Name: measuring irregular land areas
Uploaded: 2025-03-26T15:21:56.000Z
Duration: 1 min 26 s
Channel: JoVE

يتطلب حساب المناطق داخل الحدود غير المنتظمة ، مثل الأنهار أو الطرق المنحنية ، أدوات وتقنيات دقيقة.  غالبا ما ينشئ المساحون اجتياز ، وهو سلسلة من الخطوط المستقيمة التي تقترب من الحدود. يمكن حساب المنطقة المحاطة بالاجتياز باستخدام طرق قائمة على الإحداثيات ، مثل صيغة مسافة الزوال المزدوجة ، والتي تعتمد على إحداثيات كل نقطة اجتياز. يتم حساب المساحة بين الاجتياز والحدود غير المنتظمة باستخدام أدوات مثل المسطح والطرق العددية.  المسطح هو جهاز ميكانيكي يتتبع الحدود على قطعة أرض متدرجة ويدمج المنطقة المغلقة مباشرة.  عند استخدامها بشكل صحيح ، توفر هذه الأداة نتائج موثوقة بدقة تبلغ حوالي تسعة وتسعين بالمائة ، مما يجعله خيارا مفضلا لحسابات الحدود غير المنتظمة. تقدم الأساليب العددية ، مثل شبه المنحرف وقواعد الثلث لسيمبسون ، بدائل مرنة. تقسم القاعدة شبه المنحرفة المنطقة إلى شبه منحرف بناء على الإزاحات المقاسة ، وتلخصها للمساحة الإجمالية.  تستخدم قاعدة سيمبسون الثلث منحنيات مكافئة بين الإزاحات ، مما يوفر دقة أعلى مع صيغة مرجحة. يضمن الجمع بين هذه الأساليب حسابات دقيقة وفعالة للمنطقة للحدود غير المنتظمة المتنوعة.

المناطق الواقعة داخل الحدود غير النظامية

يعد حساب المناطق داخل الحدود غير المنتظمة ، مثل طول الأنهار أو الطرق المنحنية ، أمرا بالغ الأهمية في مختلف المجالات ، بما في ذلك المسح والهندسة والإدارة البيئية. غالبا ما يبدأ المساحون بإنشاء اجتياز ، وهي سلسلة متصلة من الخطوط المستقيمة التي تقترب من حدود المنطقة. إحداثيات كل نقطة اجتياز ضرورية لحساب المنطقة المغلقة. صيغة مسافة الزوال المزدوجة هي تقنية مستخدمة على نطاق واسع لهذا الغرض. تستخدم هذه الطريقة إحداثيات رأس الاجتياز لحساب المساحة الإجمالية داخل حدود الخط المستقيم التقريبية ، مما يوفر أساسا فعالا وموثوقا للحسابات اللاحقة. يتم استخدام أدوات وطرق إضافية في المنطقة الواقعة بين الاجتياز والحدود غير المنتظمة. مقياس السطح هو جهاز ميكانيكي مصمم لتتبع الحدود غير المنتظمة على خريطة مصغرة. من خلال دمج المنطقة المغلقة مباشرة ، يمكن أن يحقق مقياس السطح دقة تبلغ حوالي واحد بالمائة ، مما يجعله أداة موثوقة للمساحين والمهندسين. يتم استخدام الأساليب العددية مثل القاعدة شبه المنحرفة وقاعدة الثلث لسيمبسون لتعزيز المرونة والدقة. تقسم القاعدة شبه المنحرفة الحدود إلى أجزاء وتحسب مساحة شبه المنحرف التي تشكلت بواسطة إزاحات عمودية على خط الأساس. من خلال جمع هذه المناطق ، فإنه يقترب من إجمالي المنطقة غير المنتظمة. <figure class="image image-style-align-center image_resized" style="display:table;margin-left:auto;margin-right:auto;width:35.88%;"><img style="aspect-ratio:1355/200;" src="https://cloudfront.jove.com/files/ftp_upload/18112/Copy_of_18112_Equation_1_editor_18112.svg" alt="Copy_of_18112_Equation_1.svg"></figure> في المقابل ، تتناسب قاعدة سيمبسون الثلث مع المنحنيات المكافئة بين الإزاحات ، وتطبيق صيغة مرجحة لتحقيق دقة أعلى. هذه الطريقة فعالة بشكل خاص عندما يكون انحناء الحدود كبيرا. <figure class="image image_resized image-style-align-center" style="display:table;margin-left:auto;margin-right:auto;width:56.9%;"><img style="aspect-ratio:2154/189;" src="https://cloudfront.jove.com/files/ftp_upload/18112/Copy_of_18112_Equation_2_editor_18112.svg" alt="Copy_of_18112_Equation_2.svg"></figure>يسمح الجمع بين هذه الأساليب للممارسين بحساب المناطق بكفاءة ودقة لمختلف الحدود غير المنتظمة ، مما يضمن الدقة والقدرة على التكيف مع سيناريوهات العالم الحقيقي المعقدة.

Calculating areas within irregular boundaries, such as along rivers or curved roads, is crucial in various fields, including surveying, engineering, and ...

Education

JoVE Core

Civil Engineering

الهندسة المدنية

Unit 1

الوحدة الأولى

Traverse and Topographic Surveying

المسح الترافرسي والطبوغرافي

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

Areas Within Irregular Boundaries

measuring irregular land areas

Measuring irregular land areas often starts with a traverse. A traverse is a connected series of straight lines that follows the boundary as closely as possible. Surveyors use the coordinates of each traverse point to help calculate the enclosed area.

One common method is the double meridian distance formula. It uses the vertex coordinates of the traverse to find the area inside the straight-line boundary. This gives a practical base for later calculations.

The space between the traverse and the true irregular edge can be measured in other ways too. A planimeter is a mechanical tool that traces the boundary on a scaled map. It can measure the enclosed area directly and is accurate to about one percent. Surveyors and engineers often trust it for this kind of work.

Numerical methods also help estimate irregular areas. The trapezoidal rule divides the boundary into segments and finds the area of the trapezoids made by offsets set perpendicular to a baseline. Adding those parts gives an estimate of the full region.

Simpson's one-third rule is another option. It fits parabolic curves between the offsets and uses a weighted formula. This method works especially well when the boundary has noticeable curvature. Together, these methods give surveyors flexible and precise ways to measure irregular boundaries.

Measuring Irregular Land Areas

adjusting a traverse

Correcting Traverse Angle Errors

Correcting traverse angle errors is an important step in site surveying. In a four-sided traverse, the internal angles must add up to 360 degrees. Survey data first showed a total of 359 degrees and 48 minutes, which was 12 minutes short of the expected sum. That gap pointed to a likely measurement error from fieldwork. The correction was made by spreading the 12-minute shortfall evenly across the four internal angles. Three minutes were added to each angle, and the values were recalculated.

latitudes and departures

Balancing Traverse Latitude and Departure

Latitudes and departures are key parts of surveying that help break a traverse line into north-south and east-west parts. These projections let surveyors work with line direction, length, bearings, and area in a clear way. They are also useful for measuring and mapping land accurately. Latitude is the north-south projection of a line. It is found by multiplying the line length by the cosine of its bearing. Departure is the east-west projection. It is found by multiplying the line length by the...

area computation by the alternative coordinate method

area-computation-by-the-alternative-coordinate-method

Shoelace Formula for Traverse Area

The Shoelace Formula is a coordinate method for finding the area of a traverse. It uses Cartesian coordinates, which are x and y values on a graph, to measure the shape accurately and with a simple step-by-step setup. The points of the traverse are listed in order around the shape. Each corner is written as a fraction, with the x-coordinate on top and the y-coordinate on the bottom. The first corner is repeated at the end of the list to close the shape. Next, diagonal lines are used to...

areas within irregular boundaries

Measuring irregular land areas often starts with a traverse. A traverse is a connected series of straight lines that follows the boundary as closely as possible. Surveyors use the coordinates of each traverse point to help calculate the enclosed area. One common method is the double meridian distance formula. It uses the vertex coordinates of the traverse to find the area inside the straight-line boundary. This gives a practical base for later calculations. The space between the traverse and...

design example: marking boundaries of a site using a compass

design-example-marking-boundaries-of-a-site-using-a-compass

Compass Traverse for Site Boundary Marking

Marking a site boundary with a compass uses a traverse, which is a line-by-line surveying path. The method relies on the bearings and lengths of each boundary side. It helps surveyors place corner points with accuracy. The process begins with the site details. These include the bearing and length of every boundary line. Surveyors first calculate the latitude and departure of each side. Latitude is the north-south part of a line, and departure is the east-west part. This check shows whether the...

topographic surveying and contours

Reading Terrain with Topographic Maps

Topographic surveying records the shape of land by measuring elevation, slope, and natural and man-made features. Surveyors use these measurements to build a topographic map, which shows the terrain in a visual way. These maps are important for construction planning, water resource management, and land-use analysis. Contour lines are the key feature of a topographic map. A contour line connects points with the same elevation, so it helps show the relief of the land. The spacing between contour...

plotting of topographic maps

Drawing Contour Lines from Elevation Data

Topographic maps use contour lines to show the shape of the land from elevation data. A contour line connects points with the same elevation. This makes a two-dimensional map that shows three-dimensional terrain in a clear way. To build the map, start with a scaled grid. Mark the intersections that match the survey’s elevation data points. Then assign elevation values at those points to create the base map. Next, choose a contour interval, which is the vertical change between contour lines.

methods of obtaining topography

Topographic Surveying: Old and New Methods

Topographic surveying uses land measurements to map elevations, natural features, and artificial structures. The goal is to create an accurate picture of the terrain. Surveyors have used both traditional and modern methods to do this work, and each approach has its own strengths and limits. Traditional surveying methods included transit stadia surveys and plane table surveys. These methods used tools such as theodolites and stadia rods to measure distances and angles. Surveyors then wrote the...

design example: analyzing capacity contours for flood risk assessment

design-example-analyzing-capacity-contours-for-flood-risk-assessment

Setting Bund Height to Reduce Flood Risk

Capacity contours help engineers check flood risk when a bund is built across a small valley. A bund is a raised barrier used here to store stormwater. The contour map shows how far water could spread at a chosen level, which helps judge whether nearby homes are safe. The process starts by placing the proposed bund in the valley and estimating the high flood level. Engineers then use leveling instruments to find and mark points along the upstream side that match this water level. Those points...

key terms and concepts

Learn how surveyors estimate irregular land areas using traverses, the double meridian distance formula, planimeters, and numerical methods like the trapezoidal rule.

Measuring Irregular Land Areas | JoVE K12

JoVE Core Civil Engineering provides a foundational exploration of essential construction materials in civil engineering, focusing on bricks, stones, steel, wood, and concrete through easy-to-understand animated videos. This collection covers the properties, manufacturing processes, and practical applications of these materials. Additionally, the accompanied science-in-action videos demonstrate the research experiments performed in laboratories.

civil engineering

Measuring Irregular Land Areas

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