Chapter G. Area The line courses run between a series of . The traverse in Figure G-3 is a bit simplistic with just five sides. A simple method for area calculation uses the X and Y coordinates of the vertices. By the time all that was done, the area could have been computed by coordinates. Just as the square root of 4 can be either +2 or -2, so can the area be positive or negative. If we don't carry additional digits, we could easily increase error due to rounding. While rarely used anymore, every now and then you'll hear it mentioned so we'll spend some time going over Area by DMDs. To obtain sum2, multiply right to left. That's the math check. Note: the prismoidal formula is applicable whrn there is an odd number of sections. After all, our total station reports distances to 0.01 ft and angles to 01". EW and ELare the expected errors in the width and length. 841 Surprise. New York State Association of Professional Land Surveyors coordinates and areas. Figure 6-16(b) illustrates the technique used to compute the traverse, area. Take the absolute value of the difference of sums: While rarely used anymore, every now and then you'll hear it mentioned so we'll spend some time going over Area by DMDs. While applying the trapezoidal rule, boundaries between the ends of ordinates are assumed to be straight. 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. The Society of American Military Engineers leads collaborative efforts to identify and resolve national security infrastructure-related challenges. That's the math check. Just ome more thing to keep track of. This is done by forming trapezoids and determining their, areas. Fundamentals of Surveying week2.pdf - Week 2 Area METHODS 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 the number of sections is even, the end strip is treated separately and the area is calculated according to the trapezoidal rule. 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. To be on the safe side, we'll carry the computations to 0.1 which should be less than the expected error. Direction of travel around the traverse: clockwise or counter-clockwise doesn't matter, nor does coordinate precedence, eg, (X, Y) or (Y, X). This rule can be applied for any number of ordinates. The structure and forms of the equations used for this method are investigated in this study. The parcel area, Figure G-12, can not be determined by DMDs without additional computations. Suppose we want to evaluate the area enclosed by a traverse given parametrically as x = f (t), y = g(t), for t running from a to b, with f(a) = f(b) and g(a . the number of ordinates is odd. SUCH MONUMENTS ARE REFERRED TO AS HORIZONTAL CONTROL POINTS AND COLLECTIVELY, THEY COMPRISE THE HORIZONTAL CONTROL FOR THE PROJECT. Also the azimuth of AB has been measured at the triangulation station A, whose coordinates (XA, YA), are known. These equations look complex, more so if you expand all the terms. (2) Going in sequence around the exterior list each coordinate pair vertically, Figure G-5. This is identical to the DMD method except everything is rotated 90. Settingout Curves and Route Surveying.pdf. This is identical to the DMD method except everything is rotated 90. Area by Coordinates Method This method is used when the coordinates of all the traverse stations are know /given. 154 0 obj Backsight by Coordinate Use this method when you have 2 known survey points with the instrument established on one and the mirror target on the other survey point From the "MEAS" menu select [COORD] and then "Stn. Step (5)Use Equation (G-3) to compute the area. The base of each triangle or trapezoid coincides with the meridian. Limitation: This rule is applicable only when the number divisions is even i.e. 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. 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. To compute the area of the parcel by DMDs, you would need to determine the Lat and Dep of lines EF and FH, then compute DMDs around the perimeter. We want the the area of the parcel, not the traverse. 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. Do my homework now. 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. metric units, area is expressed in terms of square meters (m2), or hectares (ha). Until we discuss area accuracy more fully, we'll state the area as 102,935.8 sq ft. What do we use for EW andEL? Ordinates at the corners provide, the altitudes of the trapezoids. Keywords: Compass rule, double meridian distance, departure, bearing, engineer survey, latitude, transit rule 1. To compute a triangle's area, either all three sides or two sides and an included angle are needed. If we don't carry additional digits, we could easily increase error due to rounding. geometric figures such as triangles, rectangles, or trapezoids. Multiplying each line's DMD by its Latitude and summing the results will give us double the area. Lesson 8 - Area Computation | PDF | Area | Triangle 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. (3) The first coordinate pair must be repeated at the bottom of the list. Until we discuss area accuracy more fully, we'll state the area as 102,935.8 sq ft. Step (2) Multiply DMDs by Lats; add the products, Step (3) Compute the area using Equation G-6. Let us proceed to some of the basic understandings which we should all possess as land surveyors. PDF Surveying 2 - uoanbar.edu.iq There's nothing magical or sacred about point A. Figure G-7 is a continuation of the Bearing Traverse example we have been using in the past few chapters. While at first all this may look confusing, it's actually pretty easy to remember once you do it a few times. (3) The first coordinate pair must be repeated at the bottom of the list. We will now move on with our discussion on the first rule Midpoint ordinate rule with a suitable example. n = number of equal parts, the baseline is divided, d = common distance between the ordinates. determine the enclosed area of a traverse. 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. 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. 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. Step (2) Multiply DMDs by Lats; add the products, Step (3) Compute the area using Equation G-6. Which method, Coordinates or DMDs, is most accurate? That means additional calculations to obtain distances and/or an angle between lines. 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. 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. is it possible to find area of a polygon having only co-ordinate of its vertex(sides more than 5), isnt the number of equal parts n will be equal to 7 A traditional method of computing area of a closed polygonal traverse is by DMDs: Double Meridian Distances. Figure G-3 Different Triangle Combinations. A traverse is a continuous series of connected lines of known lengths related to one another by known angles. 2. Chapter G. Area The magazine remains a leading source for recounting the achievements of engineering in support of national security. 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. There's nothing magical or sacred about point A. PDF CIV2202.9: AREA AND VOLUMES - Tripod Because we're generally interested in the magnitude of the answer, we use the absolute value of the area computed. 340.65) = 36287.63 We could have stated our list at point C and traveled counter-clockwise around the traverse. Just ome more thing to keep track of. We could have stated our list at point C and traveled counter-clockwise around the traverse. Notice that the DMD of the last line is the same as the Departure of that line except with an opposite math sign. Arrows indicate "direction" of multiplication. We'll discuss the area error at the end of the chapter but for now we want to over-compute the area accuracy then report it to an appropriate resolution after we analyze it. 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.. Fundamentals of Surveying 1 Area INTRODUCTION There are a number of important reasons for determining areas. The ordinates are measured at midpoint of the division are 10, 13, 17, 16, 19, 21, 20 and 18m. method and also how to find areas by the use of the restangular coordinate method. DOCX, PDF, TXT or read online from Scribd, 0% found this document useful, Mark this document as useful, 0% found this document not useful, Mark this document as not useful, When the courses or sides of a loop traverse represent boundary lines, it is usually necessary to, compute the enclosed land area for the deed description or plotted survey plat. CLASSIFICATION OF TRAVERSE Calculation of area is carried out by any one of the following methods: Let O1, O2, O3, O4.On= ordinates at equal intervals, Area = common distance* sum of mid-ordinates, Let O1, O2, ..On=ordinates or offsets at regular intervals. <>>>/Rotate 0/StructParents 0/Type/Page>> The more traverse points, the more triangles and combinations and more inverse calculations. Multiplying each line's DMD by its Latitude and summing the results will give us double the area. See all those 1/2's? Time use of the total station system requires less than the time that is required by using the coordinate method by nearly half . Here are the five important rules (Methods) used for the calculation of areas in Surveying: Midpoint ordinate rule Average ordinate rule Simpson's rule Trapezoidal rule Graphical rule We will now move on with our discussion on the first rule "Midpoint ordinate rule" with a suitable example. horizontal curves using coordinate methods can be done using either . See all those 1/2's? The Military Engineer While rarely used anymore, every now and then you'll hear it mentioned so we'll spend some time going over Area by DMDs. 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. calculations (i.e., fewer calculations are necessary). 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. Then both the results are added to obtain the total volume. 2Engr.Shams Ul Islam (shams@cecos.edu.pk) Figure G-7 is a continuation of the Bearing Traverse example we have been using in the past few chapters. PDF Approach on Area Coordinate, Volume Coordinate and Their Usage in True Note: sometimes one or both the end of the ordinates may be zero. PDF COORDINATES & SURVEY - Land Surveying It can be applied for any number of ordinates, Total area = 89.50+106.50+158.00 = 354.00 m, Total area= 89.66+102.33+157.33 = 349.32 m, UG Courses - Agricultural Engineering (Version 2.0). The traverse turns itself inside out. Concept Software uses coordinates for area determination. of a parcel subdivided into triangles is shown in Figure 12.1. We could divide the complex polygon into a series of triangles, compute the area of each triangle, then total them, Figure G-2. Problem 1: an embankment of width 10 m and side slopes 1 :1 is required to be made on a ground which is level in a direction transverseto the centre line. and methods commonly used in surveying, in particular the knowledge and Fig 2.2 Surveying axis coordinates. We'll discuss the area error at the end of the chapter but for now we want to over-compute the area accuracy then report it to an appropriate resolution after we analyze it. measurements or additional distance measurements while in the field to simplify Chapter 1 Surveying - USDA Sum2 = (159.97 * 152.26) + (139.37 * 0.00) + (226.02 * 29.94) + (30.55 * 169.02) + (0.00 * We could have stated our list at point C and traveled counter-clockwise around the traverse. There are formulae readily available for regular polygons like, triangle, rectangle, square and other polygons. Rather than memorize each equation, it's easier to remember theirpattern and determine the area in tabular fashion. Most surveyors who solve area manually generally use coordinates also. Remember that this is equal to twice the area, so divide this number by 2. Area by coordinates Computation of area within a closed polygon is most frequently done by the coordinate method. Set the instrument coordinates with "Stn. Concept The area of a closed non-crossing plane polygon can be computed from the coordinates of the polygon's verticies. After adjustment its coordinates were used to compute the Parcel's area as 90,018.76sq ft. Software uses coordinates for area determination. which is equivalent to The area of a closed non-crossing plane polygon can be computed from the coordinates of the polygon's verticies. sides and the angle in between the sides, where C is the angle between sides a and b (C in radians). Orientation". But here the number of ordinate is even(ten). (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. The reference meridian used can be placed anywhere, but generally, it passes through the first point of the traverse. To compute a triangle's area, either all three sides or two sides and an included angle are needed. The parcel area, Figure G-12, can not be determined by DMDs without additional computations. They are normally obtained by traversing, although any method that yields the coordinates of these points is appropriate. 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 The more traverse points, the more triangles and combinations and more inverse calculations. interest, Determine the area to estimate endstream Hence simpsons rule is some times called as parabolic rule. The base of each triangle or trapezoid coincides with the meridian. METHODS OF MEASURING AREA Both field and map measurements are used to determine, area. In this procedure, coordinates of each angle point in the figure must be known. By definition, Area by DMDs is limited to travel along the traverse path so you would be determining the area of E-F-G-H-E, Figure G-13. The area of a closed non-crossing plane polygon can be computed from the coordinates of the polygon's verticies. We could approximate the area change with a 0.01' wide by 472.72 ft long rectangle - a difference of about 4.7 sq ft. That 0.01 ft offset would represent relatively small random errors in both lines CB and DA. 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. Consider this: How much would the area of the Bearing Traverse example be affected if we offset line AB by 0.01 ft? Surveying and Leveling: LESSON 14. Computation of area and volume So, the section is divided into three compartments, I= 5/2{2.50+6.10+2(3.80+4.60+5.20)} = 89.50 m2, III= 20/2{5.80+2.20+2(3.90)} = 158.00 m2, Total area = 89.50+106.50+158.00 = 354.00 m2, I= 5/3{2.50+6.10+4(3.8+5.20) + 2(4.60)} = 89.66 m2, III= 20/3{5.80+2.20+4(3.90)} = 157.33 m2, Total area= 89.66+102.33+157.33 = 349.32 m2, volume (cutting or filling), V=D/2(A1+An+2(A2+A3+.+An-1)), Volume( cutting or filling), V= D/3{A1+ An +4(A2+ A4+ An-1)+ 2(A3+ A5+.+ Ann-1)}, i.e.