8. TOPOGRAPHICAL SURVEYS - DIRECT LEVELLING

8.0 Introduction

1. In Chapters 5 and 6, you learned about various devices for measuring height differences. You also learned how to use these devices to solve three types of problems in measuring height differences, which you may face when you plan and develop a fish-farm (see Section 5.0). Now, you will learn how to plan surveys to solve these problems, how to record the measurements you make in your field-book, and how to find the information you need from these measurements.  
70.GIF (5880 byte)
     

What are elevation and altitude?

2. You have learned what the height of a ground point is. Now, however, you will need to know a more accurate definition of this term.

  • When the height of a point is its vertical distance above or below the surface of a reference plane* you have selected, it is called the elevation* of that point.
  • When the height of a point is its vertical distance above or below mean sea level (as the reference plane), it is called the altitude* of the point.

Example

Elevation of a point above a selected ground mark A
Altitude of the same point above mean sea level (amsl)

1.83 m
345 m


3. The vertical distance between two points is called the difference in elevation , which is similar to what you have learned as the difference in height (see Section 5.0). The process of measuring differences in elevation is called levelling , and is a basic operation in topographical surveys.

 
70a.GIF (6745 byte)
     

What are the main levelling methods?

4. You can level by using different methods, such as:

  • direct levelling, where you measure differences in elevation directly. This is the most commonly used method;
  • indirect levelling, where you calculate differences in elevation from measured slopes and horizontal distances.
 
Direct levelling
71.GIF (3736 byte)
     

You have already learned about indirect levelling in Section 5.0, when you learned to calculate differences in elevation from slopes or from vertical angles. Now you will learn about direct levelling.

71b.GIF (2625 byte)

 
Indirect levelling
71a.GIF (5429 byte)

What are the kinds of direct levelling?

5. By direct levelling, you can measure both the elevation of points and the differences in elevation between points, using a level and a levelling staff (see Chapter 5). There are two kinds of direct levelling:

6. In differential levelling , you find the difference in elevation of points which are some distance apart (see Section 8.1). In the simplest kind of direct levelling, you would survey only two points A and B from one central station LS. But you may need to find the difference in elevation between:

7. In profile levelling , you find the elevations of points placed at short measured intervals along a known line, such as the centre-line of a water supply canal or the lengthwise axis of a valley. You find elevations for cross-sections with a similar kind of survey (see Section 8.2).

8. You can also use direct levelling to determine elevations for contour surveying (see Section 8.3), and for setting graded lines of slope(see Section 6.9), where you need to combine both differential levelling and profile levelling.

Differential levelling
72.GIF (11290 byte)

 
Profile levelling
72a.GIF (5321 byte)

9. There are several simple ways to determine the elevations of ground points and the differences in elevation between ground points. You will use a level and a levelling staff with these methods. In the following sections, each method is fully described to help you choose between them. Table 10 will also help you to compare the various methods and to select the one best suited to your needs in each type of situation you may encounter.

 TABLE 10
Direct levelling methods

Section
Type
Method
Suitability
Remarks
Differential levelling
Open traverse
Long, narrow stretch of land
Check for closing error
Differential levelling
Closed traverse
Perimeter of land area and base line for radiation
Check for closing error.
Combine with radiating
Differential levelling
Square-grid
Small area with little vegetation
Squares 10 to 20 m and 30 to 50 m
Differential levelling
Radiating
Large area with visibility
Combined with closed traverse
Longitudinal profile levelling
Open traverse
Non-sighting and sighting level
Check for closing error
Cross-section profile levelling
Radiating
Sighting level with visibility
 
Contouring
Direct
Detailed mapping of small area with a sighting or a non-sighting level and target levelling staff
Slow and accurate.
Progress uphill
Contouring
Square-grid
Small area with little vegetation Especially if perimeter has been surveyed. Small to medium scale mapping
Terrain, scale and accuracy depend on contour interval.
Progress uphill.
Suitable for plane-tabling
Contouring
Radiating
Small to medium scale mapping of large area
Fast and fairly inaccurate. Progress uphill.
Suitable for plane-tabling
Contouring
Cross-sections
Preliminary survey of a long and narrow stretch of land
Fast, fairly inaccurate. Progress uphill.
Suitable for plane-tabling

8.1 How to level by differential

What is differential levelling?

1. You can best understand differential levelling by first considering only two points, A and B , both of which you can see from one central levelling station, LS .

  • Sight with a level from LS at the levelling staff on point A. The point where the line of sight meets the levelling staff is point X. Measure AX. This is called a backsight (BS).
 
Find AX with a backsight
74.GIF (3779 byte)
     
  • Turn around and sight from LS at the levelling staff on point B. The point where the line of sight meets the levelling staff is point Y. Measure BY. This is called a foresight (FS).
 
Find BY with a foresight
 74a.GIF (5486 byte)
     
  • The difference in elevation between point A and point B equals BC or (AX- BY) or (backsight BS - foresight FS).
 
The difference in elevation between
points A and B equals AX minus BY

74b.GIF (5383 byte)
     
  • If you know the elevation of A, called E(A), you can calculate the elevation of B, called E(B), as BS -FS + E(A).
  • But BS + E(A) = HI, the height of the instrument or the elevation of the line of sight directed from the level.
 
75.GIF (9967 byte)
     
  • Therefore,

E(B) = HI - FS


(the elevation at point B being equal to the height of the levelling instrument, minus the foresight).
 
75_a.GIF (8892 byte)

What are backsights and foresights?

It is important for you to understand exactly what "backsight" and "foresight" are in direct levelling.

2. A backsight (BS) is a sight taken with the level to a point X of known elevation E(X), so that the height of the instrument HI can be found. A backsight in direct levelling is usually taken in a backward direction, but not always. Backsights are also called plus sights (+ S), because you must always add them to a known elevation to find HI.

HI = BS + E(X)

 
76.GIF (8366 byte)
     

3. A foresight FS is also a sight taken with the level, but it can be on any point Y of the sight line where you have to determine the elevation E(Y). You will usually take it in a forward direction, but not always. Foresights are also called minus sights (-S) , because they are always subtracted from HI to obtain the elevation E of the point. Remember:

E(Y) = HI- FS

 
76a.GIF (8355 byte)
     

Surveying two points with one turning point

4. Often you will not be able to see at the same time the two points you are surveying, or they might be far apart. In such cases, you will need to do a series of differential levellings . These are similar to the type explained above, except that you will use intermediate temporary points called turning points (TP).  
77.GIF (6189 byte)
     
5. You know the elevation of point A, E(A) = 100 m, and you want to find the elevation of point B, E(B), which is not visible from a central levelling station. Choose a turning point C about halfway between A and B. Then, set up the level at LS1, about halfway between A and C.  
78.GIF (4719 byte)
     
6. Measure a backsight on A (for example, BS = 1.89 m). Measure on C a foresight FS = 0.72 m. Calculate HI = BS + E(A) = 1.89 m + 100 m = 101.89 m. Find the elevation of turning point C as E(C) = HI-FS = 101.89 m - 0.72 m = 101.17 m.  
78a.GIF (7641 byte)
     
   
78b.GIF (8669 byte)

7. Move to a second levelling station, LS2, about halfway between C and B. Set up the level and measure BS = 1.96 m, and then FS = 0.87 m. Calculate HI = BS + E(C) = 1.96 m + 101.17 m = 103.13 m. 0btain E(B) = HI- FS = 103.13 m - 0.87 m = 102.26 m.

8. You can make the calculations more easily if you record the field measurements in a table , as shown in the example. You will not make any intermediate calculations. All BS's and all FS's must be added separately. The sum FS is subtracted from the sum BS to find the difference in elevation from point A to point B.

  • A positive difference means that B is at a higher elevation than A.
  • A negative difference means that B is at a lower elevation than A.
 
79.GIF (10500 byte)
     

Knowing the elevation of A, you can now easily calculate the elevation of B. In this case, E(B) = 100 m + 2.26 m = 102.26 m; this is the same as the result in step 7, which required more complicated calculations. This kind of calculation is called an arithmetic check.

Example
Table form for differential levelling with one turning point.

GR000931.JPG (16836 byte)

 
79_a.GIF (10744 byte)

Surveying two points using several turning points

9. Often you will need to use more than one turning point between a point of known elevation and another point of unknown elevation. To do this, you can use the procedure you have just learned, but you will need to record the field measurements in a table to make calculating the results easier.

10. Knowing the elevation of point A, you need to find the elevation of B. To do this, you need for example  five turning points , TP1 ... TP5, and six levelling stations, LS1 ... LS6.

Note : the turning points and the levelling stations do not have to be on a straight line, but try to place each levelling station about halfway between the two points you need to survey from it.

11. From each levelling station, measure a backsight (BS) and a foresight (FS) , except:

 

Example
Table form for differential levelling with several turning points.
79b.JPG (20725 byte)

Using step 8 as a guideline, enter all measurements in a table and calculate the results as shown in the example below. You will find that point B is 2.82 m higher than point A and, therefore, that its elevation is E(B) = 100 m + 2.82 m = 102.82 m.

12. Even if you are careful, you may still make mistakes when you make your arithmetic calculations from the table. To reduce this kind of error, add two additional columns to your table that will make checking your calculations easy. In these columns, enter the difference (BS- FS), either positive (+ ) or negative (-), between the measurements you took at each levelling station. For example, from LS1 you measure BS (A) = 1.50 m and FS (TP1) = 1.00 m. The difference 1.50 m- 1.00 m = 0.50 m is positive, and you enter it in the (+) column on the TP1 line.

The arithmetic sum of these differences should be equal to the calculated difference in elevation D(E) = +2.82 m. These columns will also help you to calculate the elevation of each turning point , and to check on the elevation of point B more carefully.

Example
Differential levelling with several turning points
81a.JPG (28718 byte)


Making topographical surveys by straight open traverses

13. By now, you have learned enough to make a topographical survey of two distant points by measuring the horizontal distance between them and the difference in their elevation.

When you survey a future fish-farm site, you will use a very similar method. You can then prepare a topographic map of the site (see Chapter 9), which will become a useful guide for designing the fish-farm.

14. This is a survey method using straight open traverses , that is, several intermediate stations along one straight line. You know for example the elevation of starting point A, E(A) = 63.55 m. You want to know the distance of point B from point A, and its elevation. Because of the type of terrain on which you are surveying, you cannot see point B from point A, and you need two turning points , TP1 and TP2 , for levelling. Measure horizontal distances as you move forward with the level, from point A toward point B; try to progress along a straight line. If you cannot, you will need to use the broken open traverse survey method, which involves measuring the azimuths of the traverse sections as you move forward and change direction (see step 17).

 
83.GIF (16537 byte)

15. Set out a table like the one in step 12, and add two columns to it for horizontal distances. Enter all your distance and height measurements in the main part of the table. Then, in the first additional column, record each partial distance you measure from one point to the next one. In the second column, note the cumulated distance , which is the distance calculated from the starting point A to the point where you are measuring. The last number in the second column will be total distance AB.

Example
Topographical survey of a straight open traverse by differential levelling
84b.JPG (25978 byte)

16. Conclusions . Point B is 1.55 m higher than A and its elevation is 65.10 m. It is 156.5 m distant from point A. The arithmetic check from the (BS- FS) differences agrees with the calculated difference in elevation.

Making topographical surveys by broken open traverses

17. Remember, that if you survey by broken open traverses (or zigzags), you will also have to measure the azimuth of each traverse section as you proceed, in addition to distances and elevations.  
84.GIF (3266 byte)
     

18. You need for example to survey open traverse ABCDE from known point A. You require four turning points, TP1, TP2, TP3 and TP4. You want to know:

  • the elevations of points B, C, D and E;
  • the horizontal distances between these points;
  • the position of each point in relation to the others, which will help you in mapping them.
 
84a.GIF (4426 byte)
     
84c.GIF (19995 byte)

Proceed with the differential levelling as described earlier, measuring foresights and backsights from each levelling station. Measure azimuths and horizontal distances as you progress from the known point A toward the end point E. All the azimuths of the turning points of a single line should be the same. This will help you check your work.  
86.GIF (5119 byte)
     
19. Make a table similar to the one shown in step 15, and add three extra columns to it for recording and checking the azimuth values. Enter all your measurements in this table. At the bottom of the table, make all the checks on the elevation calculations, as you have learned to do them in the preceding steps.  
86a.GIF (7739 byte)
     

Example

Topographical survey of a broken open traverse by differential levelling
86b.GIF (43177 byte)


Checking on levelling errors

20. Checking on the arithmetic calculations does not tell you how accurate your survey has been. To fully check on your accuracy, level in the opposite direction , from the final point to the starting point, using the same procedure as before. You will probably find that the elevation of point A you obtain from this second levelling differs from the known elevation. This difference is the closing error .    
88.GIF (5987 byte)
     

Example

From point A of a known elevation, survey by traversing through five turning points, TP1 ... TP5, and find the elevation of point B. To check on the levelling error, survey by traversing BA through four other turning points, TP6 ... TP9; then calculate the elevation of A. If the known elevation of starting point A is 153 m, and the calculated elevation of A at the end of the survey is 153.2 m, the closing error is 153.2 m - 153 m = 0.2 m.

 
88b.GIF (4522 byte)
     
   
88a.GIF (4749 byte)

21. The closing error must be less than the permissible error, which is the limit of error you can have in a survey for it to be considered accurate. The size of the permissible error depends on the type of survey (reconnaissance, preliminary, detailed, etc.) and on the total distance travelled during the survey. To help you find out how accurate your survey has been, calculate the maximum permissible error (MPE) expressed in centimetres , as follows:

Reconnaissance and preliminary surveys:
MPE(cm) = 10D

Most engineering work:
MPE(cm) = 2.5D


where D is the distance surveyed, expressed in kilometres .

Example

You have just finished a reconnaissance survey. Your closing error was 0.2 m or 20 cm, at the closure of a traverse 2.5 km + 1.8 km = 4.3 km long. In this case, the maximum permissible error (in centimetres) equals 104.3 = 10 x 2.07 = 20.7 cm. Since your closing error is smaller than the MPE, your levelling measurements have been accurate enough for the purposes of a reconnaissance survey.

Making topographical surveys by closed traverses  

22. In the previous section, you made a topographical survey along an open traverse joining points A and B. You can survey a closed traverse , such as the perimeter of a fish-farm site, in a similar way. You should use each perimeter summit A, B, C, D, E and F of the polygon as a survey point, and plot turning points between these summits as you need to. Make a plan survey as explained in Section 7.1, and use differential levelling to find the elevation of each perimeter point.

23. If you do not know the exact elevation of starting point A, you can assume its elevation, for example E (A) = 100 m. Start the survey at point A , and proceed clockwise along the perimeter of the area. Take levelling staff readings at TP1, TP2, B, TP3, etc., until you reach starting point A again and close the traverse. At the same time, make any necessary horizontal distance and azimuth measurements. Record your measurements either in two separate tables , one for plan surveying and one for levelling, or in one table which includes distance measurements. From the (BS-FS) columns, you can easily find the elevation of each point on the basis of the known (or assumed) elevation at point A. Make all the checks on the calculations as shown in steps 15 and 16. Find the closing levelling error at point A (see step 20). This error should not be greater than the maximum permissible error (see step 21).

 
90a.GIF (7675 byte)
     

Example

Topographical survey of a closed traverse by differential levelling
90b.JPG (22227 byte)

   

 Making topographical surveys by the square grid

   

24. The square-grid method is particularly useful for surveying small land areas with little vegetation. In large areas with high vegetation or forests, the method is not as easy or practical. To use the method, you will lay out squares in the area you are surveying, and determine the elevation of each square corner.

25. The size of the squares you lay out depends on the accuracy you need. For greater accuracy, the sides of the squares should be 10 to 20 m long. For reconnaissance surveys, where you do not need to be as accurate, the sides of the squares can be 30 to 50 m long.

 
91.GIF (10395 byte)
     
26. In the field choose base line AA and clearly mark it with ranging poles. This base line should preferably be located at the centre of the site, and it should be parallel to the longest side of the site. When you work with a compass, you may find that it helps to orient this base line following the north-south direction.

27. Working uphill, chain along this baseline from the perimeter of the area, and set stakes at intervals equal to the size you have chosen for the squares, such as 20 m. Clearly number these stakes 1, 2, 3, . . . n.

 
92.GIF (8596 byte)
     
28. From each of these stakes, lay out a line, perpendicular to the base line , that runs all the way across the site.  
92_a.GIF (19821 byte)

29. Proceed by chaining along the entire length of each of these perpendiculars, on either side of the base line . Set a stake every 20 m (the selected square size). Identify each of these stakes by:
  • a letter (A, B, C, etc.) which refers to the line, running parallel to the base line, to which the point belongs;
  • a number (1, 2, 3.... n) which refers to the perpendicular, laid out from the base line, to which the point belongs.

Example

20 m from point A1, perpendicular 2 crosses line AA at point A2.
20 m to the left of point A2 lies point B2 , on line BB.

 
93.GIF (24061 byte)
     

30. Now that you have laid out the square grid on the ground, you need to find the elevation of each corner of the squares , which you have marked with stakes. First establish a bench-mark (BM) on base line AA near the boundary of the area and preferably in the part with the lowest elevation (see steps 42-44). This bench-mark can be either at a known elevation (such as one point on a previously surveyed traverse), or at an assumed elevation (such as 100 m) (see step 45).

31. You will level the square grid points in two stages.

  • Starting from the bench-mark, measure the differences in elevation for all the base points A1, A2, A3, ... An. This is called longitudinal profile levelling (see Section 8.2).
  • Then, starting at these base-line points with known elevations, measure the differences in elevation for all points of each of the perpendiculars, on each side of the base line (for example, B2, C2 and D2 followed by E2, F2 and G2). This is called cross-section levelling (see Section 8.2).
 
94.GIF (12470 byte)
     
32. If you use a sighting level you can make a radiating survey (see step 34). Set up your level at LS1 and take a backsight reading on the bench-mark (BM). Then, take foresight readings on as many base-line points as possible. From this, find the height of the instrument (HI) and point elevations, with HI = E(BM) + BS and E (point) = HI- FS. When necessary, change the levelling station and find a new HI on the last known point, which is used as a turning point. Then measure a series of foresights. Since the distances of the square grid are all fixed, you do not need to measure them any more. Note down your measurements in a table, as shown in the example.  
95.GIF (10217 byte)
     

Example

Topographical survey by square grid with a sighting level

Levelling station
Point
BS
HI
FS
Elevation

Remarks

1
BM
1.53
101.53
-
100.00
Assumed elevation
 
A1
-
101.53
1.25
100.28
 
 
A2
-
101.53
1.20
100.33
 
 
A3
-
101.53
1.15
100.38
 
2
A3
1.48
101.86
-
100.38
Turning point
 
A4
-
101.86
1.41
100.45
 
 
...
...
...
...
...
 
 
A9
...
...
...
...
 
5
A1
1.20
101.48
-
100.28
Known from A1 above
 
B1
-
101.48
0.23
100.25
 
 
C1
-
101.48
0.25
100.23
 
 
D1
-
101.48
0.28
100.20
 
6
D1
1.30
101.50
-
100.20
Turning point
 
E1
-
101.50
0.35
100.15
 
 
...
...
...
...
...
 
 
G1
-
101.50
0.47
100.03
 
9
A2
1.35
101.68
-
100.33
Known from A2 above
 
B2
...
...
-
...
 
 
...
...
...
...
...
 
12
F2
...
...
-
...
 
 
G2
...
...
-
...
 
13
A3
...
...
-
100.38

Known from A3 above

 
...
...
...
...
...
 
 

Example

Topographical survey by square-grid with a non-sighting level
95a.JPG (23533 byte)


33. If you use a non-sighting level , first follow base line AA. Start with the bench-mark as a reference point, and survey all its points A1, A2, ... A9. Then, repeat this surveying procedure along each of the perpendiculars, starting with the known base-line points as the reference points.

Enter all your measurements in a table, and find the elevation of each point of the square grid (see steps 38-41 for a further explanation).

You can check calculations and survey measurements at the bottom part of the table (see this Section, step 41).

 
97.GIF (18723 byte)

  Making topographical radiating surveys

34. When you make a radiating survey (see Section 7.2), you first need to determine the height of the instrument HI at levelling station 0. Sight at a point X of known elevation E(X), and find a backsight (BS). Then,

HI = BS + E(X)


35. Then you need to find the elevation of each of the points A, B, C and D. Sight at each of them in turn. You will find a foresight (FS) for each. Calculate their elevations as

E (point) = HI - FS


36. Record all your measurements in a table. This table may also include plan-surveying information, such as azimuths and horizontal distances. You might also use two different tables as explained in step 23. The first line of the table will refer to the known point X . This point can be one of the perimeter points which you have already determined, or it can be a benchmark (see step 42). You find the position of point 0 from the azimuth of line OX and the horizontal distance OX.

 
Use X as a point of reference
99.GIF (7909 byte)
     
GR100.GIF (9714 byte)
     

Example

Topographical radiating survey

Levelling station
Point
BS (m)
HI (m)
FS (m)
Elevation (m)
Azimuth (degree)
Distance (m)
Remarks
0
X
0.45
144.00
-
143.55
285
35.3
Known elevation
0
A
-
144.00
1.65
142.35
50
29.6
 
0
B
-
144.00
0.97
143.03
131
27.3
 
0
C
-
144.00
0.60
143.40
193
25.1
 
0
D
-
144.00
1.12
142.88
266
24.8
 

Combining traversing and composite radiating

37. This method combines radiating with a closed traverse. You can use it to gather the information you need to make a topographical map of a land area such as a fish- farm site (see Chapter 9). Using what you have learned so far about surveying, do the following:

(a) With a closed traverse, plan survey the boundaries of the area ABCDEA. Find the lengths and directions of all of its sides (see Section 7.1).
 
Fix the position of LS 1
102a.GIF (7481 byte)
     
(b) In the interior of the site, choose a series of levelling stations 1, 2, 3.... 6, from which you can survey the surrounding area by radiating.  
Choose levelling stations
 102b.GIF (2633 byte)
     
(c) Fix the position of levelling station 1 by measuring it in relation to known boundary points such as A and B. You can use the plane-tabling and triangulation methods (see Section  9.2).  
Survey the boundaries
102.GIF (5951 byte)

(d) Join all the selected levelling stations by straight lines to form a closed traverse . Survey it, using turning points as necessary, to fix the position of each station and to determine its elevation . Check for the closing error (see Section 7.1) and this section, step 20).  
Survey all the levelling stations
103.GIF (7262 byte)
     

(e) Now you are ready to start the detailed topographical survey, proceeding from each known levelling station in turn. From station 1, set up a series of radiating straight lines at a fixed-angle interval (such as 20). This means that each radiating line will be 20 from the next. Use your magnetic compass and ranging poles or stakes. Mark on the ground the north-south line. You will call this the zero-degree line . Standing on this line at station 1, measure and mark a line with a 20 azimuth. Then, moving around in a clockwise direction on the same point, measure and mark in turn lines with azimuth 40, 60, ... 340.

Note: the fixed-angle interval you use depends on how accurate a survey you need. Smaller angles will help you make a more accurate map of the site.

 
Mark radiating lines at the interval you have chosen
103a.GIF (22291 byte)
     
(f) Start at Station 1, using differential levelling , to survey ground points on each of these radiating lines. You may choose any points you want to measure, for example the intersection of the radiating line with the boundary of the site, or a point where the ground changes slope suddenly, or the location of a rock or tree. Besides finding the elevation of these points, measure the distance between each point and the levelling station, so that you will be able to map them later on.  
104.GIF (7470 byte)
     
(g) Move to each levelling station in turn (2, 3, 4, 5, 6), and repeat steps (e) and (f), measuring the elevation and distance of unknown random points along the radiating lines -, so as to survey the whole area.  
104a.GIF (7351 byte)
     

(h) Record all the measurements in a table, and calculate the elevations of all the surveyed points (see this section, step 36). You will need two additional columns in this table:

  • one column marked "Line" , where you will record the azimuth of each line;
 
105.GIF (6484 byte)
     
  • one column marked "Cumulative distances" . In this space, you can separately calculate the distance from the levelling station to the points surveyed for each line.
 
105a.GIF (6455 byte)
     

Example

Topographical survey of partial area by composite radiating


Making topographical surveys with non-sighting levels

38. You can also make topographical surveys along straight lines by using non-sighting levels , such as the line level (see Section 5.2) or the flexible-tube water level (see Section 5.3). You have already learned how to measure height differences by using the square-grid method with such levels (see this section, step 33).

Remember , when you lay out your grid, that the distance between points cannot be more than the length of your level.

 
107.GIF (19963 byte)
     
39. Work in a team of two or three with this method. Both the rear person and the front person will take measurements in the field, but only one person should be responsible for noting down these measurements in the field book.  

107a.GIF (15030 byte)

 

Example

Topographical survey with a line level (20 m)
107b.GIF (11716 byte)

40. Record the measurements in a table for each levelled section. You will be measuring horizontal distances from one point to the next, and differences in elevation between one point and the next. At both the starting point and the last point, there is only one height measurement. The rear person will measure it on the starting point, and the front person will measure it on the last point.

41. Find the cumulated distances from the starting point and the elevations of each point, as shown in the example. There are three possible checks , which you make at the bottom part of the table.

Making bench-marks for topographical surveys

42. As you have just learned, you will always start differential levelling surveys by measuring a height on a ground point of known or assumed elevation . This point becomes a bench-mark (BM) . The elevation of this bench-mark will form the basis for finding the elevation of the other points you need to survey in the area.

43. A bench-mark should be permanent . You should always establish at least one bench-mark near the construction site of a fish-farm to act as a fixed reference point or object. You may also use a bench-mark as a turning point during topographical surveys.

44. A bench-mark should be a very well-defined point . You should be able to find and recognize it easily. It should be easy to reach, so that you can hold a levelling staff on it. You can establish a bench-mark:

Note : it is best to paint the bench-mark, or set several signs near it, to show its location.

110.GIF (2831 byte)
 
110a.GIF (7209 byte)
     
110b.GIF (5007 byte)
 
110c.GIF (6720 byte)
     
45. Generally, the elevation of a bench-mark E(BM) is not known but is assumed . When you have established the first bench-mark for a building project, you give it an elevation that is a convenient whole number , such as 100 m. The number you choose should be large enough to prevent any point in the surveyed area from having a negative elevation.

Note : you have seen in previous examples that some surveys are related to previously surveyed points, This means that the measurements in the survey are based on these points. These points then become turning-point bench-marks . You find their elevations by levelling, and these then become known elevations.

 
111.GIF (6501 byte)

8.2 How to level by profile

What is the purpose of profile levelling?

1. The purpose of profile levelling is to determine the changes in the elevation of the ground surface along a definite line . (You have already learned about profile levelling used with the square-grid method in Section 8.1, step 31.) This definite line AB might be the centre-line of a water-supply canal, a drainage ditch, a reservoir dam, or a pond dike. This line might also be the path of a river bed through a valley, where you are looking for a dam site, or it might be one of several lines, perpendicular to a river bed, which you lay out across a valley when you are surveying for a suitable fish-farm site.  

Ground line AB
 112.GIF (15896 byte)

     
2. You will usually transfer the measurements you obtain during profile levelling onto paper, to make a kind of diagram or picture called a graph . This will show changes in elevation, and how they are related to horizontal distances. This kind of graph is called a ground profile. You will learn how to make one in Sections 9.5 and 9.6.  
Profile AB
112a.GIF (11882 byte)

  What does profile levelling consist of?

3. When you profile level, you are determining a series of elevations of points which are located at short measured intervals along a fixed line . These elevations determine the profile of the line.

4. There are two kinds of profiles which are commonly used in fish culture: longitudinal and cross-section profiles.

 
113.GIF (19966 byte)
     
  • You usually survey cross-section profiles along a line which is perpendicular to a surveyed longitudinal profile, using its points of known elevation as bench-marks. Cross-sections of valleys are useful in helping you locate a good fish-farm site. On a smaller scale, you can also survey cross-sections for water-supply canals, for dam construction, and for pond construction. You have already learned how to use cross-section profiles when surveying by the square-grid method (see Section 8.1, step 31).
 
113a.GIF (20314 byte)

Longitudinal profile levelling by radiating

5. You need to survey line AB, the centre-line of a water canal. You decide to make a radiating survey using a sighting level. Measure horizontal distances and mark every 25 m of the line with a stake, from its initial to its final point. Add points between the stakes where there are marked changes of slope . On each stake, clearly indicate its distance from the initial point A, that is, the cumulated distance.  
Mark out the line
114.GIF (4204 byte)
     

6. Set up your level at LS1. Take a backsight BS on a bench-mark of elevation E(BM) to determine the height of the instrument

HI = BS + E(BM)

 
Determine HI at LS 1
114a.GIF (4432 byte)
     
7. From levelling station LS1, read foresights FS on as many points (for example, six) of line AB as possible, starting from the initial point A.  
Take foresights at the points you have marked
114b.GIF (7695 byte)

8. When you need to move the level to a new station so that you can take readings on the points ahead:

  • first, choose a turning point TP and take a foresight FS to find its elevation from LS1;
  • move to the next levelling station LS2, from which you can see the turning point TP;
  • take a backsight BS on this turning point to find the new height of the instrument HI.
 
Take a foresight from LS 1 to the turning point
115.GIF (6194 byte)
     
9. Read foresights FS on as many points as possible until you reach the end point of AB. If necessary, use another turning point and a new levelling station as described in step 8.  
Take a backsight from LS 2 to the turning point
115a.GIF (6746 byte)
     
10. Note down all your measurements in a field book, using a table similar to the ones you have used with other methods. Find the elevations of the points (except for the turning point) by subtracting each FS from its corresponding HI. In the example of the table shown here, cumulated horizontal distances (in metres) appear as point numbers 00, 25, 50, 65, etc. in the first column.  

Take foresights at the points you have marked
115b.GIF (10272 byte)

     

Example

Longitudinal profile levelling with a sighting level in a radiating survey

Points(m)
BS
HI
FS
Elevation(m)
Remarks
BM
1.37
2.87
-
1.50
Nail at foot of tree stump
00
-
2.87
1.53
1.34
Beginning of canal
25
-
2.87
1.67
1.20
 
50
-
2.87
1.73
1.14
 
65
-
2.87
1.90
0.97
Marked change of slope
75
-
2.87
2.05
0.82
 
100
-
2.87
2.22
0.65
 
TP
1.80
3.07
1.60
1.27
On stone
125
-
3.07
2.27
0.80
 
150
-
3.07
2.37
0.70
 
175
-
3.07
2.57
0.50
 
200
-
3.07
2.77
0.30
 
230
-
3.07
3.00
0.07
End of canal

Longitudinal profile levelling by traversing

11. You need to survey the same line AB, the centre-line of a water canal, for profile levelling. You will use a non-sighting level, such as the flexible tube water level (see Section 5.3). Since you are using this kind of level, you will survey by traversing. Mark the line AB with stakes driven into the ground at regular intervals. The length of these intervals depends on the working length of your level (in this case, 10 m). Where there are marked changes in slope, add intermediate stakes. On each stake, mark its distance from the initial point A.

12. Level a tie-in line between bench-mark BM and the initial point A (see Section 5.3, steps 6-12). This will give you the elevation of point A, through intermediate point 1.

 
Mark the line at 10-m intervals
117.GIF (4965 byte)
     

13. Proceed with the levelling of the marked points along the line, using this method. At each point, you will make two scale readings, one rear and one forward, except at the final point where you will take only one height measurement.

14. One person should be responsible for recording the measurements in a field book, using a table similar to the one in Section 8.1, step 41. But, in this case, you will not need to enter the distances in the table, since they identify the surveyed points. Checks are made at the bottom of the table as usual. Remember that in this type of survey there is no need for turning points.

 
Level a tie-in from the bench-mark,
then level the points on the line

117a.GIF (4417 byte)
     

Example

Longitudinal profile levelling by traversing with a flexible tube water level (10 m)
118.GIF (28712 byte)


Cross-section profile levelling

15. After you have found the elevations of points along a longitudinal profile, you can proceed with the survey of perpendicular cross-sections . These cross-sections can pass through as many of the points as necessary. Cross-sections are commonly used for contouring long, narrow stretches of land (see Section 8.3).

16. You will need to have more information on some of the longitudinal profile points. Choose these points and mark them. Then, set out and mark perpendicular lines at these points (see Section 3.6), and extend these perpendiculars on both sides of the traverse as far as you need to. In this type of levelling, such perpendiculars are called the cross-section lines .

 
119.GIF (14998 byte)
     
Note : at points where the traverse changes direction (for example, at point 175 in the drawing), you should set out two perpendicular lines E and F; each line will be perpendicular to one of the traverse sections.  
At a turn, make two cross-sections
119a.GIF (5010 byte)
     

17. Choose and clearly mark the points you want to survey on each cross-section line. In this case, these points do not have to be regularly spaced. Rather, they should be at places where the terrain changes since they should mark changes in slope.

18. As you know the elevations of the traverse points from a previous survey, you may treat these points as bench-marks. Proceed with the profile levelling of selected points along the cross-section lines as explained earlier. You may survey them:

Note : you can also survey by traversing using a simple sighting level such as a bamboo sighting level (see Section 5.6) or a hand level (see Section 5.7).

 
120.GIF (4135 byte)

19. Your field notes will be similar to those shown in either step 10 or 14, depending on the levelling method you use. You will identify the points differently, however. You identify each cross-section line by the number of the traverse point of known elevation. To do this, identify the surveyed points along each cross-section line according to whether they are to the left or the right of the traverse . Also use their distance (in metres) from the traverse points as identification. The following example is of field notes and calculations for a radiating survey, where each cross-section was surveyed from a single levelling station.

Example

Cross-section profile levelling by radiating

Traverse Point

Point

BS(m)
HI(m)
FS(m)
Elevation(m)
Remarks
 
Left
Right
         
50
...
...
...
...
...
...
 
75
-
-
0.54
40.94
-
40.40
Edge of existing path
 
10
-
 
40.94
1.09
39.85
 
 
18
-
 
40.94
1.15
39.79
 
 
-
9
 
40.94
0.85
40.09
 
 
-
16
 
40.94
0.68
40.26
 
100
-
-
1.15
38.96
-
37.81
Edge of maize field
 
8
-
 
38.96
1.23
37.73
 
 
-
4
 
38.96
1.11
37.85
 
 
-
16
 
38.96
0.78
38.18
 
125
-
-
0.97
36.64
-
35.67
Edge of small forest
 
5
-
 
36.64
1.12
35.52
 
 
20
-
 
36.64
1.55
35.09
 
 
-
14
 
36.64
1.03
35.61
 
   
25
 
36.64
0.89
35.75
 
150
...
...
...
...
...
...
 

8.3 How to contour

What is a contour?

1. A contour is an imaginary continuous line or curve which joins ground points of an equal elevation. The elevation of the ground points must be measured from the same reference plane*.  
122.GIF (6855 byte)
     

Example

When you pour water into a hole in the ground, you will see that the surface of the water forms a continuous line made up of the water's points of contact with the sides of the hole. This line shows one contour for this particular water depth in the hole. A lake or a reservoir also has a surface contour which depends on its water level.

 
122a.GIF (10028 byte)
     
 

What is contouring?

2. Contouring means surveying to identify the contours on the ground, lay them out with markers, and plot them on a plan or map. You will learn more about planning and mapping contours in Section 9.4.

 
122b.GIF (8698 byte)

3. Contouring is used in fish culture to solve two kinds of problem:

  • if you have fixed the location of a point, you may have to identify the contour passing through that point;

Example

You have chosen the end-point of your water-supply canal on a fish-farm site. Now you have to identify the canal's centre-line, which usually follows a contour back to the water source (which may be a point along a river, or the outlet pipe of a pump).

 
123.GIF (14301 byte)
     
  • If you need to prepare a plan or map showing the ground relief of an area, you must find out the location of contours on the ground and be able to transfer them onto paper.

Example

You have chosen a fish-farm site. Before you can plan, design and build the farm, you will need to make a topographical map showing the location of a series of contours from which you will be able to define the ground relief of the site.

 
123a.GIF (11112 byte)
     

4. You have already learned how to find a contour on the ground from a fixed point, in the sections on contouring devices (see Sections 6.2-6.8).

5. In the following steps, you will learn how to survey contours over a land area so that you can prepare a topographical map (see Section 9.4).

 
124.GIF (13773 byte)
     

What are the main methods for contouring?

6. It would be an impossible task to identify all the contours in one area. Therefore, you will have to decide how many contours you need to identity in each area. You will have to fix the difference in elevation between contours which are next to each other. This is called the contour interval .

7. Choosing which contour interval to use depends mainly on the accuracy you need, on the scale of the map you will prepare (see Section 9.1) and on the kind of terrain you are surveying. Contour intervals usually vary from 0.25 m to 1 m . This range of intervals allows good accuracy, and makes it possible to produce large-scale topographical maps for flat or slightly sloping ground (which is usually the type of ground used for fish-culture sites). Since smaller contour intervals make contouring much more difficult, you will usually make reconnaissance and preliminary surveys with a contour interval greater than the one you use for later, more detailed surveys.

 
124_a.GIF (23205 byte)
     

Example

Relationship between the size of contour intervals and various factors

Factor

Contour intervals
Smaller
Larger
Required accuracy
High
Low
Mapping scale (Section 9.1)
Large-scale
Small-scale
Type of terrain
Flat
Sloping
 
124a.GIF (5860 byte)
     

8. There are two main methods of surveying contours:

  • a direct method; in which you trace and mark the line of each contour on the ground, and then plan survey these lines so that they can be mapped,
  • an indirect method; in which you make a topographical survey of the area to find a series of points of known elevation. Then you enter them on a map and determine the contours from this map.
 
Direct contouring
125.GIF (8238 byte)
     

Selecting the contouring method

   

9. When selecting the method you will use for contouring, remember that:

  • the direct method is much slower, but is more accurate. Use it only to contour a relatively small area which you need to map in detail, on a large scale;
  • the indirect method is faster, but it is not so accurate. Use it to contour large areas that you will map on a medium or small scale. It should preferably be combined with plane-tabling (see Section 7.5).
 
Indirect contouring
125a.GIF (16172 byte)

Laying out contours on the ground with a sighting level

You will now learn the direct method of contouring which will enable you to lay out a number of points on the ground which have exactly the same elevation.

10. Start your contouring survey of site ABCDEA at a point of known elevation, such as an existing bench- mark BM . If there is no such point of known elevation in the area, you can establish one:

  • either by differential levelling from a bench-mark outside the area to a point within the area;
  • or by assuming a convenient elevation for your bench-mark (such as 100 m) so that you will not have points with negative elevation later.

Note : try to establish this bench-mark in the middle of the lowest ground of the area, so that you can survey uphill.

 
Establish a bench-mark in the lowest part of the site
126.GIF (7178 byte)
     

11. Through this bench-mark BM at point F, lay out and mark a straight line FG . Make sure you follow the direction of the greatest ground slope . The line should cross the entire site.

12. At regular intervals, set out a series of lines parallel to FG. To choose the interval between parallels, use:

  • 10 m or less , if the contour interval is to be 0.25 to 0.50 m;
  • 25 to 30 m , if the contour interval is to be 1 to 1.5 m;
  • 50 m , if the terrain has a very gentle or regular slope.
 
Lay out line FG from the bench-mark,
and parallel lines at regular intervals

127.GIF (14763 byte)
     
13. If you know the elevation E(BM) of the benchmark BM from a previous survey, first find the point on the line with an elevation that corresponds to a multiple of the contour interval you have selected. You can use a sighting level together with a target levelling staff.The method will enable you to set the target on the staff in the right position for identifying the first contour on the ground.  
Take a backsight at the bench-mark and
calculate the nearest contour line

128.GIF (9044 byte)
     

Example

  • BM is at elevation 59.36 m.
  • With a sighting level set up at LS1 and a levelling staff held on BM, read BS = 3.23 m.
  • Choose the contour interval, for example Cl = 0.25 m.
  • Calculate the multiple of Cl (= nCl) closest to E(BM) = 59.36 m as follows:
    (a) E(BM) Cl = 59.36 m 0.25 m = 237.44 ... or the round number n = 238;
    (b) n x Cl = 238 x 0.25 m = 59.50 m.
  • The difference between E(BM) and n(Cl) equals 59.50 m - 59.36 m = 0.14 m.
  • Set the target on a target levelling staff at the height of BS minus this difference or
    3.23 m - 0.14 m = 3.09 m.
  • Find the position of the first contour at the elevation 59.50 m.
 
Set the target at E (BM) - n (Cl)
below the line of sight

128a.GIF (5474 byte)
     
   
When the target is in the line of sight,
you have found a point on the first countour line

128b.GIF (6102 byte)

14. You will need an assistant for this method. At LS1, the point from which you can survey as many surrounding points as possible, set up the level. Holding the adjusted target levelling staff , your assistant walks slowly uphill from the bench-mark along the central line FG . Sight with the level at the target, and signal to your assistant to stop when the sighting line lines up with the target line. The ground point X where the levelling staff stands should be at elevation 59.50 m. This is the first point of the 59.50 m contour. Direct your assistant to mark this point with a stake. Remember also to indicate clearly the elevation of the point on the stake.  
Mark the point
129.GIF (8971 byte)
     
15. Your assistant then moves with the levelling staff to another parallel line, where you determine and mark a second point Y at elevation 59.50 m in the same way. This procedure is repeated on all the parallel lines, until you have marked contour 59.50 m completely on the ground across the site.  
Survey other points on the same contour
129a.GIF (11340 byte)
     

16. To determine the next contour, you must change the position of the target on the staff. As you are moving uphill , using a selected contour interval of 0.25 m, you will lower the target by 0.25 m to a height of 3.09 m - 0.25 m = 2.84 m. In this position, the target will show the ground points at elevation 59.50 m + 0.25 m = 59.75 m, if you continue surveying from the same levelling station LS1 .

 
Lower the target by the chosen interval
130.GIF (4106 byte)
     

17. From LS1, find all the points on the parallel lines at elevation 59.75 m, and mark a second contour on the ground. Again lower the target by 0.25 m to the height of 2.84 m - 0.25 m = 2.59 m to determine points at the next elevation of 60 m.

 
Survey the next contour
130a.GIF (11216 byte)
     

18. If you need to change the levelling station but continue to survey the same contour:

  • ask your assistant to hold the levelling staff on one of the points of that contour;
  • move the level to a new, more convenient levelling station;
  • tell your assistant to adjust the target height until it lines up with the line of sight of the level;
  • continue to survey the same contour.
 
To continue on the same contour, move the level,
then adjust the target

131.GIF (5878 byte)
     

19. If you need to change the levelling station at the same time you are ready to determine another contour:

  • ask your assistant to keep the levelling staff on a point of the last surveyed contour;
  • move the level to its new station; adjust the target height to the new line of sight;
  • change this target height to determine the new contour (by lowering it 0.25 m, for example, see step 16).
 
For a new contour, set the target lower than
the line of sight and...

131a.GIF (5634 byte)
     
   

...Find the new contour
131b.GIF (5658 byte)

20. When you have determined the various contours at their intersection with each parallel line, you will have to measure the horizontal distances between all the marked points. To do this, you can chain along the parallel lines starting from the area boundaries (see Section 2.6). These measurements will help you to prepare a topographical map of the area (see Section 9.4).

Measure the horizontal distance between the points
132.GIF (22059 byte)

Laying out contours with a non-sighting level

21. When you use a non-sighting level (such as a line level or an A-frame level) to lay out contours over an area of land, you first need to establish a bench-mark BM near the boundary of the area. As usual, this bench-mark may be either of known elevation or of assumed elevation. It should also be located in the part of the area with the lowest elevation (see Section 8.1, steps 42-44).

22. Set out a line FC through BM , and set out lines parallel to it at a selected distance, as described in steps 11- 12 above.

Example

Selected distance between parallels = 10 m.

 

Set out a line through the bench-mark,
and parallels at regular intervals

133.GIF (12544 byte)

     

23. If you are using a bench-mark with a known elevation , proceed as shown above in step 13 to calculate the elevation of the first contour you will survey near the bench-mark. Also calculate the difference between the elevation of this first contour and the elevation of the bench-mark.

Example

  • BM elevation E(BM) = 127,85 m
  • Selected contour interval = 0.50 m
  • Multiple of E(BM): 127.85 m 0.50 m = 255.7 and therefore you choose n = 256
  • First contour will be at elevation 256 x 0.50 m = 128 m
  • Difference in elevation between E(contour) and E(BM): 128 m - 127.85 = 0.15 m.
 
Calculate the nearest contour line
134.GIF (3338 byte)
     

24. Then, next to the bench-mark , place some objects (such as bricks, stones, wooden planks, a tin or a box) that will provide the elevation calculated for the first contour.

 
Find the difference in height
134a.GIF (6047 byte)
     

Example

Next to BM, place some bricks and adjust their top height at 0.15 m higher than E(BM), using a straight-edge and a mason's level (see Section 5.1). The top of these bricks will be at the 128 m elevation.

 
Use bricks to make up the height difference at BM
134b.GIF (5766 byte)
     

25. Find a ground point X which is near BM, is located on the line CF passing through BM, and has the same elevation as the objects piled near BM. To do this, use one of the methods described earlier (see Sections 5.1, 6.2-6.4 and 6.6). This ground point X is the first point of the contour 128 m.

Example

Using a straight-edge level, transfer the level 128 m from the top of the bricks to a ground point X on the line CF passing through BM.

 
Finding the contour from a known bench-mark
135.GIF (7583 byte)
     

26. If you are using a bench-mark with an assumed elevation , and are working uphill, determine the point X of the line passing through BM in the same way. The elevation of this point will equal assumed E(BM) plus the contour interval Cl.

Example

  • If E(BM) = 100 m and Cl = 0.50 m, pile bricks 0.50 m high at BM.
  • Locate nearby point X where E(X) = 100 m + 0.50 m = 100.50 m.
 
Finding the contour from an assumed bench-mark
135a.GIF (8307 byte)

27. Start contouring from point X using one of the methods described in Chapter 6. With a stake , mark each point where the contour you are following intersects with one of the parallel lines . On each stake, clearly indicate the elevation of the ground point.

28. Each time you finish laying out a contour, determine the first point Z, of the next contour by using a method like the one described in step 24. At known point X, where the last contour line crosses central line CF, place objects with a total height equal to the contour interval . Transfer this new level horizontally along line CF to point Z on the next contour. If the contour interval is large, you may have to use intermediate points to do this in stages.

 
Mark the intersections of the contour and the parallels
136.GIF (7605 byte)
     

Example

  • Cl = 0.50 m.
  • Transfer first E(contour) by + 0.25 m, from X to Y.
  • Repeat again from Y to Z, to total + 0.50 m = 2 x 0.25 m.

29. When you have laid out all the contours on the ground with stakes, measure, from stake to stake, the horizontal distances along the parallel lines. This will help you to prepare a topographical map (see Section 9.4).

 
Transfer the elevation of the contour Interval
136a.GIF (5847 byte)
     
   
Measure the horizontal distances between the points
136b.GIF (12038 byte)
     

Contouring by the indirect method

30. You can also contour by the indirect method . In this method, you make a topographical survey of the area, using a definite pattern, such as..

  • a square grid to determine elevations for points located at the intersections of a grid made of square or rectangular blocks;
  • radiating to determine elevations for random points located on lines which radiate at a selected angle interval from a known point;
  • cross-sections to determine elevations for points located on short lines laid out at right angles to a surveyed base line.
 
Square grid
137.GIF (5195 byte)
     

31. You learned earlier that the square-grid pattern is commonly used to contour relatively small areas, particularly if their perimeters have already been surveyed (see Section 8.1, steps 24-33).

32. You also learned about the radiating pattern , which is particularly useful for large areas (see Section 8.1, steps 34-36).

 
Radiation
137a.GIF (4969 byte)
     
33. Finally, you learned about cross-sections. These are commonly used in preliminary surveys, where you need a contoured plan of a long narrow stretch of land to select the best possible route for your purpose. You lay out lines about 30 to 100 m apart and about 50 to 100 m long on either side of a main compass traverse, and at right angles to it. Then you can find elevations of points along these cross-sections (see Section 8.2, steps 15- 19).  

Cross-sections
137b.GIF (3478 byte)