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

أثناء التسوية، بسبب انحناء الأرض، يكون خط رؤية المستوى عموديا على خط راسيا عند نقطة واحدة فقط وينحرف أكثر عن خط المستوى.يتم تحديد هذا الانحراف، C، من خلال النظر في مثلث قائم الزاوية مع الأضلاع E، يمثل نصف قطر الأرض، D، الذي يمثل مسافة أفقية تتوافق مع الانحراف C، والوتر E + C. من المعادلة التي تربط بين أضلاع المثلث وتتجاهل قيمة C2 حيث أن حجمها أقل بكثير مقارنة بحجم E2 ، يتم اشتقاق تعبير عن الانحراف. يشير هذا التعبير إلى أن انحناء الأرض يتسبب في انحراف خط أفقي بمقدار 0.0785 متر على مسافة كيلومتر واحد، ويزداد مع مربع المسافة.أيضا, أثناء التسوية, يتسبب الانكسار الجوي في انحناء خط الرؤية لأسفل بحوالي 0.011 متر في 1 كيلومتر, حوالي سبع تأثير انحناء الأرض.مجتمعة, تأثير الانحناء والانكسار الجوي, يتسبب في انحراف خط رؤية المستوى بحوالي 0.0675 متر في 1 كيلومتر, تختلف مع مربع المسافة الأفقية.

تأثير انحناء الأرض وانكسار الغلاف الجوي على التسوية

أثناء التسوية ، يؤدي انحناء الأرض وانكسار الغلاف الجوي إلى حدوث انحرافات في خط الرؤية عن مرجع أفقي حقيقي. عندما يتم تسوية خط الرؤية ، فإنه يظل عموديا على الخط الراسيا عند نقطة واحدة فقط. علاوة على ذلك ، فإنه ينحرف بسبب انحناء الأرض ، الذي يمثله التصحيح C. بالنسبة لمسافة البصر D ، يمكن اشتقاق الانحراف باستخدام العلاقة:<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="18021_Equation_1.svg"></figure> توضح هذه العلاقة أن الانحراف يزداد تربيعيا مع المسافة. على مسافة أفقية قدرها 1 كيلومتر ، يبلغ طولها حوالي 0.0785 متر. بالإضافة إلى الانحناء ، ينحني الانكسار الجوي خط الرؤية لأسفل ، مما يؤدي إلى انحرافه عن الأفقي الحقيقي. تأثير الانحناء هو ما يقرب من سبع انحراف انحناء الأرض ، حيث يبلغ حوالي 0.0112 مترا على مسافة كيلومتر واحد. ينشأ هذا الانكسار من التغيرات في معامل الانكسار للهواء مع الارتفاع ، مما يتسبب في انحناء أشعة الضوء قليلا.  التأثير المشترك لانحناء الأرض وانكسار الغلاف الجوي هو حوالي 0.0675 مترا على كيلومتر واحد. كما هو الحال مع الانحناء وحده ، يزداد هذا التأثير المشترك مع مربع المسافة ، الأمر الذي يتطلب تعديلات دقيقة أثناء عمليات التسوية للحفاظ على الدقة. يعد تصحيح هذه الانحرافات أمرا بالغ الأهمية للتطبيقات عالية الدقة ، مثل تحديد الارتفاعات المعيارية وإنشاء مستويات أفقية على مسافات طويلة.

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

الهندسة المدنية

Unit 1

الوحدة الأولى

Leveling

تسوية

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الرئيسية

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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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...

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Leveling Errors in Survey Measurements

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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...

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

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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.

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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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3.3.9-12.S

Curvature and Refraction in Survey Leveling

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