# Chapter 8 Topographical surveying.

OBJECTIVES

After reading this chapter, you should be able to:

* Explain the features of a topographic map.

* Understand the importance of selecting the right locations for stations.

* Understand the difference between the two main types of topographical surveys.

* Draw topographic maps.

* Know the characteristics of contour lines.

* Know how to interpolate between two points.

TERMS TO KNOW

topographic map

contour lines

hachure marks

interpolating

INTRODUCTION

Topographical surveying is used to collect the information required to draw topographic maps. A topographic map is drawn with distances to scale, as a road map, but it also includes information about the surface of the earth in the map area. The information for the surface will include the relief (elevation) and the position of the natural and man-made features. The relief is described using lines of constant elevation called contour lines. The use of contour lines is the distinguishing characteristic of topographic maps. The use of contour lines produces a three-dimensional map on a two-dimensional surface. The natural and man made features are represented by a system of symbols, and the map may include their elevations. This chapter will discuss uses of topographic maps, methods of collecting data for topographic maps, and the procedures for drawing topographic maps.

TOPOGRAPHIC MAPS

Topographic maps are very useful for planning construction and land use because they are three-dimensional. With a topographic map, the reader can determine the elevation of any point on the map, the distance between any two points and the slope between any two points. A topographical map can also be used to draw a profile of any route across the map. Topographic maps are the preferred source of information for landscape design and community planning.

The United States government has produced topographic maps of the entire country. A common size of map is called a 7.5 minute quadrangle. These maps are called 7.5 minute quadrangle maps because they cover 7.5 minutes of latitude and longitude. The amount of detail provided by the map is determined by the scale that is used. For the United States Geological Survey (USGS) maps the common scales are 1:24,000, 1:100,00, and 1:250,000. The 1:24,000 scale is very popular. It shows sufficient detail to meet the needs of hikers, campers, hunters, and large scale-planning.

Maps with larger scale are required for construction and planning purposes because the amount of detail that can be shown is proportionate to the scale of the map. Usually, these maps must be produced for each specific job. These maps are used for planning roads, sidewalks, retaining walls, and other types of construction. More information is presented on map scales in a later section in this chapter.

Topographic Map Symbols

Topographic maps use symbols to represent different man-made and natural features. The symbols show the location and give an estimate of the size of the features. Symbols are used for features such as lakes, roads, buildings, towers, benchmarks, and bogs. Figure 8-1 is an example of the symbols commonly used by the USGS. Other government and private agencies also use symbols. These may not be the same as the USGS symbols, but they will be similar.

Contour Lines

Contour lines are used to show the relief of the earth's surface. A contour line is an imaginary line that connects points of equal elevation. The points may be on dry land and/or on the land surface underwater. Before contour lines can be drawn, the survey crew must record the location and elevation of numerous points within the area being surveyed. In addition, the survey party should determine the contour interval that will be used. The decision on contour spacing is another judgement based on the volume of the data and the use of the data. A contour interval of two or five feet is very common, but there are situations where an interval of six inches or 10 feet would be appropriate. This is discussed more in the following section on collecting data.

CHARACTERISTICS OF CONTOUR LINES

Government agencies and other groups that draw contour lines have established several guidelines for individuals producing topographic maps.

* Contour lines are continuous. Some contour lines may close within the map, but others will not. In this case, they will start at a boundary line and end at a boundary line.

* Contour lines are relatively parallel unless one of two conditions exists. They will meet at a vertical cliff and they will overlap at a cave or overhang. If contour lines overlap the lower elevation contour should be dashed for the duration of the overlap.

* A series V shape indicates a valley and the V's point to higher elevation.

* A series U shape indicates a ridge. The U shapes will point to lower elevation.

* Evenly spaced lines indicate an area of uniform slope.

* A series of closed contours with increasing elevation indicates a hill, and a series of closed contours with decreasing elevation indicates a depression.

* Closed contours may be identified with a +, hill, or -, depression.

* Closed contours may include hachure marks. Hachures are short lines perpendicular to the contour line. They point to lower elevation.

* The distance between contour lines indicates the steepness of the slope. The greater the distance between two contours, the less the slope. The opposite is also true.

* Contours are perpendicular to the maximum slope.

* A different type of line should be used for contours of major elevations. For example at 100, 50, and 10 foot intervals. Common practice is to identify the major elevations lines, or every fifth line, with a bolder, wider line.

[FIGURE 8-1 OMITTED]

COLLECTING INFORMATION FOR TOPOGRAPHIC MAPS

The equipment and procedures used to collect the data are influenced by the scale of the map and the contour interval that will be used. Before the instruments are set up someone must decide on the type of topographic survey that will be conducted and the contour interval. Knowing the contour interval is important because it may be misleading to produce a map with small contour intervals when the stations were selected on a larger interval. Drawing a map with two foot intervals when the survey crew collected the data using changes in elevation of 10 feet or more can result in bad designs and costly mistakes. There is less potential for this to occur when most maps are drawn by hand because the person drawing the map and the surveyor learned the importance of communicating with each other. Computers and computer programs are now the method of choice for professional surveyors and engineers. Topographic-mapping programs allow the operator to specify the contour interval. The operator can produce any number of maps with different contour intervals from the same data set. This can result in topographic maps that do not represent the topography.

The selection of the contour interval will also influence the amount of data that must be collected. Figure 8-2 illustrates the number of stations that are required to define a hill. It can also be used to illustrate the effect of contour interval. As discussed earlier, the change in elevation for the stations in the field should be related to the contour interval of the map. For the example in Figure 8-2, the number of stations would increase from 19 to 25 or more if the interval were reduced by half. It should be noted that it is better to err on the side of collecting too much data. It is easier to throw out data that is not needed than to collect data that is missing.

The choice of whether to produce a topographic map by hand or by computer hinges on several factors. First, to draw a topographic map by computer, you must have the computer, the program, and the ability to use both. Second, maps are usually drawn on paper larger than 8.5 by 11.0 inches. This requires a different printer from what is normally used, or a plotter. Third, drawing a map by hand will require more time and some drawing ability. A hand-drawn topographic map represents many hours of work. Computer drawn maps are worth their cost for large and/or complicated areas, but hand-drawn maps are still useful for small areas and for individuals who do not have a computer or computer program and have the time to hand-draw maps. A discussion of topographic-map-drawing computer programs is beyond the scope of this text. For this information, the reader should consult professional magazines or such programs' information. This chapter will discuss how to draw simple maps by hand.

Map Scales

All maps are drawn to scale because it is not practical to have a map the same size as the area. Various scales are used for different agencies and purposes, but they are always integers and usually multiples of five or 10. A common way of expressing the scale of a map is to use the notation of a number, usually one, a colon and a second number. The scale on a map could be written as 1:10. On a map with this scale, each foot on the map represents 10 feet on the ground. The common USGS scale of 1:24,000 means that each foot on the map represents 24,000 feet on the ground, or each inch on the map represents 24,000 divided by 12, or 2,000 feet. It is important for the reader to study the map scale to ensure that he or she is interpreting the distances correctly.

The mapmaker must decide the appropriate size and scale for the size of the area surveyed and the amount of detail that is required. A map scale that uses multiples of 10 reduces the complexity of the math when one is hand-drawing a map.

Number of Stations

One aspect of topographic surveys that is constant across all methods is the care that must be taken when selecting the stations. Often, the first response is to take all you think you need and then a few more. It is important to remember that three items of information must be measured and recorded for each station, two for the location and one for the elevation. An excessive number of stations will greatly increase the time required to record the data and the volume of data. If an insufficient number of stations are recorded, the user of the map may not have sufficient information to make accurate decisions. The optimum number of stations is the minimum required to define the topography, and the additional sites, for the use of the data.

[FIGURE 8-2 OMITTED]

The intended use of the data is a very important factor to consider. Assume that the purpose of the survey is to develop a map that will have a large scale and will primarily be used for general planning. In this situation, the number of stations can be fewer because the precision of the map will be low. For example, it is not necessary to measure small changes in elevation. It would be appropriate in some situations for elevation changes of two feet or less not to be recorded. The opposite is true if the purpose of the survey is to develop a map that will be used to produce a drainage plan for an area that has very little slope. In this case, it may be necessary to record changes in elevation of six inches or less. Recording elevation changes as small as six inches, coupled with needing a small scale, will result in a large number of stations. A large area using these criteria will result in a very large data set and a large map. These criteria are used for this situation because it is important to measure small changes in elevation.

DETERMINING THE NUMBER OF STATIONS

Ensuring that the optimum number of stations is used is an important aspect of topographical surveying. It is possible that the person drawing the map has not seen the site. The only information he or she has is what has been recorded by the surveyors. The person drawing the map must assume that all of the manmade and natural features have been documented and that the surface between any two stations is a straight line. A depression or tree that was left out of the data will not appear on the map. This kind of mistake can lead to very expensive errors during the design and construction phase of a project. It is the responsibility of the survey team to record the appropriate data. The ability to select the right stations is more of an art than a science. For this reason, it is usually done by the most experienced member of the team.

In Chapter 6, an example illustrated the care that must be taken to ensure that a ditch is appropriately defined. Greater care must be taken when the surveying team records surface features such as ditches, hills, and depressions for topographic maps. It is important to remember that topographical maps are three-dimensional. To draw or plot in three dimensions you must be able to locate each station and know the elevation for each station. Locating each station will require at least two dimensions, or an angle and a distance, (X and Y). The third piece of information is the elevation of the station (Z).

Not only must the team decide on the number of stations needed to define a natural or man-made feature, such as a ditch, they must also remember that the length and shape of many features are not constant. As the shape and elevation of the feature changes, additional information must be collected to define the changes. Figure 8.2 illustrates that, where small changes in elevation are important to the survey, 15 or more stations may be required to define the shape of a small hill. It is also possible that the presence of this hill is of no consequence for the construction being planned. In this case, it would be ignored. The determining factor is always the use of the data.

In summary, selecting the stations is a very important part of topographical surveying. The surveying team must balance the uses of the data against the amount of resources required to collect the data. Even so, it is better to error on the side of collecting too much data than not enough. Someone must reconnoiter the site, and with an understanding of the purpose for the data, determine the location of the stations.

Instrument Site

Selecting the optimum site for the instrument can have a dramatic effect on the time required to complete the survey. The ideal site is one that will allow the instrument to see all of the stations for the survey. The stations will include:

* all of the corners on the property

* the stations required to define the topography

* the stations that are used to locate and establish the elevation of the man-made and natural features of the property

For a small area, devoid of trees or structures, site selection will be easy. As the area being surveyed becomes larger and the number of trees and other features increases, site selection becomes more complicated. If the property will not allow all of the stations to be seen from one location, then one or more turning points will be required. The use of turning points will increase the time required to complete the survey and increase the opportunity for errors. In addition, the location of the instrument for each turning point must be carefully documented when the angle and distance method is used. This will be discussed in greater detail in the next section.

When turning points are used, the note keeper must ensure that sufficient information is recorded to determine weather or not the turning point can be used as one of the stations for the map. When the top of a stake is used as a turning point, that elevation cannot be used as a station in the map because the elevation doses not represent the elevation of the earth at that point. When a mark on a sidewalk, manhole cover, or so on is used as a turning point, the elevation of the turning point can be included in the topographic map. This point can be included because the elevation of the turning point represents the elevation of the earth's surface. It is very important to record the structure used for the turning point in the notes for the survey. The structure used and the location of the turning point is part of the sketch. It is important to include this information on the sketch to prevent someone from using the data incorrectly. A well-drawn and documented sketch is the key to understanding the data.

Control Point

When turning points are used, it is helpful to use at least one control point. A control point is very similar to a turning point. It is a station in the survey that is used for more than one instrument setup. Because of its similarity to a turning point, a control point should be marked as a turning point, and the same rules apply for including the elevation in the topographic map. The use of a control point serves as a check for error when using turning points in an angle and distance topographic survey and as a check for instrument height when using the grid method. These two methods will be explained in detail in a later section of this chapter.

In Figure 8-3, station H is a control point. At instrument position one (IP1), the location and elevation of the turning point was recorded to extend the survey. In addition, the location and elevation of station H were also recorded. Station H may be a point that will be included in the topographic map, or it may not be included. The determining factor is the type of structure that was used to mark the location of the station. During the survey, data would be collected to determine the elevation and location of station H. Before the instrument is moved from IP1, data is also collected to determine the elevation and location of the turning point (TP).After the instrument is moved to IP2, the data for elevation and location are collected again for the turning point and station H. These measurements will aid in locating IP2 when you draw the map and provide a check on the accuracy of the height of the instrument because the difference in the elevation between TP and station H at IP1 and the location of TP and station H must be the same at IP2. If they are not the same, there is a high probability that an error occurred in moving and setting up the instrument at IP2. When this occurs the instrument should be re-leveled and the readings repeated. In surveys requiring a high level of precision it is common practice to use more than one control point.

Control points also help blend more than one set of data. When a large area, or an area with a large number of stations, is surveyed it may not be possible to complete the survey in one day. Using a common benchmark is standard practice when combining data, but including at least one control point will reduce the chance of errors when the two data sets are combined.

[FIGURE 8-3 OMITTED]

INTERPOLATING

Interpolating is the process of locating the position of a contour line between the elevations of two stations. Interpolating uses proportions to determine the correct position of the contour line. A contour line is extended across the map by calculating the proportion for each pair of stations that it passes through. Drawing maps by hand requires the individual to complete each calculation by hand. This is one of the benefits of computer topographic programs. The program completes all of the calculations.

Interpolating for a Grid

Assume that a 100-foot contour will pass between two stations. One station is at an elevation of 99 feet, and the second station elevation is 101 feet. In this example, the 100-foot contour would be an equal distance from both stations, so it would be drawn half-way between the two stations. Unfortunately, topographic interpolating is not always this easy. Determining the location of a 100-foot elevation contour between stations of 103.5 and 97.2 feet will require the use of a calculator or a computer spreadsheet.

For those situations that require a calculator, a formula can be used. The formula determines the proportional distance for the contour line from the highest elevation.

Proportion = High elevation-Contour elevation/High elevation-Low elevation

The proportion determined by the formula, times the distance between the two stations on the map, determines the distance between the station with the highest elevation and the contour line.

Interpolating Example

Determine the location of a 98.0-foot contour line between two stations that are at 101.0 feet and 96.0 feet elevation. The map is drawn with a scale that results in 1 inch between stations.

Proportion = 101-98/101-96 = 0.6 0.6 x 1 inch = 0.6 inches

The contour line crosses an imaginary line between the two stations a distance of 0.6 inches from the station with the highest elevation (see Figure 8-4).

The same process is used when the distance between the grid stations is not equal to 1 inch. For example when interpolating the diagonals for a grid survey. A map with a 1-inch grid will have 1.4 inches between the diagonal stations.

[FIGURE 8-4 OMITTED]

a = [square root of [b.sup.2] + [c.sup.2]]

= [square root of [1.sup.2] + [1.sup.2]]

= 1.4 in.

The location of the contour line is determined by multiplying the proportion times the distance between the two stations on the map.

06. x 1.4 in. = 0.84 in.

The contour line crosses an imaginary line between the two diagonal stations at 0.84 inches from the station with the highest elevation (see Figure 8-5).

This process is repeated for each pair of stations and the grid diagonals that the contour passes between until the contour line is completed or it intersects a boundary.

Interpolating for Angle and Distance Surveys

Interpolating for angle and distance surveys uses the same formula. The primary difference is the distance between stations is more variable, and the map drawer must be careful not to miss some stations. Some of the stations may be several inches apart on the map.

TYPES OF TOPOGRAPHIC SURVEYS

The data for topographic maps can be collected using several different methods. A popular method, especially for a large area, is aerial photography. Using special cameras and computers, surveyors can fly over an area and develop topographic maps from the photographs. This method is time-consuming and expensive, but for difficult terrain that will require a large number of human resources, it can be more economical.

[FIGURE 8-5 OMITTED]

Land-based topographic surveys are usually divided into three types based on the method used to identify the location of the stations. Three common methods are grid, angle and distance, and points on the contour. The grid and angle and the distance methods will be explained in this chapter. If you are interested in the third method, or any other, you should consult an engineering surveying textbook.

Topographical Survey by Grid

In the grid method, the first step is to identify and locate the boundary corners for the parcel being surveyed. This is an example of a place where a traverse survey would be used. Information on traverses is included in the next chapter. After the boundaries are located, a grid is established, as shown in Figure 8.6. Elevations are recorded at each point the lines cross and at each intersection of a grid line with the property line. A common practice for identifying the stations is to use the rows and columns identified by letters and numbers. The grid identification system used is not important as long as it results in a unique identification for each station. For example, the identification for the station marked by a circle in Figure 8-6 is C3, and the station marked by a diamond is J8.

[FIGURE 8-6 OMITTED]

When establishing the grid it should be aligned with the longest boundary. This will reduce the number of atypical grids. In the illustration in Figure 8-6, stations J2 through J9 and A11 through C11 are atypical grids. The distances between the atypical station and the nearest station on the grid must be recorded. Otherwise, these stations will located incorrectly on the topographical map. When atypical grids are used and not identified the person using the data will assume that all of the stations were on the standard grid, and the boundary of the area will not be drawn correctly. Figures 8-6 and 8-7 illustrate this situation. Figure 8-6 is the grid of the area being surveyed. Figure 8-7 shows how the map would be drawn if the mapmaker didn't know that the data contained atypical grids. Figure 8-7 would be a major mistake.

The grid is the reference for locating all stations and features. In the grid method, the location of the instrument is not important when drawing the map, but it is good practice to identify the location(s) of the instrument in the sketch that accompanies the data in the field book.

SPOT ELEVATIONS

Spot elevations are stations that are not part of the grid. These elevations may be taken to record the location and elevation of additional man-made or natural features that are important to the survey, but are not located at a grid point. Spot elevations can be located by trilateration from two grid stations. The rock in the illustration in Figure 8-8 is located 32.8 feet SE from station C2 and 43.3 NE feet from station C3.

[FIGURE 8-7 OMITTED]

Trilateration requires three dimensions. The third dimension is the grid spacing, which was previously defined by the positions of C2 and C3.The data table could include the spot elevations with the grid elevations. It would also be appropriate to include a separate table of spot elevations. The surveyor must also include the information that was used to locate the spot elevation in the field book.

Data Table

There is more than one way of organizing topographic data. What is important is for the data to be identified, clear, complete, and easy to read and understand. Figure 8-19 (see page 129) is an example of a notebook page for a topographic survey. It is an example of a uniform grid. In the field, this rarely happens. The data table for the example in Figure 8-8 would have the appropriate number of rows and tiers, but there should not be a place to record the elevation for A1, C5, and E5. These stations do not exist on the parcel of land being surveyed.

[FIGURE 8-8 OMITTED]

GRID SPACING

A very important decision when using the grid method is determining the size of grid. If it is too small an excessive amount of resources

will be used when collecting data; if it is too large important information will be missed. The determining factors are the steepness of the slopes and the contour interval that will be used. Steep slopes and a small contour interval require a small grid. A smooth surface and a large contour interval indicate that a large grid should be used. To illustrate this point, study Figures 8-9 and 8-10. Both figures use the same set of data. The difference is that in Figure 8-10 every other row and column was left out to simulate the effect of doubling the grid size. There is a clear difference in the two maps.

The issue of appropriate grid size becomes more confusing because under the right circumstances either one of these two maps would be appropriate. The smaller grid size in Figure 8-9 reveals four areas of lower elevation that are not visible in Figure 8-10. Not knowing the location of the three lower areas would probably not seriously affect construction if the purpose of the survey were to develop the area for a building. The engineer would determine the elevation of the building floor and then have the construction crew level the area at the desired elevation.

[FIGURE 8-9 OMITTED]

[FIGURE 8-10 OMITTED]

If on the other hand, the purpose of the survey was to design a park and the design included a sidewalk, then the location of the four lower areas would be important. They would change the slope of a sidewalk and possibly cause the sidewalk to exceed the desired standards. If the 100-foot grid survey were all that was available, the designer would not know the three depressions even existed. A small area, 10 acres or less, with very little variability could be surveyed with a grid spacing of 50 or 100 feet. If the surface were more variable, it might be necessary to use a 25-foot or smaller grid.

It is always important to remember that the grid size determines the number of stations that will be recorded. Ten acres with a 50-foot grid will result in 196 stations. If the grid is reduced to 25 feet, the number of stations increases to 729. Increasing the number of stations dramatically increases the time and other resources that will be required to collect and manage the data. For large areas, it is customary to use a grid spacing of 100 feet or more. For example, 100 acres surveyed with a 25-foot grid result in 7,056 stations. It is not good business for a surveying team to spend the amount of time required to record 7,000+ stations unless the use of the data dictates this requirement. The selection of grid size may ultimately be decided by the client or the personal preferences of the head surveyor.

Topographical Survey by Angle and Distance

Locating the stations by angle and distance is an alternative. In this method, all of the stations are spot elevations because the only elevations that are recorded are the points that are important to the survey. When conducting an angle and distance topographic survey, the stations are usually identified by numbers, and/or letters, and the stations are located by measuring the angle and distance from the location of the instrument. Therefore, it is very critical that the location of the instrument be measured and recorded. A common practice is to locate the position of the instrument by measuring the distance from two or more of the boundary corners. The location of the instrument could also be recorded by using the angle and distance from two or more boundary corners.

An angle must be measured from a point or line. Before stations in an angle and distance topographic survey can be identified, the survey crew must determine what will be used as the backsight for the angles. Historically, transits were the instrument of choice for angle and distance surveys, because they measure angles accurately and most styles of transits included a compass in the base. The compass could be used to orient the instrument to magnetic or geographical north. North could be used as the backsight for all angles. An alternative is to use an easily identifiable, permanent landmark as the backsight for the angles. This could be a utility pole, corner post, tower, or any structure that is easy to locate. When a landmark is used, it is important to ensure that it is identified in the field notes, and its location must be carefully noted.

As with the grid method, someone must determine the number and location of stations. The station selection must provide adequate data to define all of the man-made and natural features that are important for the use of the data.

One of the characteristics of the angle and distance method is measuring the distance from the instrument to each of the stations. The selection of the method for measuring distance will greatly affect the time required to collect the data. Chaining the distances would be acceptable for a small area, but it would be a time-consuming process for a large area. The use of a transit would allow the use of a compass for orientation of the angles, and the distance could be measured by stadia. This would only be acceptable for low-precision surveys because of the limitation of distances to a precision of 0.1 feet. This is a situation where a total station would be the instrument of choice. It produces accurate, precise data for distances and angles. Another plus is that higher-end units can be operated by a single person.

ANGLE AND DISTANCE EXAMPLE

The following example will illustrate the process for completing an angle and distance topographic survey. Figure 8-11 is an illustration of an area of land encompassing about 1.9 acres.

The first step is to locate and record the corners of the property and their elevations. This is accomplished by selecting a site for the instrument and determining the angles and distances, and elevations for the six corners.

Measuring Angle and Distance The process of determining the angles and distances for the corners from the instrument position is illustrated in Figures 8-12 and 8-13. In this example, a compass was used to establish the backsight for all of the angles.

The sequence for recording data will depend on the methods used. The angles and distances can be recorded simultaneously if the distances are measured by stadia or EDM. If not, then two separate operations will be required to record the angles and distances. Several options also exist for recording the elevations. The elevations for the six corners could be recorded in a separate operation, using a laser for example, or they could be recorded when the angles and/or the distances are measured. An advantage of using a total station is that all of the data can be recorded simultaneously. Using equipment that requires the survey to be broken down into several operations will increase the amount of time required to complete the survey.

[FIGURE 8-11 OMITTED]

Regardless of the methods used, the survey crew must ensure that all of the necessary data is recorded and that it is accurate. The data must be recorded in an appropriate table.

DATA TABLE FOR SAMPLE PROBLEM

The format of the data table is flexible as long as the requirements for recording data are met. All of the data for an angle and distance survey could be included in one table, but separating them into two tables will make the data easier to read.

Table 8-1 contains sufficient data to draw a topographic map, but it would only be accurate if the surface of the 1.9 acres was uniform. Any hills, ditches, or other structures within the boundaries of the property would not be evident because there is no data to locate them and define their shape. Any person reading the data table would make the assumption that no other features or structures exist on the property.

A review of the data reveals that only the corners of the property were located and recorded (see Figure 8-14). This type of data should be suspect. Just the addition of one point with an elevation different from the elevations on the map would make a dramatic difference. Assume that an additional point was recorded in the middle of the property and that it had an elevation of 99.8 feet. Figure 8-15 illustrates the results of adding this one station.

With the addition of this one point, the appearance of the map changes. The more difference there is in the new data as compared to the existing data--the more dramatic the change will be in the topographic map. To emphasize this point one step further, assume that an additional point is included halfway between stations A and B and that the elevation of this station is 98.0 feet. Figure 8-16 illustrates the effect of adding this station to the data set. This causes a dramatic change.

Comparing Figure 8-15 and Figure 8-16 illustrates the effect that one additional station can have on a topographic map. If Figure 8-16 represents the property, then any design or planning using the map in Figure 8-14 would have serious flaws.

DRAWING TOPOGRAPHIC MAPS

Drawing topographic maps by hand is a slow, tedious process. A computer program should be used if maps will be drawn frequently or if large maps are being used. The advantages of computer-drawn maps include better quality and more accurate interpretation of the data. The disadvantage is the program restraints on the data input format and map output.

Hand-Drawing Maps

Drawing maps by hand is a useful skill for small areas or for quick low-precision maps that can be used for planning and estimating. Drawing a topographic map by hand is a two-step process that requires two sheets of paper. The first sheet is used to record all of the information. This includes the boundaries, the locations of the stations, and the elevations of the stations. The second sheet is used to draw the map.

Mapping Supplies

Before starting to draw a topographic map, make sure the necessary materials are available. Both topographical methods require pens or pencils and a scale. A scale that is graduated in tenths is easier to use than one graduated in fractions. The angle and distance method will also require a protractor and compass. The paper should be large enough to contain the map, and one piece should be thin like tracing paper. Typing and drawing paper can be used if a good light source is available such as a light table or a window with strong light behind it.

Topographic Maps by Grid

The first step is to draw the boundaries to scale. It is very important to coordinate the scale of the map and the size of paper that will be required. Before selecting the paper size the map maker must analyze the date and determine the dimensions of the parcel of land being mapped. The grid method expedites this process because it is easy to tell from the data the number of rows and columns that were used. This information and the grid spacing provide the information necessary for determining the size of the map. Data collected by angle and distance must be carefully studied to determine the outlying points. This may require drawing a sketch of the area before the size of the paper can be determined. In addition, the drawing must be orientated on the paper. Remember the convention for maps is place north at the top of the page.

The second step is to lay out the grid and write in the elevations for every point. Next, the tracing paper or second sheet is taped over the first. The second paper should only be taped along one edge so that it can be lifted out of the way when it becomes necessary to refer to the data on the first sheet. The first step in drawing the map is transferring the boundary lines from the first sheet to the second sheet. The last step is drawing the contour lines.

DRAWING CONTOUR LINES

Contour lines can start at any one of the desired intervals, but it is important to study the elevations to ensure that some are not missed. Review the elevations for the minimum and maximum numbers and pick one of the desired contour elevations that falls within this range. Start on a boundary or at an interior point, and trace the line across the map. Remember that contour lines must be closed inside the map or extend to a boundary line. A contour line cannot stop at any interior point. The line is extended by interpolating between points.

A confusing part of drawing contour lines is determining their route between stations. Remember, contour lines represent points of equal elevation. Study Figure 8-17. The 100-foot contour starts between A1 and B1. The difficulty is determining the next point. Remember that for a contour to cross between two stations, one station must have an elevation greater than the elevation of the contour, and the elevation of the other station must be less than the elevation of the contour.

The contour is extended by comparing the elevations of the next pair of stations that have a higher and lower elevation. In Figure 8-17 the elevation of stations B1 and B2 is greater than 100 feet. The contour line doesn't cross between these two stations. Also, note that the elevations of stations A1 and A2 are less than 100 feet. The 100-foot contour will not cross between these two. That leaves stations A2 and B2. In this example, the elevation of station A2 is less than 100 feet and the elevation of station B2 is greater than 100 feet. The 100-foot contour crosses the imaginary line between these two stations. The intersection is located using interpolation.

[FIGURE 8-12 OMITTED]

Continue drawing the contour lines until the map is complete. Remember to look for small hills and depressions that are complete within the map and for contour lines that may enter and exit the map a short distance apart. The process of drawing contour lines will be illustrated with a sample problem.

SAMPLE PROBLEM--TOPOGRAPHIC BY GRID

Study the page from the field notes illustrated in Figure 8-19 (see page 129). In many situations, the person drawing the map was not part of the surveying crew and the only information he or she has is the notes from the field book. This is why it is so critical that the notes are complete.

Conceptualizing a Map

The first step in drawing a map is to picture in your mind what the area looks like. The two primary clues are the data table and the sketch. The sketch shows that the field is rectangular and that it is orientated north to south. A note with the sketch also states that two of the boundaries were defined by a fence. These are important clues when you start to draw the map. The data table shows that the stations range from A1 to E7. The data includes a benchmark that was not part of the survey. The data also shows that station C4 was used as a turning point. What is not clear is whether the structure used for the turning point represented the surface of the earth. This information should be included with the sketch. In this example, we will assume that the turning point can be included in the map.

[FIGURE 8-13 OMITTED]

Also, note the station identification that was used. For this survey, rows were identified by numbers and columns were identified by letters. This is important to remember when the elevations are written on sheet one of the map. An additional factor that must be remembered when drawing this map is that no man-made or natural features were identified and measured during the survey.

The purpose of this sample problem is to show the process of drawing a topographic map; therefore a simple rectangular area was used. The process is the same for larger sets of data and shapes that are more complex; it just takes more time and care to lay out the boundaries and the station locations on the drawing.

Paper Size and Scale

The next step is to determine the size of paper that will be needed to draw the map to the desired scale. The note below the sketch, shown in Figure 8-19, indicates that a 100-foot grid was used. Five columns and seven rows equate to an area of 400 feet x 600 feet. A map scale of 1:100 would produce a map that measured 4 inches x 6 inches. This would be a small map, and it would not be very useful for construction or planning purposes. An alternative is to use a different scale. A scale of 1:10 would result in a map that was 40 inches x 60 inches. This is not a practical size. The options are to use a small map or a scale different from a multiple of ten. For example, a scale of 1:50 would result in a map that is 8 inches x 12 inches. For this example, the scale of 1:100 will be used because the small map is large enough to demonstrate the principles of drawing contours and it will fit on standard 8 1/2 inch x 11 inch paper.

Drawing the Map

The manual method of drawing topographic maps works best if two sheets of paper are used. The first sheet is used to record the location and elevations for all of the survey, and the second sheet is used for the map. If all of the station elevations are included in the final map, the map becomes cluttered and is confusing to use. It may be desirable to include spot elevations for man-made or natural features on the contour map.

Sheet One

The first task is to locate station A1 on the paper so that the map will be centered on the paper when it is complete. For this example, the width of the map is 4 inches. Subtracting the width of the map from the width of the paper, 8.5 inches, leaves 4.5 inches. Dividing 4.5 inches by 2 produces a left and right margin of 2.25 inches. Completing the same calculations for the top and bottom margin results in 2.5 inches ((11 - 6)/2). This results in a location of station A1 2.25 inches from the left margin and 2.5 inches from the top of the paper.

[FIGURE 8-14 OMITTED]

[FIGURE 8-15 OMITTED]

[FIGURE 8-16 OMITTED]

The next task is to draw the boundaries. The top boundary, A to E, is drawn parallel, starting with the location of A1, with the top edge of the paper. The left boundary, rows 1 to 7, is drawn starting at the location of A1 and parallel with the left side of the paper. Station E7 is located by measuring 4 inches from station A7 and 6 inches from station E1. The point where these two dimensions meet is the location of station E7. Drawing a line connecting station E7 to E1 and A7 completes the boundary. Next, the grid is drawn. A scale of 1:100 and a grid distance of 100 feet result in a grid distance on the paper of 1 inch.

After the grid is drawn, the station elevations are added to the grid. The elevations must be plain and legible because they must be read through the second sheet when the contour lines are drawn.

The last step for sheet one is to locate the intersections of the contour lines and the grid lines. This is accomplished by placing a mark at the appropriate spot where the contour line intersects a horizontal or vertical grid line. The location of the contour line should also be marked for where the contour intersects an imaginary diagonal between either two pairs of stations. The intersections and the contour line for the intersections are included in Figure 8-20 (see page 130).

Sheet Two

The next step is to tape one edge of the second piece of paper over the first sheet. Both sheets of paper should be taped to a light table or to a surface that will provide enough back lighting to see the elevations through the second sheet. Make sure that the second sheet can be lifted up, without removing the tape, to expose the first sheet. The boundaries should be traced onto the second sheet, and then the contour lines can be drawn. It will be less confusing if the contours are completed one at a time, instead of locating all the intersections for the entire map first and then drawing all of the smooth curves for the contours.

Figures 8-21 and 8-22 (see pages 131 and 132) show the process of locating the first two intersections. For intersection one, the equation produces a proportion of 0.72. The scale of the map is 1 inch equals 100 feet, therefore the location of intersection one from the station with the highest elevation is 0.72 x 1 inch, or 0.72 inches, as shown in Figure 8-21 (see page 131).

The procedure for locating intersection two is slightly different because it is a diagonal. The interpolation equation produces a proportional distance of 0.68. The distance between stations A6 and B7 is 1.4 inches. Therefore, the distance between the station A6 and the intersection with the contour line is 0.68 x 1.4 inches, or 0.95 inches.

The remaining intersections are located and marked using the same method. The math required to locate the intersections is not difficult--just tedious. The calculations for a 100-foot contour are included to aid you in understanding the example problem. The intersections were numbered starting with the location between A7 and B7 as 1 and then moved counterclockwise around the contour until the contour left the map between stations B7 and C7.

1. 103.8-100/103.8-98.5 = 0.72

2. 103.2-100.0/103.2-98.5 = 0.68

3. 103.2-100.0/103.2-99.6 = 0.89

4. 102.9-100.0/102.9-99.6 = 0.88

5. 102.9-100.0/102.9-99.7 = 0.91

6. 102.6-100.0/102.6-99.7 = 0.90

7. 102.6-100.0/102.6-99.9 = 0.96

8. 102.3-100.0/102.3-99.9 = 0.96

0.96 x104 = 1.3

9. 100.5-100.0/100.5-99.9 = 0.83

10. 101.1-100.0/101.1-99.9 = 0.92

0.92 x 104 = 1.3

11. 104.6-100.0/104.6-99.9 = 0.97

12. 104.6-100.0/104.6-99.7 = 0.94

13. 105.2-100.0/105.2-99.7 = 0.94

14. 105.2-100.0/105.2-99.6 = 0.93

15. 105.2-100.0/105.2-99.7 = 0.94

16. 104.5-100.0/104.5-99.7 = 0.94

0.94x1.4 = 1.3

17. 104.1-100.0/104.1-99.7 = 0.93

18. 104.2-100.0/104.2-99.7 = 0.93

0.93x104 = 1.3

19. 103.8-100.0/103.8-99.7 = 0.93

20. 103.8-100.0/103.8-99.6 = 0.90

0.90x1.4 = 1.3

21. 103.8-100.0/103.8-98.5 = 0.72

[FIGURE 7-17 OMITTED]

[FIGURE 7-18 OMITTED]

The intersection points are connected by a smooth, curved line. The map with the completed 100-foot contour can be seen in Figure 8-23 (see page 133).

The remaining contours are completed using the same procedures. After all of the contour lines are located and drawn, the map is finished with the appropriate labels and legends.

PROFILE GRAPH FROM TOPOGRAPHIC MAP

Topographic and profile surveys have one thing in common. They both are used to define the topography of the earth's surface. The difference is that topographic surveys collect the information to define the surface of an area, and profile surveys only define the topography for a route, a line. Because of their similarity, a profile graph can be drawn from a topographic map. There are two common methods of producing the profile of a route from a topographic map:

* determining the values for distance and elevation from the map

* transferring the information from the topographic map to the profile

[FIGURE 8-19 OMITTED]

[FIGURE 8-20 OMITTED]

[FIGURE 8-21 OMITTED]

It must be pointed out that neither of these two methods is as precise as a profile survey. Both methods are useful for selecting a route and or initial planning and design work. Many situations would require the completion of a profile survey along the desired route before the final designs are completed.

DRAWING A PROFILE BY DETERMINING VALUES

In Chapter 6, the requirements for drawing a profile were determined to be a value for distance and a value for elevation. Numbers for these two values can be determined from a topographic map. The task is to determine the appropriate stations on the topographic map, and a distance and elevation for each one.

Determining Stations

Stations must be points where the distance from the initial point and the elevation can be determined. Distances can be determined at any point along the route, by measuring with a rule and using the maps scale to convert the measurement to the distance, but the only elevations are the contour lines. Therefore, the stations are the junctions of the route and a contour line. The stations can be identified in the same way, by their distance from the initial point, but any system is acceptable as long as it is consistent and clear. Refer to Appendix I for more information on drawing graphs by hand.

[FIGURE 8-22 OMITTED]

EXAMPLE OF A PROFILE BY DETERMINING DISTANCE AND ELEVATION

Figure 8-24 illustrates a topographic map with the route of the desired sidewalk drawn on the map. This illustration contains all of the information needed to draw a profile of the proposed sidewalk.

The first step is to determine the distance for each station from the initial point of the survey. This is accomplished by placing a ruler along the route and determining the distance for each junction with a contour line, as shown in Figure 8-25.

[FIGURE 8-23 OMITTED]

This is an example of were using a table for the data will help organize it and reduce the chance for errors.

Note that in Table 8-2 the information for station A is complete, except for the elevation. The start of the sidewalk is not at a contour line. The elevation of this point must be interpolated. In this example, the elevation of station A is 89.4 feet. The information for all of the stations is included in Table 8-3.

[FIGURE 8-24 OMITTED]

[FIGURE 8-25 OMITTED]

Knowing the distance from the initial point and the elevation of the station, the information can be plotted on a graph, Figure 8-26.

DRAWING A PROFILE BY TRANSFERRING THE INFORMATION

This method of producing a profile graph from a topographic map is easier to produce, but it is not as useful because the distance for each station is not known. It also requires the profile graph to be the same width as the length of the route on the topographic map. It is still useful for visualizing what the profile will look like.

In this method, the X- and Y-axis are drawn on the paper and the paper is folded along the X-axis. The folded edge is aligned with route of the sidewalk on the topographic map (see Figure 8-27). Ensure that the corner of the X-Y axis is aligned with the initial point of the sidewalk. Move along the sidewalk and mark the location of each contour line on the X-axis of the graph.

[FIGURE 8-26 OMITTED]

Remove the graph paper and mark the elevation for each contour line (see Figure 8-28). Connect the marks, attach the appropriate titles, legends, and labels, and the profile is complete.

Marking the contour lines on the Z-axis identifies their location on the graph. This method does not allow the elevations to be transferred. They must be established following the manual methods of drawing a graph. The first step is establishing the scale for the Y-axis. In this method, the Y-axis scale is the same as the scale for the map. This eliminates the vertical exaggeration that is normally used with profile graphs, but it does provide a visual image of the profile. The graph is completed by connecting the elevations with a straight line and labeled.

This is another example of where the use of a computer would save time in surveying. Several computer-surveying programs allow the operator to input the coordinates of the route and the program will draw the profile. One big advantage is the ability to change the position of the route and almost instantaneously see the new profile.

[FIGURE 8-27 OMITTED]

[FIGURE 8-28 OMITTED]

SUMMARY

The object of this chapter was to acquaint the reader with the principles and methods of topographical surveys and topographic maps. These are the preferred maps for construction, landscape architects and for land use planning. Producing a topographic map requires a large amount of resources. Careful planning must be completed before any equipment is set up and used. As with most surveying activities, many of the aspects of topographical surveying are as much of an art as a science. There is no substitute for experience, but if a beginning surveyor takes care to adhere to recommended principles and practices he or she will be able to produce usable topographic maps.

STUDENT ACTIVITY

Draw a topographic map for the data in the following table. Start with even elevations and use a contour interval of 2 feet.
```STA   BS    HI     FS     ELEV

BM    2.3   52.3          50.0
A1          52.3   14.3   38.0
A2          52.3   12.3   40.0
A3          52.3   1.1    51.2
A4          52.3   11.1   41.2
A5          52.3   12.7   39.6
A6          52.3   14.8   37.5
B1          52.3   13.8   38.5
B2          52.3   12.2   40.1
B3          52.3   10.0   42.3
B4          52.3   6.5    45.8
B5          52.3   6.4    45.9
B6          52.3   4.1    48.2
C1          52.3   16.3   36.0
C2          52.3   10.8   41.5
C3          52.3   10.3   42.0
C4          52.3   7.9    44.4
C5          52.3   3.8    48.5
C6          52.3   2.8    49.5
D1          52.3   18.3   34.0
D2          52.3   9.9    42.4
D3          52.3   10.3   42.0
D4          52.3   7.7    44.6
D5          52.3   3.5    48.8
D6          52.3   2.3    50.0
E1          52.3   13.8   38.5
E2          52.3   9.5    42.8
E3          52.3   8.8    43.5
E4          52.3   6.8    45.5
E5          52.3   4.3    48.0
E6          52.3   2.3    50.0
F1          52.3   11.1   41.2
F2          52.3   10.0   42.3
F3          52.3   8.5    43.8
F4          52.3   7.1    45.2
F5          52.3   3.8    48.5
F6    3.3   53.5   2.1    50.2
BM                 3.5    50.0

Table 8-1 Angle and distance data

Station   Angle (1)   Distance

A         -25.7 (2)   175.48
B         56.1        264.09
C         119.4       243.43
D         176.3       116.96
E         178.1       142.47
F         -152.2      162.17

(1) Magnetic North

Station   BS    HI      FS    IFS   Elevation

BM        5.2   105.2               100
A                             3.1   102.1
B                             3.2   102.0
C                             4.2   101.0
D                             5.6   99.6
E                             5.7   99.5
F                             4.8   100.4
BM                      5.2         100.0

(2) Notice that two of the angles are recorded as "-" angles.
Refer to Chapter 7 if you need to review why this symbol is used.

Table 8-2 Sample table for creating a profile from
a topographic map

STA   Measurement   Distance        Elevation

A     0.0           0.0
B
C
D
E
F
G
H
I

Table 8-3 Data for example

STA   Measurement   Distance (ft)   Elevation

A     0.0           0.0             89.4
B     0.4           40              90
C     1.4           140             92
D     1.95          195             94
E     2.2           220             96
F     2.4           240             98
G     3.55          355             100
H     4.3           430             102
I     5.4           540             102
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