web chapter 3design and draw the following types of charts and graphs: rectilinear, surface, column,...

OBJECTIVESAfter completing this chapter, you will:

■ Design and draw the following types of charts and graphs:rectilinear, surface, column, pie, polar, nomographs, trilin-ear, flow, distribution, and pictorial.

■ Use a computer-aided design and drafting system to designand draw a chart from engineering specifications andsketches.

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WEB CHAPTER Engineering Charts

and Graphs

3

T H E E N G I N E E R I N G DESIGN A P P L I C AT I O N

Given the following statistical data, design a rectilinearchart that will represent the information.

Projected population of the United States from 1985to 2165. The source is World Bank data, projected assum-ing constant fertility and migration. The year is followedby the population in millions: 1985—238, 1995—255,2005—269, 2015—282, 2025—290, 2035—291,2045—287, 2055—283, 2065—279, 2075—273,2085—269, 2095—264, 2105—259, 2115—255,2125—251, 2135—247, 2145—243, 2155—240,2165—239.

Step 1. Establish the range of units. In this case the low-est unit in years is 1985 years and the highest is2165 years. The lowest unit in population is238 million and the highest is 291 million.

Step 2. Determine the vertical scale to accommodatethe range; for example, 230 to 300 million asshown in Figure 1.

Step 3. Determine the horizontal scale. In this case thereis a set of data every ten years. The horizontalscale will be divided into units representing ten-year modules. It is best to make the horizontalscale approximately equal to the vertical unitswithout crowding. In this case there are morehorizontal than vertical units, so the ten-yeardivisions will be closer than preferred; however,the thirty-year divisions will be the main units asshown in Figure 2.

Step 4. Plot the points and draw the curve as shown inFigure 3.

Step 5. Complete the chart by labeling the title and anyrequired captions. (See Figure 4.)

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FIGURE 1 ■ Step 2—determine the range for the vertical scale units.

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FIGURE 2 ■ Step 3—determine the horizontal scale and estab-lish the grid.

(Continued)

Charts are graphic representations of any measurable data.Charts, graphs, and diagrams are all synonymous with thegraphic representation of numerical data. Charts may be morespecifically defined as illustrations that give information thatwould otherwise be arranged in a table (tabular form). Graphsand diagrams are a series of points, a line, a curve, or an arearepresenting the comparison of variables. The advantage ofcharts and graphs is that technical data may be shown in amanner that quickly and graphically communicates the infor-mation.

Professionals in any field can use charts and graphs tographically explain or demonstrate the results of statistics. Sta-tistics is the science of the collection, arrangement, and inter-pretation of quantifiable information. Statistics has two areas orbranches: descriptive statistics and inferential statistics. Descrip-tive statistics is the summarizing and organization of data.Inferential statistics includes making inferences (drawing con-clusions) about a whole population based on informationobtained from a sample. Many engineers, quality-control peo-ple, and managers are beginning to understand that to really

interpret data, they need the statistics and a picture of the datain the form of a chart or graph. Many people have difficultyunderstanding and interpreting statistical data unless the quan-tities are shown on a chart or graph.

The accurate preparation of charts and graphs requires adegree of knowledge of the topic related to the data and anunderstanding of where, how, and why the chart is used. Thereare two fundamental applications for charts: analysis and pres-entation. Analytical charts are used to analyze, examine, andexplore data, or the information is used to calculate specificrequired values. Presentation charts are generally more artisticin appearance and are used to demonstrate or present informa-tion. Presentation charts are used in advertising and may bepictorial for easy communication of data for laypeople. Whilethere may be two classifications of charts, there is a crossover.For example, analytical charts may be used for presentation,and presentation charts often contain analytical data.

ASA According to the American Standards Associationdocument ASA Y15.2, the following questions should beanswered before a chart design is started:

1. What is the general purpose of the chart?

2. What kind of data are to be presented?

3. What features of the data is the chart to identify?

4. For what audience is the chart intended?

5. What method will be used to show the chart to the audience?

The selection of the specific type of chart is the designer’schoice. Not all chart design questions are applied to each chart.Some charts may be designed to focus on one or more of therelated design questions. One of the most important factors inchart design is simplicity. Keep the chart as simple as possibleby avoiding the presentation of too much information or detail.

Charts may be designed for any purpose to accurately com-municate numerical data from a simple line format to a pictorialpresentation. The selection of the chart type depends on theaudience, the intent of the presentation, and the type of data.The basic types of charts include rectilinear (line) charts, sur-face charts, column (bar) charts, pie charts, polar charts, nomo-graphs, trilinear charts, flowcharts, distribution charts, and pic-torial charts.

RECTILINEAR CHARTSRectilinear charts, also known as line charts, are the most com-mon type of chart used for the presentation of analytical data.The rectilinear chart is commonly set up on a horizontal andvertical grid where the horizontal axis or scale representsamounts of time or other significant independent values. Thevertical axis identifies the dependent quantities or valuesrelated to the horizontal values. The horizontal axis is calledthe X axis or abscissa, and the vertical axis is called the Y axisor ordinate. The line formed by connecting the data elements iscalled the curve. (See Figure 5.) Rectilinear charts are referredto as a slope curve when the data represent points in time that

2 ■ Engineering Charts and Graphs

T H E E N G I N E E R I N G DESIGNA P P L I C AT I O N (continued)

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2301985 2015 2045 2075 2105 2135 2165

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2301985 2015 2045 2075

YEARSWORLD BANK DATA PROJECTED ASSUMING

CONSTANT FERTILITY AND MIGRATION

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PROJECTED POPULATION OF THEUNITED STATES FROM 1985–2165

2105 2135 2165

FIGURE 3 ■ Step 4—plot points from given data and draw thecurve. Note points are exaggerated for emphasis.Should be plotted very lightly.

FIGURE 4 ■ Step 5—complete the chart by labeling the titleand required captions.

are not backed by mathematical computations. (See Figure 6a.)Step curves are established by data that change abruptly. (SeeFigure 6b.) In some applications a smooth curve is used whenthe data plotted form a consistent pattern, or when the averageof the calculated points is represented. A smooth curve gener-ally acknowledges an empirical relationship between the dataand the curve. Empirical refers to information that is based onobservation and measurement rather than theory. (See Figure 6c.)A type of rectangular chart where greatly varying data do not fitinto a defined curve is called a rectangular coordinate distribu-tion chart or scatter chart. The term scatter is used to describethese charts because the plotted data are scattered around onthe chart. The purpose of these charts is to observe the distri-bution of data and to identify any areas of concentration. (SeeFigure 6d.)

Scales

The selection of horizontal and vertical scales is one of themost important aspects of chart design. There should be a goodbalance between the scales. If one scale is exaggerated out ofproportion, then the resulting curve may be misleading. Scaleselection greatly affects chart design. For example, the twocharts shown in Figure 7 contain the same data; however, thechart in Figure 7a has a smaller vertical scale than the chart inFigure 7b. Notice the extreme difference in curve representa-tion between the two charts.

When selecting the proper scale, the first consideration isthe range of data. The scale range extends from the smallestvalue to the largest value. Charts often, but not always, begin atzero and extend beyond the largest Y value and are at least aslong as the largest X value. The scale should include zero whena comparison of two or more curve magnitudes is made. Thescales may not necessarily show zero when the intent of thechart is to show the relationship between one group of unitsand another, or when the general shape of one curve is com-pared to another.

The selection of a beginning and ending scale value alsodepends on the range of values to be displayed. For example, ifthe display values range from 500 to 1500, then a zero begin-ning may be too far removed from the first value of 500. Whenzero does not begin the scale, the first numerical value shouldbe labeled with bold letters or otherwise clearly identified sothe reader does not assume a zero beginning. The scale divi-sions are usually established as convenient units such as0,2,4 . . . ; or 0,5,10. . . . The scale should also be selected sothe curve is well distributed throughout the chart. Thisrequires that the scale range be extended beyond the value lim-its. (See Figure 8.) As previously shown in Figure 7b, too muchrange is also not desirable because it provides an excessiveamount of blank area in the chart. In some situations a certainamount of blank space may be necessary to accommodatenotes, details, or other information. When this is appropriate,add enough scale units to provide this space.

ENGINEERING CHARTS AND GRAPHS ■ 3

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HORIZONTAL UNITS

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RTI

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CURVE

X AXIS(ABSCISSA)

Y AXIS(ORDINATE)

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FIGURE 5 ■ Elements of a rectilinear chart.

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0(c) SMOOTH CURVE

MATHEMATICAL DATA

(a) SLOPE CURVE

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COORDINATE DISTRIBUTION(SCATTER) DIAGRAM

(b) STEP CURVE

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FIGURE 6 ■ Rectilinear curves.

(a) GOOD

M T W TH F M T W TH F

(b) POOR

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FIGURE 7 ■ Scale selection may greatly affect chart design.

When one or more charts are compared, the designer shouldset the scales of all charts the same by starting with the chartthat has the greatest range of values. The only potential prob-lem is that some of the curves may be flat; however, this maybe necessary to provide a realistic comparison. Figure 9 showstwo charts placed for comparison. Another method to show thecomparison of two or more curves is to place each curve on thesame chart. When the curves do not cross, the curve lines maybe drawn all the same thickness as shown in Figure 10.

When the curves to be compared intersect each other, atechnique should be used to differentiate each curve. Figure 11shows curve comparison on the same chart by using differentline thicknesses. Another common method used to distinguishcurves in a comparative chart is to show the curves using dif-ferent line representations; for example, solid line, dash line,and dotted line as shown in Figure 12. It is not normally a goodidea to design a chart with unusual patterns or shapes. Thesetypes of designs often clutter the chart or may be difficult todifferentiate without careful analysis. (See Figure 13.) Anothertechnique for charts with the same horizontal and verticalscales is to prepare the charts separately on clear polyester filmand overlay them for comparison.

The previous discussion and examples have shown chartswhere numerical values along the abscissa and ordinate havebeen positive, beginning with zero on the X and Y axis. Many

charts that are designed from mathematical data do not followthis layout pattern. When numerical values exist as negativequantities, the chart must reflect the quantities below zero asshown in Figure 14. Some applications exist where plotted val-ues are negative X and Y, or positive X and Y, or positive X andnegative Y, or negative X and positive Y values. When thisoccurs, the chart will be set up in quadrants as shown in Fig-ure 15. Quadrant 1 shows positive X and Y values. Quadrant 2provides negative X and positive Y values. Quadrant 3 displaysnegative X and Y values. Quadrant 4 shows positive X and neg-ative Y values.


(a) POOR; TOTALRANGE NOT SHOWN

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(b) GOOD; FULLRANGE SHOWN

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FIGURE 8 ■ Scale range selection affects chart design.

(a)

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FIGURE 9 ■ (a) Charts placed side-by-side for comparison; same scale range. (b) Comparativecharts stacked to save space.

FIGURE 10 ■ Noncrossingcurves may be drawn the samethickness for comparison.

FIGURE 11 ■ Curve com-parison using different linethicknesses.

Ratio Scales

Ratio scales are special scales that are referred to as logarithmic andsemilogarithmic scales. The scales that were discussed previouslyare arithmetic scales where equal distances represent equalamounts. Arithmetic scales are used to display the absolute dimen-sion of values. Ratio scales represent a different function where therate of change of the variables is more important than the absolutevalues or amount of change. Logarithmic charts use a logarithmicscale for both the X and Y axis. Semilogarithmic charts use a log-arithmic scale for the Y axis and an arithmetic scale for the X axis.The advantage of ratio scales exists when it is desirable to displaychanges at one level either relatively larger or smaller than changesat another level, or for showing a pattern of relative changes. Log-arithmic scales are established by making the divisions propor-tional to the logarithms of the arithmetic scales. A comparison ofthe arithmetic and logarithmic scales is shown in Figure 16.

There are a variety of logarithmic scales available. The scalesmost commonly used for chart design are one-cycle, two-cycle,and three-cycle. (See Figure 17.)

Logarithmic charts may be prepared directly on preprinted log-arithmic paper or designed to fit any required area. Preprinted logscales may be used to divide the given area into proportional divi-sions by the same technique used when dividing a space into equalparts (Chapter 4), or using scales set up in the CADD program.


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(a) PATTERNS OF THIS TYPEARE MORE DIFFICULT TO

DRAW AND CLUTTERTHE CHART.

(b) PATTERNS OF THIS TYPEARE DIFFICULT TODIFFERENTIATE.

FIGURE 12 ■ A comparative chart using different line representations.

FIGURE 13 ■ Charts designed with unusual patterns or line desig-nations should be avoided.

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FIGURE 14 ■ Chart showing negative values.

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FIGURE 15 ■ Chart set up in quadrants on an X–Y axis.

(a)ARITHMETIC SCALE—

EQUAL AMOUNTS

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(b)LOGARITHMIC SCALE—

EQUAL RATIOS

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FIGURE 16 ■ A comparison of the arithmetic and logarithmic scales.

Grids

The grid is the horizontal and vertical lines that form the chart lay-out. The grid lines are determined by the scales and are used to aidin both drawing and reading the chart. Charts and graphs may beprepared on preprinted grid paper or designed to fit specific needs.The actual grid format depends on the purpose of the chart. Inmost applications the following guidelines should be considered:

1. A grid with wide horizontal and short vertical incrementsis used for data that cover a long period of time.

2. A grid with narrow horizontal and high vertical incre-ments is used for data that represent short periods of timeor rapid value changes.

3. Most applications work out well if the horizontal and ver-tical grids are approximately equal. (See Figure 18.)

Grid lines are generally thin. The thickness of these lines mayincrease as the distance between them increases. Close gridlines should usually be drawn very thin.

Certain horizontal or vertical grid lines may be distinguishedfrom other lines by drawing them either thicker or as a dashedline. For example, manufacturing quality control often usescomputerized monitoring of dimensional inspections in statisti-cal process control (SPC). When this is done, a chart that showsfeature dimensions obtained at inspection intervals is developed.

The chart shows the expected limits of sample averages as twodashed, parallel horizontal lines as shown in Figure 19.

It is important not to confuse control limits with tolerances—they are not related to each other. The control limits come fromthe manufacturing process as it is operating. For example, if youset out to make a part 1.000 ± .005 in., and you start the run andperiodically take five samples and plot the averages (x) of thesamples, the sample averages will vary less than the individualparts. The control limits represent the expected variation of thesample averages if the process is stable. If the process shifts or aproblem occurs, the control limits signal that change.

Notice in Figure 19 that the x values represent the average ofeach five samples; is the average of averages over a period of sam-ple taking. The upper control limit (UCL) and the lower controllimit (LCL) represent the expected variation of the sample aver-ages. A sample average may be “out of control” yet remain withintolerance. During this part monitoring process, the out-of-controlpoint represents an individual situation that may not be a problem;however, if samples continue to be measured out of the control lim-its, the situation must be analyzed and the problem rectified. Whenthis process is used in manufacturing, part dimensions remainwithin tolerance limits and parts will not be scrapped. Statisticalprocess control is discussed further in Chapters 11, 12, and 16.

Line Chart Labeling

There are standard guidelines for the placement of labels andcaptions. In general, however, labels should be large enough for

x=


(a) ONE-CYCLE (b) TWO-CYCLE (c) THREE-CYCLE

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FIGURE 17 ■ Logarithmic scales.

POOR POOR RECOMMENDED

FIGURE 18 ■ Grid spacing.

AVERAGE OF AVERAGES (X)

OUT-OF-CONTROL POINT

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FIGURE 19 ■ A chart showing feature dimensions at inspectionintervals.

easy reading and placed to avoid cluttering the chart. The mostimportant feature of the chart should be emphasized by bolddisplay or special effects such as color. For example, the title ora predominant curve may be emphasized. Avoid overemphasiz-ing a particular feature to the extent that other items are lost.

Chart Titles

Chart titles are generally aligned with the left edge of the paperor centered at the top of the chart. Title lettering is higher andbolder than other labels and captions.

Labeling Scales

The scales are usually identified with numerical values next tothe corresponding grid lines. Abscissa scale numerals areplaced below the horizontal scale and ordinate scales arelabeled to the left or right of the chart. Very long or high chartsmay have scales labeled at both grid limits. The horizontal andvertical units are identified next to the numerical values orbelow the X values and directly above the column of Y values.Figure 20 shows several examples.


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CENTERINTERMEDIATENUMERALS ONGRID LINES

DROP TOP NUMERAL TOALIGN WITH CHART TOP

RAISE BOTTOMNUMERAL TOALIGN WITHCHARTBOTTOM

VERTICALSCALECAPTION

TITLE

ALIGN LEFT SIDE

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FIGURE 20 ■ Chart labeling.

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POOR RECOMMENDED POOR RECOMMENDED

10 THOUSAND THOUSAND MILLION BILLION

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FIGURE 21 ■ Scale identification.

Scale identification should be kept as simple as possible. Forexample, long scale numerals should be shortened using theeasiest format for the reader to understand and proper abbrevi-ations should be used when appropriate. (See Figure 21.)

Curve Captions

Curve captions are necessary when two or more curves are dis-played on the same chart. Single curves are labeled only if identi-fication is not otherwise apparent by other captions and titles. Thelettering for curve labels is generally smaller than titles and largerthan general notes. Place curve labels on the face of the chart inareas that clearly avoid crowding or confusion. (See Figure 22.)

Subtitles and Notes

Subtitles and general notes are subordinate captions that relate tothe entire chart. These items may be placed below the title, in thefield of the chart, or below the chart, depending on the designinfluence of the information and the space requirements. Specificnotes relate to individual items on the chart and may be placedin the field of the chart or keyed to the chart by identificationsymbols and placed in the area of general notes. (See Figure 23.)

(a) POOR

CURVE B

CURVE A

(b) RECOMMENDED

CURVE B

CURVE A

(c) POOR

DEPT B

(d) PREFERRED

DEPT A

DEPT C

DEPT BDEPT A

DEPT C

FIGURE 22 ■ Curve captions.

Missing or Projected Data

When some data are omitted due to missing or unavailableinformation, the estimated curve representing the missing datashould be shown as demonstrated in Figure 24.

There are some applications when the function of the chartshows current data and provides an estimate of projected val-ues. This may be done by continuing the curve into a futureinterval as shown in Figure 24.

In some unique situations there may be one or more valuesthat fall well out of the normal distribution of values. Whenthese freak values occur, they may completely alter the appear-ance of the chart unless intentionally left beyond the gridboundaries. When this is done, the numerical designation ofthe freak value is labeled as shown in Figure 25. Freak valuesshould be carefully evaluated for possible error because inactual practice this approach is uncommon.

SURFACE CHARTSSurface charts, also known as area charts, are designed to showvalues that are represented by the extent of a shaded area. The onlydifference between a surface chart and a line chart is that the areabetween the curve and the X axis or the area between curves isshaded for emphasis. The advantage of surface charts is that theymore clearly define the difference between curves or the extent ofa single curve. Surface charts should be avoided when accuratereadings are required, or when greatly irregular layers exist. Sur-face charts are designed much like line charts, except that transferfilms or computer graphics hatching techniques are used to createshading. Some of the common design layout and labeling tech-niques used with surface charts are shown in Figure 26.

One of the best design considerations for surface charts existswhen the intent of the chart is to show a margin between twocurves. (See Figure 27.) Another design characteristic is the


NOTES:

NOTE

NOTE

GENERAL NOTES

NOTES:

GENERAL NOTES

TITLESUBTITLE

CURVE B

SPECIFIC NOTES:

SPECIFIC NOTES MAYALSO BE KEYED BYOTHER SYMBOLS,LETTERS, OR NUMERALS.

CURVE A

TITLESUBTITLE

1

2

1

2

1960 1965 1970 1975 1980 1985 1990

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PROJECTED VALUES

MISSING DATA

FIGURE 23 ■ Subtitles and notes.

FIGURE 24 ■ Missing and projected data.

JAN F M A M J

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92

FREAK VALUE

FIGURE 25 ■ Technique for freak values. Avoid this method whenever possible.

(b) LEGEND USED TO LABELTHE CHART VALUES

LABEL A LABEL CLABEL B

(a) LABELING THE VALUESON THE CHART FACE

LABEL B

LABEL A

LABEL C

FIGURE 26 ■ Surface chart design and layout techniques.

implementation of a surface chart that shows the net increase orthe net decrease between two sets of values. (See Figure 28.)

COLUMN CHARTSColumn charts are commonly referred to as bar charts. A barchart is used to represent numerical values by the height orlength of columns. The data presented usually represent totalperiods of time or total percentages as opposed to various peri-ods of time shown in line charts. Bar charts provide less detailthan line charts, but provide a more dramatic and easy-to-understand display for nontechnical readers.

The columns of a bar chart may be placed either horizontallyor vertically; the vertical application is most common. The designof the bar chart vertical scale is similar to the technique used forline charts. For vertical column charts the horizontal grid isdetermined by the range of data and vertical grids are replaced bythe columns. The design of the columns should assist and notdistract from reading the chart. Chart columns should not be toobold or too thin as shown in Figure 29. The column chart shownin Figure 29c is used a lot in quality control and is referred to asa histogram. The vertical scale is the frequency of occurrence andthe horizontal scale is the value measured.

Subdivided column charts are used to show the values to indi-vidual components within total quantities of column data. Thecomponent values in each column are shaded to stand out asdifferent quantities. The column subdivisions may be labeledon the face of the chart within the designated areas or withleaders pointing to the area, or a legend may be used that dif-ferentiates the components. Caution should be exercised whenusing these charts as they may be deceiving, and hard to readand interpret. (See Figure 30.)


MARGIN

FIGURE 27 ■ Emphasizing the difference between two curves.

FIGURE 28 ■ Emphasizing the net difference between two curves.

INCREASE

DECREASE

NETINCREASE

NETDECREASE

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FIGURE 29 ■ Column chart techniques.

DISTRIBUTION OF INCOMEIN MILLIONS OF DOLLARS

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TAXES ON INCOMEDIVIDENDSADDITION TO RETAINED EARNINGS

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FIGURE 30 ■ Subdivided column chart. Courtesy Computer SupportCorporation.

Grouped column charts are used to compare two quantities atdifferent intervals. Two columns are attached to show the com-parison at the given periods as shown in Figure 31.

One hundred percent column charts are used to show the rela-tionship between the distribution of components where the totalsare always equal values, such as 100 percent of any given unit.(See Figure 32.) These charts are effective in some applications,but may be hard to read. It is usually better to separate the data.


GROUP B

GROUP A

UNIT C

UNIT A

UNIT B

FIGURE 31 ■ Grouped column chart.

FIGURE 32 ■ One hundred percent column chart.

PERCENTVARIANCE

ACTUAL 2000VS. PLAN 2000

01 VS 0000 VS PLANAS OF 9/1/01

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FIGURE 33 ■ Over-under column chart. Courtesy Computer Support Corporation.

AVERAGE

FIGURE 34 ■ Range column chart.

Over-under column charts are used to emphasize the differencebetween two variables or the difference between a variable and agiven standard. The over-under column chart has columns thatoriginate at a common value or standard line as shown in Fig-ure 33.

The previously discussed bar charts have been index chartswhere each of the columns originate at a common base. Anothertype of bar chart is the range bar, where individual columns rep-resent segments of the total applicable range. Range columncharts are used to emphasize the difference between valueswhere one value is always higher or larger than the other. Manyapplications of range bar charts also show the average value foreach column. (See Figure 34.) These charts show the centraltendency (average) of data and the variability (range) of thedata. Range bar charts are also used with median values, ratherthan average values, marked, and with control limits the sameas the chart in Figure 19.

PIE CHARTSPie charts are used for presentation purposes and are one of themost popular methods of making graphic representations ofdata for people to understand. It is easy to understand how theportions of a pie represent quantity. Even without reference tothe values of the pieces, readers can quickly determine the rela-tionship between large and small portions. Pie charts are alsoreferred to as 100 percent circle charts because the entire pie orcircle represents 100 percent of the total and each piece of pierelates to a percentage of the total. For example, a pie chart mayrepresent 100 percent of 2001 computer graphics market ship-ment, where the percentage of each segment’s shipment isshown as a piece of the pie. (See Figure 35.)

Pie Chart Design

Given the following information, design a pie chart that willgraphically display the data:

2001 agricultural sales for Washington County:Nursery crops = 44%Vegetable crops = 26%Fruits and berries = 11%Grain and hay = 8%Greenhouse crops = 6%Miscellaneous crops = 5%

Step 1. Draw a circle with a diameter of approximately 4 inches.The diameter of the circle depends on the sheet size andthe information to be included. Individual judgmentmust be used.

Step 2. Convert each category into degrees. There are 360° in thecircle representing 100% of the values.Use the formula 3.6 × % = degrees.Nursery crops = 3.6 × 44 = 158.4°.Vegetable crops = 3.6 × 26 = 93.6°.Fruits and berries = 3.6 × 11 = 39.6°.


BUSINESSGRAPHICS

45%

CAD/CAMGRAPHICS

42%

OTHERGRAPHICS

13%

200122.3 BILLION

COMPUTER GRAPHICS MARKET SHIPMENT VALUEBY APPLICATIONS SEGMENTS

SOURCE: ADVANCED RESOURCES DEVELOPMENT

FIGURE 35 ■ Comparative pie charts. Courtesy MICRO-GRAFX.

5%18°

8%28.8° 6%

21.6°

26%93.6°

11%39.6°

44%158.4°

FIGURE 36 ■ Pie chart design and layout.

VEGETABLE CROPS

226%

FRUITS AND BERRIES

NURSERY CROPS

44%

GREENHOUSECROPS

GRAIN AND HAY

MISCELLANEOUSCROPS

5%% 8%66%

1111%%%%

FIGURE 37 ■ Pie chart design shading and labeling.

Grain and hay = 3.6 × 8 = 28.8°.Greenhouse crops = 3.6 × 6 = 21.6°.Miscellaneous crops = 3.6 × 5 = 18°.

Step 3. Using the degrees calculated in step 2, lay out each pieceof the pie on the scale as shown in Figure 36. Notice thatat least one of the small pie parts is separated from thegroup of small parts for ease in labeling later.

Step 4. Add the title, notes, and captions, and do any shading tosuit the design. (See Figure 37.)

POLAR CHARTSPolar charts are designed by establishing polar coordinatescales. Polar coordinates are points determined by an angle anddistance from a center or pole. There are two scales on the polarchart. The first scale is related to the degrees or radians of a cir-cle and these radiate from the pole. The second scale representsdistances from the center. Each distance is represented by aconcentric circle. (See Figure 38.) Polar coordinate charts areused to display the effects of data that radiate from a source.The applications may include the range of intensity of a lightsource or the effective range of communication signals.

where b = 15. Project to the left and locate the c value at the Yaxis. The answer should be 20. This is an extremely simplifiedversion of the concurrency chart; however, the technique isthe same for more complex versions.

Alignment Charts

Alignment charts are designed to graphically solve mathematicalequation values using three or more scaled lines. The known val-ues are aligned on a combination of scales and the solution isfound when the line is extended or aligned with the additionalscale. The alignment chart scales are typically vertical lines; how-ever, other combinations of scale arrangements are used. Todemonstrate the alignment chart principle, the equation a + b = cis used again as shown in Figure 42. Notice that if a line is drawnbetween the 5 on the “a” scale and the 10 on the “b” scale, theunknown value of the “c” scale is 15. Therefore, 5 + 10 = 15.

Scales may have equal graduations. These graduations arecalled uniform scales. When the scales resulting from the solu-tion of the equation variables are not uniform, they are calledfunctional scales.

TRILINEAR CHARTSTrilinear means consisting of three lines. A trilinear chart isdesigned in the shape of an equilateral triangle. These chartsare used to show the interrelationship between three variableson a two-dimensional diagram. The amounts of the three vari-ables, usually presented as percentages, can be represented asshown in Figure 43. The corners of the triangle labeled A, B,and C correspond to 100 percent values of A, B, and C. Theside of the triangle opposite the corner labeled A representsthe absence of A values. Therefore, the horizontal lines acrossthe triangle show increasing percentages of A from 0 percent atthe base to 100 percent at the A vertex. In a similar interpreta-tion the percentages of B and C, respectively, are given by thedistances opposite the two sides of the vertices at either B orC. From the three scales of the triangle the value correspon-ding to any point can be read and the total of the three valuesat any given point is always 100 percent. This is possiblebecause of the geometric result that the sum of the three per-pendicular distances from any point to the three sides of thetriangle is equal to the height of the triangle.

FLOWCHARTSFlowcharts are used to show organizational structure, steps in aseries of operations, the flow of something through a system, orthe progression of materials through manufacturing processes.Organizational charts show the relationship of the different lev-els of an organization as shown in Figure 44.

Production control or process charts are used for planning andcoordinating a series of activities such as a marketing planningcycle as shown in Figure 45.


SCALE DISTANCEFROM CENTER

60

70

50

40

30

20

10

315

300

285

270

255

240

225

45

60

75

90

105

120

135

ANGULAR SCALES

210 195 180 165 150

POLE

FIGURE 38 ■ Polar coordinate scales.

NOMOGRAPHSNomographs are graphic representations of the relationshipbetween two or more variables of a mathematical equation.Nomographs are used as a quick graphic reference whereunknown values of a given equation may be determined byaligning given numerals on a series of scales. There are twogeneral types of nomographs. The most elementary is a concur-rency chart, also known as a rectangular Cartesian coordinatechart. The other type of nomograph is called an alignment chart.Nomographs are generally designed only when the chart willget a great deal of use; otherwise the mathematical solution ofunknown values would be the easiest and fastest approach.Nomographs, in general, are difficult and time-consuming todesign. A nomograph is shown in Figure 39.

Concurrency Charts

The concurrency chart uses the X and Y axis, as previouslydescribed in the discussion on rectilinear charts, to graphicallysolve values for given mathematical equations. For example,given the equation a + b = c, a series of curves is establishedon a rectilinear chart where each line represents one of theequation values. (See Figure 40.) The chart is used to solve foran unknown value by selecting any two known values. UseFigure 40 to solve the formula a + b = c when a = 5 and b = 15.Find 5 on the X axis. Then project directly up to the curve


1000 10 200,000 2000

1000

500400300

200

100

504030

20

10

543

2

1

.5

.4

.3

.2

100,000

50,00040,000

30,000

20,000

10,000

500040003000

2000

1000

500400300

200

100

504030

20

30

40

50

60

708090100

150

200

300

400

500

6007008009001000

1500

2000

3000

987

6

5

4

3

2

1.9.8.7

.6

.5

.4

.3

.2

.1

500

400

300

200

100

50

40

30

20

10

15

“HP

” H

OR

SE

PO

WE

R

“T”

TO

RQ

UE

–PO

UN

D F

EE

T

“RP

M”

T = 5252 × HPRPM

Nomogram Horsepower to Torque Conversion Table

NomogramHorsepower to TorqueConversion Table

FIGURE 39 ■ Nomograph. Courtesy Lovejoy, Inc., Downers Grove, Illinois.

35

30

25

20

15

10

5

00 1 2 3 4 5 6

c V

ALU

ES

a VALUES

FIGURE 40 ■ Concurrency chart where a + b = c.

EXAMPLES:1. Problem: Find the HP

with 3 ft.–lb. torque at 1750 RPM.

Solution: Using a straight edge, placeone end at 1750 RPM andthe middle at 3 ft. torque(right side of “T” scale).Read right side of HP scale.

Answer: 1 HP.

2. Problem: Find the torque in ft.–lbs.of a 100 HP at 1750 RPM.

Solution: Using a straight edge, placeone end at 100 HP on leftside of HP column and the other end at 1750 RPM.Read the left column of the“T” torque scale.

Answer: 300 ft.–lb. torque.

NOTE: Always use corresponding sides of “HP” and “T” scales to arrive at correct solution.


CA

DD

APPLIC

ATION

S

GRAPHICS

The examples displayed in this chapter have been designedand plotted or printed by computer. CADD software isavailable that transforms numerical data into presentation-quality graphics using any desired format; for example,line, bar, pie, or pictorial charts. Charts may be designedwith any grid, scales, line type, shading technique, or textsize and style. Programs are available that allow the

designer to use a variety of predetermined symbols fortwo- or three-dimensional applications. Using a CADDsystem of this type to design charts is the same as having aportfolio of artwork that can be automatically used in anydesired configuration for unlimited creativity. With CADD,scales may be automatically reduced, enlarged, or other-wise changed to accommodate any format. (See Figure 41.)

75

50

25

00 5 10 15

OR

DIN

ATE

100

10

1

OR

DIN

ATE

100

10

1

OR

DIN

ATE

ABSCISSA

ARITHMETIC SCALE SEMILOGARITHMIC GRAPHLOGARITHMIC SCALE ALONG ORDINATEARITHMETIC SCALE ALONG ABSCISSA

LOGARITHMIC GRAPHLOGARITHMIC SCALES

ALONG BOTH AXES

0 5 10 15ABSCISSA

1 2 4 6 10ABSCISSA

(b) (c)(a)

CADD GRAPH PROGRAMS ARE AVAILABLE THAT ALLOW YOU TO AUTOMATICALLY CHANGE THE SCALE OF EITHER AXIS,ENLARGE, REDUCE, OR DESIGN ANY TYPE OF GRAPH OR CHART WITH TEXT, SYMBOLS, AND PICTORIALS.

FIGURE 41 ■ Computer-generated charts automatically change the scales by changing the ordinate and abscissa require-ments:(a) arithmetic scale; (b) semilogarithmic scale; (c) logarithmic scale.

5

4

3

2

1

0

30

25

20

15

10

5

0

25

20

15

10

5

0

a c b

FIGURE 42 ■ Alignment chart where a + b = c. FIGURE 43 ■ Trilinear chart scales.

0%C

20%C

40%C

60%C

80%C

0%B 20%B 40%B 60%B 80%B 100%BC

80%A

60%A

40%A

20%A

B100%C 0%A

100%AA

DISTRIBUTION CHARTSDistribution charts are used to display data based on geograph-ical region. The data may be defined by outlining geographicareas. These charts are often in the form of maps to providelocational information. For example, the average frost depth inthe United States is shown in Figure 46a. Another use of thedistribution chart is placing dots or other symbols to definespecific locations as shown in Figure 46b.


FIGURE 44 ■ Organizational charts. Courtesy Computer SupportCorporation.

FIGURE 45 ■ Production control or process chart. Courtesy Com-puter Support Corporation.

EXTREME FROST PENETRATION(IN INCHES)

BASED UPON STATE AVERAGES

45°

125° 120° 115° 105°110° 100° 95° 90° 80°85° 75° 70° 65°

115° 110° 105° 100° 95° 90° 85° 80° 75°

45°

50°

40°

35°5"

5"5"0"

0"

5"

30°

0"0"

25°

40°

30°

25°

35° 10"

10"20"

30"40"

50"60"

70"80"

90"100" 90"

80"

70"

60"50"40"

30"20"

100"

100"90"

100"90"

24

18

5

23

10

18

61

31

56

4430

80

50

44

1215

74

6550

58

20 14

4

65

4

1018

3236362030

48

64

8

10

(a)

++

++

+

+

+ +

+

+

++

+ +

+

+

+ +

+

++

+ + ++

+

++++

+

+

+

ALBUQUERQUE, NMATLANTA, GAAUSTIN, TXBALTIMORE, MDBIRMINGHAM, ALBOSTON, MABUFFALO, NYCHICAGO, ILCINCINATTI, OHCLEVELAND, OHCOLUMBUS, OHDALLAS, TXDENVER, CODES MOINES, IADETROIT, MIDULUTH, MNEL PASO, TXFORT WORTH, TXFRESNO, CAGREENVILLE, NCHOUSTON, TXHARTFORD, CTINDIANAPOLIS, INJACKSON, MSJACKSONVILLE, FLKANSAS CITY, MOKNOXVILLE, TNLAS VEGAS, NVLOS ANGELES, CALOUISVILLE, KYMADISON, WI

MEMPHIS, TNMIAMI, FLMILWAUKEE, WIMOBILE, AL NASHVILLE,TNNEW ORLEANS, LANEW YORK, NYNORFOLK, VAOKLAHOMA CITY, OKOMAHA, NEPHILADELPHIA, PAPHOENIX, AZPITTSBURGH, PAPORTLAND, ORRALEIGH, NCRICHMOND, VAROCHESTER, NYSACRAMENTO, CAST. LOUIS, MOSALT LAKE CITY, UTSAN ANTONIO, TXSAN DIEGO, CASAN FRANCISCO, CASAN JOSE, CASEATTLE, WASPOKANE, WASYRACUSE, NYTAMPA, FLTULSA, OKTUSCON, AZWASHINGTON, DC

(b)

63 SALES OFFICES!

...TO SERVE YOU NATIONWIDE

FIGURE 46 ■ Distribution charts. (a) Average frost depth in theUnited States. (b) National sales offices. Part b cour-tesy Computer Support Corporation.

PICTORIAL CHARTSAny chart type may be designed in a pictorial manner. Pictorialcharts are used for advertising promotions where the pictorialrepresentation is more important than the data presented. Pic-torial charts are used to enhance the meaning of the data usingtwo- or three-dimensional graphics, photography, or color. Anypictorial representation may be used to help the reader visual-ize the intent of the chart. Pictorial bar charts may be drawnwith the bars shown three-dimensionally or with pictorial rep-resentations of the product as shown in Figure 47. Pie charts


$136$139

$116

$107

$87$78$83

$71

150

120

90

60

30

01994 1995 1996 1997 1998 1999 2000 2001

DO

LLA

RS

MONTHLY ELECTRIC BILLAVERAGE AMERICAN HOUSEHOLD

2000(ESTIMATED)

ABT10 BILLION

51.5%

NONCOMPATIBLE (D&F)5.5 BILLION

28%

PCMs2.5 BILLION

13%

PCMs1.4 BILLION7%

PCMsD 60 MILLIONF NEGLIGIBLE

1.3%

ABT2.9 BILLION

65%

NONCOMPATIBLE(D&F)

1.5 BILLION33.6%

1998

ABT7.6 BILLION

61%

NONCOMPATIBLE (D&F)2.5 BILLION

20%

PCMs1.5 BILLION

12%

PCMs.9 BILLION

7%

1990

F

F

D

D

D = DOMESTICF = FOREIGN

CURRENT ANNUALGROWTH RATES

ABTNONCOMPATIBLEPCM

15%13%19%

SOURCE: THE DETTMAR GROUP

PCMS CUT ABT’S MARKET SHARENUMBER OF SYSTEMS SHIPPED

FIGURE 47 ■ Pictorial bar chart. Courtesy Computer Support Corporation.

FIGURE 48 ■ Pictorial pie chart. Courtesy Computer Support Corporation.

COMBINED

TEMPERATURE (°C)

300

200

100

0∆

R/R

(PP

M)

180 500 1000 1500 2000

TIME (H)

CHANGE IN RESISTANCE AFTER 2000 HOURS OF OPERATION

140100

60

RESISTANCE

VS

TEMPERATURE

RESISTANCEVS

TIME

FIGURE 49 ■ Pictorial line chart. Courtesy Computer Support Corporation.

P R O F E S S I O N A LPERSPECTIVE

Following are some professional tips that can make yourcharts and graphs accurate for the intended audience.

■ Make your graphs and charts clean and simple, avoid-ing unnecessary detail and information.

■ Do not misrepresent the facts.

■ Keep all sets of data proportional.

■ Avoid distorting the data.

■ Study the background of the data to ensure you under-stand the intended representation.

■ Know the audience and know what they want to havethe graph or chart represent. If you display one set ofinformation and they want something else, then yourwork is useless.

■ Be sure the numbers you are representing are accurateand appropriate.

You should consider taking some classes in statistics, orhave someone who understands statistics available to evalu-ate your designs to ensure the data are represented accurately.If you are unprepared or if the data are misrepresented, some-one will question the quality of the presentation.

may be easily shown pictorially by drawing the pie isometri-cally as shown in Figure 48. The designer may also prepare cre-ative pictorial line charts as shown in Figure 49. The chartdesign, format, and layout may serve any function, using a vari-ety of symbols to pictorially depict recognizable features asshown in Figure 50.


RESIDENTIALCOMMERCIAL

METALLUGICAL

SYNTHETICFUEL

INDUSTRYTHERMAL

ELECTRICUTILITIES

CHEMICALFEEDSTOCKS

MARKETS

DOMESTIC USE

FOREIGN USE

COAL MINE &PREPARATION PLANT

COAL CHAINS AND MARKETS

RAIL–UNITRAIL–MIXEDBARGEPIPELINETRUCK

DOMESTICTRANSPORT

COAL EXPORTTERMINAL

MARINETRANSPORT

COAL IMPORTTERMINAL

INTERNALTRANSPORT/TRANSSHIPMENT

FIGURE 50 ■ Pictorial flowcharts using symbols. Courtesy Computer Support Corporation.

There are a variety of chart and graph software packagesthat work within your regular CADD program. For exam-ple, Figure 51 shows a bar chart application being usedinside AutoCAD. Creating schedules for presentations orproposals is easy. All you have to do is add activities andtheir corresponding dates for automatic display in the

drawing. Additionally, the information is stored in a data-base for editing as needed. Other advantages includeadding a title block and inserting an existing drawing toenhance the presentation of your chart. Figure 52 showsa bar chart created in this manner.

CADD PROGRAMS FOR CHART DESIGN

CA

DD

APPLIC

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S

FIGURE 51 ■ A bar chart application being used inside AutoCAD. Courtesy PROJECAD, Inc. (Continued)


CADD APP L ICAT IONS (continued)

FIGURE 52 ■ A bar chart created using CADD software. Courtesy PROJECAD, Inc.

EQUATION OF A STRAIGHT LINE

CADD computers and all other computers are designed tofollow the established math rules when drawing a graph.For a straight line, the equation used is y = mx + b,where m is a number for the slope and b is the point wherethe line crosses the y-axis (ordinate).

Problem: Find the slope of the rectilinear graph shown inFigure 53 and write its mathematical formula.

Solution: Mathematical slope is the same as engineeringslope; both are rise divided by run. Lines that slant upand to the right have positive slope, those that slant downand to the right have negative slope, and a horizontal linehas zero for a slope. From the scaling, the line rises 2 units for every 10 units to the right; so its slope mustbe 2 ÷ 10, or .2. Also, the y-intercept is 2. Then for thisgraph, m = .2, b = 2; so the equation is y = .2x + 2.

MA

TH

APPLIC

ATION FIGURE 53 ■ Rectilinear graph requiring an equation.


Engineering Charts and Graphs TestDIRECTIONSAnswer the questions with short complete statements or drawings as needed.

3WEB

CHAPTER

QUESTIONS1. Define statistics.2. Name and define the two fundamental applications for

charts.3. Identify at least four questions that should be answered

before a chart design is started.4. What is another name for the X axis?5. What is another name for the Y axis?6. How does the range of data affect chart scales?7. Logarithmic and semilogarithmic scales are also referred

to as _____ scales.8. How are grid lines laid out for most applications?9. What is the general guideline used for chart labeling?

10. When should curve captions be used?11. Rectilinear charts are also referred to as ______ charts.

12. Surface charts are also known as _____ charts.13. What is the best design consideration for surface chart use?14. Column charts are commonly referred to as _____ charts.15. What are subdivided column charts used to show?16. What are column charts that show the relationship

between the distribution of components where the totalsare always equal values called?

17. Define range bar chart.18. What are pie charts used for?19. How many degrees of a pie chart would a value equal to

36 percent occupy? Show the formula and calculations.20. What is the purpose of a polar chart?21. Define nomograph.22. What are the two types of nomographs?23. Identify at least three applications for flowcharts.24. For what general purpose are pictorial charts used?

Engineering Charts and Graphs ProblemsDIRECTIONSGiven the data for the following chart problems, design and draw the charts using a CADD system or manualdrafting tools.

3WEB

CHAPTER

PROBLEM 1 Draw the following line chart. Set up the horizon-tal scale for the nine years ending last year, and project thisyear and next year. Courtesy Computer Support Corporation.

PROBLEM 2 Redesign similar to the format shown in Fig-ure 30, and draw the following column chart. CourtesyComputer Support Corporation.

EXPENSES

PROPERTY PLANT AND EQUIPMENT

NET SALES

ACQUIRED REGULUS, INC.FEBRUARY 1980

ACQUIRED HYPONIX, LTD.JUNE 1990

ACQUIRED TENSOR CORP.MAY 1950

175

150

125

100

75

50

25

019 19 19 19 19

TEN YEAR HISTORY19 19 19 19 20 20

MIL

LIO

NS

OF

DO

LLA

RS

APPROXIMATE ANNUAL SALESAT TIME OF ACQUISITION:

HYPONIX, LTD.TENSOR CORP.REGULUS, INC.

$22 MILLION$16 MILLIOM$1 MILLION

GROWTH IN SALES, EXPENSES, AND FIXED ASSETS

15

10

5

1980 1985 1990

IMPACT OF PERSONAL COMPUTERSON PRODUCTIVITY

PRESENTATIONGRAPHICS

1995 2001(projected)

0

DATA BASEAPPLICATIONS

WORDPROCESSING

FORECASTING ANDANALYSIS

RELATIVEPRODUCTIVITY

1980 = 1.0 1.9

4.7

7.1

12.9

1.0 1.62.8

4.45.5

6.8

PROBLEM 3 Design a rectilinear chart that represents theincrease in recommended current amperage with theincrease in round solid copper wire gauge size.

PROBLEM 6 Design a surface semilogarithmic chart fromthe following information: Ten years of community collegegraduates with technical Associate of Science (AS) degreesvs. transfer Associate of Arts (AA) degrees.


RECOMMENDED MAXIMUMAGW GAUGE SIZE CURRENT IN AMPERES

28 .42726 .72524 1.12322 1.82120 31918 4.51716 71514 121312 181110 30

SPEED (MPH)ENGINE SPEED (RPM) 1ST GEAR 2ND 3RD 4TH 5TH

1000 10 17 25 30 402000 20 34 48 62 783000 38 50 74 92 1164000 38 67 97 122 1555000 47 84 121 152 1926000 56 100 145 182 2307000 66 105 168 212 268

YEAR AS AA YEAR AS AA1989–90 266 37 1995–96 232 241990–91 214 24 1996–97 233 141991–92 225 26 1997–98 242 181992–93 225 34 1998–99 263 301993–94 269 32 1999–00 270 361994–95 265 33

STATE NUMBER OF FORTUNE 500 HEADQUARTERSNY 75IL 49

CA 38OH 37CT 35PA 34

YEAR 1992 1993 1994 1995 1996Net Sales in Millions 1400 1500 1600 1825 2150Income/Share $ 1.39 1.56 1.85 1.87 2.06

YEAR 1997 1998 1999 2000 2001Net Sales in Millions 2275 2500 2900 3225 3475Income/Share $ 2.00 2.36 2.61 1.55 2.62

EXPENSE REVENUE EXPENSE REVENUEUnited States 343.2 651.7 France 239.4 302.7England 264.8 466.9 Taiwan 201.6 224.3Canada 301.6 485.2 Hong Kong 214.7 102.5Mexico 241.8 413.3 Brazil 225.0 88.2Australia 213.7 339.9

PROBLEM 4 Design a comparative rectilinear chart showingthe five-speed transmission diagram for the Porsche 911Carrera (establish straight line curve average for each gear).

Tire size: 185/70-VR15, 215/60 VR15

Note: This diagram shows guiding values, based on a mediumeffective rolling radius. Slight deviations due to tire toler-ance, variations in the rolling radius, wear and skidding onthe wheels have not been taken into account.

PROBLEM 5 Design a chart similar to Figure 19 showing fea-ture dimensions of a part obtained at inspection intervalsbased on the following information:

1. Average of samples taken at given intervals (x): 2.6248,2.6252, 2.6250, 2.6250, 2.6244, 2.6248, 2.6251.

2. Upper control limit (UCL) = 2.6253.3. Lower control limit (LCL) = 2.6243.4. Determine the average of averages ( ).x=

PROBLEM 7 Design a column chart based on the followinginformation: Where top companies reside; more than halfof the USA’s Fortune 500 companies are headquartered insix states. Information courtesy USA Today.

PROBLEM 8 Design a column chart that shows net saleswith values on the left vertical scale and a step curve toshow income per share with values on the right verticalscale. The horizontal scale shows the range of years from1992 to 2001 for Dial Industries, ten-year summary ofoperations and financial review.

PROBLEM 9 Design an expense/revenue over-under columnchart for Precision Manufacturing, Ltd. by country ($ inmillions).

PROBLEM 10 Design a range bar chart that represents valuesfor surface roughness in microinches and micrometers pro-duced by common processing methods.

PROBLEM 13 Design a nomograph that may be used todetermine grades for the Engineering Drafting I class draft-ing projects and term tests based on the following assump-tions. Total points for drafting projects equal 500 and totalpoints for tests equal 300. Grades are based on the follow-ing percentages: A = 100–91%; B = 90–81%; C = 80–71%;D = 70–61%; F = below 60%.

PROBLEM 14 Design a flowchart for the chain of commandof your school or company.

PROBLEM 15 Design a pictorial chart that provides the fol-lowing information: 25 years in space from 1960 to 1985.More than 200 people—mostly from the USA—have flownin space since Soviet cosmonaut Yuri Gagarin became thefirst to do so. Tally of space travelers: (Tip: Rockets leavingthe earth might be considered.)

USA citizens = 124Soviet citizens = 62Foreigners on USA flights = 8Foreigners on Soviet flights = 11Source: Congressional Research Service.

PROBLEM 16 Design and draw an alignment chart for theformula a + b = c.

PROBLEM 17 Design and draw a distribution chart showingthe cities in the United States with populations over500,000. Research is required.

PROBLEM 18 Review your family electric bills over the pastyear and design and draw a pictorial chart similar to theone shown in Figure 47.

PROBLEM 19 Research the monthly average rainfall in yourstate over the past year and design and draw a pictorial chart.

PROBLEM 20 Design a graph or chart of your own selectionto display the capture rate of recent district high schoolgraduates to the local community college based on the fol-lowing information:


RANGE AVERAGEPROCESS MICROINCH MICROMETER MICROINCH MICROMETER

Flame cutting 2000-250 50-6.3 1000-500 25-12.5Snagging 2000-125 50-3.2 1000-250 25-6.3Sawing 2000-32 50-0.80 1000-63 25-1.6Planing,

shaping 1000-16 25-0.40 500-63 12.5-1.6Drilling,

chemical milling,elect. discharge machining 500-32 12.5-0.80 250-63 6.3-1.6

Milling 1000-8 25-0.20 250-32 6.3-0.80Broaching, reaming 250-16 6.3-0.40 125-32 3.2-0.80Electron beam, laser 250-8 6.3-0.40 250-32 6.3-0.80Electrochemical 500-2 12.5-0.05 125-8 3.2-0.20Boring, turning 1000-1 25-0.025 250-16 6.3-0.40Barrel finishing 125-2 3.2-0.05 32-8 0.80-0.20Electrolytic grinding 32-4 0.80-0.10 20-8 0.60-0.20Roller burnishing 32-4 0.80-0.10 16-8 0.40-0.20Grinding 250-1 3.2-0.025 63-4 1.6-0.10Honing 63-1 1.6-0.025 32-4 0.80-0.10Electropolish 63-0.5 1.6-0.012 32-4 0.80-0.10Polishing 32-0.5 0.80-0.012 16-4 0.40-0.10Lapping 32-0.05 0.80-0.012 16-2 0.40-0.05Superfinish 32-0.05 0.80-0.012 8-1 0.20-0.025

YEAR CAPTURE RATE1992 18.5%1993 20.2%1994 23%1995 22.5%1996 23.5%1997 24%1998 21.5%1999 18.3%2000 18.3%2001 21.2%

Note: The ranges indicated are typical of the process; higher orlower values may be obtained under special conditions.

PROBLEM 11 Design a pie chart that represents the agricul-tural sales for Washington County during 2001.

Nursery crops = 44%Vegetable crops = 26%Small fruit and berries = 11%Other crops = 8%Miscellaneous animals = 6%Greenhouse crops = 5%

PROBLEM 12 Design a pie chart that represents ProductRevenue by category for 2001. Data courtesy Computer Sup-port Corporation.

Automated process equipment = 28%Marine products = 20%Energy services = 17%Sports products = 13%Electronic controls = 9%Specialty products = 6%Wheel goods = 4%

MATH PROBLEMSPROBLEM 21 What are the slope and y-intercept of the line

with this equation: y = 2x – 7?

PROBLEM 22 Which of the following pairs of equations willgraph as parallel lines? (Hint: Parallel lines have the sameslope.)

a. y = 2x – 7 and y = 2x + 6b. y = 5x + 2 and y = 3x + 2c. y = –2x – 3 and y = –2x + 4d. y = 17x + 5 and y = 17x – 5

PROBLEM 23 Which of the pairs of equations from Prob-lem 22 cross the y-axis at the same point?

PROBLEM 24 Find the slope and equation of the graphshown.

PROBLEM 25 Find the equation of the following graph.

PROBLEM 26 Which of the following equations wouldgraph as a horizontal line?

a. y = 6xb. y = 7c. y = 2x + 5d. y = –4x – 3

PROBLEM 27 Which of the equations from Problem 26 passthrough the origin (0,0)?


web chapter 3design and draw the following types of charts and graphs: rectilinear, surface, column,...

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