Over time, surveyors and engineers have developed several methods of levelling, each suited to different conditions and requirements. These methods vary in their approach, equipment used, accuracy, and applicability to different terrains and project scales. The choice of levelling method depends on factors such as the required precision, the nature of the terrain, the size of the area to be surveyed, and the available resources.
Based on the principle used, levelling can be categorized into the following methods:
- Spirit Levelling (Direct Levelling)
- Trigonometric Levelling (Indirect Levelling)
- Barometric Levelling
- Hypsometric Levelling
i. Spirit Levelling (Direct Levelling)
Spirit levelling is the most common and precise method of determining elevation differences between points. It relies on the fundamental principle of establishing a horizontal line of sight and measuring vertical distances relative to this line. The process involves establishing a horizontal line using an instrument called a spirit level, while the vertical distances above or below this line are measured using a graduated levelling staff.
Spirit levelling may be classified as :
1. Differential levelling
2. Check levelling
3. Profile levelling
4. Cross-sectioning levelling
5. Reciprocal levelling
6. Precision levelling.
7. Fly levelling
1. Differential Levelling (Compound or Continuous Levelling)
Differential levelling refers to the process of determining the difference in elevation between two or more points, irrespective of their horizontal alignment. This method is employed when:
- The points are far apart.
- There is a significant difference in elevation between the points.
- An obstacle obstructs the direct line of sight between the points.
Procedure of Differential Levelling
In differential levelling, the level instrument is set up in several intermediate positions between the points of interest. A backsight (B.S.), intermediate sight (I.S.), and foresight (F.S.) are taken at each stage to progressively determine the height differences.
- Backsight (B.S.): The reading taken on a point with a known elevation, such as a benchmark (B.M.). It is used to establish the height of the instrument (H.I.) relative to the reference point.
- Intermediate Sight (I.S.): Readings taken at intermediate points between the backsight and foresight to monitor height changes.
- Foresight (F.S.): The reading taken at the final point whose elevation is to be determined.
The process involves moving the level to different positions between the points, repeating the readings until all points have been connected. The sum of the backsight readings is added to the benchmark elevation, while the foresight readings are subtracted to determine the elevation at each point.
2. Check Levelling
Check levelling is a process used to verify the accuracy and stability of previously established benchmarks. This method involves running a level line over a known set of benchmarks to ensure that their elevations remain consistent over time. By comparing the new measurements to the original values, surveyors can determine if any of the benchmarks have shifted or if there were errors in earlier levelling work.
The Purposes of check levelling are :
- To confirm the accuracy of existing benchmarks
- To detect any errors in previous levelling work
- To identify any changes in benchmark elevations due to settlement or other factors
- To validate the day’s levelling work
Best Practices for Check Leveling
- Use different instrument setups from the original levelling work
- If possible, employ a different surveyor or team for check levelling
- Conduct check levelling under similar environmental conditions as the original work
- Keep detailed records of both original and check levelling results
Example of Check Levelling
Starting at Point A with an elevation of 92.5 m, levels were taken along a section to Point B, where the reduced level (R.L.) was found to be 98.15 m. The difference in elevation from A to B was 5.65 m.
When check levels were run back from B to A along the shortest route, the observed difference in elevation was 5.45 m, indicating an error of 0.2 m. This error may result from minor instrument or procedural inaccuracies and should be corrected if within acceptable limits.
3. Longitudinal or Profile Levelling
Longitudinal or profile levelling is a surveying technique used to determine the elevations of points at known intervals along a specified line, providing an accurate representation of the ground surface profile. This technique is essential for various civil engineering projects such as the construction and design of sewers, pipelines, highways, railways, and canals.
The Purposes of profile levelling are :
- To create vertical sections of the ground surface along a surveyed line
- To provide essential data for designing and constructing linear infrastructure projects
- To determine cut and fill volumes in earthwork calculations
- To compare alternative routes for cost and feasibility analysis
Procedure of Profile Levelling
- Establish a baseline or centerline for the project
- Set up levelling instrument and take readings at:
• Regular intervals (stations)
• Points where ground slope changes
• Critical points (e.g., stream crossings, road intersections) - Record both elevation readings and chainage (horizontal distance) for each point
- Use differential levelling principles, including: • Backsights on known points or change points • Intermediate sights along the profile • Foresights to establish new change points
- Note important features along the profile (e.g., streams, roads, structures)
Key Considerations in Profile Levelling
- Accuracy is crucial for subsequent design and construction work
- Multiple profiles may be needed to compare alternative routes
- Attention to detail in recording both elevations and horizontal distances is essential
- Understanding of local topography and project requirements helps in identifying critical points for measurement
4. Cross Sectional Levelling
Cross-sectioning is a levelling technique used to determine the elevation of points located perpendicular to the main line of a proposed route, typically at right angles on either side of the centerline. This method helps create a vertical profile of the ground surface. Cross-sectioning is often performed radially on curves and provides essential data for understanding the variations in elevation across the terrain.
This information is critical in engineering projects as it allows for the accurate calculation of earthwork volumes. The cross-sections are plotted similarly to longitudinal sections, with both horizontal and vertical measurements being drawn to the same scale, ensuring a precise representation of the land’s contour.
5. Reciprocal Levelling
Reciprocal levelling is a method used to accurately determine the difference in elevation between two points by performing two sets of reciprocal observations. Reciprocal levelling is used to accurately determine the elevation difference between two points when direct levelling is impractical or prone to significant errors. This technique is particularly useful in situations where an obstruction, such as a valley or river, prevents setting up the levelling instrument between the two points.
Procedure of Reciprocal Levelling
First Setup: The instrument is first positioned near point A on one side of the obstruction. A reading is taken on the staff held at point A (let’s call it reading a, which is error-free due to the short distance) and on the staff held at point B on the opposite side of the valley (reading b, which may contain an error e due to curvature, refraction, and collimation).
Second Setup: The instrument is then moved near point B, and a new set of readings is taken. A reading is taken on the staff at B (let’s call this c, which is error-free) and again on the staff at A (reading d, which contains an error e).
Formula for True Elevation Difference
The true difference in elevation (h) between points A and B can be calculated as:
h = 1/2 * [(b – a) + (c – d)]
This formula accounts for the errors in the readings. The error e due to curvature, refraction, and collimation can also be computed as:
e = 1/2 * [(b – a) – (c – d)]
In deriving these equations, it is assumed that atmospheric refraction has the same effect during both sets of observations. However, if only one instrument is used, there may be a time delay in moving the instrument, which could result in changes in the refraction. To mitigate this, it is recommended to use two instruments—one at each point—so that observations can be made simultaneously.
Although using two levels provides more accurate results, each instrument may have its own collimation error. To account for this, it is advisable to interchange the instruments and repeat the procedure. The mean of the four readings will yield the most accurate difference in elevation between the two points.
6. Precise Levelling
Precise levelling is a method of levelling that provides the highest degree of accuracy. It is primarily used for establishing a network of permanent benchmarks in a country for future reference. This method is typically carried out by national surveying organizations, such as the Survey of India. While the principles of precise levelling are similar to those of ordinary levelling, it uses specialized instruments and includes the application of corrections to minimize errors. The levelling staves used in precise levelling are graduated to very fine measurements, often 0.1 mm or finer, whereas ordinary levelling staves are graduated to 0.05 cm.
Precise levelling is defined as the process of levelling done using instruments designed to allow readings with greater precision. The most commonly used tool is a parallel-sided plate micrometer fitted to a telescope with about 30x magnification, accompanied by a tubular bubble with high sensitivity for precise alignment.
Classification of Precise Levelling
Precise levelling is classified based on the degree of accuracy required:
Primary Levelling (First Order Levelling):
- Description: This is the most accurate type of levelling, where the maximum permissible error is ± 4 √K mm, where K is the total distance of the level line in kilometers.
- Maximum Staff Distance: The distance from the instrument to the staff should not exceed 50 to 60 meters.
Secondary Levelling (Second Order Levelling):
- Description: For second-order precise levelling, the permissible closure error is ± 8 √K mm, where K is the length of the level circuit in kilometers.
- Maximum Staff Distance: The distance from the instrument to the staff is limited to 60 to 70 meters.
Tertiary Levelling (Third Order Levelling):
- Description: Third-order levelling involves a permissible closure error of ± 12 √K mm, where K represents the total length of the level circuit.
- Maximum Staff Distance: The staff distance from the instrument should not exceed 90 meters.
In precise levelling, accuracy is paramount, and the limitations on staff distance and allowable error reflect the need to maintain precision throughout the survey process.
7. Fly Levelling
Fly levelling is a type of levelling operation where a line of levels is quickly run to determine approximate elevations along a specific route. This method is primarily used for reconnaissance or preliminary surveys of linear structures such as roads, railways, tunnels, and canals. The purpose is to gather basic elevation data to assist in the planning and design stages of such infrastructure projects.
Fly levelling provides a general idea of the terrain but lacks the precision required for detailed construction work.
ii. Trigonometric Levelling (Indirect Levelling)
Trigonometrical levelling is an indirect method of determining the difference in elevation between points by using observed vertical angles and measured distances. The vertical angles are measured with a transit, while the distances can either be measured directly or calculated using trigonometric formulas.
This method is especially useful in topographical surveys, where it is used to determine the elevations of structures such as buildings, chimneys, and church spires. Additionally, it proves advantageous in challenging terrains, such as mountainous areas, where direct levelling methods may be impractical.
Since field conditions and the capabilities of available instruments vary, there are numerous possible scenarios for using trigonometrical levelling. The approach can be adapted to fit different cases, many of which can be solved through practical applications by surveyors.
From the right-angled triangle CFE: h = D * tan(θ)
Where: h = FE (height difference between instrument and top of object)
D = CE (horizontal distance)
θ = angle of elevation
Final Elevation Calculation:
R.L. of F = R.L. of BM + S + h
= R.L. of BM + S + D * tan(θ)
Limitations of Trigonometric Levelling
- Less precise than direct levelling methods for short distances
- Accuracy depends on the precision of angle and distance measurements
- Affected by atmospheric refraction, especially over long distances
iii. Barometric Levelling
Barometric levelling operates on the principle that the elevation of a point is inversely proportional to the weight of the air column above the observer. However, the relationship between air pressure and elevation is not linear because air is compressible. Factors such as temperature, humidity, and weather conditions (especially storms) also affect air pressure, making this method less precise. Barometric levelling is particularly suited for rough terrains where high precision is not required. It is also used for converting slope distances to horizontal distances in electronic measurements.
The instrument used to measure atmospheric pressure is a barometer. A modified version of the barometer, called an altimeter, is used to determine the relative elevations of points on the earth’s surface. Though simple in operation, altimeters are sensitive to atmospheric pressure changes.
Single Base Method
n this method, two altimeters are used:
- Control Altimeter: One altimeter, along with a thermometer, is placed at a control point with a known elevation. Readings are taken at regular intervals.
- Roving Altimeter: The second altimeter is used to take readings at the points where the elevation is to be determined.
The readings from the roving altimeter are adjusted based on the changes in temperature and atmospheric pressure observed at the control point. The difference in elevation between the two points is calculated using the following formula:
H = 18336.6 * (log₁₀h₁ – log₁₀h₂) * (1 + (T₁ + T₂) / 500)
Where:
- H = difference in elevation between the two points (in meters)
- h₁, h₂ = barometric readings (in cm) at the lower and higher points, respectively
- T₁, T₂ = air temperatures (in °C) at the lower and higher points, respectively
This method is useful for estimating elevation changes, though it is less accurate due to sensitivity to atmospheric conditions.
Limitations of Barometric Levelling
- Lower accuracy compared to geometric or trigonometric levelling
- Sensitive to atmospheric conditions (temperature, humidity, weather)
- Requires frequent calibration and corrections
iv. Hypsometric Levelling
Hypsometric levelling is used to determine the reduced levels of various points over long distances in hilly or mountainous terrain. This method relies on a device called a thermo-barometer, also known as a hypsometer, and is based on the principle that “a liquid boils when its vapour pressure equals the atmospheric pressure.”
The boiling point of a liquid, particularly water, depends on the pressure to which it is subjected. As altitude increases, atmospheric pressure decreases, causing the boiling point of water to lower. By measuring the boiling point of water at different locations, hypsometric levelling helps in estimating elevation differences.
Principle of Hypsometric Levelling
The boiling point of water decreases as altitude increases due to lower atmospheric pressure. The hypsometer is used to measure this boiling point at various points where elevation needs to be determined.
Hypsometer Setup
A hypsometer is essentially a highly sensitive thermometer, graduated to 1/5 degree Fahrenheit or 1/10 degree Celsius. During observation, the hypsometer is held vertically by a telescopic tube and suspended over a small boiler filled with rainwater. A spirit lamp heats the water until it boils, and the hypsometer measures the temperature of the steam just above the water surface. A second thermometer is used to measure the surrounding air temperature.
The boiling point of pure water at sea level is 100°C (212°F) when the atmospheric pressure is 76 cm of mercury (29.92 inches) and the air temperature is 0°C (32°F).
Calculations
- Barometric Pressure Calculation: Barometric height (cm of mercury) = 76.00 ± 2.679 t₁ Where t₁ = difference of observed boiling point from 100°C
- Elevation Difference Calculation: H = 18336.3 * (log h₁ – log h₂) * (1 + (T₁ + T₂) / 500) Where: H = Elevation difference h₁, h₂ = Barometric heights at lower and higher points T₁, T₂ = Air temperatures at lower and higher points
Limitations of Hypsometric Levelling
- Less accurate than traditional levelling methods
- Sensitive to atmospheric conditions and water purity
- Requires careful calibration and operation
