Name: curvature and refraction in survey leveling
Uploaded: 2025-03-26T15:16:57.000Z
Duration: 1 min 26 s
Channel: JoVE

K12 Standards

Pennsylvania State Academic Standards

9-12

Earth and Space Science

Weather and Climate

3.3.9-12.E

influence-of-earth-s-curvature-and-atmospheric-refraction-on-leveling

Influence of Earth's Curvature and Atmospheric Refraction on Leveling

While leveling, due to Earth's curvature, the level&#8217;s line of sight is perpendicular to a plumb line only at one point and deviates further from the level line.This deviation, C, is determined by considering a right-angled triangle with sides E, representing the Earth&#8217;s radius, D, representing a horizontal distance corresponding to a deviation C, and hypotenuse E + C.&#160;From the equation connecting the sides of the triangle and neglecting the value of C2 as its magnitude is much less compared to the magnitude of E2, an expression for the deviation is derived.&#160;This expression indicates that the Earth's curvature causes a horizontal line to deviate by 0.0785 meters over 1 kilometer, increasing with the square of the distance.Also, during leveling, the atmospheric refraction causes the line of sight to bend downwards by about 0.011 meters in 1 kilometer, about one-seventh of the Earth&#8217;s curvature effect.Combined, the effect of curvature and atmospheric refraction, cause the level's line of sight to deviate by approximately 0.0675 meters in 1 kilometer, varying with the square of the horizontal distance.

influenza della curvatura terrestre e della rifrazione atmosferica sul livellamento

Durante il livellamento, la curvatura terrestre e la rifrazione atmosferica introducono deviazioni nella linea di mira da un vero riferimento orizzontale. Quando la linea di vista &#232; livellata, rimane perpendicolare alla linea a piombo solo in un singolo punto. Oltre questo, devia a causa della curvatura terrestre, rappresentata dalla correzione C. Per una distanza di vista D, la deviazione pu&#242; essere derivata utilizzando la relazione:<figure class='image image-style-align-center image_resized' style='display:table;margin-left:auto;margin-right:auto;width:9.51%;'><img style='aspect-ratio:197/150;' src='https://cloudfront.jove.com/files/ftp_upload/18021/18021_Equation_1_editor_18021.svg' alt='18021_Equation_1.svg' /></figure>Questa relazione, mostra che la deviazione aumenta quadraticamente con la distanza. Su una distanza orizzontale di 1 chilometro, &#232; di circa 0,0785 metri.Oltre alla curvatura, la rifrazione atmosferica piega la linea di vista verso il basso, deviandola ulteriormente dal vero orizzontale. L'effetto di piegatura &#232; di circa un settimo della deviazione della curvatura terrestre, pari a circa 0,0112 metri su 1 chilometro. Questa rifrazione deriva dalle variazioni dell'indice di rifrazione dell'aria con l'altitudine, che causano una leggera curvatura dei raggi luminosi.L'influenza combinata della curvatura terrestre e della rifrazione atmosferica &#232; di circa 0,0675 metri su 1 chilometro. Come con la sola curvatura, questo effetto combinato aumenta con il quadrato della distanza, il che richiede attente regolazioni durante le operazioni di livellamento per mantenere la precisione. La correzione di queste deviazioni &#232; fondamentale per applicazioni ad alta precisione, come la determinazione delle elevazioni di riferimento e la definizione di piani orizzontali su lunghe distanze.

Influenza della Curvatura Terrestre e della Rifrazione Atmosferica sul Livellamento

During leveling, the Earth's curvature and atmospheric refraction introduce deviations in the line of sight from a true horizontal reference.&#160;When ...

Education

Didattica

JoVE Core

Civil Engineering

Ingegneria Civile

Unit 1

Unità 1

Leveling

Livellamento

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

curvature and refraction in survey leveling

Earth’s curvature and atmospheric refraction affect leveling measurements. These effects change the line of sight away from a true horizontal reference. Surveying over long distances must account for both sources of error to keep elevation readings accurate.

When a line of sight is leveled, it stays perpendicular to the plumb line only at one point. Farther away, Earth’s curved surface causes the sight line to deviate. This deviation is called the curvature correction, C, and it grows with the square of the sight distance, D.

At a horizontal distance of 1 kilometer, the curvature effect is about 0.0785 meters. Atmospheric refraction adds another shift because air has a changing refractive index with altitude. This makes light bend slightly downward.

The refraction effect is about one-seventh of the curvature deviation. Over 1 kilometer, it is about 0.0112 meters. Together, curvature and refraction produce a combined deviation of about 0.0675 meters at 1 kilometer.

Like curvature alone, the combined effect also increases with the square of the distance. That is why careful correction is needed during leveling. These adjustments matter in high-precision work, such as finding benchmark elevations and setting horizontal planes over long distances.

Curvature and Refraction in Survey Leveling

curvature-and-refraction-in-survey-leveling

introduction and methods of leveling

Surveying Elevation with Leveling Methods

Leveling is a surveying method used to find elevation differences between distant points. Elevation is the vertical distance above or below a reference datum, usually mean sea level (MSL). In the United States, elevations are often tied to the mean sea level station at Father Point Rimouski along the St. Lawrence Seaway. Surveyors use permanent markers called benchmarks to make that datum available in the field. These benchmarks have known elevations. If one point in a region has a known...

leveling equipment

Level Rods and Automatic Levels

Leveling uses a level rod and a level to measure vertical distances from a horizontal line of sight. The level rod is the graduated rod used for vertical measurements. The level provides the horizontal sight line needed for accurate readings. A level includes a high-powered telescope and a leveling system. The instrument is adjusted so the line of sight stays horizontal when the bubble in the spirit level is centered. This setup helps the user make precise measurements in the field. Level...

differential leveling

Surveying Elevation with Level Rods

Differential leveling measures elevation differences in surveying using a level instrument and a level rod. Surveyors use it to find accurate vertical measurements for level surfaces and grade lines. Those measurements are important when planning and building roads, bridges, and buildings. The process starts by setting up and leveling the instrument at a point where the benchmark can be seen. A benchmark, or BM, is a known reference point with a known elevation. The level rod is placed on the...

influence of earth's curvature and atmospheric refraction on leveling

Earth’s curvature and atmospheric refraction affect leveling measurements. These effects change the line of sight away from a true horizontal reference. Surveying over long distances must account for both sources of error to keep elevation readings accurate. When a line of sight is leveled, it stays perpendicular to the plumb line only at one point. Farther away, Earth’s curved surface causes the sight line to deviate. This deviation is called the curvature correction, C, and it grows with the...

common leveling mistakes and errors

Leveling Errors in Survey Measurements

Leveling errors in survey measurements can change the calculated elevation difference between Point A and Point B. A survey team uses a leveling instrument and a leveling rod to measure uneven terrain. When several mistakes happen during the same run, the final result can be far from the true value. One common mistake is misreading the rod. At Point A, the rod is partly hidden by tall grass during a backsight reading, which is the first reading taken from a known point. Instead of 1.135 m, the...

profile leveling and cross sections

Surveying Terrain for Roads and Railways

Profile leveling and cross sections are surveying methods used to map terrain elevations for roads, railroads, canals, and pipelines. They help surveyors plan earthwork and set the alignment of a proposed route. These measurements show how the land rises and falls along a path and across it. In profile leveling, the surveyor measures elevations along a fixed line to build a vertical profile of the ground. The level instrument is set up at a benchmark, or BM, which is a known reference point. A...

design example: maintaining level of an embankment

design-example-maintaining-level-of-an-embankment

Surveying Fill Heights for an Embankment

Surveying fill heights for a roadway embankment helps keep the structure level on uneven ground. Surveyors use a leveling instrument and a staff to measure ground elevations and work out how much fill is needed at each point along the embankment line. This supports stability and proper drainage. The process starts by placing the leveling instrument near a benchmark, which is a point with a known elevation. A backsight reading is taken first to set the instrument height. That height becomes the...

key terms and concepts

Learn how Earth’s curvature and atmospheric refraction change leveling measurements, why the error grows with distance, and how surveyors correct for it.

Curvature and Refraction in Survey Leveling | JoVE K12

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civil engineering

Louisiana Student Standards for Science

High School

Earth Science

Earth’s Systems

HS-ESS2-3

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During leveling, the Earth's curvature and atmospheric refraction introduce deviations in the line of sight from a true horizontal reference.&nbsp;When ...

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3.3.9-12.S

Curvature and Refraction in Survey Leveling

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