2. Area By Coordinates - Page 2 Knowing what we do about how errors occur and accumulate, does it make sense to state an area of 90,018 sq ft to an accuracy of that square? 156 0 obj With ADVANCED SURVEY MATH. Figure G-11 shows the example Bearing Traverse with the previously computed adjusted Latitudes and Departures. measurements or additional distance measurements while in the field to simplify Because the area of a rectangle is length times width, the Error of a Product can be used to approximate an accuracy, Figure G-14. For land area. Step (1) Start at point E and going clockwise around the parcel, list the coordinates. Arrows indicate "direction" of multiplication. 155 0 obj Using the simplified error propagation, Equation G-10 allows the surveyor to express area to a reasonable level of uncertainty. Introduction Almost all surveying requires some calculations toreduce measurements into a more useful form fordetermining distance, earthwork volumes, land areas,etc. PDF Approach on Area Coordinate, Volume Coordinate and Their Usage in True Parallel distances are determined from an E/W reference line (a parallel) and multiplied by the latitudes. Sum1 = (340.65 * 139.37) + (152.26 * 226.02) + (0.00 * Fundamentals of Surveying 1 Area INTRODUCTION There are a number of important reasons for determining areas. This total sum is multiplied by the common distance. If surveying software is available, a sensitivity analysis can be done: vary multiple measurements by introducing reasonable errors into them and examine how the area changes. You'll sometimes see reference to Area by DPDs (Double Parallel Distance). Area by coordinates method surveying pdf. So, simpsons rule is applied from O1 to O9 and the area between O9 and O10 is found out by the trapezoidal rule. With a crossing traverse, one must be careful when listing the coordinates. sides and the angle in between the sides, where C is the angle between sides a and b (C in radians). With its national office in Alexandria, Va., SAME provides its more than 30,000 members extensive opportunities for training, education and professional development through a robust offering of conferences, workshops, networking events and publications. Starting with line AB and use Equation G-4 to computed the DMDs. Why then the Double Meridian Distance? You'll sometimes see reference to Area by DPDs (Double Parallel Distance). While at first all this may look confusing, it's actually pretty easy to remember once you do it a few times. Figure G-3 demonstrates that there can be quite a few possible triangle combinations for a five sided traverse. Arrows indicate "direction" of multiplication. The rule states that if the sum of all the ordinates taken at midpoints of each division multiplied by the length of the base line having the ordinates (9 divided by number of equal parts). We generally have a tendency to overstate area accuracy: it's not uncommon to see a computer generated map with areas expressed to 0.01 sq ft. Surveyors sometimes get caught up in equipment specifications and forget about the propagated errors when multiple measurements are combined. <>stream Orientation". Area By Coordinates a. We generally have a tendency to overstate area accuracy: it's not uncommon to see a computer generated map with areas expressed to 0.01 sq ft. Surveyors sometimes get caught up in equipment specifications and forget about the propagated errors when multiple measurements are combined. PDF Total Station Setup and Operation - University of South Alabama A traditional method of computing area of a closed polygonal traverse is by DMDs: Double Meridian Distances. Cartesian coordinates needtwo lines within anorthogonal system. It happens because of their combination of area and precision that both examples have 12 sq ft error. Figure G-2 Traverse Divided into Triangles. In this article, we will list out different methods to calculate the areas in Surveying and also study each of the method in depth We will also explain each method with a suitable example for your better understanding. The area equations, depending on coordinate format used, are shown here as Equations G-1 and G-2. Download full-text PDF Read full . The Society of American Military Engineers leads collaborative efforts to identify and resolve national security infrastructure-related challenges. Persons with disabilities who require alternative means for communication of program information (Braille, large print, audiotape, etc.) Multiplying each line's DMD by its Latitude and summing the results will give us double the area. With a crossing traverse, one must be careful when listing the coordinates. Using the simplified error propagation, Equation G-10 allows the surveyor to express area to a reasonable level of uncertainty. geometric figures such as triangles, rectangles, or trapezoids. (4) Cross multiply the coordinates and sum the products, Figure G-6. The common area coordinate are triangular area coordinate and quadrangular area coordinate. See all those 1/2's? In this rule, the boundaries between the ends of ordinates are assumed to form an arc of parabola. We can approximate the errors using the traverse precision. The traverse in Figure G-3 is a bit simplistic with just five sides. The best way to determine area accuracy is to propagate all measurement and setup errors into it. Rather than memorize each equation, it's easier to remember theirpattern and determine the area in tabular fashion. PDF Math for Surveyors - Esri Step (1)Start at point A and going clockwise around the traverse list the coordinates: Step (2) Cross multiply in one direction: Step (3) Cross multiply in the other direction, Step (5) Using Equation G-3 compute the area. Concept Software uses coordinates for area determination. endobj A sketch of the figure will aid in the computations. SUCH MONUMENTS ARE REFERRED TO AS HORIZONTAL CONTROL POINTS AND COLLECTIVELY, THEY COMPRISE THE HORIZONTAL CONTROL FOR THE PROJECT. The reference meridian used can be placed anywhere, but generally, it passes through the first point of the traverse. Most surveyors, however, prefer to use the coordinate method to. Which method, Coordinates or DMDs, is most accurate? Let O1, O2, O3, O4.On= ordinates at equal intervals l=length of base line d= common distance between ordinates h1,h2,..hn=mid-ordinates Area by coordinates Computation of area within a closed polygon is most frequently done by the coordinate method. As with other surveying calculations, we need a systematic, repeatable, and reliableapproach to determine traverse area. The area of the square in Figure G-15 on your screen should be 0.01 sq ft; it is 0.1 ft (approx 1.2") on a side(Your browser's magnification and display may affect the square's displayed size. You'll sometimes see reference to Area by DPDs (Double Parallel Distance). Using only triangles divides the area into fewer pieces and simplifies Midpoint-ordinate rule endobj No additional calculations besides the area computations, More calculations: need coordinates before area computations, Numbers can be huge if using large coordinates. Step (1)Start at point A and going clockwise around the traverse list the coordinates: Step (2) Cross multiply in one direction: Step (3) Cross multiply in the other direction, Step (5) Using Equation G-3 compute the area. metric units, area is expressed in terms of square meters (m2), or hectares (ha). The base of each triangle or trapezoid coincides with the meridian. A. Hydrographic Surveying B. If the thumb, the forefinger and the second finger of the right hand are placed mutually at right angles then the thumb points in the Z-direction, the forefinger points in the X-direction and the second finger points in the Y-direction. endstream Instrument and reflector centering errors and measurement errors could easily exceed 0.01 fterror per line. By multiplying both sides of each MD equation by 2, the 1/2's all go away and we're left with Double Meridian Distances (DMDs) on each left side, Equation G-5. The Parcel's area uncertainty is12 sq ft so show it as 90,018 sq ft. Figure G-13 Crossing Traverse For the Parcel. 154 0 obj (3) The first coordinate pair must be repeated at the bottom of the list. A meridian distance (MD) is the distance from a reference meridian to the center of a line; it is measured in the East (X) direction, Figure G-10. Most surveyors who solve area manually generally use coordinates also. Don't assume all areas will have the same error. endobj To be on the safe side, we'll carry the computations to 0.1 which should be less than the expected error. Multiplying each line's DMD by its Latitude and summing the results will give us double the area. The lengths of the lines are determined by direct measurement of horizontal distances, slope measurement, or by indirect measurement using the methods of stadia or the subtense bar. That means our area uncertainty would be expressed to two sig fig: 12 sq ft. Absolute value of the sum1 - sum2 = twice the area. When the tract of land is formed by straight lines only, it is possible to divide up the tract into, adjacent triangles, rectangles, and trapezoids and to compute the sum of the areas of all those, regular geometric figures. By the time all that was done, the area could have been computed by coordinates. Step (1)Start at point A and going clockwise around the traverse list the coordinates: Step (2) Cross multiply in one direction: Step (3) Cross multiply in the other direction, Step (5) Using Equation G-3 compute the area. Number of equal parts of the baseline, n = 8, Length of baseline, L = n *d = 8*10 = 80m. Figure G-8 shows the Crossing Traverse we've been using as another running example. A simplified approach can be used which uses basic error propagation along with the traverse precision. 1.2 shows two interconnected triangles ABC and BCD.All the angles in both the triangles and the length L of the side AB, have been measured. The Military Engineer was launched under its current masthead in 1920 (after previously being published as Professional Memoirs, a Corps of Engineers publication) and immediately carried the message of the new association of engineers and was a vital tool in communicating with engineers across the country and helping establish the Post network, which became the bedrock of SAME. coordinates should be used in small areas, if there are triangulation stations within or near the local area to be surveyed, these stations should be used as a basis for the survey, as they not only furnish an accurate control but also serve to join the local sur-vey to the triangulation of the whole country. sides shown in Figure are known, the area enclosed by the traverse can be calculated from the following expression . 178 0 obj Also the azimuth of AB has been measured at the triangulation station A, whose coordinates (XA, YA), are known. 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