaying text in a CAD drawing is one of the easiest things to do. You can quickly type in the text you want to display and select the font, height, slant, and rotation angle. That part is easy, but annotations are useless if nobody can read them.

When you create drawings that will be plotted on different sized sheets or at different scales, sizing the text can require a lot of planning. Take the architectural plan drawing shown in Figure A for example. When plotted to scale 1/2″ = 1′, the text showing dimensions is clearly visible. But when shown at one tenth of that size, scale 1/2″ = 10′, that same text becomes illegible.

Figure shows an architectural plan drawing.

(A) When plotted to a scale of 1/2= 1on an 11″ × 8.5sheet, the text showing the dimensions is clearly visible. (Courtesy of Centermark Industries, Inc.)

The ability to reuse the same CAD data at different scales without having to recreate the drawing is one of its big advantages over pen and paper drawings. Yet, cumbersome workarounds were once necessary to make legible text at different scales. One workaround was to have several different sizes of the same text, which the user would turn on or off depending on what drawing scale was used.

Now, AutoCAD software provides a feature called annotation scaling. Here is how it works: Drawing objects that are commonly used to annotate drawings (provide text information) can have their annotation property turned on. This allows you to create one annotative object that displays at different sizes, based on scale properties.

In the AutoCAD software, object types that can have annotative object properties include text, mtext, dimensions, hatches, tolerances, multileaders, leaders, blocks, and attributes.

Screenshot of the Annotation Object Scale window is shown.

(B) The annotation scaling feature of AutoCAD software allows annotative text to be made legible at various scales. (Autodesk screen shots reprinted courtesy of Autodesk, Inc.)



Portfolio

Figure depicts the assembly directions for the instructions on squaring chassis assembly.

Assembly Drawing. An assembly drawing showing a revision block and a standard title block. (Courtesy of Dynojet Research, Inc.)

Figure shows a sketch of a civil drawing.

A Civil Drawing. The drawing shows approval blocks and engineers’ stamp. (Courtesy of Perliter and Ingalsbe Consulting Engineers and Calleguas Municipal Water District.)

Figure shows the window and door schedules.

Window and door schedules are used in architectural drawings to specify the type of window or door, rough opening size, manufacturer, and other information. (Courtesy of Frog Rock Design, LLP.)


Key Words

Approval Block

Architects’ Scale

Construction Lines

Decimal Inch

Decimal-Inch Scale

Drawing Lines

Drawing Number

Drawing Scale

Drawing Size

Drawing Title

Engineers’ Scale

Font

Freehand Line

Guidelines

Inclined

Italic

Kerned Pairs

Layout

Lettering

Measurement Systems

Mechanical Engineers’ Scale

Media

Multiview Projection

Name

Oblique Projection

Orthographic Projections

Parallel Projections

Perspective Projections

Piercing Points

Plane of Projection

Projectors

Roman

Sans Serif

Scale

Scales

Serif

Sheet Number

Sheet Revision Block

Sheet Sizes

Station Point

Thick Lines

Thin Lines

Title Blocks

Vertical

Weight

Zone Numbers

Chapter Summary

Now that you have completed this chapter you should be able to:

• Understand the basic principles of projection used in drawings.

• Demonstrate the lineweights (thickness) and types (dashed or solid) of lines used in the alphabet of lines that specify meaning in technical drawings.

• List the two main systems of measurement used on drawings.

• Use different types of scales to make measurements.

• Note the scale for a drawing in the title block. Paper drawings are scaled before they are drawn. CAD drawings are scaled when they are to be printed.

• List the advantages of several different drawing media and the qualities that distinguish them.

• Add legible and quick notes and dimensions to sketches using uppercase letters drawn by hand.

• Lay out a sheet and fill in the information in the title block using standard letter shapes.

Review Questions

1. Draw the alphabet of lines and label each line.

2. What are the main advantages of polyester film as a drawing media?

3. What are the four standard types of projections?

4. Which drawing lines are thick? Which are thin? Which are very light and should not reproduce when copied?

5. What font provides the shape of standard engineering lettering?

6. Describe the characteristics of good freehand lettering.

7. Why should guidelines be used for lettering?

8. List the standard items found in a title block.

Chapter Exercises

Drawing Exercises

Practice your skills for making measurements, laying out drawing sheets, and forming neat standard lettering with these drawing exercises.

These problems are designed to fit easily on a sheet. (See the inside front cover of this book). Draw all construction lines lightly, using a hard lead (4H to 6H), and all required lines dense black with a softer lead (F to H). Draw your construction lines lightly so that they do not need to be erased.

In Exercises 2.12.3 you will practice measuring, and in Exercises 2.42.6 you will practice drawing layouts.

__________________________________________________________________________

___________________________________________

__________________________________________________________

___________________________________

_________________________________________________________

______________________________________________________________

Exercise 2.1 Measure the lines shown above and list their lengths using millimeters. List the inch measurements for each in square brackets [ ] to the right of the millimeter measurement.

___________________________________

____________________________________________________

__________________________________________________________________________

____________

____________________________________________________________

____________________

Exercise 2.2 Measure the lines shown above and draw them at Scale 1:2, Scale 2:1, and list their scales below them using the form Scale: X:X.

Exercise 2.3 Measure the overall interior dimensions of your room. Letter the measured length neatly in the first column as shown in the example. In the second column list how long you would draw that line at a scale of 1/4″ = 1′, third column at 3/8″ = 1′, fourth column at 1″= 1′, fifth column at 1:100 metric scale (10 mm = 1 meter).

Measurement

1{{#}}8729;4″ = 1′

3{{#}}8729;8″ = 1′

1″ =1′

1:100 Metric

10′-6″

2.625″

3.9375″

10.5″

32mm

Exercise 2.4 Create the layout for an 8.5″ × 11″ sheet as shown at right.

Figure shows a large grid square.

Exercise 2.5 Create the layout for the 210 mm × 297 mm sheet shown at right.

Figure shows an drawing sheet with a title block.

Exercise 2.6 Design a title block and layout for a C-size sheet. Create a name and logo for your company. Use an attractive but legible font for the titles on your layout. If assigned, design a special north arrow to be used on your drawings.

Lettering Exercises

Layouts for lettering problems are given in Exercises 2.72.11. Draw complete horizontal and vertical or inclined guidelines very lightly. Draw the vertical or inclined guidelines through the full height of the lettered area of the sheet. For practice in ink lettering, the last two lines and the title strip on each sheet may be lettered in ink, if assigned by the instructor. Omit all dimensions.

Exercise 2.7 Letter the words to your favorite song, joke, or inspirational quote of 50 words or more. Use 1/8″ tall UPPERCASE engineering lettering. Center the words near the middle of the sheet. Make sure to leave a row of space between each row of lettering. Make sure that the subject you choose is professional and appropriate.

Figure shows letters written on a sheet.

Exercise 2.8 Lay out sheet as shown. Add vertical or inclined guidelines and fill in vertical or inclined capital letters as assigned. For decimal-inch and millimeter equivalents of given dimensions, see the inside back cover.

Figure shows letters written on a sheet.

Exercise 2.9 Lay out sheet as shown. Add vertical or inclined guidelines and fill in vertical or inclined capital letters as assigned. For decimal-inch and millimeter equivalents of given dimensions, see the inside back cover.

Figure shows letters written on a sheet.

Exercise 2.10 Lay out sheet as shown. Add vertical or inclined guidelines and fill in vertical or inclined lowercase letters as assigned. For decimal-inch and millimeter equivalents of given dimensions, see the inside back cover.

Figure shows letters written on a sheet.

Exercise 2.11 Lay out sheet as shown. Add vertical or inclined guidelines and fill in vertical or inclined numerals and fractions as assigned. For decimal-inch and millimeter equivalents of given dimensions, see the inside back cover.

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