Chapter 19 Topographic Surveying and Mapping

Topography refers to the characteristics of the land surface. These characteristics include relief, natural and artificial (or man-made) features. Relief is the configuration of the earth’s surface and includes such features as hills, valleys, plains, summits, depressions, trees, streams, and lakes. Man-made features are highways, bridges, dams, wharfs, buildings, and so forth.

This lesson introduces the methods and procedures used to perform topographic surveying and to prepare topographic maps. A topographic map is a drawing that shows the natural and artificial features of an area. A topographic survey is conducted to obtain the data needed for the preparation of a topographic map.

When you have completed this lesson, you will be able to:

1. Describe the different types of topographic surveying control mechanisms.
2. Describe the methods for conducting topographic mapping.


1.0.0 Topographic Surveying

2.0.0 Topographic Mapping




The field work in a topographic survey has two aspects:

1.1.0 Topographic Control

Topographic control consists of two parts: horizontal control, which locates the horizontally fixed position of specified control points, and vertical control, which establishes the elevations of specified bench marks. This control provides the framework from which topographic details, such as roads, buildings, rivers, and the elevation of ground points, are located.

1.1.1 Horizontal Control

Locating primary and secondary horizontal control points or stations may be accomplished by traversing, by triangulation, or by the combination of both methods. On an important, large-area survey, there may be both primary control, in which a number of widely separated primary control points are located with a high degree of precision, and secondary control points, where stations are located with less precision within the framework of the primary control points.

The routing of a primary traverse should be considered carefully. It should follow routes that will produce conveniently located stations. Such routes might run along roads, ridges, valleys, edges of wooded areas, public land lines, or near the perimeter of tracts of land. This latter route is particularly important for small areas. When all the details in the area can be conveniently located from stations on the primary traverse, secondary traverses are not needed. However, the size or character of the terrain usually makes secondary traverses necessary. Consider, for example, the situation shown in Figure 19 -1. This figure shows a tract bounded on three sides by highways and on the fourth side by a fence. For simplification, the figure shows only the items to be discussed. An actual complete plan would include a title, date, scale, north arrow, etc.

The primary traverse ABCD runs around the perimeter of the tract. If this tract was sufficiently small and level, then details within the whole tract could be located from only the primary control points which includes stations A, A1, B, B1, C, C1, D, and D 1.

Figure 19-1 – Primary and Secondary Traverse.

However, in this example the size or perhaps the character of the terrain made it necessary to establish additional control points inside the perimeter of the tract. The additional controls points are D2, A2, and B2. These points were established by running traverse lines (called crossties) across the area from one primary traverse station to another. It should be noted that, since each secondary traverse closes on a primary control point, errors cannot accumulate any farther than the distance between the primary stations.

Field notes for the survey sketched in Figure 19 -1 must contain notes showing the horizontal locations of the stations and level notes for determining the elevations of the stations.

1.1.2 Vertical Control

In topographic surveying, bench marks serve as starting and closing points for the leveling operations when locating details. Although for some surveys the datum may be assumed, it is preferable that all elevations be tied to bench marks which are referred to the sea-level datum. In many areas, particularly in the United States, series of permanent and precisely established bench marks are available. A surveyor must make an effort to tie surveys to these bench marks to ensure proper location and identification. Often, the established horizontal control marks are used as the bench marks because the level routes generally follow the traverse lines.

Vertical control is usually carried out by direct leveling; however, trigonometric leveling may be used for a limited area or in rough terrain. Topographic maps for construction projects must be based on accurate horizontal and vertical data. The degree of precision of a topographic map is related to the scale of the land area depicted in the map. When establishing the primary vertical control to use in a topographic survey for an intermediate-scale map, four degrees of precision are used as follows:

First - 0.05 foot distance in miles. This order is used as the standard for surveys in flat regions when the contour interval is 1 foot or less. It is also used to determine the gradient of streams or to establish the grades for proposed drainage and irrigation systems.

Second- 0.1 foot distance in miles. This order is used in a survey when the contour interval of the map is 2 feet.

Third- 0.3 foot distance in miles. This order is used for a contour interval of 5 feet.

Fourth- 0.5 foot distance in miles. This order is used for a contour interval of 10 feet and may be done by stadia leveling, a method that is very advantageous in hilly terrain. Stadia will be discussed later in this lesson.

The third or fourth order of precision is used for a large-scale map that generally has a contour interval of 1 or 2 feet. For an extensive survey of a large area, the third order is used. Surveys of smaller areas use the fourth order.

Once the topographic control has been established, the next major step in a topographic survey is to locate the details horizontally and vertically in the vicinity of each control point or station. These details consist of (1) all natural or artificial features that appear on the map and (2) enough ground points and spot elevations to make the drawing of contour lines possible.

The methods and the instruments used in topographic surveys depend upon the purpose of the survey, the degree of precision needed, the nature of the terrain to be covered, the map scale, and the contour interval. For a high degree of accuracy,  19-5 azimuths should be located with a theodolite or transit. Horizontal distances should be measured with a chain or an electronic distance measurement (EDM) device. Elevations are determined with a level.

The following sections discuss two methods commonly used to locate topographic details.

1.2.0 Locating Details by Transit and Tape

Another manual in this series, Direct Linear Measurements and Field Survey Safety, describes the procedures used to tie in and locate points using a transit and tape. These same procedures are used for tying in and locating topographic details.

To begin, determine the vertical location (or elevation) of the detail points by using direct or trigonometric leveling procedures. Then horizontally locate the details either by directions or distances or a combination of both. Use a method or a combination of methods that requires the least time in a particular situation. Directly measure the dimensions of structures, such as buildings, with tapes. When many details exist, assign each one a number in the sketch and key the detail to a legend to avoid overcrowding. For directions, use azimuths instead of deflection angles to minimize confusion. Locate details as follows:

  1. Measure the angle and distance from transit stations.
  2. Measure angles from two transit stations.
  3. Measure distances from two known points.
  4. Measure an angle from one station and distance from another station.
  5. Measure swing offsets and range ties.

Detailing by transit and tape is a time-consuming process that requires chaining many distances and taking many level shots. This is necessary when a high degree of accuracy is required. For lower-precision (third and fourth order) surveys, a less time-consuming method is to locate the details by transit and stadia.

1.3.0 Locating Details by Transit and Stadia

Most of the topographic surveying conducted by an EA requires a lower degree of accuracy, and thus is well suited to the transit and stadia method. In this method, horizontal distances and differences in elevation are indirectly determined by using subtended intervals and angles observed with a transition and a leveling rod or stadia board. The following sections discuss the principles of stadia and then examine field procedures used in stadia work.

1.3.1 Stadia Equipment Terms, and Principles T

his section addresses the equipment, terminology, and principles used in stadia surveying. Although the discussion of stadia surveying is included here,, as an EA, you should be aware that stadia can be used in any situation where horizontal distances and differences in elevation must be determined indirectly. The results, though, are of a lower order of precision than is obtainable by taping, EDM, or differential leveling. However, the results are adequate for many purposes, such as lower -order trigonometric leveling.

A thorough understanding of stadia is important to any surveyor. To supplement the knowledge gained from this section, read other books, such as Surveying Theory and Practice, by Davis, Foote, Anderson, and Mikhail. Stadia Rods

Where sight distances do not exceed 200 feet, a conventional rod such as a Philadelphia rod is adequate for stadia work. A stadia rod is used for longer distances. Stadia rods usually have large geometric designs on them so they may be read at distances of 1,000 to 1,500 feet or even farther. Some rods do not have any numerals on them. From the geometric pattern on the rod, intervals of a tenth of a foot and sometimes a hundredth of a foot can be seen. Stadia Hairs

The telescope of transits (as well as theodolites, plane-table alidades, and many levels) is equipped with two hairs (called stadia hairs) that are in addition to the regular vertical and horizontal cross hairs. Figure 19-2 shows two types of stadia hairs as viewed through a telescope. As shown in this figure, one stadia hair is located above and the other an equal distance below the horizontal (or middle) cross hair. On most equipment, the stadia hairs are not adjustable and remain equally spaced.

Figure 19-2 – Stadia Hairs. Stadia Interval

When viewed through a transit telescope, the stadia hairs appear to intercept an interval on the stadia rod. The stadia interval or stadia reading is the distance on the rod between the apparent positions of the two stadia hairs. Determine stadia intervals by sighting the lower stadia hair at a convenient foot mark and then observing the position of the upper stadia hair. For example, the lower hair might be sighted on the 2.00 foot mark and the upper hair might be in line with 6.37. After subtraction (6.37 -2.00), the stadia reading is 4.37. When a stadia reading is more than the length of the rod, you should take the observed half-interval and multiply it by 2 to get the stadia reading. Stadia Constant

Light rays that pass through the lens (objective) of a telescope come together at a point called the principal focus of the lens. Then these light rays continue in straight-line paths, as shown in Figure 19-3.

The distance between the principal focus and the center of the lens is called the focal length (f) of the lens. For any particular lens, the focal length does not change. Dividing the focal length by the distance between the stadia hairs (i), yields the stadia constant (k). The stadia constant is also called the stadia factor or stadia interval factor. A convenient value to use for the stadia constant is 100. Stadia hairs are usually spaced so that the interval between them makes the stadia constant equal to 100.

Figure 19-3 – Light rays converge at principal focus of a lens. Stadia Distance

The distance from the principal focus to the stadia rod is called the stadia distance. As shown in Figure 19-3, this distance is equal to the stadia constant (k) times the stadia reading (s). Instrument Constant

The distance from the center of the Transit telescope instrument to the principal focus is the instrument constant. This constant is determined by the manufacturer of the instrument. This information is typically stated on the inside of the instrument box. Externally focusing telescopes are manufactured so that the instrument constant may be considered equal to 1. For internally focusing telescopes, the objective in the telescope is so near the center of the instrument that the instrument constant may be considered zero. This is a distinct advantage of internally focusing telescopes. Most modern instruments are equipped with internally focusing telescopes. Stadia Reduction Formulas

Stadia work is concerned with finding two values:

  1. The horizontal distance from the center of the instrument to the stadia rod
  2. The vertical distance or difference in elevation between the center of the instrument and middle-hair reading on the rod. Stadia reduction formulas are used to find these values.

Stadia Formula for Horizontal Sights To calculate a horizontal sight, first determine the horizontal distance between the center of the instrument and the stadia rod. Find this distance by adding the stadia distance to the instrument constant as follows:

Write ks for the stadia distance and (f + c) for the instrument constant. Then the formula for computing horizontal distances when the sights are horizontal becomes:

h = ks + (f + c)


h = horizontal distance from the center of the instrument to a vertical stadia rod
k = stadia constant, usually 100
s = stadia interval
f = focal lengths of the lens
c = distance from the center of the instrument to the center of the lens
f + c = instrument constant (zero for internally focusing telescopes, approximately 1 foot for externally focusing telescopes)

The instrument constant is the same for all readings. Using an externally focusing instrument with an instrument constant of 1.0 and a stadia interval of 1 foot, the horizontal distance would be:

h = (100) (1) + 1 = 101 feet

If the stadia interval is 2 feet, the horizontal distance is:

h = (100) (2) + 1 = 201 feet

If you are using an internally focusing instrument, the instrument constant is zero and can be disregarded. This is the advantage of an internally focusing telescope. So, if the stadia interval is 1 foot, the horizontal distance is simply the stadia distance, which is 100 feet. For a stadia reading of 2 feet, the horizontal distance is 200 feet. Horizontal distance usually is stated to the nearest foot. Occasionally for short distances under 300 feet it may be specified that tenths of a foot be used.

Stadia Formulas for Inclined Sights Since most often the sights needed in stadia work are not horizontal, it is necessary to incline the telescope upward or downward to acquire a vertical angle. This vertical angle (α) may be either an angle of elevation or an angle of depression, as shown in Figure 19-4.

Figure 19-4 – (A) Angle of elevation and (B) Angle of depression.

When the line of sight is elevated above the horizontal, it is an angle of elevation. If the line of sight is below the horizontal, the vertical angle is an angle of depression.

In either case, use the following formulas to find the horizontal and vertical distances:

h = ks cos 2α + (f +c) cos α

v = 1/2 ks sin 2α+ (f + c) sin α

Those two expressions are called the stadia formulas for inclined sights in which

h = horizontal distance
v = vertical distance
h = stadia distance
a = vertical angle
f + c = instrument constant

Refer to Figure 19-5 for clarification of the terms in the stadia formulas for inclined sights.

Figure 19-5 – Stadia interval – inclined sight. Distance and Elevation for Inclined Sights

The following example describes the use of the stadia reduction formulas for inclined sights. Assume a stadia interval of 8.45 and an angle of elevation of 25º 14’, as shown in Figure 19-6. Let the instrument constant be 1.0.

Substituting the known values in the stadia formula for the horizontal distance yields the following:

h = ks cos2α + (f + c) cos α

h = 100 (8.45) (0.90458)2 + (1) (0.90458) = 692.34

So the horizontal distance is 692 feet.

Substituting the known values in the formula for the vertical distance yields:

v = 1/2 ks sin 2α + (f + c) sinα

v = 50 (8.45) (0.77125) + (1) (0.42631)

v = 326.28

The vertical distance to the middle-hair reading on the rod is 326.28 feet.

To find the elevation of the ground at the base of the rod, subtract the center-hair rod reading from this vertical distance and add the height of instrument (HI) as depicted in the example in Figure 19-6. If the HI is 384.20 feet and the center-hair rod reading is 4.50 feet, then the ground elevation is

326.28 - 4.5 + 384.20 = 705.98 feet.

Figure 19-6 – Ground elevations – telescope raised.

If the angle of inclination was depressed, the center-hair rod reading is added to the vertical distance. The sum is then subtracted from the HI. Using this equation, the ground elevation of Figure 19-7, would be:

384.2 - (326.28 + 4.5) = 53.42 feet.

Figure 19-7 – Ground elevation – telescope depressed. Stadia Tables

Horizontal distance and the vertical distance (difference in elevation between two points) can also be determined by using the stadia reduction tables.

Editor's Note

I am omitting the discussion of stadia tables from this lesson, primarily because the source material is not to our usual standard of clarity.  A second, and equally compelling reason for omitting this particular section is because--in this day of powerful hand-held calculators--it is no longer necessary to use logarithm-like tables. Approximate Forms of Stadia Formulas

 Because of the errors inherent in stadia surveying, it has been found that approximate stadia formulas are precise enough for most stadia work. Refer again to Figures 19-5, 19-6 and 19-7, and notice that it is customary to hold the stadia rod plumb rather than inclined at right angles to the line of sight. Failure to hold the rod plumb introduces an error causing the observed readings to be longer than the true readings. Another error inherent in stadia surveying is caused by the unequal refraction of light rays in the layers of air close to the earth’s surface. The refraction error is smallest when the day is cloudy or during the early morning or late afternoon hours on a sunny day. Unequal refraction also causes the observed readings to be longer than the true readings.

To compensate for these errors, topographers often regard the instrument constant as zero in stadia surveying of ordinary precision, even if the instrument has an externally focusing telescope. In this way, the last terms in the stadia formulas for inclined sights vanish, that is, become zero. Then the approximate expressions for horizontal and vertical distance are

h = ks cos2 α

v = (1/2)ks sin 2α

1.3.2 Field Procedures


 Figure 19-8 – Difference in elevation.

Figure 19-8 illustrates a situation where the difference in elevation between an instrument station of known elevation and a ground point of unknown elevation needs to be determined. In Figure 19-8, (A) The elevation of instrument station P is known and the difference in elevation between P and the rod station P1 needs to be determined. The horizontal center-line height of the instrument (H.I.) above point P is equal to PA. This H.I. is different than the H.I. typically used in direct leveling.

The rod reading is P1B.

The difference in elevation (DE) between P and P1 can be expressed as:

DE = PA = BC – P1b


DE = h.i. = BC – P1B

Therefore, the ground elevation at P1 can be expressed as:

Elev. P1 = Elev. P + (h.i. + BC – P1B)

Now sight on the rod such that P1B = PA = h.i. In this case, a similar triangle (PC1P1) is formed at the instrument station P. From observation of these similar triangles, it be can seen that the DE= P1C1 = BC. Therefore, the ground elevation at P1 can be expressed as follows:

 Elev. P1 = Elev. P + BC

 This is an important concept to understand when shooting stadia from a station of known elevation. It illustrates that when the center cross hair is sighted on a rod graduation that is equal to the h.i. before reading the vertical angle, then calculating the difference in elevation is greatly simplified. However, if the line of sight is obstructed and you cannot sight on a rod graduation that is equal to the h.i., then you must sight on some other graduation.

In addition, in Figure 19-8, (B) The difference in elevation between two points on the ground (P1 and P2) from an instrument station (E) that is located between the two points needs to be determined.

Assume in this case that a backsight is taken on a rod held at P1 and then a foresight is taken to P2. Now the difference in elevation (DE) between the two points can be written as follows:

DE = P1A + AB + CD – P2D

In reverse, if a backsight was taken to P2 with a foresight to P1, then the expression for DE can be written as:

DE = CD – P2D – AB – P1A

Figure 19-9 shows field notes for locating topographic details by transit and stadia. The details shown by numbers in the sketch on the Remarks side are listed on the data side by numbers in the column headed Obj. At the top of the page on the data side, control point D1 was used as the instrument station. Immediately below this, from instrument station D1, the transit was backsighted to point A and that all horizontal angles were measured to the right from the backsight on A.


Figure 19-9 – Notes for locating topographic details by transit and stadia.

In the third line from the top on the data side, the known elevation of D1 is 532.4 feet and the vertical distance (h.i.) from the point or marker at D1 to the center of the instrument above D1 is 4.8 feet. This vertical distance was carefully determined by measurement with a tape or rod held next to the instrument.

Begin with point 1 to see how each of the objective points was detailed. Remember, in this example D1 is the instrument station from which all observations are made.

To determine the direction of point 1, train the transit telescope on A and match the zeros. Next, turn the telescope right to train on point 1 and read the horizontal angle (30º10’). For the horizontal distance and elevation of point 1, set a rod on the point, and train the lower stadia hair of the transit telescope on a whole-foot mark on the rod so the center hair is near the 4.8 graduation. (This is a common practice in stadia work that makes reading the stadia interval easier.) Then read and record the stadia interval (in this case 6.23 feet). Next, rotate the telescope about the horizontal axis until the center hair is on the 4.8 rod graduation. Lock the vertical motion and read and record the vertical angle (-3026’). Be sure to record each vertical angle correctly as plus or minus. While you are reading and recording the vertical angle, the rodman can be moving to the next point. This will help speed up the survey.

From the stadia interval and the vertical angle reading, the horizontal distance (entered in the fifth column of Figure 19-11) and the difference in elevation (in the sixth column) are determined from a stadia reduction table. Table 19-2 shows the page from a stadia reduction table that applies to the data for point 1 in Figure 19-9.

For this point, the vertical angle is –3026’, and the stadia interval is 6.23 feet. In the table under 3° and opposite 26’, note that the multiplier for horizontal distance is 99.64, while the one for difference in elevation is 5.98. If the final distance is ignored, the horizontal distance is 6.23 X 99.64 = 620.75 (or 621feet). The difference is elevation is 6.23 X 5.98 = 37.3 feet. Add the corrections for focal distance given at the bottom of the page to these figures. For an instrument with a focal distance of 1 foot, add 1 foot to the horizontal difference (making a total horizontal distance of 622 feet) and 0.06 foot to the difference in elevation. This makes the difference in elevation round off to 37.4 feet, and since the vertical angle has a negative (-) sign, the difference in elevation is recorded as –37.4 feet. In the first column on the remarks side of Figure 19-9, enter the elevation of each point, computed as follows. For point 1, the elevation equals the elevation of instrument station D1 (532.4 feet) minus the difference in elevation (37.4 feet), or 495.0 feet. Subtract the difference in elevation, in this case, because the vertical angle you read for point 1 was negative. For a positive vertical angle (as in the cases of points 12 and 13 through 17 of your notes), add the difference in elevation. The remainder of the points in this example are detailed in a similar manner except for point 13. When a detail point is at the same, or nearly the same, elevation as the instrument station, the elevation can be determined more readily by direct leveling. This is the case for point 13. As seen in the vertical-angle column of the notes, the vertical Table 19-2 – Horizontal distances and elevations from stadia.  19-17 angle was 0° at a rod reading of 5.6 feet. Therefore, the elevation of point 13 is equal to the elevation of the instrument station (532.4 feet) plus the H.I. (4.8 feet) minus the rod reading (5.6 feet), or 531.6 feet. In the above example the transit was initially backsighted to point A and the zeros were matched. This was because the azimuth of D1A was not known. However, if you knew the azimuth of D1A, you could indicate your directions in azimuths instead of in angles right from D1A. Suppose, for example, that the azimuth of D1A was 26°10’. You would train the telescope on A and set the horizontal limb to read 26°10’. Then when you train on any detail point, read the azimuth of the line from D1 to the detail point.

Test Your Knowledge

1. Which of the following elements is representative of topographic maps?

A. Earth’s surface.
B. Earth’s natural features
C. Man-made features
D. All of the above

2. By what manner are control points located?

A. Triangulation only
B. Traversing only
C. Both A and B
D. Indirect leveling

3. When topographic maps require a high degree of accuracy, what method of finding details is recommended?

A. Transit and tape
B. Transit and stadia
C. Transit and trigonometric leveling
D. EDM and level

4. Which of the following actions should you take to avoid overcrowding and confusion when sketching details during fieldwork?

A. Use azimuths instead of deflection angles.
B. Use numbers and legends for a large number of details.
C. Both A and B
D. Estimate distances and angles.

5.  Philadelphia rods should be used for stadia work for distances up to 1,500 feet.

A. True
B. False

6. When your stadia reading is more than the length of the rod, what procedure should you use?

A. Read a half-interval using the middle cross hair; then multiply by 2.
B. Hold two rods together.
C. Make a rod in the BU shop that will be long enough.
D. Shorten your sighting.

7. Unequal refraction caused by the sun’s rays will affect your data by causing what differences in readings?

A. Longer distances than actual.
B. Shorter distances than actual
C. Reversed vertical angles
D. Smaller vertical angles than actual


The following sections address how a draftsman prepares a topographic map. Additional field methods used by surveyors are also presented.

2.1.0 Representation of Relief

One of the purposes of a topographic map is to depict relief. Relief is the term for variance in the vertical configuration of the earth’s surface. You have seen how relief can be shown in a plotted profile or cross section. These, however, are views on a vertical plane, but a topographic map is a view on a horizontal plane. On a map of this type, relief may be indicated by the following methods, shown in Figure 19-10. A relief model is a three-dimensional relief presentation of a molded or sculptured model, developed in suitable horizontal and vertical scales, of the hills and valleys in the area. Shading is a pictorial method of showing relief by the use of light and dark areas to suggest the shadows that would be created by parallel rays of light shining across the area at a given angle. Hachures are a pictorial method similar to shading except that the light-and-dark pattern is created by short hachure lines drawn parallel to the steepest slopes. Relative steepness or flatness is suggested by varying the lengths and weights of the lines. Contour lines are lines of equal elevation. Each contour line on a map is drawn through a succession of points that are the same elevation. Figure 19-10 – Methods of indicating relief.  19-19 The contour-line method is the most commonly used topographic map.

2.2.0 Contour Lines

Contour lines indicate a vertical distance above or below a datum plane. Contours begin at sea level, normally the zero contour, and each contour line represents an elevation above (or below) sea level. The vertical distance between adjacent contour lines is known as the contour interval. Starting at zero elevation, the topographer draws every fifth contour line with a heavier line. These are known as index contours. At some place along each index contour, the line is broken and its elevation is given. The contour lines falling between index contours are called intermediate contours. They are drawn with a finer line than the index contours and usually do not have their elevations given. Examples of index contours and intermediate contours are shown in Figure 19-11.

2.3.0 Ground Point Systems

The essential data for showing relief by contour lines consists of the elevation of a sufficient number of ground points in the area. Methods of determining the horizontal and vertical locations of these ground points are called ground point systems. The systems most frequently used are the following:

In practice, combinations of these methods may be used in one survey.

2.3.1 Tracing Contours

In the tracing contours system, points on a given contour are plotted on the map, and the contour line is drawn through the plotted points. The method may be illustrated by the following simple example.

Refer to the traverse shown in Figure 19-11. In this figure, assume that the traverse runs around the perimeter of a small field. The elevations at corners A, B, C, and D are as shown. The ground slopes downward from AB toward DC and from AD toward BC.


Figure 19-11 – Traverse with contour lines.

In this example the contour interval is 1 foot. Therefore, the 112-foot contour line is plotted, the 111-foot contour line, the 110-foot contour line, and so forth.

Also in this example, assume that the required order of precision is low, as encountered in a reconnaissance survey, for example, and therefore a hand level is used. The elevation of station A is determined to be 112.5 feet. Assume that the vertical distance from the level to the ground is 5.7 feet. Then, the H.I. at station A is

112.5 + 5.7= 118.2 feet.

If a level rod is set up anywhere on the 112.0-foot contour, the reading from station A would be

118.2 – 112.0= 6.2 feet.

Therefore, to determine the point where the 112.0-foot contour crosses AB, the rodman backs out from point A along AB until reaching the point where 6.2 feet is read on the rod. The point where the 112.0-foot contour crosses AD can be determined the same way. You can measure the distance from A to each point and then record the distance from A to the 112.0-foot contour on AB and AD.

When all of the contours have been located on AB and AD, shift to station C and carry out the same procedure to locate the contours along BC and CD. Now all the points are located where contours at a one-foot interval intersect the traverse lines. If the slope of the ground is uniform (as it is presumed to be in Figure 19-11), the contour lines can be plotted by simply drawing lines between points of equal elevation, as shown in the figure. If the slope has irregularities, send the rodman out along one or more lines laid across the irregular ground, to locate the contours on these lines as you located them on the traverse lines.

2.3.2 Grid Coordinate System

In the grid coordinate system, the area is laid out in squares of convenient size, and the elevation of each corner point is determined. While this method lends itself to use on relatively level ground, ridge or valley lines must be located by spot elevations taken along the lines. The locations of the desired contours are then determined on the ridge and valley lines and on the sides of the squares by interpolation. This gives a series of points through which the contour lines may be drawn. Figure 19-12 illustrates this method.


Figure 19-12 – Grid system of ground points.

Assume that the squares in Figure 19-12 measure 200.0 feet on each side. Points a, b, and c are points on a ridge line, also 200.0 feet apart. You need to locate and draw the 260.0-foot contour line. By inspection, you can see that the 260.0-foot contour must cross AD since the elevation of A is 255.2 feet and the elevation of D is 263.3 feet. However, at what point does the 260.0-foot contour cross AD? This can be determined by using a proportional equation as follows.

Assume that the slope from A to D is uniform. The difference in elevation is 8.1 feet (263.3 – 255.2) for 200.0 feet. The difference in elevation between 255.2 and 260.0 feet (elevation of the desired contour) is 4.8 feet. The distance from A to the point where the 260.0-foot contour crosses AD is the value of x in the proportional equation: 8.1:200 = 4.8:x or x = 118.5 feet. Lay off 118.5 feet from A on AD and make a mark.

In the same manner, you locate and mark the points where the 260.0-foot contour crosses BE, EF, EH, and GH. The 260.0-foot contour crosses the ridge between point b (elevation 266.1 feet) and point c (elevation 258.3 feet). The distance between b and c is again 200.0 feet. Therefore, you obtain the location of the point of crossing by the same procedure just described.

You now have six plotted points: one on the ridge line between b and c and the others on AD, BE, EF, EH, and GH. A line sketched by hand through these points is the 260.0- foot contour line. Note that the line is, in effect, the line that would be formed by a horizontal plane that passed through the ridge at an elevation of 260.0 feet. Note, too, that a contour line changes direction at a ridge summit.

2.3.3 Control Points

This explanation illustrates the fact that any contour line may be located by interpolation on a uniform slope between two points of known elevation a known distance apart. The example also demonstrates how a ridge line is located in the same manner.

By locating and plotting all the important irregularities in an area (ridges, valleys, and any other points where elevation changes radically), a contour map of an area can be drawn by interpolating the desired contours between the control points.

A very elementary application of the method is shown in Figure 19-13. Point A is the summit of a more or less conical hill. A spot elevation is taken here, and then also at points B, C, D, E, and F, which are points at the foot of the hill. It is desired to draw the 340.0-foot contour. Point a on the contour line is interpolated on the line from A to B, point b is interpolated on the line from A to C, point c is interpolated on the line from A to D, and so on.

Figure 19-13 – Control point method of locating contour.

Figure 19-14 shows a more complicated example in which contours are interpolated and sketched between controlling spot elevations taken along a stream.

Figure 19-14 – Sketching contours by interpolation.

2.3.4 Cross Profiles

In the cross-profile system, elevations are taken along selected lines that are at right angles to a traverse line. Shots are taken at regular intervals or at breaks, or both, in the ground slope. The method is illustrated in Figure 19-15. The line AB is a traverse along which 100-foot stations are shown. On each of the dotted cross-section lines, contours are located. The particular contour located at a particular station depends on (1) the ground elevations and (2) the specified contour interval. In this instance, it is 2 feet. The method used to locate the contours is the one described earlier for tracing a contour system. 

Figure 19-15 – Cross profiles.

When the even-numbered 2-foot interval contours are located on all the cross-profiles lines, the contour lines are drawn through the points of equal elevation.

2.4.0 Characteristics of Contour Lines

A contour line is a line of equal elevation; therefore, two different lines must indicate two different elevations. Two different contour lines cannot intersect or otherwise contact each other except at a point where a vertical or overhanging surface, such as a vertical or overhanging face of a cliff, exists on the ground. Figure 19-16 shows an overhanging cliff. The segments of contour lines on the cliff are made as dotted (or hidden) lines. Aside from the exception mentioned, any point where two different contour lines intersect would be a point with two different elevations.

When you are forming a mental image of the surface configuration from a study of contour lines, it is helpful to remember that a contour line is a level line, that is, a line that would be formed by a horizontal plane passing through the earth at the indicated elevation.

A contour line must close on itself somewhere, either within or beyond the boundaries of the map. A line that appears on the map completely closed may indicate either a summit or a depression. If the line indicates a depression, this fact is sometimes shown by a succession of short hachure lines drawn perpendicular to the inner side of the line. An example of a depression is shown in Figure 19-16. A contour line marked in this fashion is called a depression contour.

On a horizontal or level plane surface, the elevations of all points on the surface are the same. Therefore, since different contour lines indicate different elevations, there can be no contour lines on a level surface. On an inclined plane surface, contour lines at a given equal interval will be straight, parallel to each other, and equidistant. 

Figure 19-16 – Typical contour formations.

 Generally, the spacing of the contour lines indicates the nature of the slope. Contour lines that are evenly spaced and wide apart indicate a uniform, gentle slope, as shown in Figure 19-17.

Figure 19-17 – Uniform gentle slope.

Contour lines that are evenly spaced and close together indicate a uniform, steep slope, as shown in Figure 19-18.

Figure 19-18 – Uniform steep slope. 

The closer the contour lines are to each other, the steeper the slope. Contour lines closely spaced at the top and widely spaced at the bottom indicate a concave slope, as shown in Figure 19-19.

Figure 19-19 – Concave slope.

Contour lines widely spaced at the bottom indicate a convex slope, as shown in Figure 19-20.

Figure 19-20 – Convex slope. 

A panoramic sketch is a pictorial representation of the terrain in elevation and perspective as seen from one point of observation. This type of map shows the horizon, which is always of military importance, with intervening features, such as crests, woods, structures, roads, and fences. Figures 19-21 through 19-27 show panoramic sketches and maps. Each figure shows a different relief feature and its characteristic contour pattern. Each relief feature illustrated is defined in the following paragraphs.

A hill is a point or small area of high ground, as shown in Figure 19-21. When you are on a hilltop, the ground slopes down in all directions.

Figure 19-21 – Hill.

A stream course that has at least a limited extent of reasonably level ground and is bordered on the sides by higher ground is a valley, as shown in Figure 19-22. The valley generally has maneuvering room within it. Contours indicating a valley are U-shaped and tend to parallel a major stream before crossing it. The more gradual the fall of a stream, the farther apart are the parallel contour lines. The curve of the contour crossing always points upstream.

Figure 19-22 – Valley and draw.

A draw is a less-developed stream course where there is essentially no level ground and, therefore, little or no maneuvering room within its sides and towards the head of the draw. Draws occur frequently along the sides of ridges at right angles to the valley between them. Contours indicating a draw are V-shaped with the point of the V toward the head of the draw.

A ridge is a line of high ground that normally has minor variations along its crest, as shown in Figure 19-23. The ridge is not simply a line of hills. All points of the ridge crest are appreciably higher than the ground on both sides of the ridge.

Figure 19-23 – Ridge and spur.

Figure 19-23 also shows a spur, which is usually a short continuously sloping line of higher ground normally jutting out from the side of a ridge. A spur is often formed by two roughly parallel streams that cut draws down the side of the ridge.

A saddle is a dip or low point along the crest of a ridge, as shown in Figure 19-24. A saddle is not necessarily the lower ground between the two hilltops; it may be simply a dip or break along an otherwise level ridge crest. 

Figure 19-24 – Saddle.

A depression is a low point or sinkhole surrounded on all sides by higher ground, as shown in Figure 19-25.

Figure 19-25 – Depression.

Cuts and fills are man-made features that result when the bed of a road or railroad is graded or leveled off by cutting through high areas and filling in low areas along the right-of-way, as shown in Figure 19-26.

Figure 19-26 – Contour cut and fill.

A vertical or near vertical slope is a cliff. As described previously, when the slope of an inclined surface increases, the contour lines become closer together. In the case of a cliff, the contour lines can actually join, as shown in Figure 19-27. Notice the tick marks shown in this figure. These tick marks always point downgrade.

Figure 19-27 – Cliff.

2.5.0 Map Scales and Contour Intervals

A topographic map is called either large scale, intermediate scale, or small scale by the use of the following criteria:


The designated contour interval varies with the purpose and scale of the map and the character of the terrain. Table 19-3 shows the recommended contour intervals used to prepare a topographic map.

Table 19-3 – Recommended Contour.

Types of Topographic Map Nature or Terrain Recommended Contour Interval
Large Scale  Flat 0.5 or 1
Rolling 1 or 2
Hilly 2 or 5
Intermediate Scale Flat 1,2 or 5
Rolling 2 or 5
Hilly 5 or 10
Small Scale Flat 2,5 or 10
Rolling 10 or 20
Hilly 20 or 50
Mountainous 50, 100 or 200

2.6.0 Contour Map Construction

If engineering techs can perform ordinary engineering drafting chores, they will not have any difficulty in constructing a topographic map. To some degree, topographers must draw contour lines by estimation. Their knowledge of contour line characteristics and the configuration of the terrain that the contour lines represent is a great help. Topographers must use their skill and judgment to draw the contour lines so that the lines are the best representation of the actual configuration of the ground surface.

Basically, the construction of a contour map consists of three operations:

  1. Plot horizontal control that will serve as the framework of the map.
  2. Plot details, including the map location of ground points of known ground elevation. These ground points or contour points will be used as guides for the proper location of the contour lines.
  3. Construct contour lines at given contour intervals.

Take special care in the field to locate ridge and valley lines because these lines are usually drawn first on the map before plotting the actual contour points, as shown in Figure 19-28, View A. Since contours ordinarily change direction sharply where they cross these lines and the slopes of ridges and valleys are fairly uniform, these lines aid in drawing the correct contour lines. After plotting the ridge and valley lines, space contour crossings (by interpolation) along them before making any attempt to interpolate or to draw the complete contour lines, as shown in Figure 19-28, View B.

 Figure 19-28 – Plotting detail and contouring.

Draw contour lines freehand with a contour pen to yield uniform widths. Leave breaks in the lines to provide spaces for the elevations. Write the elevation numbers so they may be read from one or two sides of the map. Some authorities prefer that elevations also be written in a way that the highest elevation numbers are arranged from the lowest to the highest uphill. Show spot elevations at important points, such as road intersections.

Figure 19-28, View C shows the completed contour map. For more refined work, the EA must trace the map using a contour pen on tracing paper or other appropriate medium, to allow reproduction of more copies.

The true shape of features to scale can be better represented on a large-scale map. On small-scale maps, however, symbols are used to represent buildings and other features. Center the symbol on the true position, but draw it larger than the scale of the map.

Detail of this type is portrayed on the map by means of standardized topographic symbols, such as shown in Figure 19-29.

Figure 19-29 – Commonly used map symbols.

When plotting contours, remember that streams and ridge lines have a primary influence on the direction of the contour lines. Remember also that the slope of the terrain controls the spacing of the contour lines. Contour lines crossing a stream follow the general direction of the stream on both sides, then cross the stream in a fairly sharp V that points upstream. Finally, remember that contour lines curve around the nose of ridges in the form of a U pointing downhill and cross ridge lines at approximate right angles.

2.7.0 Interpolating Contour Lines

In the examples of interpolation previously given, a single contour line was interpolated between two points of known elevation a known horizontal distance apart, by mathematical computation. In actual practice, usually more than one line must be interpolated between a pair of points, and large numbers of lines must be interpolated between many pairs of points. Mathematical computation for the location of each line would be time-consuming and would be used only in a situation where contour lines had to be located with an unusually high degree of accuracy.

For most ordinary contour-line drawings, one of several rapid methods of interpolation is used. In each case it is assumed that the slope between the two points of known elevation is uniform.

Figure 19-30 shows the use of an engineer’s scale to interpolate the contours at 2-foot intervals between A and B. The difference in elevation between A and B is between 11 and 12 feet. Select the scale on the engineer’s scale that has 12 graduations for a distance and comes close to matching the distance between A and B on the map. In Figure 19-30 this is the 20 scale. Let the 0 mark on the 20 scale represent 530.0 feet. Then the 0.2 mark on the scale will represent 530.2 feet, the elevation of A. Place this mark on A, as shown. If the 0 mark on the scale represents 530.0 feet, then the 11.7 mark represents

530.0 + 11.7, or 541.7 feet,

the elevation of B. Place the scale at a convenient angle to the line from A to B, as shown, and draw a line from the 11.7 mark to B. You can now project the desired contour line locations from the scale to the line from A to B by drawing lines from the appropriate scale graduations (2, 4, 6, and so on) parallel to the line from the 11.7 mark to B.

Figure 19-30 – Interpolating contour lines with a scale.

Figure 19-31 shows a graphic method of interpolating contour lines. On a transparent sheet, draw a succession of equidistant parallel lines. Number the lines as shown in the left margin. The 10th line is number 1, the 20th, number 2, and so on. Then the interval between each pair of adjacent lines represents 0.1 feet.

Figure 19-31 – Graphic method of interpolating contour lines.

Figure 19-31 shows how to use this sheet to interpolate contour lines at a 1-foot interval between point A and point B. Place the sheet on the map so that the line representing 1.7 feet (elevation of A is 500.0 + 1.7, or 501.7 feet) is on A, and the line representing 6.2 feet (elevation of B is 500.0 + 1.7, or 506.2 feet) is on B. You can see how you can then locate the 1-foot contours between A and B.

For a steeper slope, the contour lines would be closer together. If the contour lines are too close, it is advisable to give the numbers on the graphic sheet different values, as indicated by the numerals in the right-hand margin. The space between each pair of lines represents 0.2 foot. Points A´ and B´ have the same elevations as points A and B, but the fact that the horizontal distance between them is much shorter shows that the slope between them is much steeper. You can see how the 1-foot contours between A´ and B´ can be located using the line values shown in the right margin.

A third method of rapid interpolation involves the use of a rubber band marked with the correct, equal decimal intervals. The band is stretched to bring the correct graduations on the points.

2.8.0 General Requirements for Topographic Maps

The scale and contour interval of a map are specified according to the purpose for which the map will be used. A map used for rough design planning of a rural dirt road would be on a smaller scale and have a larger contour interval than one to be used by builders to erect a structure on a small tract in a built-up area. The following guidelines suggest the nature of typical map specifications.

A map should present legibly, clearly, and concisely a summation of all information needed for the use intended, such as planning, design, construction, or record.

Topographic maps for preliminary site planning should have a scale of 1 inch = 200 feet and a contour interval of 5 feet. These maps should show all topographic features and structures with particular attention given to boundary lines, highways, railroads, power lines, cemeteries, large buildings or groups of buildings, shorelines, docking facilities, large rock strata, marshlands, and wooded areas. Secondary roads, small isolated buildings, small streams, and similar minor features are generally less important.

Topographic maps for detailed design for construction drawings should show all physical features, both natural and artificial, including underground structures. Scales commonly used are 1 inch= 20 feet, 1 inch= 40 feet, and 1 inch = 50 feet. The contour interval is 1 foot or 2 feet, depending on the character and extent of the project and the nature of the terrain. Besides contour lines, show any spot elevations required to indicate surface relief.

Additional detail features that are usually required include the following:

  1. Plane coordinates for grid systems, grid lines, and identification of the particular system or systems.
  2. Directional orientation, usually indicated by the north arrow.
  3. Survey control with ties to the grid system, if there is one. This means that the principal instrument stations from which details were located should be indicated in a suitable manner.
  4. All property, boundary, or right-of-way lines with identification.
  5. Roads and parking areas, including center-line location and elevation, curbs, gutters, and width and type of pavement.
  6. Airport runways, taxiways, and apron pavements, including center-line locations with profile elevations and width and type of pavement.
  7. Sidewalks and other walkways with widths and elevations.
  8. Railroads, including center-line location, top-of-rail elevations, and any turnouts or crossovers.
  9. Utilities and drainage facilities, such as gas, power, telephone, water, sanitary sewer and storm sewer lines, including locations of all valve boxes, meter boxes, handholes, manholes, and the invert elevations of sewers and appurtenances.
  10. Locations, dimensions, and finished floor (usually first floor) elevations of all structures.


Test Your Knowledge

8. What is the definition of relief as it applies to surveying?

A. Difference in elevation of the earth’s surface
B. Variation in the natural and man-made features of the earth’s surface
C. Variation of natural features of the earth’s surface
D. Man-made variations of the earth’s surface

9. What term is used for the type of line on a map representing the same elevation for all points on the line?

A. Contour
B. Elevation
C. hachure
D. Grid

10. What term is used for the difference between the values of adjacent contour lines?

A. Index contour
B. Contour interval
C. Intermediate contour
D. Elevation interval

11. The grid coordinate system works best on what type of features?

A. Slopes
B. Relatively level ground
C. Valleys
D. Shorelines and cliffs

12. What type of area is represented on a topographic map by contour lines that are evenly spaced and wide apart?

A. Valley
B. Gentle, uniform slope
C. Steep, uniform slope
D. Ridge

13. In what manner does a panoramic sketch shows the terrain?

A. In contour lines
B. In elevation
C. In perspective
D. Both B and C

14. What type of lines are drawn before the actual contour lines are plotted on a topographic map?

A. Spur and ridge
B. Vertical control and spur
C. Spur and valley
D. Ridge and valley

15. Which of the following devices is useful for interpolating contour lines rapidly?

A. Engineer’s scale
B. Tracing cloth
C. Graduated rubber band
D. All of the above



This lesson discussed the characteristic of topography including relief, natural features, and artificial features. This lesson also introduced you to the methods and procedures used to perform topographic surveying and to prepare topographic maps. You learned that a topographic map is simply a drawing that shows natural and artificial features of an area and that topographic survey is a survey conducted to obtain the data needed to prepare a topographic map.

Review Questions

1. In a topographic survey of an area, what kind of control is established by crossties from one side of the area to another?

A. Primary
B. Secondary
C. Horizontal
D. Vertical

2. Vertical control is normally established by what type of leveling?

A. Direct
B. Trigonometric
C. Barometric
D. Indirect

3. When time is more critical than a high degree of accuracy, what method of locating details is recommended?

A. Transit and tape
B. Transit and stadia
C. Transit and trigonometric leveling
D. EDM and level

4.  The stadia method provides horizontal distances of a higher precision than those obtained by taping, EDM, or differential leveling.

A. True
B. False

5. The stadia interval is defined as the ________.

A. reading on the rod between the stadia hairs.
B. distance to the stadia rod.
C. reading between the upper stadia hair and the middle cross hair.
D. reading between the lower stadia hair and the middle cross hair.

6. Stadia distance is equal to the ________.

A. rod reading.
B. rod reading divided by the stadia constant.
C. stadia interval.
D. stadia interval times the stadia constant.

7. Stadia horizontal distances are normally recorded to what degree of accuracy?

A. To 0.01 foot with a target
B. To 0.1 foot over 300 feet
C. To the nearest foot
D. As close as possible 

8. How do you compensate for refraction?

A. By ignoring the instrument constant
B. By taking all readings at two different times of the day
C. By shading the instrument
D. By using the refraction compensation formula

9. Which of the following methods are used for relief maps?

A. 3-D models
B. Hachure lines
C. Shading representing shadows
D. All of the above

10. Contour lines are used to show what type of information on a topographic map?

A. Quickest route
B. Boundaries
C. Rivers and streams
D. Relief

11. In a topographic survey, what term is used for the system in which the actual contour points on the ground are located and plotted?

A. Cross profiles
B. Control points
C. Grid control
D. Tracing contours

12. When drawing contour lines by using control points, what must you do to locate contour lines?

A. Scale
B. Interpolate
C. Average
D. Randomize

13. In what direction does the curve of a contour line cross a stream?

A. Upstream
B. Westward
C. Downstream
D. Eastward

14. What do contour lines represent in relation to the earth’s surface?

A. Horizontal planes
B. Vertical planes
C. Grid lines
D. Different points of elevation

15. Which of the following scales represents a large-scale topographic map?

A. 1 inch = 50 feet
B. 1 inch = 120 feet
C. 1 inch = 500 feet
D. 1 inch = 1,000 feet

16. Which of the following operations is NOT one of the basic operations for construction of a topographic map?

A. Plotting horizontal control
B. Plotting details and ground points
C. Determining slope distances
D. Drawing contour lines

17. For clarity on small-scale maps, how should buildings and other features be shown?

A. To scale
B. Larger than scale and true to shape
C. Larger than scale and by symbols
D. By location in the notes

18. Topographic maps used for the design of construction drawings normally use what contour interval, in feet?

A. 1 or 2
B. 1, 2, or 5
C. 10
D. 20