If we don't carry additional digits, we could easily increase error due to rounding. 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. After adjustment its coordinates were used to compute the Parcel's area as 90,018.76sq ft. To be on the safe side, we'll carry the computations to 0.1 which should be less than the expected error. The area should be expressed to a level compatible with the uncertainty: 102,936 sq ft. Instrument and reflector centering errors and measurement errors could easily exceed 0.01 fterror per line. 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. 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. If you examine the Deps and DMDs computations above, you should see a pattern to the computations. Let O1, O2, ..On=ordinate at equal intervals, and d= common distance between two ordinates. 1. If we multiply a distance by the precision, p,it gives us an expected error in that distance. In this case, if you list the coordinates along the original traverse path, E-F-G-H-E, you will be able to compute an area but it will be nonsensical. EW and ELare the expected errors in the width and length. Area by coordinates method surveying pdf. Notice that the DMD of the last line is the same as the Departure of that line except with an opposite math sign. Midpoint-ordinate rule Calculation of area is carried out by any one of the following methods: a) Mid-ordinate method b) Average ordinate method c) Trapezoidal rule d) Simpson's rule The mid-ordinate rule Consider figure. The more traverse points, the more triangles and combinations and more inverse calculations. As long as we remember to repeat the initial point at the bottom of the list, we will come up with the same area although one could be positive and the other negative. 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. the number of ordinates is odd. Area by coordinates method surveying pdf | Math Applications Area by DMD & DPD method Copyright: All Rights Reserved Available Formats Download as DOC, PDF, TXT or read online from Scribd Flag for inappropriate content Save Share Download now of 1 Example Problems in Elementary Surveying Example: Using DMD and DPD Methods in Lot Area Computation Example: hb`````*d`f`Ngc@ >+_f Until we discuss area accuracy more fully, we'll state the area as 102,935.8 sq ft. Different Methods for the Calculation of Areas in Surveying Direction of travel around the traverse: clockwise or counter-clockwise doesn't matter, nor does coordinate precedence, eg, (X, Y) or (Y, X). <>stream But for determining the areas of irregular polygons, different methods are used. n = number of equal parts, the baseline is divided, d = common distance between the ordinates. They are normally obtained by traversing, although any method that yields the coordinates of these points is appropriate. The area coordinate is calculated by ratio of triangle area with the polygon area, the triangle is enclosed by moving point and a boundary edge. 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. With a crossing traverse, one must be careful when listing the coordinates. The traverse turns itself inside out. Problem 3: the following offsets are taken from a survey line to a curves boundary line, and the first and the last offsets by: here the intervals between the offsets are not reglar through out the length. DIRECTIONS ARE DETERMINED A TRAVERSE IS CURRENTLY THE MOST COMMON OF SEVERAL POSSIBLE METHODS FOR ESTABLISHING A SERIES OR NETWORK OF MONUMENTS WITH KNOWN POSITIONS ON THE GROUND. Step (1) Start at point E and going clockwise around the parcel, list the coordinates. That should result in an uncertainty smaller than 12 sq ft, shouldn't it? Well if we start at point A in Figure G-10 and begin computing meridian distances, we see a pattern start to develop, Equation G-4. While rarely used anymore, every now and then you'll hear it mentioned so we'll spend some time going over Area by DMDs. By the time all that was done, the area could have been computed by coordinates. This type of surveying in which the mean surface of the earth is considered as a plane, or in which its spheroidal shape is neglected, with regard to horizontal distances and directions. Introduction Almost all surveying requires some calculations toreduce measurements into a more useful form fordetermining distance, earthwork volumes, land areas,etc. Coordinates In order to describe theposition of a point, twocoordinates are required. 2Engr.Shams Ul Islam (shams@cecos.edu.pk) In Figure G-5, the surveyor started at point A and then ended on point A. Let us proceed to some of the basic understandings which we should all possess as land surveyors. 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). The central heights at 40 m intervals are as follows: Calculate the volume of earth work according to, Solution: the c/s areas are calculated by, (a) Volume according to trapezoidal formula, V= 40/2{10.22+ 9.58+2(14.84+28.43+34.38+23.63+16.23)}. While at first all this may look confusing, it's actually pretty easy to remember once you do it a few times. Two common methods exist for determining the area of triangles: (1) in which the length of all three sides are known, and (2) in which two sides and their joining angle is known. Step (1) Start at point E and going clockwise around the parcel, list the coordinates. Figure G-13 Crossing Traverse For the Parcel. metric units, area is expressed in terms of square meters (m2), or hectares (ha). The Military Engineer Using the simplified error propagation, Equation G-10 allows the surveyor to express area to a reasonable level of uncertainty. If that's the case, draw a 1.2" square on a piece of paper to visualize it.). Figure G-11 shows the example Bearing Traverse with the previously computed adjusted Latitudes and Departures. But here the number of ordinates must be odd. This total sum is multiplied by the common distance. Download full-text PDF Read full . SUCH MONUMENTS ARE REFERRED TO AS HORIZONTAL CONTROL POINTS AND COLLECTIVELY, THEY COMPRISE THE HORIZONTAL CONTROL FOR THE PROJECT. 5 Area by Triangles Formula A = a.b sinC A = s(s-a)(s-b)(s-c) where s = (a+b+c) Area by Triangles 1 2 3 6 Methods of Determining Land Area 2. (1) Select a start point (it doesn't matter where you start) (2) Going in sequence around the exterior list each coordinate pair vertically, Figure G-5. Which method, Coordinates or DMDs, is most accurate? Just like area by coordinates it looks pretty confusing, but there is a pattern that helps guide the calculations. 340.65) = 36287.63 The area of a, triangle whose lengths of sides are known can be computed by the formula, where a, b, and c are the lengths of sides of the triangle and Another formula for the area of a. where C is the angle included between sides a and b. of a triangle: one-half the product of the base and the altitude. Note: the prismoidal formula is applicable whrn there is an odd number of sections. The base of each triangle or trapezoid coincides with the meridian. The units of the cross products are square linear units - if coordinates are in feet, cross products are sq ft. (5) Using Equation G-3, compute the traverse area. endobj In both triangle combinations of Figure G-3, the red lines must be computed by inversing. This method will be discussed more in detail in next month's column. We can approximate the errors using the traverse precision. Prior to adjustment we determined its precision to be 1/11,900; area computed by coordinates is 102,935.8sq ft. 187952513-Surveying.pdf. (4) Cross multiply the coordinates and sum the products, Figure G-6. The area equations, depending on coordinate format used, are shown here as Equations G-1 and G-2. A simple method for area calculation uses the X and Y coordinates of the vertices. hbbd``b`:$@.` "@01 @"f``bd~ p After adjustment its coordinates were used to compute the Parcel's area as 90,018.76sq ft. TME has followed the trends of engineering from the development of our nations transportation infrastructure through Cold War-era construction and the birth of computer-aided design to the current era of sustainable development and infrastructure resilience. FE Civil Course https://www.directhub.net/civil-fe-exam-prep-course/ FE Exam One on One Tutoring https://www.directhub.net/fe-exam-tutoring/https://www.. Just ome more thing to keep track of. If you know the length of all Why then the Double Meridian Distance? Polar coordinates need aline and an angle. The volume of the remaining strips is calculated in the usual manner by the prismoidal formula. Arrows indicate "direction" of multiplication. (PDF) SETTING OUT OF CURVES AND ROUTE SURVEYING FOR A ROAD - ResearchGate These equations look complex, more so if you expand all the terms. Another important application is determining end areas for . 187952513-Surveying.pdf. You'll sometimes see reference to Area by DPDs (Double Parallel Distance). What do we use for EW andEL? Here let me remark that the underlying mathematics is directly related to the coordinate method. You'll sometimes see reference to Area by DPDs (Double Parallel Distance). 841 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. With . In S.1 units the area is measured in square meters, hectares or square Kilometers. 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. Once a loop traverse has been adjusted, how can its area be determined? There's nothing magical or sacred about point A. Thus the areas enclosed between the base line and the irregular boundary line are considered as trapezoids. If the number of sections is even, the end strip is treated separately and the area is calculated according to the trapezoidal rule. Substituting those numbers into Equation G-11: Recall that throughout our calculations, up to that of the area, we carried an additional digit to minimize rounding errors. Field measurement methods are the more accurate and include (1) division of the tract, into simple figures (triangles, rectangles, and trapezoids), (2) offsets from a straight line, (3). The area coordinate is a kind of 2D local coordinate, which is composed by a sequence of ratios of small triangles with a polygon, the small triangle is surround by a moving point and one edge of the polygon. Step (5)Use Equation (G-3) to compute the area. AMS :: Feature Column from the AMS - American Mathematical Society New York State Association of Professional Land Surveyors coordinates and areas. The reference meridian used can be placed anywhere, but generally, it passes through the first point of the traverse. Rather than memorize each equation, it's easier to remember theirpattern and determine the area in tabular fashion. After all, our total station reports distances to 0.01 ft and angles to 01". There may be hundreds of The Parcel's area uncertainty is12 sq ft so show it as 90,018 sq ft. endobj There's nothing magical or sacred about point A. Traditionally, the The area should be expressed to a level compatible with the uncertainty: 102,936 sq ft. distance, bearing, boundaries, and area are necessary to visualize the shape & exact location of the land. Just as the square root of 4 can be either +2 or -2, so can the area be positive or negative. The vector. 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. Get Started. While at first all this may look confusing, it's actually pretty easy to remember once you do it a few times. Step (2)-(4) Cross multiply in both directions; sum the columns. Figure G-3 demonstrates that there can be quite a few possible triangle combinations for a five sided traverse. No additional calculations besides the area computations, More calculations: need coordinates before area computations, Numbers can be huge if using large coordinates. Ordinates at the corners provide, the altitudes of the trapezoids. Adding the areas, some of which are negative based on the latitude and meridian distance, results in the area of the polygon. Surveying Notes | PDF | Surveying | Compass - Scribd (3) The first coordinate pair must be repeated at the bottom of the list. The objective is to determine the coordinates of the Why then the Double Meridian Distance? Some Land Surveying Problems While rarely used anymore, every now and then you'll hear it mentioned so we'll spend some time going over Area by DMDs. 2. Area By Coordinates - Page 2 Remember that this is equal to twice the area, so divide this number by 2. Consider this: How much would the area of the Bearing Traverse example be affected if we offset line AB by 0.01 ft? As long as we remember to repeat the initial point at the bottom of the list, we will come up with the same area although one could be positive and the other negative. (4) Cross multiply the coordinates and sum the products, Figure G-6. Envision a rectangular parcel which includes the same area as the traverse. Area Computation by Coordinates | Journal of Surveying Engineering Software uses coordinates for area determination. 178 0 obj This pattern is shown using colored arrows below. So, the area between the first two divisions, Similarly, the area of next two divisions, Total area = d/3[O1+On+4(O2+O4+) + 2(O3+O5)], Thus the rule may be stated as the follows. Figure G-11 shows the example Bearing Traverse with the previously computed adjusted Latitudes and Departures. It can be especially interesting approach with a concave traverse, Figure G-4, having one or more situations where triangle areas should be subtracted instead of added. One is to include the acreage of a parcel of land in the deed describing the property.
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