FIJI NATIONAL UNIVERSITY
TDA1 Trimester 2 2011
AEG 511 – Surveying, Structure & Processing
DIFFERENTIAL AND PROFILE LEVELING
Surveying is used for two specific purposes:
1. Planning - In which a site is surveyed to provide the information needed to develop the maps, charts, and
drawings necessary to lay out buildings, roads, drains, etc,
2. Layout - Where surveying is used to establish the boundaries, lines, and elevation for the construction of
Importance of Leveling in surveying:
One of several procedures of surveying and it is the process of determining the elevation of points such as
the ground, the tops of stake, or parts of building.
It ranks next to the measurement of distance in importance as a surveying technique.
Bench Mark (BM) - is a permanent object whose elevation above sea level is known or assumed to be known.
It is the reference point for all of the elevations for a survey.
It is important to select an object for a bench mark that will not be disturbed.
If the bench mark elevation is accidentally changed, all surveys that used it must be redone.
The U.S. Geological Survey (USGS) has established a nationwide network of bench marks in the US, all
referenced to mean sea level.
When using a local bench mark, the survey crew must select and establish its location.
Two rules should be followed. The object selected should :
1. Be reasonably permanent for as long as it will be needed, and not easily moved or otherwise
2. Be capable of being described in such a way that it can be easily relocated.
Back Sight (BS)
It is a rod reading taken on a point of known elevation.
It is the vertical distance between the line of sight and the point of known elevation on which the rod is held.
The reading is used to establish a new height of instrument.
Height of Instrument (HI) - is the elevation of the line of sight when the instrument is level.
It is found by adding a backsight rod reading to the elevation of the point on which the backsight was taken.
HI = BS + Elev
Foresight (FS) - is a rod reading taken on any point of unknown elevation.
In differential leveling, there is only one foresight for each instrument setup, whereas profile leveling may
have several foresights per instrument setup.
The FS is important to find the elevation of an unknown point.
Turning Point (TP) - is a temporary bench mark upon which foresight and backsight rod readings are taken for the
purpose of continuing the line of the survey.
In long lines several turning points may be needed.
They should be selected with care and must not be moved until the instrument is moved forward and the
new HI determined.
A solid object such as a stake or a large solid rock should be used. Do not set the rod on the ground when
making a turning point; doing so could result in a serious error.
Elevation (Elev) – is the vertical distance above or below from assumed level surface or datum.
To find the elevation of an unknown point: FS is subtracted from the HI.
Elev = FS - HI
The equipment used in leveling consists of the following:
Common type of level:
1. Engineer’s or a Dumpy level – is the most common type of level.
The leveling instrument is a telescope containing both vertical and horizontal cross – hairs and one or more
spirit levels (bubble in a liquid – filled tube) to indicate when the instrument base is horizontal.
The entire assembly of the Leveling instrument consist of the major components:
Spirit level - can be “leveled” by turning the three or four leveling screws that hold the frame in position
above the tripod head.
Figure 1. Dumpy level showing the major components
A spirit level or bubble level is an instrument designed to indicate whether a surface is level or plumb.
A Bull's eye level is a type of spirit level that allows for the leveling of planes in two dimensions - both the 'pitch'
and 'roll' in nautical terms.
Spirit level or bubble level Bull's eye level
Figure 2. Two (2) Types of Spirit Level
Reading Rod - is used to measure the vertical distance between the line of sight, established by the instrument, and
the object on which the rod is resting.
Requirement for an accurate ror reading:
To provide an accurate reading it must be held in an upright position.
Failure to hold the rod in a vertical position is a common error in surveying.
The easiest way to ensure that the rod is vertical is to use a rod level.
Figure 3. Reading a rod
Techniques in reading a rod ( See Figure 3.):
One method is for the rod person to slowly rock the rod forward (F) and backward (B).
The instrument person records the shortest reading. This is illustrated in Figure 3.
The shortest reading will occur when the rod is vertical. D 1 will always be less than distance D2.
The type of rod we are using have the following features:
This rod has four (4) sections, each 1 meter long, that can be extended to give continuous readings from
zero at the base to 4 metres at the top.
Each Section have black and red colours
The graduations consist of blackor red marks painted on a white background.
The graduations are spaced 0.1 metre apart.
The size of the graduations allows the rod to be red, to the nearest 0.01 metre, directly for distances up to 4
1.866.0m 5.1 m
Figure 4a. Reading the Staff or Measuring Rod
Figure 4b. Reading the Philadelphia rod Figure 4b. Reading the rod with a target
Setting Up a Surveying Level
Many different types and variations of levels are used for surveying.
The following procedure for setting up a dumpy or engineer’s level
When not in use, the instrument is housed in a case for protection.
To be used, it must be removed from this case and carefully threaded on the tripod head.
The tripod legs are set about 4 feet apart and pushed firmly into the ground, thereby providing a stable base
for the instrument and helping to ensure an accurate survey.
If the tripod is set up with the head nearly horizontal, leveling of the instrument will be much easier and
faster than it otherwise would be.
To level a three-legged instrument, the position of the telescope is not critical. The instrument is leveled
with the adjusting screws and the spirit level, and then the telescope is slowly rotated to check the accuracy
of the leveling.
The procedure is repeated until the bubble remains centered for any position of the telescope. The leveling
screws should not over tighten, or they will bind and put excessive strain on the instrument frame.
LEVELING FIELD NOTES
The Standard Note keeping procedures have been developed to simplify and systematize record keeping for
(STATION) BACKSIGHT HEIGHT OF FORESIGHT ELEVATION REMARKS
STA (BS) INSTRUMENTS (HI) (FS) (ELEV)
Leveling notes are a simple form of bookkeeping with the following simple rules:
1. Eeach point where a rod reading is made is identified by its station name, and whether it is a foresight or a
2. All pertinent information about a point is shown on the same horizontal line.
3. The height of instrument is recorded on the next line below the backsight reading and the foresight reading
from this setup.
Differential leveling - is the process of finding the difference in elevation between two points.
If the two points are within the limits of the instrument, two readings are taken.
The difference in rod readings represents the difference in elevation between the two points.
If one o the point is beyond the range of the telescope, temporary stations called turning points must be
established to allow the instrument to be moved.
One of the most common applications of differential leveling - is to run a circuit of sights to determine the
elevations of one or more bench marks relative to a previously established bench mark.
The procedure for differential leveling will be described using this type of circuit, illustrated schematically in Figure
Figure 5. Differential Leveling
The diagram shows the following:
That the three instrument setups were made in traveling from BM1 to BM2.
Also note that a “return check” was made between BM2 and BM1,
And that three more setups were made in this phase of the survey.
Procedures in Differential Leveling:
1. The survey begins with the instrument person going forward a convenient distance (not over 400 feet) and
setting up the level, following the procedure previously described.
2. The instrument person sights on the rod while it is held on the top of BM1 by the rod person, and notes a
center cross hair reading of 3.03 feet.
3. This is a backsight, so the 3.03 feet rod reading is added to the BM1 elevation (assumed 100.00 ft),
resulting in a height of instrument (HI) of 103.03 feet.
4. The rod person then goes forward past the instrument and selects a turning point, TP1.
5. The rod reading to this TP, 3.86 feet, is a foresight (elevation of an unknown point).
6. The foresight is subtracted for the HI, and the elevation of TP1 is found to be 99.17 feet.
7. The instrument can now be moved forward and set up at a new position.
8. A backsight rod reading of 2.60 feet is observed on TP1 and added to the TP1 elevation of 99.17 feet, and
the HI for the second setup is found to be 101.77 feet.
9. Again a new turning point, TP2, is selected, and a rod reading of 4.53 feet is recorded.
10. This rod reading is subtracted from the HI of 101.77 feet, and an elevation of 97.24 feet is obtained for
11. This process is repeated a third time, and the elevation of BM2 is found to be 95.30 feet.
12. We now know that the difference in elevation between BM1 and BM2 is 100.00 feet minus 95.30 feet, or
In summary, the procedure for differential leveling is:
1. Set up the instrument.
2. Establish BM1, and take the BS reading.
3. Establish the TP, and take the FS reading.
4. Move the instrument, and set up again.
5. Establish the next TP, and take FS reading.
6. Move the instrument, and set up again.
7. Repeat steps 5 to 7 until the survey is complete.
The results of this survey are recorded in the field notes (Table 1)
Table 1. Data for Differential Leveling
STA BS HI FS ELEV
BM1 3.03 100.00
TP1 2.60 3.86 99.17
TP2 4.22 4.53 97.24
BM2 6.43 6.16 95.30
TP3 3.85 4.44 97.29
TP4 5.11 2.96 98.18
BM1 3.30 99.99
The left hand page of surveying field notebooks contain six columns.
Five columns are needed for differential leveling; from left to right the column headings are station (STA),
backsight (BS), height of instrument (HI), foresight (FS), and elevation (ELEV).
The sixth column is used to record additional information, for example, the distance for each sight.
In surveying, it is important to eliminate as many errors as possible.
For differential leveling surveys two error checks should be conducted:
1. Note check of the allowable error of closure.
2. Calculation of the allowable error of closure.
Note Check of the allowable error of closure
The note check is conducted to catch any mathematical errors in the notes. For checking notes, the absolute value of
the sum of the foresights minus the sum of the backsights should equal the difference ( ) in elevation for BM1
(beginning and closure elevation).
∑FS - ∑BS = Elevation (Equation 1)
Problem: Are the field notes in Table 1 accurate?
Solution: Using Equation 1:
∑ FS ∑ BS
25.25 minus 25.24 equals 0.01 ft.
Elevation = BM1 beginning - BM1 ending
= 100.00 – 99.99
= 0.01 ft
The difference in the summation of the foresights minus the summation of the backsights equals the difference in
beginning and ending elevations for BM1; therefore, the notes have no math errors.
Calculation of the allowable error of closure
The second check is for the error of closure. The allowable error of closure for differential leveling depends on the
accuracy required for the survey.
For most agricultural surveys the allowable error can be determined by:
AE = 0.10 M
AE = Allowable error
0.10 = A constant
M = Distanced traveled (mi)
If a higher level of accuracy is required, a smaller number than 0.10 is used for the constant.
Problem: Is the closure error of 0.01 feet for the differential leveling survey in Figure (3) acceptable if the total
distanced surveyed, out and back, was 3600 feet?
Solution: Using Equation (15-2):
AE = 0.10 M
= 0.10 3600 ft x 1 mi
= 0.10 0.682 mi
= 0.082 ft
The closure error is acceptable (0.01 < 0.082).
Profile leveling is the process of determining the elevation of points at measured distances along a selected line.
When the information is plotted on a graph, it will give the following information:
Profile of the line and will enable one to establish grades.
Find high or low spots, and make estimates of cuts and fills.
Procedures for profile leveling and the way to record the data:
1. Before a profile can be made, the surveying crew establishes the stations by setting a stake where the rod
readings are to be taken.
2. The stakes are usually set a fixed distance apart (25.50m or 100 feet), depending upon the irregularity of
the ground and the amount of detail required.
3. Because the purpose of the profile is to show the true slope of the ground, the irregularity of the terrain will
largely determine where the stations should be established.
4. If there is a definite chance in the slope of the ground, the crew should set a stake and determine the
elevation, even if it does not fall on the preselected distance.
5. Once the centerline of the ditch, terrace outlet, channel, road or other line to be profiled is established, the
distance from the starting point to each station is accurately measured.
6. For higher level surveys, 2 x 2 inch stakes may be driven flush with the ground surface, and rod set directly
on the ground.
7. Next, the level is set up, readings are taken, and elevations are established for each staked point along the
line. A turning point is established when it becomes necessary to move the instrument to make another
series of measurements.
8. Finally, a closing circuit of readings must be made to check the accuracy of the survey.
9. This is done by running a line of differential levels back to the bench mark where the survey began.
10. If no turning points are used, a sight is taken at the bench mark used to establish the height of instrument,
and compared with the original backsight.
Figure 6 and Table 2 illustrate the procedures for conducting a profile leveling survey.
Figure 6. Profile Leveling
Procedures for conducting a profile leveling survey:
With the level set up near the line to be profiled, the rod is held on the bench mark and a reading of 6.02
feet is recorded.
This establishes the height of the instrument
At the station 2+90 a stake is set flush with the surface so it can be used to record the elevation and also be
used as a turning point.
The elevation of each point is calculated by subtracting the rod reading from the height of instrument.
Notice that the same HI is used for all stations up to and including 2+90, as all readings are made from the
same instrument setup.
Because the surveying crew anticipated in advance the need for a turning point, the profile leveling exercise
is continued by moving the instrument to a new location to provide a view of the remaining stations.
A backsight of 1.72 feet is observed, establishing a new height of instrument as 107.40 feet.
The survey continues by recording the rod readings for stations 3+40, 4+00, and 4+60.
A stake is set at TP2, and a foresight of 5.35 feet is observed. The procedure is repeated to complete the
survey from TP2 to BM1.
At the completion of the survey it is noted that an error of 0.02 foot has accumulated during the survey.
Table 2 contains a set of notes for this survey. Note the similarities and differences between these notes and
Table 1 (data for differential leveling).
Table 2. Data for profile leveling.
STA BS HI FS ELEV
BM1 6.02 106.02 100.00
0+00 7.34 98.68
1+00 5.76 100.26
2+25 3.67 102.35
2+90 1.72 107.40 (0.34) 105.68
3+40 4.03 103.37
4+00 6.65 100.75
4+60 4.00 107.28 (4.12) 103.28
TP2 3.34 105.27 (5.35) 101.93
BM1 (5.25) 100.02
∑ BS = 15.08 ∑ FS = 15.06
∑ FS - ∑ BS = 0.02
Elevation = 100.02 - 100.00 = 0.02
Acceptable Error = 0.10 460 + 5280 = 0.03
= 0.02 < 0.03
Because profile leveling notes usually have more foresights than backsights, the method of checking for
arithmetic mistakes is slightly different from that for differential leveling.
The only foresights to be included when calculating the sum of the foresights (∑FS ) are those taken on
turning points, including bench marks if they were used as TP’s. In the sample notes (Table 2) the
foresight readings that are to be used for checking are shown in parentheses.
The data in Table 2 indicate there were no arithmetic errors in the survey, and the closure error was
This procedure provides a check on the turning points only – not the intermediate foresights.
There is no way to check those foresights not used for TP’s except to rerun the entire profile.
Extreme care must be used to prevent mistakes in reading and recording the rod readings and in
calculating the elevations at all stations.
The results of profile leveling surveys are most useful when they are plotted on graph paper.
The principal purposes for plotting a profile are:
1. To aid in the selection of the most economical drain the lines, sewer lines, roads, etc,; and
2. To determine the amount of cut or fill required for these installations.
The graph is plotted with the elevation on the ordinate (vertical scale) and the stations on the abscissa (horizontal