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. 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. 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.

influence of earth's curvature and atmospheric refraction on leveling

During leveling, the Earth's curvature and atmospheric refraction introduce deviations in the line of sight from a true horizontal reference. When the line of sight is leveled, it remains perpendicular to the plumb line only at a single point. Beyond this, it deviates due to the Earth&#8217;s curvature, represented by the correction C. For a sight distance D, the deviation can be derived using the relationship:<figure class="image image-style-align-center image_resized" style="display:table;margin-left:auto;margin-right:auto;width:9.53%;"><img style="aspect-ratio:197/150;" src="https://cloudfront.jove.com/files/ftp_upload/18021/18021_Equation_1_editor_18021.svg" alt="Mathematical formula: C = D&#178;/2E, equation for calculating specific scientific constants." data-altupdatedat="1762173717000" data-alt="18021_Equation_1.svg" /></figure>This relationship shows that the deviation increases quadratically with distance. Over a horizontal distance of 1 kilometer, it is approximately 0.0785 meters.In addition to curvature, atmospheric refraction bends the line of sight downward, further deviating it from the true horizontal. The bending effect is approximately one-seventh of the Earth's curvature deviation, amounting to about 0.0112 meters over 1 kilometer. This refraction arises from variations in the refractive index of air with altitude, causing light rays to curve slightly. The combined influence of Earth's curvature and atmospheric refraction is approximately 0.0675 meters over 1 kilometer. As with curvature alone, this combined effect increases with the square of the distance, which requires careful adjustments during leveling operations to maintain accuracy. Correcting for these deviations is critical for high-precision applications, such as determining benchmark elevations and establishing horizontal planes over long distances.

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

Education

JoVE Core

Civil Engineering

Unit 1

Leveling

KEY TERMS AND CONCEPTS

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

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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...

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Leveling Errors in Survey Measurements

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

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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

JoVE Core Civil Engineering offers a foundational exploration of essential construction materials such as bricks, stones, steel, wood, and concrete, along with fluid mechanics topics like flow over immersed bodies, open channel flow, and dimensional modeling. It also covers key surveying concepts, including leveling, traverse adjustments, curve design, topographic mapping, and geospatial technologies (GPS & GIS). Science-in-action videos showcase laboratory research on materials, fluids, and surveying practices in real-world engineering systems.

civil engineering

Louisiana Student Standards for Science

High School

Earth Science

Earth’s Systems

HS-ESS2-3

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3.3.9-12.S

Curvature and Refraction in Survey Leveling

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