CIVL 3056 Surveying

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Introduction

SURVEYING

Surveying may be defined as the art of making measurements of the relative positions of natural

and man-made features on the earth's surface, and the presentation of this information either

graphically or numerically.

• Surveying plays an essential role in the planning, design, layout, and construction of our

physical environment and infrastructure. Infrastructure is commonly used to represent all

the constructed facilities and systems that allow human communities to function and thrive

productively.

• Simply stated, surveying involves measuring distance and angles:

• Measurements form the basis of traditional plane surveying:

(1) horizontal and vertical distances.

(2) horizontal and vertical (or zenith) angles.

(3) slope distances.

• In the following figure.

OAB and ECD are horizontal planes,

and OACE and ABDC are vertical planes.

horizontal angles. such as angle AOB,and horizontal distances. OA and OB, are

measured in horizontal planes:

vertical angles, such as AOC, are measured in vertical planes: zenith angles. such as

EOC, are also measured in vertical planes: vertical lines (elevations). such as AC and

BD, are measured vertically (in the direction of Gravity):

and slope distances, such as OC, are determined along inclined planes.

Distances may be measured on slopes, but they must be converted to a corresponding

horizontal distance.

• By using combinations of these basic measurements, it is possible to compute relative

positions between any points.

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• Equipment and procedures for making each of these basic kinds of measurements will be

the main subject of our course.

• Computations of primarily positions, direction, area and volume require the applications of

geometry, trigonometry and basic algebra.

• The term Geomatics is the same as Surveying but is now more currently used due to

technology advances and diverse areas that this contains.

The work of the surveyor

1. Selecting the method, equipment, reconnaissance of site and so on.

2. Field work or data acquisition. Making measurement recording data in the

field.

3. Computing or data processing. Performing calculations on the recorded data to

determine locations, areas, volume and so on.

4. Mapping or data representation. Plotting measured and computed values to

produce a map, plan or chart, or present the data in a numerical or computer

format.

5. Marking. Placing monuments to delineate boundaries and guide construction

operations.

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HISTORY OF SURVEYING

• The oldest historical records indicate that this science had its beginning in Egypt.

• Herodotus says Sesostris (about 1400 B.C.) divided the land of Egypt into plots for the

purpose of taxation. He appointed the early surveyors were called rope-stretchers since their

measurements were made with ropes having markers at unit distances to relocate the lost

boundaries after flooding.

• The magnetic compass was first used as a surveying instrument in the thirteenth century, to

establish the directions of boundary lines.

DEFINING HORIZONTAL AND VERTICAL DIRECTIONS

• The earth has the approximate shape of an ellipsoid:

The solid generated by an ellipse rotated on its minor axis.

Polar axis is slightly shorter than axis passing through the equator.

• We can consider the earth to be a perfect sphere with a constant diameter.

• If we ignore the surface irregularities (like mountains, etc…), the surface of the sphere is

represented by the average level of the ocean, or mean sea level, MSL.

• The curved surface of the sphere is termed a level surface.

• The direction of gravity is perpendicular or normal to this level surface at all points.

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• As shown in the figure, the direction of all plumb lines converge at the center of the earth; at

no points are the plumb lines actually parallel.

• The vertical direction is taken to be the direction of gravity. Therefore, it is incorrect to

define vertical as simply "straight up and down,".

• The horizontal direction is the direction perpendicular (at an angle of 90°) to the vertical

direction of gravity.

PLANE AND GEODETIC SURVEYING

• Most surveying measurements are carried out as if the surface of the earth were perfectly flat.

• We make our measurements as if the lines of force due to gravity were everywhere parallel

to each other, and as if underneath the irregular ground surface there existed a flat, horizontal

reference plane. This is illustrated in the following figure.

In plane surveying, the curvature of the earth is neglected, and vertical distances are

measured with reference to a flat plane.

The method of surveying based upon this assumption is called plane surveying:

• In plane surveying, we neglect the curvature of the earth, and we use the principles of plane

geometry and plane trigonometry to compute the results of our surveys.

• The use of plane surveying methods simplifies the work of the surveyor, and for surveys of

limited extent, very little accuracy is lost. Within a distance of about 20 km, the effect of

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the earth's curvature on our measurements is so small. The difference between the length of

arc and the chord length is only about 6 mm for a 20 km distance.

• As it turns out, the vast majority of ordinary private surveys are performed well within these

limits.

• A survey that takes the earth's curvature into account is called a geodetic survey. These

types of surveys are usually conducted on national level.

• The geometry and trigonometry (advanced mathematics and spherical trigonometric

formulas) of figures on a curved surface differ considerably from the geometry and

trigonometry of plane or flat figures. For example, in a plane triangle, the interior angles

always add up to 180°. But this is not the case with a triangle on a curved surface.

• Geodetic surveying methods are generally used to map large areas and to establish large-

scale networks of points on the earth for horizontal and vertical control. The relative

positions of these points are measured with a high degree of precision and accuracy, both in

longitude and in latitude, as well as in elevation. They are used as points of reference for

many other local surveys that require a lower degree of accuracy.

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SURVEYING APPLICATIONS

Property Surveying

• It is performed to establish the positions of boundary lines and property corners.

Topographic Surveying

• Performed to determine the relative positions (horizontal and vertical) of existing natural and

constructed features on a tract of land.

• The data is plotted as scaled maps, called a topographic map, or topo map. The shape of the

ground is shown with contours, or lines of equal elevation

Construction Survey

• Also called a layout or location survey, and is performed to mark the position of new points

on the ground. The points represent the location of building corners, road centerlines, and

other facilities that are to be built.

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Control Survey

• There are two kinds of control surveys: horizontal and vertical. In a horizontal control

survey, several points are placed in the ground by the surveyor. The relative horizontal

positions of these points are established, usually with a very high degree of precision and

accuracy; this is done using traverse, triangulation, or trilateration survey methods.

• In a vertical control survey, the elevations of relatively permanent reference points are

determined by precise leveling methods. Marked points of known elevation are called

elevation benchmarks (BMs).

Reconnaissance Survey

• A reconnaissance survey is a preliminary survey conducted to get very rough data regarding

a tract of land.

• Distances may be approximated by pacing, and spot elevations may be obtained with the use

of only a hand level.

• Examination of aerial photographs may also serve as part of a reconnaissance survey.

Cadastral Survey

A cadastral survey is a boundary survey applied specifically to the relatively large-scale Public

Lands Survey system. It also refers to the surveying and identification of property in political

subdivisions.

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Photogrammetric Survey

Photogr-ammetric surveying uses relatively accurate methods to convert aerial photographs into

useful topographic maps.

GEOGRAPHICAL INFORMATION SYSTEM GIS

A geographical information system (GIS) is an information management process for organizing

spatially related data.

1. The data are stored in different layers.

2. One of the layers is a digital map.

3. The collection of the data is superposed onto the map

4. Relation between the different data on different layers can be established and used in the

analysis of the data.

UNITS OF MEASUREMENTS

Most countries use SI metric units of measurement; SI stands for "Systeme International." In

the United States, a gradual transition from the English or U.S. customary units to SI units is still

in progress.

Angles

Degrees, Minutes, and Seconds

• The most common system is the sexagesimal system:

A complete rotation of a line (or a circle) is divided into 360 degrees of arc(°)

1 degree is divided into 60 minutes (′)

1 minute is further divided into 60 seconds of arc (″)

35° 17' 46" (35 degrees, 17 minutes, 46 seconds).

• A right angle (two perpendicular lines) = 90°00' 00".

• To add two angles 35° 17' 46" and 25° 47' 36", the degrees, minutes,

and seconds are first combined separately, resulting in 60° 64' 82".

But this must be converted to 61° 05' 22" because 82" = 01' 22", and 65' =1° 05'.

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• When subtracting angles, it may be necessary to first "borrow" 60 minutes from a degree and

60 seconds from a minute. For example, to subtract 35° 17' 46" from 90° 00' 00", we must

write

• Calculators normally accept angular values expressed directly in degrees, minutes, and

seconds. You can convert degrees, minutes, and seconds to degrees and decimal parts of a

degree, or vice versa.

For example, an angle of 35° 30' 35.5°, since 30/60' = 0.5°.

An angle of 142.125° 142° 07' 30", since 0.125° = 0.125 x 60' = 7.5', and 0.5 = 0.5' x

60" = 30".

Grads (gon)

• The centesimal system: A complete rotation is divided into 400 grades, or grads, written as

400g.

• Calculator mode: GRAD

• For conversions, 1g = 0.9°.

Radian (rad)

• One radian is equivalent to the angle formed between two radii in a circle, when the arc

length between the radii is the same as the radius.

• The circumference of a circle = 2πR, there must be 2π (about 2 x 3.14 = 6.28) rad in a

circle.

• 6.28 rad = 360°, and 1 rad = 57.3°.

Distance

• In the U.S. Customary system, the basic unit for distance or length is the foot (ft).

• In the SI system of units, length or distance is measured primarily in terms of meters (m) or

fractions of m.

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• The Gunter's chain, for example, has long been used as a unit of linear measure for land

surveys in the US.

One chain is equivalent to 66 ft.

One quarter of a chain is called a rod, perch, or

pole; = 16.5 ft.

The chain contains exactly 100 links.

In the southwest part of the United States, another

unlit, called the vara (equivalent to about 33 in), was used in many past surveys.

1 nautical mile = 6076.10 feet; 1 fathom = 6 feet; units of area is derived from the basic unit

of length.

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1. Measuring Horizontal Distances

1. DISTANCE MEASURING TECHNIQUE

1. Pacing

2. Odometer

3. Tapes, Chains

4. Stadia (Tacheometry)

5. Substense Bar

6. EDM (Electronic Distance Measurment)

2. ROUGH DISTANCE MEASUREMENT

Pacing

Pacing involves counting steps or paces while walking naturally along the line to be measured.

All surveyors and construction technicians should know their own personal unit pace value.

Example

A surveyor has a unit pace of 0.8 m/pace and walks a line while counting 86.5 paces, the

distance is computed as:

Distance = 0.8 x 86.5 = 69.2 m z 69 m

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Fiberglass Cloth Steel

Measuring Wheel

• A simple measuring wheel mounted on a rod can be used to

determine distance by pushing the rod and rolling the wheel

along the line to be measured. An attached device called an

odometer serves to count the number of turns, or revolutions, of

the wheel.

• This device is particularly useful for rough measurements of

distance along curved lines.

3. TAPING

Chains

When North America was first surveyed (in the 18th and 19th centuries), the distance measuring

device in use was the Gunter's chain. It was 66 ft long and was comprised of 100 links. The

length of 66 ft was apparently chosen because of its relationships to other units in the Imperial

System:

Tapes

Tapes can be cloth, fiberglass or steel. For precise tape measuring, steel tapes are always used.

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Accessories for Taping

Plumb bob

When taping horizontal distances, the tape very often must be held above the ground at one or

both ends. The plumb bob is used to project the horizontal position of a point on the ground up

to the tape, or vice versa.

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Ranging Rods (poles)

Range poles serve to establish a line of sight and keep the

surveyors properly aligned. A range pole would be placed

vertically in the ground behind each endpoint of the line to be

measured. Made of wood, metal, or fiberglass, range poles are

about 2.5 m, in length, and are painted with red and white bands

for easy sighting. It can be used with tripods to support them on

hard soil.

Pins (arrows)

Steel taping pins (also called chaining pins or surveyor's arrows) are used to mark the end of

the tape, or an intermediate point, when taping over grass or unpaved ground. They are

generally carried in a set of 10 or 11 pins

Crayon (Keel)

To mark temporary points on paved surfaces, a pencil line or scratch circled with a yellow

lumber crayon, often called keel, may be used.

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Hand Level

When taping horizontal distances, it is necessary to hold the

tape as close to a horizontal position as possible. To

reduce errors caused by an excessively sloped tape,

some surveyors make use of a hand level. A horizontal

line of sight can be easily obtained by using a small

level vial and looking through the level toward the

surveyor at the higher end of the tape.

Tension Handle

Applying the correct tension is particularly important if high

accuracy is required. It is measure by a spring-balance

tension handle.

Tape Thermometer

For precise taping, temperature corrections must be made. It is attached to the tape near one

end; the bulb should be in contact with the steel.

Tape Clamp Handle

A tape clamp handle is used for providing a firm grip on the tape at

any intermediate point, without causing damage to the tape or injury

to the surveyor from the steel edge.

Pegs

Pegs are dowel bars, typically used for marking permanent points.

If the tape is damaged, tape repair kits are available for splicing broken tapes; a spliced tape must

first be recalibrated or standardized before being put back in use, to avoid systematic errors.

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4. MEASURING THE LENGTH OF A LINE

To measure the line AB, position ranging rods at A and B

A group of 3 men are needed, 3 rods, a tape and 10 arrows. (Leading chainman, Follower and

a Surveyor)

1. Leader drags his end to A1 and holds the ranging rod 0.3 m short of the end.

2. The follower holds his end of the band firmly against station A. The surveyor lines in

the Leader’s pole between A and B, by closing one eye and sighting Poles A and B and

signaling the leader until he brings his pole into line AB.

3. The leader straightens the band past the rod by sending gentle snakes down the band.

4. The follower indicates the band is straight and the leader puts an arrow at the end A1.

5. The leader drags his end to A2 taking 9 arrows and his pole.

6. The follower moves to A1 and puts his pole behind the arrow. The surveyor again lines

in from here or from A.

7. The above procedure is repeated, the follower picking up the first arrow before moving

from A1. The leader moves to A3 carrying eight arrows. The follower moves to A2

carrying the arrow from A1.

Upper path

Lower path

Walking dir.

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5. SETTING OUT RIGHT ANGLES

Cross staff

• It Consists of an octagonal brass box with slits cut in each

face so that opposite pairs form sight lines. The instrument

may be mounted on a short ranging rod.

• This is mounted on a short ranging rod which is stuck in the

ground at the point at which the right angle is to be set out.

• The cross staff is turned until a sight is obtained along the

survey line and the normal is then set out by sighting

through the slits at right angles to this.

Optical Square

Two mirrors set at 45° in a cylindrical body. The eye looking through the small eye hole

will see ½ the object at O1, and ½ the object at O2 as reflected through mirror B (half

silvered, half plain). Mirror A is fully silvered. It is used as already described, being either

held in the hand or else on a short ranging rod.

90°

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Setting Right Angles with a tape

Put the free end of the tape at P. Strike an arc

to cut the survey line at A and B. Bisect AB.

Pythagoras’theoerm (3, 4, 5 rule or any

multiple, 9, 12, 15). Put the zero of the tape at

P. Measure 12 m to find A. Take 24 mark at

A ( 9 +15). Pull both parts of the tape tight to

Q. APQ = 90°.

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6. PROCEDURE FOR TAPE AND OFFSET SURVEY

Tape and offset surveying consists of measuring with the tape the lengths of a series of straight

lines, and then locating points on the ground relative to these lines by measuring two other lines,

known as ties, or by measuring offsets at right angles to the main survey line. Ties and offsets

should not exceed one tape length.

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MEASUREING SLOPES

Abney Level

It consists of a sighting tube with a graduated arc.

There is a small buble tube which can be seen through

sighting. The device can be used to measure vertical

angles.

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ERRORS

In all surveying operations, errors are likely to occur, and so far as is possible they must be

guarded against or their effects corrected for. The types of error that can occur have been

classified as follows:

mistakes,

random errors

systematic errors

Mistakes

• These are due to inexperience or to carelessness on the part of the surveyor or the chainmen,

and are quite random in both occurrence and magnitude.

• By careful work, and by taking suitable check measurements, it should be possible to make a

survey that is free from mistakes. Typical mistakes in measuring the length of a line are:

Omitting an entire band length in booking. This is prevented by noting down each band

length, and by the keeping careful count of the arrows, as described earlier.

Misreading the steel band. It is best if two people make important readings.

Erroneous booking sometimes occurs; it is prevented by the chainman carefully calling out

the result and the surveyor repeating it, paying attention when calling 5 or 9, 7 or 11.

Random or Accidental Errors

This group of errors, acting independently on observations, arises from:

• Lack of perfection in the human eye.

• The method of using equipment.

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Systematic or Cumulative errors

1. Standard

• Has the tape changed length ± due to: wear out (and stretch more), or when it become bent or

spliced? The end points still read 0 and 30 but the correct length is different.

• By checking the band against a standard tape called Invar, the exact error per band length is

known.

• A correction can be applied which will enable the effect of the error to be removed.

Correction = SL

SLCLxlengthmeasured )( −

The length of the standard is, of course, usually 30 m or 50 m. It would be good practice to

discard any steel band that differed from the standard by more than 6 mm in 30 m.

Accidental errors occur when the tape is (a) misaligned or (b) off level.

CL =Correct length

SL = standard length

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Example:

A measurement was recorded as 171.278 m with a 30-m tape that was only 29.996 m under

standard conditions. What is the corrected measurement?

Solution:

Correct length = measured length x TapeLengthStnd

lengthTapeCorrect.

Correct length = 171.278 x 30996.29 = 171.255 m

Correction = 171.278 x m023.030

)30996.29(−=

−

Note that:

Correct length = Measured length + Correction (+ve or –ve)

2. Sloping Ground

• All measurements in surveying must either be in the horizontal plane, or be corrected to give

the projection on this plane.

• Lines measured on sloping land are longer than lines measured on the flat, and if the slope is

excessive, then a correction must be applied. There are two methods.

Stepping On ground that is of variable slope this is the best method, and needs no

calculation. The measurement is done in short lengths of 5-10 m, the leader holding the length

horizontal. The point on the ground below the free end of the band is best located by plumb bob,

as shown next.

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Measuring along the slope This method is applicable where the ground runs in long

regular slopes. The slope is measured either by an instrument such as the Abney level, or by

leveling. (α) or h are known.

(If α is small then tan α = sin α = α in radians = h/L, α2 = h2/L2

Correction = - L

h2

2

= 2

2Lα−

If α is not known but the height (h) is known the correction by Pythagorous theorem is

Correct length = 22 hL −

Slope can be express as 1/n (vertical to horizontal) = tan α = α in Rad.

Example:

Horizontal distance = 22 hL −

tan θ = 1.5/100

θ = 0.859° (θ = 0.015 rad.)

H = L cos θ = 156.77 cos 0.859 = 156.759 m

L h

L cos α

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Tape standardization

• For very accurate work a spring balance should be attached to one end of the steel band. The

purpose of this is to ensure that the band is tensioned up to the value at which it was

standardized: i.e. if the band is 30 m long at 20 °C under a 5 kg (50 N) pull on the flat, then

a tension of 5 kg should be applied to eliminate any correction for pull.

• All good-quality bands should have a standardization certificate.

3. Tension

As mentioned, the correct tension can be applied to the band by attaching a spring balance to the

handle at one end. If the standard tension is not applied a correction should be made since the

length of the tape will have changed:

Correction = (P - Ps) .L /AE

where P, Ps = field and standard tension respectively

A = cross-sectional area of band, E = Young's modulus of elasticity for the band, L = length

measured.

Example

E = 20 x 1010 N/m2

Solution:

Correction = mxx

xx 0038.0102002.0

1030)50100(10

4

+=−

4. Temperature

If the tape temperature, t, is not equal to the standard temperature, ts.

Correction = α L(t—ts)

Where, α = coefficient of linear expansion.

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If the temperature during measurement is greater than the standard temperature, the tape will

expand; the reading will be too low. A positive correction is thus required.

Example:

A distance measured with a 30-m steel tape and recorded as 96.345 m. The average tape temp.

was 5° C. Standard temperature is 20° C, coefficient of linear expansion = 1.16 x10-5 / °C/m

Solution

Correction = 1.16 x 10-5 x 96.345 x (5-20) = -0.01676 m

Correct distance = 96.345 – 0.01676 = 96.328 m

5. Deviation from the straight (alignment)

Corrections can be applied for misalignment but since this would require actually measuring the

misalignment, it is generally easier to take more care and line in the band.

6. height above mean sea level;

The length of the line as measured can be reduced to its equivalent

length at mean sea level.

Correction = -L RH

7. Sag, if the tape has been standardized on the flat, not in catenary.

If the highest accuracy is required, rather than lay the band along the ground, it can be suspended

between tripod heads, i.e. hung in catenary, and a correction for the sag in the tape applied if the

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tape has been standardized on the flat. The next figure shows a simple arrangement that could be

used.

Correction for sag = - w2L3/(24 P2)

where w = weight per unit length of the tape, L is the measured length of span. If the tape has

been standardized in catenary no correction is required for sag so long as the field tension P is

the same as the standard tension, Ps.

Example

Solution:

0532.010024

000.50)807.963.1(2

2

−=−

=x

xxCorrection

The length between supports = 50 – 0.0532 = 49.947 m

Comprehensive Example

A 30 m steel tape standardized at 20°C on the flat under a tension of 5.45 kg was found to be

30.012 m long. A = 0.050 cm2 , w = 0.03967 kg/m. The tape was held horizontal and used to

measure 3 segments in catenary with a tension of 9.09 kg. Correct for tape length, tension,

temperature and sag and determine the correct length of the line.

E= 20 x 1010 N/m2

Standard Temp. = 20°C

α = 1.16 x 10-5 / °C/m

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Solution:

Tape length

Tension

Temperature

∑ .Temp

Sag

∑ =sag

Correct distance AB = Measured distance AB + All corrections.

mAB 131.810503.00048.000289.003246.0151.81 =−−++=

- 0.00208 m

- 0.0048 m

2 x - 0.0214 m

- 0.0503 m

0.03246 m

0.00289 m

- 0.00174 m -0.00098 m

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2 - LEVELING

LEVELING

Levelling is the general term applied to any of the various processes by which elevations of points or

differences in elevation are determined.

LEVELLING RESULTS ARE USED TO:

(a) Design highways, railways and canals having grade lines that best conform to existing

topography;

(b) Layout construction projects according to planned elevations;

(c) Calculate volumes of earthwork;

(d) Investigate drainage characteristics of an area

(e) Develop maps showing general ground configurations.

DEFINITIONS: BASIC TERMS USED IN LEVELLING ARE

(a) Vertical Line: A line that follows the direction of gravity as indicated by a plumb line.

(b) Level Surface: A curved surface that at every point is perpendicular to the plumb line (the

direction in which gravity acts). Level surfaces are approximately spherical in shape.

(c) Level Line: A line in a level surface; therefore, a curved line.

(d) Horizontal Plane: A plane perpendicular to the direction of gravity. In plane surveying, a

plane perpendicular to the plumb line (see Introduction section, page 4).

(e) Horizontal Line: A line in a horizontal plane perpendicular to the vertical.

(f) Datum: Any level surface to which elevations are referred (for example, mean sea-level).

(g) Mean Sea-Level (MSL): The average height of the sea's surface for all stages of the tide

(over a 19-year period). It can be derived from readings, usually taken at hourly intervals,

at coastal tide gauges. For example, in Australia, the average of 30 tide gauage stations

was used to produce the national levelling datum.

(h) Elevation: The vertical distance from a datum to a point or object. If the elevation of

point A is 802.46m, A is 802.46 m above some datum!

(i) Bench-Mark (BM): A relatively permanent object, natural or artificial, having a marked

point whose elevation above or below an adopted datum is known or assumed. Normally

BM are supplied at 5 every km2 (rural) or 40 per km2 (urban).

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(j) Levelling: The process of finding elevations of points or their difference in elevation.

(k) Vertical Control: A series of bench-marks or other points of known elevation established

throughout a project, also termed basic control or level control.

METHODS TO DETERMINE DIFFERENCES IN ELEVATIONS

Difference in elevations can be determined using taping, differential leveling, barometric

leveling, and trigonometric leveling.

Differential Levelling

A horizontal line of sight is established. A telescope with suitable magnification is used to read

vertical distances from fixed points with a graduated staff. The next figure shows an instrument

setup z half-way between BM rock and point X.

• A Level is setup at a point halfway through BM and point X.

• The elevation of BM is known = 825.00 m

• The reading on the staff at BM = 3.42 m called Back Sight (BS) or + sight (+S).

• Backsight = reading at a point of known or assumed elevation.

• The first observation in a leveling run is always a BS, and is used to compute the height of

the instrument (HI) or height of collimation. It is the vertical distance from a datum to

the instrument line of sight.

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• Add a BS of 3.42 m to BM elevation of 825.00 m gives HI of 828.42 m

• Turning the telescope to bring into view the staff held on point X, a foresight (FS) or -

sight (- S) is obtained at 0.20 m.

• Foresight = is defined as the staff reading on a point whose elevation is desired.

• Subtracting the FS (0.20 m) from the HI, 828.42, gives the elevation of point X = 828.22 m.

LEVELLING EQUIPMENT

There are four types of levels (in addition to hand level!):

• Dumpy level

• Tilting level

• Automatic level

• Digital level

Theodolites can also be used for leveling.

Telescopes

The telescopes of leveling instruments define the line of sight and magnify the view of a

graduated rod against a reference reticle, thereby, enabling accurate readings to be obtained.

The components of a telescope are mounted in a cylindrical tube.

Line of Collimation

3.42 m

0.2 m

828.22 m

825.00 m

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Its four main components are the:

• objective lens

• negative lens.

• reticle,

• eyepiece.

Two of these parts: the objective lens and eyepiece, are external to the instrument.

Objective Lens.

This lens, securely mounted in the tube's object end has its optical axis concentric with the tube

axis. Its main function is to Gather incoming light rays and direct them toward the negative

focusing lens.

Negative (focusing) Lens.

The negative lens is located between the objective lens and reticle, and mounted so its optical

axis coincides with that of the objective lens. Its function is to focus rays of light that pass

through the objective lens onto the reticle plane. During focusing, the negative lens slides back

and forth along the tube axis.

Reticle (Diaphram or cross-hairs)

The reticle consists of a pair of perpendicular reference lines

etched on a thin round glass plate (usually called cross hairs).

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• The glass plate is held in place in the main cylindrical tube by two pairs of opposing screws,

which are located at right angles to each other to facilitate adjusting the line of sight.

• Two additional lines parallel to and equidistant from the primary lines are commonly added

to reticles for stadia (we will talk about it later).

• The point of intersection of the cross hairs together with the optical center of the objective

system forms the so-called line of sight, also sometimes called the line of collimation.

• The reticle is mounted within the main telescope tube with the lines placed in a horizontal-

vertical orientation.

Eyepiece.

The eyepiece is a microscope (usually with magnification from about 25 to 46 x) for viewing the

image.

• To Focus a Telescopic Sight, Three steps are required to focus a telescopic sight for

greatest accuracy.

1. Aim the telescope at a white piece of paper in front of the objective lens, and regulate

the eyepiece until the cross hairs are in sharp focus.

2. Aim the telescope at the object to be viewed and, while keeping the eye focused on the

cross hairs, regulate the focusing lens until the object is clear.

3. If both focusing have been carried out correctly the cross hair appears to be

superimposed on the object (staff).

4. If one or both focus adjustments have been made improperly the resultant error is

known as Parallax. The cross hair appears to move up or down as the observer’s head

moves slightly up and down.

5. To eliminate parallax, change the focus of the objective until the apparent motion is re-

versed. Continue focusing back and forth, reducing the apparent motion each time until

it is eliminated. It may then be necessary to adjust the eyepiece slightly to make the

image and the cross hairs appear clear-cut.

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Note: When the eyepiece has been set for a particular observer after the parallax has been once

eliminated, it is common practice to keep the eyepiece in this position throughout the work and

to rely on focusing the objective so that both the cross hairs and the object are in sharp focus

simultaneously, to eliminate parallax (unless the eye tires).

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Level Vials

Level vials are used to orient many different surveying instruments with respect to the direction

of gravity. There are two basic types:

• The “Spirit” tube vial and

• The circular or so-called "bull's-eye''.

• Tube vials are used to precisely orient the line of sight horizontal prior to making rod

readings. Bull's-eye vials are also used on tilting levels, and on automatic levels for quick,

rough leveling, after which precise final leveling occurs. The principles of both types of

vials are identical.

• A tube level is a glass tube manufactured so that its upper inside surface precisely conforms

to an arc of a given radius. The tube is sealed at both ends, and except for a small air

bubble, it is filled with a sensitive liquid. The liquid must be nonfreezing, quick-acting, and

maintain a bubble of relatively stable length for normal temperature variations. Purified

synthetic alcohol is generally used.

• As the tube is tilted, the bubble moves, always to the highest point in the tube because air is

lighter than the liquid.

• The axis of the level vial is an imaginary longitudinal line tangent to the upper inside

surface at its midpoint. When the bubble is centered in its run, the axis should be a

horizontal line.

• For a leveling instrument that uses a level vial, if it is in proper adjustment, its line of sight is

parallel to its level vial axis. Thus by centering the bubble, the line of sight is made

horizontal.

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• The following figure shows a coincidence-type tube level vial used on precise

equipment. The bubble is centered by bringing the two ends together to form a smooth

curve. A prism splits the image of the bubble and makes the two ends visible

simultaneously. This arrangement enables bubble centering to be done more

accurately.

• Bull's-eye level vials are spherical in shape (see next figure). Like the tube version,

when the bubble is centered in the smallest circle, the axis should be horizontal. They

are used in rough leveling of tilting and automatic levels, and other equipment. Their

sensitivity is much lower than that of tube vials.

Circular (Bull’s eye) spirit level

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TYPES OF LEVELS

• The three leveling footscrews which rest on the base plate allow the telescope axis to be set

in a horizontal plane. Some older instruments have four screws. Some have a ball-and

socket joint which enables faster but less accurate levelling of the instrument.

Dumpy Level

• In a dumpy level, the telescope and vertical axis are cast as one piece.

• There is no facility to finely adjust the bubble centering but instead, before any readings are

taken, the telescope has to be set horizontal in all directions using the foot screws.

The general principle of this temporary adjustment: the telescope, and hence the bubble tube, is

placed parallel and at 90° to a pair of foot screws, the bubble being centered in each case as

shown in the next figure.

Diaphragm

screws

Ball and Socket Joint footscrews

Base plate

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• The dumpy level is not particularly popular with engineers: it takes too much time to level

and dislevellment occurs between initial setting and subsequent readings.

Tilting Level

• Quick leveling is achieved using a bull’s eye bubble, and the leveling screws or ball and

socket joint. Before every reading, the telescope bubble is centered using the tilting screw.

Slight lateral movement to the left or right of this line is made with the 'slow motion' or

'tangent' screw.

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Optical

micrometer

Telescope

eyepiece Focus

Ball and

socket joint

Circular

spirit level

Hz. Motion

screw

Tilting

screw

Objective

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Automatic

• Automatic levels incorporate a self-levelling feature.

• Rough leveling using a three-screw levelling head or ball and socket joint approximately centers

a bull's-eye bubble. After the bull's-eye bubble is manually centered, a compensator takes over,

automatically levels the line of sight and keeps it level.

• No further leveling is required at that particular instrument location; the instrument, then, may

be described as being "self-leveling."

• Automatic levels have become popular for general use because of the ease and rapidity of their

operation.

• They are typically accurate and easy to use, and they can be set up and leveled relatively

quickly.

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Compensator for self-levelling level

Digital Level

• They reduce human error that occurs in vertical

distance measurements.

• Using a digital level and a special bar-coded rod,

instrument operators can collect and store accurate

backsight, foresight, and distance data in as little as

3-4 seconds, without observation or calculation

errors.

• It is an automatic level as it uses a pendulum

compensator to level itself. They can still be used to

obtain readings manually.

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TRIPODS AND HEADS

Tripods are made of wood or metal, fixed or adjustable length.

LEVEL STAFFS

Level staffs are made of wood, fiberglass or metal and have graduations in meters and decimals.

Two main classes of staffs are:

(1) Self-reading staffs: which can be read by the instrument operator while sighting through the

telescope and noting the apparent intersection of the cross-wire on the staff. This is the most

common type and shown.

Tripod head adaptor

Adjustable leg straight leg

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(2) Target staffs: having a moveable target that is set by a field assistant at the position indicated

by signals from the level operator.

• The staff should be held vertically. Sometimes handles are provided in the sides to assist

with the field operation.

Examples for Reading the Staff

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Rod level Rod level mounted on leveling rod

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2- DIFFERENTIAL LEVELING

SETTING UP THE INSTRUMENT

• Unscrew the tripod screws.

• Pull the tripod up to a desired height.

• Hold one leg down and pull the other two towards you.

• The tripod should be set up with the legs well spread and

pressed firmly into the ground.

• The legs should be adjusted so that the head of the tripod is

roughly horizontal.

• Remove the instrument from its case, carefully lifting it by the base.

• Screw the lower plate of the instrument on the head of the tripod.

• The circular bubble should be brought to its central position, using

the foot screws or 'ball and socket' assembly.

• Eliminate the Parallax (focus).

Notes:

• For tilting level, you need to center the coincidence bubble before every reading.

• For leveling work, the instrument need not be set up precisely over a particular point

or station.

• When the level is to be moved to another position, it need not be removed from the tripod

(except perhaps for very expensive and precise instruments), In a clear area, hold the tripod

in a vertical position.

• Direct the telescope toward the rod by

sighting over the top of the telescope

(Sighting Collimator).

• A rod may be waved back and forth

and the lowest reading observed.

• Do not touch the tripod when taking

readings.

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HEIGHT OF COLLIMATION METHOD

The next section before the example is similar to page 2 of the handout “2 – leveling”

• A Level is setup at a point halfway through BM and point X.

• The elevation of BM is known = 825.00 m

• The reading on the staff at BM = 3.42 m called Back Sight (BS) or + sight (+S).

• Backsight = reading at a point of known or assumed elevation.

• The first observation in a leveling run is always a BS, and is used to compute the height of

the instrument (HI) or height of collimation. It is the vertical distance from a datum to

the instrument line of sight.

• Add a BS of 3.42 m to BM elevation of 825.00 m gives HI of 828.42 m

• Turning the telescope to bring into view the staff held on point X, a foresight (FS) or -

sight (- S) is obtained at 0.20 m.

• Foresight = is defined as the staff reading on a point whose elevation is desired.

• Subtracting the FS (0.20 m) from the HI, 828.42, gives the elevation of point X = 828.22 m.

Height of collimation = Elevation + BS

Elevation = Height of Collimation – FS

• Datum = MSL

• On small works, an arbitrary datum can be chosen.

Line of Collimation

3.42 m

0.2 m

828.22 m

825.00 m

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Example:

• We need to produce the longitudinal section of the road centerline.

• We setup the level at P and a benchmark is observed.

• Reduced Level = Referred Level = Level of a point referred to a datum level, normally MSL

• Reading at a point of knonwn Level is Backsight BS (BM)

• Reading at a point to obtain its level = intermediate sight IS (A, B, C)

• Reading at the last point = Forsight FS (D)

• Turning Point (TP) = a point which has both FS and BS

• The change in level position is required because change in ground level or some obstruction

to the line of sight.

Station +

BS

-

IS

-

FS

Ht. of

Collimation

Reduced

Level

Distance

BM 0.663 98.760

A 1.946 0

B 1.008 20

C 1.153 40

D

(change

point)

2.787 1.585 60

E 2.270 80

F 1.218 100

G 0.646 120

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Station +

BS

-

IS

-

FS

Ht. of

Collimation

Reduced

Level

Distance

BM 0.663 99.423 98.760

A 1.946 97.477 0

B 1.008 98.415 20

C 1.153 98.27 40

D

(change

point)

2.787 1.585 100.625 97.838 60

E 2.270 98.355 80

F 1.218 99.407 100

G 0.646 99.979 120

Check 3.450

-2.231

2.231 99.979

-98.760

1.219 1.219

Level at P

Ht of Collimation = BM Level + BS = 98.760 + 0.663 = 99.423 m

RLA = Ht of Collimation – FS (A) = 99.423 – 1.946 = 97.477 m

Station +

BS

-

IS

-

FS

Ht. of

Collimation

Reduced

Level Distance

BM 0.663 98.760

A 1.946 0

B 1.008 20

C 1.153 40

D (TP) 2.787 1.585 60

E 2.270 80

F 1.218 100

G 0.646 120

TP

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Check

∑ ∑ −=− RLFirstRLLastFSBS

Misclosure

• The leveling process is checked by carrying out a fly-out level to the starting point. The

error in closure is estimated.

• The normally accepted maximum misclosure for a line of ordinary leveling closing back on

the starting point is ± 12 K mm where K is the length of the circuit in km.

• When the specified value has been exceeded, re-leveling should be undertaken.

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2 – Leveling

Example: (Height of Collimation method)

Station +

BS

-

FS

HI (bet. BS and

following line

FS)

RL

(of station)

BM A 1.33 2054.51 2053.18

TP1 0.22 8.37 2064.36 2046.14

TP2 0.96 7.91 2039.42 2038.45

TP3 0.46 11.72 2028.16 2027.69

BM Oak 8.71 2019.44

Check 2.97

- 36.71

36.71 2019.44

- 2053.18

-33.74 -33.74

A

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DISTANCE WITH THE USE OF A LEVEL: STADIA (TACHEOMETRY)

• Stadia is a form of indirect measurement that uses a telescopic cross-hair configuration to

assist in determining distances.

• Additional cross hairs (stadia hairs) are positioned in the telescope an equal distance above

and below the main cross hair such that when the interval (as measured on a leveling rod)

between the upper and lower stadia hairs is multiplied by a constant (usually 100), the

ground distance is determined.

Upper stadia hair

Lower stadia hair

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USE OF LEVELLING

The main uses of leveling are:

Longitudinal Profiles

The objective is to produce on paper the existing ground profile along a particular line, such as

the centerline or roads, railway, road canal, sewer, or main water line.

• Levels should be taken every distance along the centerline (10, 20, or 30 m)

and at Points of change in direction of grade change.

• The profile, line showing ground elevation at a vertical section along a survey line, is drawn

typically for the CL versus distance (chainage).

• It shows the natural ground level (and possibly the finished road level, in case of a roadway

project)

• Scales vary but typically a 10X exaggeration is used for the vertical scale.

• Level is setup off the centerline so that sights of uniform length can be produced.

Avg. gradient between C and D (in our first example) = 20

97.838-98.27 *100 = 2.16 %

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Cross sections

• Works such as roads, railways, embankments and large tanks, will necessitate the use of

ground on either side of the centre line.

• Information regarding relative ground levels is obtained by taking cross-sections at right

angles to the centre line.

• The longitudinal spacing of the sections should be constant if earthworks are to be

computed. A spacing of 20 m is common. The centre line is first set out.

• Pegs (or arrows) are placed at points where cross- sections are required; Cross-sections are

then set out using an optical square or similar instrument to set out right angle.

• Arrows or ranging rods mark the points where levels are required.

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Contouring

• A contour is a line drawn on a plan joining points of equal

elevations.

• Difference between contours elevations is the vertical interval

• Gradient = vertical interval / Horizontal distance

• Close together, steep gradients exist, and as they open, the gradients flatten.

• Contour lines are continuous lines.

• Two contour lines of different value cannot intersect or cross (except at cliff or overhang).

• They close even though outside the area of interest

• Spot elevations may be used instead of contours for flat terrain over large areas.

Contour plot for Old Alkohd Wadi

3D conour plot

for Old Alkohd

Wadi (Digital

Terrain Model)

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a) Contours equally spaced – uniform gradient

b) Slope steeper at the top

c) Slope steeper at the bottom

d) V shape, points upstream - River valley

e) V shape, points downward, forming a nose

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Methods of Contouring

Gridding

• Squares of 10-20 m side are setout.

• Levels are taken at the corners.

• Two sets of lines may be established using ranging rods. To locate a particular corner the

staff man aligns himself in using pairs of ranging rods.

• The reduced levels are plotted on a plan with the same grid.

• Interpolation is used to generate the line of equal elevations (contours).

Radiating Lines

• Rays are setout on the ground from a central point in a known direction.

• Levels are taken along these lines at measured distances from the center.

• Interpolation is used to give the contour lines

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Direct Contouring

1. Can be used in any case, especially in hilly terrain.

2. The level is set up at some position, and the height of collimation is established from a

point of known level (e.g. 33.99 Above MSL).

3. To locate a point 33 m Above MSL, the surveyor directs the staff man up or down the hill

until the staff reads 0.99 (i.e. 33.99-33.00=0.99).

4. The staff man sticks an arrow with colored tape into the ground (one colour being used

for one particular contour line), and moves to another point on the contour.

5. A series of staff readings of 33.99—32= 1.99 would enable the 32 m contour to be set

out, and so on.

6. The positions of the arrows are later surveyed by any suitable method, such as tape and

offset survey, traverse survey, or tacheometry.

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2 - LEVELLING

FALL AND RISE METHOD

Case (a)

• Reading at A = 3.222

• Reading at B = 1.414

• Diff in level = 3.222 – 1.414 = 1.808 m

• This is a rise of land at B relative to A

Case (b)

• Reading B is greater, this represent a fall

at B relative to A by

3.222 – 3.484 = -0.262 m

Case (a) Level at B = Level at A + Rise

128.480 + 1.808 =

130.288 m above MSL

Case (b) Level at B = Level at A – Fall

128.480 – 0.262 =

128.218 m above MSL

Let’s solve the previous example with this method.

Above MSL

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Station BS IS FS Rise Fall RL Distance

BM 0.663 98.760

A 1.946 0

B 1.008 20

C 1.153 40

D (TP) 2.787 1.585 60

E 2.270 80

F 1.218 100

G 0.646 120

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Station BS IS FS Rise Fall RL Distance

BM 0.663 98.760

A 1.946 1.283 97.477 0

B 1.008 0.938 98.415 20

C 1.153 0.145 98.27 40

D (TP) 2.787 1.585 0.432 97.838 60

E 2.270 0.517 98.355 80

F 1.218 1.052 99.407 100

G 0.646 0.572 99.979 120

Check 3.450

-2.231

3.079

-1.86

99.979

-98.760

1.219 1.219 1.219

Check

∑ ∑ −=− RLFirstRLLastFSBS = ∑ ∑− FallsRises

Misclosure

• The leveling process is checked by carrying out a fly-out level to the starting point. The

error in closure is estimated.

• The normally accepted maximum misclosure for a line of ordinary levelling closing back on

the starting point is ± 12 K mm where K is the length of the circuit in km.

• When the specified value has been exceeded, relevelling should be undertaken.

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CURVATURE AND REFRACTION

From the definition of horizontal and level lines, the horizontal departs from the level because of

earth curvature (deviation BD).

It is estimated as:

C = 0.0785 k2K2

C = departure in m

K =distance in km

Q? A and B have the same elevation (on the same level line), If you place a level at A, and

leveling staff at B, would it read D or B (neglecting refraction effect)?

Answer:

Light rays passing through the earth atmosphere are bent or refracted towards the earth’s surface.

The actual line of sight and therefore the reading on the staff will not be at H but at R.

R = 0.011 K2

R = refraction in m

K = distance in km.

It is about 1/7 the effect of curvature

Combined Effect = C + R = (0.0785 – 0.011) K2 = 0.0675 K2

Proper field procedure can eliminate both effects.

B′

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Example:

Calculate the error due to curvature and refraction for the following distances:

a) 1.8 km

b) 100 m

Solution

a) C = +0.0785 * 1.82 = 0.254 m

R = - 0.011 * 1.82 = - 0.036 m

C+R = 0.254 – 0.036 = +0.218 m

b) C+R = 0.0675 * 0.12 = 0.000675 m = 0.675 mm

Notes:

• It is unlikely that we will survey over large areas, effect of curvature is small!! However,

Horizontal distances of BS and FS should be approximately equal by pacing or any other

method.

• This will eliminate the errors due to instrument maladjustment and combined effect of

curvature and refraction.

• In case of (C+R), e1 in BS is added and e2 in FS is subtracted. They are equal if D1 = D2,

then the effect will be eliminated.

• Sight length of no more than 50 m is permitted for first order Class I, and up to 90 m in third

order.

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SOURCES OF ERROS:

1. Instrument

2. Natural

3. Personal

INSTRUMENT

Line of Sight

• A properly adjusted leveling: line of sight and level vial axis parallel.

• Automatic level: the compensator should be operating properly.

• These errors are systematic and canceled if the horizontal lengths of plus and minus sights

are kept equal.

Cross Hair Not Exactly Horizontal

• Reading the rod near the center of the horizontal cross hair will eliminate or minimize this

potential error.

Rod (Staff) Not Correct Length

• Similar to those resulting from incorrect markings on a measuring tape.

• Uniform wearing of the rod bottom makes HI (height if the instrument) values too large.

but the effect is canceled when included in both plus (BS) and minus (FS) sights.

• Rod graduations should be checked by comparing them with those on a standardized tape.

Tripod Legs Loose

NATURAL

Curvature of the Earth

• The effect of curvature of the earth is to increase the rod reading. Equalizing lengths of

plus and minus sights in differential leveling cancels the error due to this cause.

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Refraction

• This decreases rod readings. Balancing the length of plus and minus sights usually

eliminates errors due to refraction.

Temperature Variations

• Heat causes leveling rods to expand, but the effect is not important in ordinary leveling.

• If the level vial of a tilting level is heated, the liquid expands and the bubble shortens. This

does not produce an error (although it may be inconvenient). Unless one end of the tube is

warmed more than the other, and the bubble therefore moves.

• Other parts of the instrument warp because of uneven heating, and this distortion affects

the adjustment.

• Shading the level by means of a cover when carrying it, and by air umbrella when it is

setup will reduce or eliminate heat effects. These precautions are followed in precise

levelling.

• Air boiling or heat waves near the ground surface or adjacent to heated objects make the

rod appear to wave and prevent accurate sighting. Raising the line of sight by high tripod

setups, taking shorter sights, avoiding any that pass close to heat sources (such as buildings

and stacks), and using the lower magnification of a variable-power eyepiece reduce the

effect.

Wind

• Strong wind causes the instrument to vibrate and makes the rod unsteady. Precise leveling

should not be attempted on excessively windy days.

Settlement of the Instrument

• Setups on spongy ground should be avoided if possible.

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PERSONAL (MISTAKES)

Bubble Not Centered

• Particularly on long sights.

• If the bubble runs between the BS and FS sights, it must be recentered before the FS is

taken. Experienced observers develop the habit of checking the bubble before and after

each sight.

Parallax

• Results in incorrect rod readings.

Faulty Rod Readings

Rod Handling

• Serious errors caused by improper plumbing of the rod are eliminated by using a rod level

• Banging the rod on a turning point for the second (plus) sight may change the

elevation of a point.

Holding the Rod in Different Places for the Plus and Minus Sights on

a TurningPoint

• The rod person can avoid such mistakes by using a well-defined point or by outlining

the rod base with lumber crayon.

Reading a meter too High

Recording Notes

Touching Tripod or Instrument during Reading Process

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REDUCING ERRORS AND ELIMINATING MISTAKES

Errors in running levels are reduced (but never eliminated) by carefully adjusting and

manipulating both instrument and rod and establishing standard field methods and

routines. The following routines prevent most large errors or quickly disclose mistakes:

(1) Work early

(2) Checking the bubble before and after each reading (if an automatic level is not being

used).

(2) Shade the level

(3) Using a rod level.

(4) Keep reading above 0.3 m

(5) Taking the three hair reading

(6) Keeping the horizontal lengths of plus and minus sights equal,

(7) Running lines forward and backward.

(8) Making the usual field-book arithmetic checks.

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2 - LEVELLING

TWO-PEG TEST (PERMANENT ADJUSTMENT OF TILTING LEVEL)

• This test is to ensure that the bubble tube axis is parallel to the telescope axis.

• When the bubble is centered, the line of sight should be horizontal.

• This test would also work with a dumpy level or an Automatic level but the adjustment in

this case would be using the diaphragm (reticle) screws to move the cross hair vertically.

o On flat site, two pegs are set at A and B approx. 50 m apart.

o Setup the level halfway between them.

Staff reading at A = a1

Staff reading at B = b1

o Move the level to Q beyond AB by 25 m.

Staff reading at A = a2

Staff reading at B = b2

• Assuming the line of sight is not horizontal then the collimation error (angle) e:

e (in rad.) = tan e

Horizontal line

Line of sight (collimation)

Horizontal line

Line of sight

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Note: elevationinDifferenceTruehAB =∆

Level at P

)()( 2111 edbedahAB −−−=∆

21 dd =

11 bahAB −=∆

• Even when the instrument is not in correct adjustment, the difference in height is

correct when the points are equidistant.

Level at Q

][])([ 323212 edbedddahAB −−++−=∆

eddbahAB )()( 2122 +−−=∆

Equate the two equations

eddbabahAB )()( 212211 +−−=−=∆

)()()(

21

1122

ddbabae

+−−−

=

• If e is < |0.00005| then no adjustment is necessary.

• If the error is greater than this, the level should be adjusted.

• With the instrument still set at Q a horizontal line of collimation would give a reading on the

staff at A of:

a2 - (d1+d2+d3)e

• Using the tilting screw, the line of collimation is lowered (or raised if e is negative) to the

correct staff reading and then the bubble is brought to its central position using the capstan

screws, which alter the alignment of the bubble with respect to the telescope.

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Example: Checking the adjustment of a tilting level

• Pegs at A, P, B and Q were set out to lie on a straight line such that AP = PB = BQ = 30 m.

• The level was set up at P and readings taken to a staff at A and then at B.

• The level was then moved to Q and readings again taken to a staff held first at A and then at

B.

• Check whether the level is in adjustment and recommend the correction if needed.

Staff Reading, m Instrument

position B A

b1=1.462

b2=1.945

a1= 1.926

a2=2.445

P

Q

Solution

From P: Apparent (=True) difference in elevation AB = 1.926 - 1.462 = 0.464 m

From Q: Apparent difference in elevation AB = 2.445 - 1.945 = 0.500 m

Clearly the instrument is in error.

To adjust, first calculate the collimation error

.0006.060

464.0500.0 Rade =−

=

• Note that the difference in height between A and B is greater when deduced from the staff

readings with the level at Q than at P. This implies that the staff reading of 2.445 is too high

and so the collimation error is upward.

Adjustment

• With the instrument set at Q a horizontal line of collimation would bisect staff at A at

2.445 - (0.0006 x 90) = 2.391 m

• This staff reading is set using the tilting screw and the bubble brought to its central (level)

position using the bubble adjusting screws.

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RECIPROCAL LEVELLING

In situations where it is difficult to keep the BS and FS short and equal, this technique can be

used. Going back to the effect of curvature, E = error reading on the staff due to curvature and

refraction.

a) )( 11 EYXhXY −−=∆ = EYX +− 11 =Apparent difference in elevation + correction

b) EYXYEXhXY −−=−−=∆ 2222 )( =Apparent difference in elevation – correction

True difference in elevations = 0.5 (sum of Apparent difference in elevation)

This corrects for effects of curvature, refraction (and instrument error).

E

E

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Example:

In levelling a cross a river, reciprocal levelling observations gave the following results for staffs

held vertically at A and B from level stations X and Y on each bank respectively:

Level at X Level at Y

Reading at A = 1.753 2.080

Reading at B = 2.550 2.895

If the RL of A is 90.37 above MSL, find RL of B.

Solution:

• Note that staff reading at B is higher than A Fall.

• Instrument at X: Apparent difference in elev. = 1.753 – 2.550 = - 0.797 m

• Instrument at Y: Apparent difference in elev.= 2.080 - 2.895 = - 0.815 m

• Therefore the True difference in elev. = 0.5*[-0.797 + -0.815] = - 0.806 m

• Therefore RL of B = 90.37 - 0.806 = 89.564 above mean seal level.

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LEVEL OF BRIDGES

An inverted staff is hung from the bridge roof and a reading is taken and recorded with negative

sign in the booking (see the Fig. Below)

• RL of bridge roof = 56.520 - (-2.535) = 59.055 m above MSL

• The clearance of the bridge = 1.555+2.535 = 4.09 m

OTHER TYPES OF LEVELLING TECHNIQUES

Trigonometric leveling

By measuring the horizontal or inclined distance between two points + vertical angle a.

HAB = HI + DC Sin EDC – CB

If DE is used, the equation involves “tan α”.

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Taping or Electronic Methods

Tape can be used to measure vertical lines such as depth of mine shaft, floor elevations, layout of

multistory buildings. EDM devices can replace the tape for measuring vertical distances on

construction sites.

Reflectorless EDM used to measure elevation differences in construction applications

Barometric Levelleing

Barometer is an instrument that measures air pressure. Using this property, the elevation can be

obtained. This needs calibration and it generally provides a scale of 0.5 to 1.0 m. This is not an

accurate method.