An In-Depth Analysis of Leveling Techniques in Surveying: Methods, Instruments, and Applications

What Is Leveling?

Leveling is the most widely used method for obtaining this elevation of ground points relative as a reference datum & is usually carried out as a separate procedure from that used for fixing a planimetric position.

Leveling involves the measurement of a vertical distance relative to a horizontal line of sight. Therefore it requires a graduated staff for the vertical measurements and an instrument that will provide a horizontal line of sight.

Leveling Methods in Surveying.

1. Direct Leveling (Spirit Leveling)
2. Barometric Leveling
3. Hypsometric Leveling
4. Stadia Leveling 
5. Indirect Leveling (Trigonometric Leveling) 

1. Direct Leveling (Spirit Leveling)

Direct leveling is a common form of leveling. In this method, the telescope is made horizontal, and the horizontality is checked using a spirit level. Horizontal sight is taken on a graduated staff held at the point. Reading helps in finding the difference in elevation.

Types of Direct Leveling

1. Simple Leveling
2. Differential Leveling
3. Reciprocal Leveling
4. Precise Leveling
5. Fly Leveling

1.1. Simple Leveling

It’s the simplest operation in levelling when it’s necessary to locate the difference in elevation between two points, each of which is visible from a single position of the level. The readings can be obtained on a staff held successively upon these points.

The precise situation of the level is immaterial, but to eliminate the instrumental error, the sight distances to the two staff positions should be kept as nearly equal as possible. The level is set on a firm ground anywhere, not necessarily in the same vertical plane as that of the two staff positions.

Sampling leveling

1.2. Differential Leveling

Determining this difference in elevation between two or more points without any regard to the alignment of the points is called differential leveling. It is used when:

1. Two points are a large distance apart (as below fig -1)
2. The difference in elevation between the two points is large (as below fig -2) and
3. Some obstacle intervenes between the points (as below fig-3)

Differential leveling (Point far apart) fig-1

Differential leveling (Point with large difference of elevation) fig-2

Differential leveling (Point having an obstacle in between ) fig-3

1.3. Reciprocal Leveling

It is the operation of leveling where the difference in elevation between two points is accurately determined by two sets of reciprocal observations. This method is very useful when the instrument cannot be set up between the two points because of an obstruction such as a valley, river, etc., and if the sights are much longer than are ordinarily permissible.

For such long sights, the errors of reading the staff, the curvature of the earth, and the imperfect adjustments of the instrument become prominent. Special methods like reciprocal leveling should be used to minimize these errors.

Reciprocal Leveling

1.4. Precise Leveling

This is the operation of leveling in which precise instruments are used. In principle, there is no difference between ordinary and precise leveling. In the former, the distances between checkpoints are relatively short, and the elevations obtained are satisfactory for routine purposes.

However, for precise leveling, the level loop may be of substantial length, and efforts are made to control all the sources of errors. The most important error control in precise leveling is the balancing of foresight and backsight distances.

1.5. Fly Leveling

It is an operation of leveling in which a line of levels is run to determine the approximate elevations along a route. It is carried out for reconnaissance of linear structures such as roads, railways, tunnels, canals, etc.

Fly Levelling

2. Barometric Leveling

The principle used in barometric leveling is that the elevation of a point is inversely proportional to the weight of the air column above the observer. However, the relationship between pressure and elevation is not constant as air is compressible. Sudden changes in temperature, humidity, and weather conditions due to storms also affect the pressure.

The barometric methods are particularly suited for work in rough country, where high precision is not desirable. These are also used to reduce the slope distances to horizontal when measured electronically. The instrument used for measuring pressure is called a barometer. The modified form of a barometer used to find relative elevations of points on the surface of the earth is called altimeter.

It is simple in operation but very sensitive to changes in atmospheric pressures. The method used to measure elevations with an altimeter is known as a single base method. Two altimeters are required. One altimeter, along with a thermometer, is placed at a point of a known elevation called the control point, where the readings are taken at regular intervals.

The other altimeter, called roving altimeter, is taken to the points whose elevations are desired. Readings of the roving altimeter taken at the desired points are adjusted later in accordance with changes in temperature and the like observed at the control point. The difference in elevation between the two points may be obtained by the following formula:

H = 18336.6 x (log10 h1 – log 10 h2) x (1+ ( (T1 + T2)/500))

H = The difference in elevation between the two points.

h1. h2 = The Barometric (in cm) at the lower and higher point respectively, &

T1.T2 =Tempratuers pf air (in ⁰C) at the lower and higher points respectively

Type of Barometric Leveling

1. Barometer 
2. Mercurial Barometric

2.1. Barometer 

Barometers are used in leveling for a rough determination of elevations, a difference of elevations, and the flying height of aeroplanes in aerial photogrammetry. They are also used for calculating the refraction correction in certain kinds of astronomical observations.

Since leveling with the barometer is not very accurate, it is normally used only for topographical and reconnaissance surveys on a small scale, where great accuracy in the determination of elevations is not essential. Two kinds of barometers, the mercurial and the aneroid, are available (as per below fig.). The former is more accurate but is inconvenient to carry and breaks easily.

Barometer 

2.2. Mercurial Barometric

The Mercurial barometer depends on the principle of balancing a column of mercury against the atmospheric pressure, the atmospheric pressure at the point of observation being a function of the elevation of this point above mean sea level.

There are two main types of mercurial barometers—cistern and siphon. Mercurial barometers need to be supported vertically and are therefore often suspended by some form of gimbal mounting attached to a special tripod.

In the cistern type of barometer, the mercury is contained in a glass tube about 85 cm long, the upper end of which is closed, whereas the lower open end is immersed in a cistern containing mercury open to the atmosphere. The tube is exhausted of air so that the space above the level of the mercury in the tube is a vacuum.

Since the pressure on the mercury in the cistern is atmospheric and there is no pressure on the upper end of the column of mercury in the tube, a column of mercury is maintained in the tube; the height of which depends upon the pressure on the surface of the mercury in the cistern.

In the syphon type of mercury barometer, the tube containing mercury is bent into a U-shape at the lower end. One of the branches of the U-tube is kept shorter than the other. A small opening is provided in the upper end of the short branch to admit air, while the long branch is closed at the top with the vacuum at its top. This type of barometer is inferior to the cistern type and is not much in use.

3. Hypsometric Leveling

The altitudes of various points may be obtained by using an instrument known as a hypsometer. It works on the principle which a liquid boils when its vapor pressure is equal to the atmospheric pressure.

It may be noted that the boiling point of water is lowered as the pressure decreases, i.e., as a higher altitude is attained. The method, therefore, consists in determining the boiling point temperatures at various stations.

The corresponding atmospheric pressures may be obtained from the tables. In the absence of tables, the following approximate formula may be used:

h = 76.00 ± 2.679 t

t is the difference of boiling point from 100°C, and It is the pressure in cm.

The difference in elevations may be obtained by using the formula given below formula.

H = 18336.6 x (log10 h1 – log 10 h2) x (1+ ( (T1 + T2)/500))

H = The difference in elevation between the two points.

h1. h2 = The Barometric (in cm) at the lower and higher point respectively, &

T1.T2 =Tempratuers pf air (in ⁰C) at the lower and higher points respectively

The hypsometer (as per above fig.) consists of a thermometer graduated to 0.1°C. It is fitted inside a telescopic tube and is suspended over a small boiler filled with distilled water.

The thermometer is kept in steam and is adjusted so as not to touch the water. The temperature of this air in the shade is also observed simultaneously with a detached thermometer.

4. Stadia Leveling

It is also known as Tacheometric Surveying. This common method of measuring horizontal distances is chaining, and that for measuring vertical distances is differential leveling.

Both of these methods give results to the required accuracy. Chaining, however, on rough grounds does not furnish very accurate results. When the ground is rough and more observations at a faster rate with ordinary precision are acceptable, then the tachometer is the choice.

An example of the use of a tachometer for the above-said conditions is the collection of data to draw contours on a topographic map. As compared to chaining on flat grounds, the accuracy of tachymetric distances is low, but on rough and steep grounds, the accuracy is more.

A tachometer is defined as an optical distance measurement method. Though less accurate, this method of surveying is very rapid and convenient. The other names given to the tachometer are tachymetry or telemetry. The primary object of a tachymetric survey is the preparation of a contoured plan.

It is particularly suitable for filling at details on topographical maps, preliminary location surveys (e.g., for railways, roadways, canals, reservoirs, etc.) and surveying steep grounds, broken boundaries, and water stretches, etc.

Also, on surveys of higher accuracy, it may be used to provide a ready check on distances measured with a chain or tape. A tachometer is essentially a transit theodolite, the diaphragm of which is furnished with stadia wires in addition to the cross-wires.

Observations are made on stadia rod, usually a level staff but with a larger least count (1 cm), and horizontal as well as vertical distances are computed from these observed readings.

Stadia digraph

5. Indirect Leveling (Trigonometric Leveling) 

This is an indirect method of leveling in which the difference in elevation of the points is determined from the observed distances measured and vertical angles.

The vertical angles are measured with transit, and the distances are measured directly or computed trigonometrically. Trigonometrical leveling is commonly utilized in topographical work to find out the elevation of the top of buildings, chimneys, church spires, etc.

Also, it may be used to its advantage in difficult terrains like mountainous areas. Depending on the field conditions and the measurements which may be made with the instruments available, there may be innumerable cases. An attempt has been made to solve a few cases, and many more can be solved by the reader himself.

5.1. The base of the Object Accessible—The Object may be Vertical or Inclined

In as per below fig., AF is the vertical object, D is the horizontal distance between the object and instrument, S is the reading on the leveling staff held vertical on the B.M., h1 is the height of the instrument, h is the height FE, and θ is the angle of elevation on the top of the object.

Reduce the level of the top of a vertical object

From triangle CEF,

1. EF = CE tan θ
2. h = D tan θ
3. Reduced Level of F = R.L of B.M. + S +h
4. Reduced Level of F = R.L of B.M. + S + D tan θ 

In as per below fig., AF is the inclined object, x is the distance between the foot of the object and the projection F’ of the top, O1 and O2 are the instrument stations such that O1, O2 and A are in the same vertical plane, D1 and D2 are the distances of the foot of the object from the instrument stations O1 and O2, respectively.

S1 and S2 are the staff readings on B.M. from instrument positions at O1 and O2, respectively,  and θ1 and θ2 are the angles of elevation from O1 and O2, respectively.

Reduce the level of the top of an inclined object

Reduced Level of F = R.L of B.M. + S1 +h1

Reduced Level of F = R.L of B.M. + S + (D1 + x) tan θ 1

Reduced Level of F = R.L of B.M. + S1 +h1

Reduced Level of F = R.L of B.M. + S + (D2 –  x) tan θ 2

x = ( S2 – S1 ) + D2 tan θ2 – D1 tan θ1 / tan θ1 + tan θ2

5.2. The base of the Object Inaccessible—The Instrument Stations and the Elevated Object are in the Same Vertical Plane

When the horizontal distance between the instrument and the elevated object is inaccessible, the observations are made from two instrument stations. Assuming the two instrument stations and the object to be in the same vertical plane, the following two cases arise.

5.2.1. Instrument Axes at Same Level

In as per below fig, h is the vertical distance FA’, S is the staff reading on the B.M., θ1 and θ2 are the angles of elevation from the instrument stations O1, and O2 respectively, D is the horizontal distance between O1 and the object, and d is the horizontal distance between the two stations.

h = D tan θ1

h = (D + d) tan θ2

Reduced Level of F = R.L. of B.M. S + h

D = d tan θ2 / (tan θ1 – tanθ2 )

5.2.2. Instrument Axes at Different Level

Depending upon the terrain, three cases arise:

1. Instrument axis at O2 higher than that at O1
2. Instrument axis in O1 higher than that at O2
3. Instrument axes at very different levels

5.2.2.1. Instrument axis at O2 higher than that at O1 (as per below fig.)

h1 – h2  = S2 – S 1 = S

From triangle O1′ A” F, h1 = D tan θ1

From triangle O2′ A” F, h2 = (D + d) tan θ2

Reduced Level of F = R.L. of B.M. S1 + h1

D = (S+ d tan θ2) /(tan θ1 -tan θ2)

5.2.2.2. Instrument axis in O1 higher than that at O2

h2 – h1  = S1 – S 2 = S

From triangle O1′ A” F, h1 = D tan θ1

From triangle O2′ A” F, h2 = (D + d) tan θ2

Reduced Level of F = R.L. of B.M. S1 + h1

D = (d tan θ2 – S) /(tan θ1 -tan θ2)

5.2.2.3. Instrument axes at very different levels (as per below both fig. )

If the difference at elevation (S2 – S1) between the two instrument stations is too large and cannot be measured on staff at the B.M., then the following procedure is adopted:

Set up this instrument at O1 and measure the vertical angle at point F (as per below fig.).

Transit the telescope and establish a point O2, at a distance d from O1.

Shift this instrument to O2 and measure the vertical angle at point F.

Observe the staff reading r with respect to horizontal cross-wire on the staff at O1 (as per below fig). Let S be the difference at a level between the two axes in O1 and O2.

S = h2 – h1

D = ( d tan θ2 – S) / ( tan θ1 – tan θ2 )

Reduced Level of F = R.L. of B.M. S1 + s + h1

Reduced Level of F = R.L. of B.M. S1 + d tan θ – r + h’ +h1

Frequently Asked Questions (FAQ)

What Is Leveling in Surveying?

Leveling in surveying is a method used to determine the elevation of ground points relative to a reference datum. It involves measuring vertical distances from a horizontal line of sight using a graduated staff and a leveling instrument.

What Are the Primary Methods of Leveling?

The primary methods of leveling include:

1. Direct Leveling (Spirit Leveling)
2. Barometric Leveling
3. Hypsometric Leveling
4. Stadia Leveling
5. Indirect Leveling (Trigonometric Leveling)

What Is Direct Leveling and How Is It Performed?

Direct Leveling, or Spirit Leveling, involves using a leveling instrument to take horizontal sights on a graduated staff. The instrument’s horizontal line of sight is used to measure the vertical distance between points.

What Are the Types of Direct Leveling?

Types of Direct Leveling include:

1. Simple Leveling
2. Differential Leveling
3. Reciprocal Leveling
4. Precise Leveling
5. Fly Leveling

How Does Barometric Leveling Work?

Barometric Leveling relies on measuring atmospheric pressure with a barometer. The elevation of a point is inferred from the air pressure, with adjustments made for temperature and other atmospheric conditions.

What Is Hypsometric Leveling?

Hypsometric Leveling uses a hypsometer to determine altitude based on the boiling point of water, which changes with atmospheric pressure. The boiling point temperature is used to calculate the elevation.

What Is Stadia Leveling and When Is It Used?

Stadia Leveling, or Tachymetric Surveying, involves using a tachometer to quickly measure horizontal and vertical distances. It’s particularly useful for surveying rough or steep terrain and creating topographic maps.

How Does Indirect Leveling (Trigonometric Leveling) Differ from Other Methods?

Indirect Leveling, or Trigonometric Leveling, determines elevation differences using measured distances and vertical angles. It is used in challenging terrains and for surveying tall structures.

What Instruments Are Used in Leveling?

Instruments commonly used in leveling include:

1. Leveling Instruments (e.g., theodolites and spirit levels)
2. Barometers
3. Hypsometers
4. Tachometers

What Are the Key Considerations When Choosing a Leveling Method?

Considerations include:

1. Accuracy Requirements
2. Terrain Type (e.g., flat, rough, or steep)
3. Distance Between Points
4. Environmental Conditions