Mapua Institute of TechnologySchool of Civil Engineering and Environmental and Sanitary EngineeringElementary SurveyingFIELD MANUAL

FIELDWORK NO. 4DETERMINING THE AREA OF A POLYGONAL FIELD USING ONLY THE TAPE

CE120-0 / A4Submitted by Cayanan, Jonas I.2013102552 Group 1Cabarce, Christian July 27, 2015August 29, 2015Submitted to Engr. Balmoris

GRADE

Table of Contents

Introduction2Objectives and Instruments3Procedures5Computations7Preliminary Data Sheet8Final Data Sheet10Research and Discussion14Conclusion17

Introduction

Almost all surveying requires some calculations to reduce measurements into a more useful form for determining distance, earthwork volumes, land areas, etc. Basic field operations performed by a surveyor involve linear and angular measurements. Through application of mathematics (geometry and trigonometry) and spatial information knowledge, the surveyor converts these measurements to the horizontal and vertical relationships necessary to produce maps, plans of engineering projects. In this fieldwork we will use surveying in determining the area of a certain field using points. Points on the ground or on a map are related to each other through a horizontal distance and a horizontal angle (or direction.) Horizontal angular measurements are made between survey lines to determine the angle between the lines. A horizontal angle is the difference between two measured directions. Horizontal angles are measured on a plane perpendicular to the vertical axis (plumb line).Vertical angular measurements are measured to determine slope of survey lines from the horizontal plane (level line). When the vertical angle is applied to the slope distance, the horizontal and vertical distances may be calculated. Vertical angles are measured on a plane passing through the vertical axis perpendicular to the horizontal plane. In order to facilitate the trigonometric calculations of horizontal and vertical distance, the reference or zero angle is on the vertical axis directly above the instrument, which is termed the zenith angle.

Objectives1. To develop the skills in determining the horizontal distance of an evenground by breakingthe tapemethod up anddown the slope.2. To acquire the skills in determining the horizontal distance of a sloping ground by usingthe tape and the automatic level.3. To apply the value of excellence and patience in measuring the distance of the ground.

InstrumentsRange PolesSurveying instrument consisting of a straight rod painted in bands of alternate red and white each one foot wide. Used for sighting by surveyors

Chalkis a soft, white, porous sedimentary carbonate rock, a form of limestone composed of the mineral calcite.

50 meter tapeused insurveyingfor measuring Horizontal, vertical or slope distances. Tapes are issued in various lengths and widths and graduated in variety of ways.

Plumb-bob / PlummetAplumb-bobor aplummetis a weight, usually with a pointed tip on the bottom that is suspended from a string and used as a vertical reference line, orplumb-line.

PROCEDUREs1. Determination of the area of triangle components using the basic formula. A= B x H 21. The students designate the locations of 5 random points that is likely to be a pentagonal shape.1. The chief of party divides the field area into convenient triangular components and calls them A1, A2 and A3.1. For first trial use the basic formula to compute the field and designate this as the base of the triangle.1. Determine the length of the altitude to this base. The determination of the altitude is done by locating a point on this base after dropping a line perpendicular to this from opposite vertex by swaying.1. Record the length of the base and altitude in the fieldwork computation sheet provided.1. Repeat the same procedures 4-6 with the rest of the triangular components of the polygonal field and the sum up the areas.

1. Determination of the triangles by using the formula. Area=absinC 21. The same triangular field will be used for this second trial but change the naming of the vertices of polygonal filed. 1. The chief of party divides the field area into convenient triangular components and calls them A1, A2 and A3.1. For second use the basic formula in B to compute the field and designate this as the base of the triangle.1. Determine the measurement of the angles between the lines.1. Record the lengths of two sides and included angle in the field work. Record in the data.1. Repeat procedures 4-6 with the rest of triangular components of the polygonal area to compute the entire area.

1. Determination of the area using the formula.

1. The same triangular field will be used for this second trial but change the naming of the vertices of polygonal filed. 1. The chief of party divides the field area into convenient triangular components and calls them A1, A2 and A3.1. For third use the basic formula in C the herons formula to compute the field and designate this as the base of the triangle.1. Record the lengths of the three sides of each triangle.1. Repeat procedures 3-5 with the rest of the triangular components until the data is complete.

COMPUTATIONSA triangle= b x h 2

WhereA = area of the triangle in square metersb = base of the triangle in metersh = altitude of the triangle in meters

A triangle= absinC 2

Where A = area of the triangle in square metersa and b = any 2 sides of the triangles in metersSin C = sine of any included angle of the measured sides a and b

A triangle=

WhereA = area of the triangle in square meterss = half the perimeter of the triangular components in metersa, b and c = sides if the triangular components in meters

Preliminary data sheetDate: July 27, 2015Group No. : 1Time: 1:00Location: Intramuros WallsWeather: SunnyProfessor: Engr. Balmoris

A. Method: BY BASE AND ALTITUDE METHOD

TRIANGLEBASEALTITUDEAREA

14m7.43m14.86m2

23.36m7.49m12.58m2

32.76m8.04m11.10m2

TOTAL38.54m2

B. COMPUTATIONSA1 = ( b * h ) / 2 = ( 4m * 7.43m ) / 2= 14.86 mm2A2 = ( b * h ) / 2 = ( 3.36m * 7.49m ) / 2 = 12.58 mm2A3 = ( b * h ) / 2 = ( 2.76m * 8.04m ) / 2 = 11.10 mm2Atotal = 38.54 mm2

C. Method: BY TWO SIDES AND THE INCLUDED ANGLETRIANGLEANGLESIDESAREA

Theta in degreesab

130.93o7.49m7.31m14.07m2

249.25o9.45m4.9m12.77m2

351.36o4m7.31m11.42m2

TOTAL38.26m2

D. COMPUTATIONSA1 = a * b * sin (theta) = (7.49m)(7.31m)( sin (30.93o))= 14.07 mm2A2 = a * b * sin (theta) = (9.45m)(4.90m)( sin (49.25o))= 12.77 mm2 A3 = a * b * sin (theta) = (9.45m)(4.90m)( sin (49.25o))= 11.42 mm2Atotal = 14.07 mm2

E. Method: BY THREE SIDES (HERONS FORMULA)TRIANGLESIDESHALF PERIMETERAREA

abc

18.04m5.50m7.30m10.42m19.51m2

24.50m4.00m7.30m7.90m7.93m2

34.00m8.04m8.04m8.95m11.14m2

TOTAL38.58m2

F. COMPUTATIONS1 = (a + b + c) / 2 = (8.04 + 5.50 + 7.30) / 2= 10.42 mmS2 = (a + b + c) / 2 = (4.50 + 4.00 + 7.30) / 2= 7.90 mmS3 = (a + b + c) / 2 = (4.00 + 8.04 + 8.04) / 2= 8.95 mm

A1 = s*sqrt(s(s-a)(s-b)(s-c)) = 10.42m*sqrt(10.42m(10.42m-8.04m)(10.42m-5.50m)(10.42m-8.04m))= 19.51m2A2 = s*sqrt(s(s-a)(s-b)(s-c)) = 7.93m*sqrt(7.93m(7.93m-4.50m)(7.93m-4.00m)(7.93m-7.30m))= 7.93m2A3 = s*sqrt(s(s-a)(s-b)(s-c)) = 8.95m*sqrt(8.95m(8.95m-4.00m)(8.95m-5.50m)(8.95m-8.04m))= 11.14m2ATotal = 38.58m2

G. SKETCH

FINAL data sheetDate: July 27, 2015Group No. : 1Time: 1:00Location: Intramuros WallsWeather: SunnyProfessor: Engr. Balmoris

A. Method: BY BASE AND ALTITUDE METHOD

TRIANGLEBASEALTITUDEAREA

14m7.43m14.86m2

23.36m7.49m12.58m2

32.76m8.04m11.10m2

TOTAL38.54m2

B. COMPUTATIONSA1 = ( b * h ) / 2 = ( 4m * 7.43m ) / 2= 14.86 mm2A2 = ( b * h ) / 2 = ( 3.36m * 7.49m ) / 2 = 12.58 mm2A3 = ( b * h ) / 2 = ( 2.76m * 8.04m ) / 2 = 11.10 mm2Atotal = 38.54 mm2

C. Method: BY TWO SIDES AND THE INCLUDED ANGLETRIANGLEANGLESIDESAREA

Theta in degreesab

130.93o7.49m7.31m14.07m2

249.25o9.45m4.9m12.77m2

351.36o4m7.31m11.42m2

TOTAL38.26m2

D. COMPUTATIONSA1 = a * b * sin (theta) = (7.49m)(7.31m)( sin (30.93o))= 14.07 mm2A2 = a * b * sin (theta) = (9.45m)(4.90m)( sin (49.25o))= 12.77 mm2 A3 = a * b * sin (theta) = (9.45m)(4.90m)( sin (49.25o))= 11.42 mm2Atotal = 14.07 mm2

E. Method: BY THREE SIDES (HERONS FORMULA)TRIANGLESIDESHALF PERIMETERAREA

abc

18.04m5.50m7.30m10.42m19.51m2

24.50m4.00m7.30m7.90m7.93m2

34.00m8.04m8.04m8.95m11.14m2

TOTAL38.58m2

F. COMPUTATIONS1 = (a + b + c) / 2 = (8.04 + 5.50 + 7.30) / 2= 10.42 mmS2 = (a + b + c) / 2 = (4.50 + 4.00 + 7.30) / 2= 7.90 mmS3 = (a + b + c) / 2 = (4.00 + 8.04 + 8.04) / 2= 8.95 mm

A1 = s*sqrt(s(s-a)(s-b)(s-c)) = 10.42m*sqrt(10.42m(10.42m-8.04m)(10.42m-5.50m)(10.42m-8.04m))= 19.51m2A2 = s*sqrt(s(s-a)(s-b)(s-c)) = 7.93m*sqrt(7.93m(7.93m-4.50m)(7.93m-4.00m)(7.93m-7.30m))= 7.93m2A3 = s*sqrt(s(s-a)(s-b)(s-c)) = 8.95m*sqrt(8.95m(8.95m-4.00m)(8.95m-5.50m)(8.95m-8.04m))= 11.14m2ATotal = 38.58m2

G. SKETCHIn these pictures, we determined the distance of one point to another. These points served as the vertex for our pentagon. We used the chalk to connect the two points after determining their distance from one another.

We started creating triangles using the vertices of the polygon; these triangles will be used to determine the area of the polygon we created.

For the first part of the fieldwork we formed the first 3 triangles and measured its altitude, knowing the lengths of the altitudes and the bases of the triangles we can compute their individual area and we can obtain the area of the polygon.

For the second part of the fieldwork we again formed the second 3 triangles and measured a semi- triangle on one of the vertex per triangle and computed its included angle.

For the last part of the fieldwork we again formed the third 3 triangles and knowing the distances of the sides of the triangles formed. We can compute there individual area as well as the area of the

Research and discussion

PRINCIPLE There are several ways that we can measure the distance of the ground. It can be accomplished by breaking the tape method, by making a irregular polygon. A horizontal line of sight is established if the bubble is centered while sighting through the tube. This device is simply a level adopted for measuring vertical angles. Vertical aide is acted on where angles are read. It gives the value and the slope in terms of arc measure. Surveying can be used to calculate areas of different fields; this is under topographical surveying. We have different ways in determining the area of a certain field Topographic surveying is determining the relative location of points on the earths surface by measuring horizontal distances, differences in elevation and directions. Using this we can determine the area of a tract land where we can build a certain building or infrastructure that we want. Knowing also how to use topographical map we can determine the area of our reservoir and watersheds. Knowing the areas of cross-section profiles to calculate the amount of earthwork you need to do. To determine the areas can be either directly from field measurements, or indirectly from a plan or a map. "Land is ordinarily bought and sold on a basis of cost per unit area. For this reason as well as many others, an accurate determination of tract area is often necessary." The surveyor measures angles and distances. Once a "closed traverse" has been accomplished, i.e. a series of line segments that comes back to its initial point, the enclosed area (the "traverse area") may be computed. In the first case, you will find all the measurements of distances and angles you need by surveying and you will calculate the areas from them. In the second case, you will draw a plan or map first. Then you will get the dimensions you need from the scale, and determine the area on that basis. There are several simple methods available for measuring areas. Some of these aregraphic methods,where you compare the plan or map of the area you need to measure to a drawn pattern of known unit sizes. Others aregeometric methods, where you use simple mathematical formulas to calculate areas of regular geometrical figures, such as triangles,trapeziums*, or areas bounded by an irregular curveMethodRemarks

StripsGraphic method giving rough estimate

Square-gridGraphic method giving good to very good estimates

Subdivision into regular geometric figures such as, triangles, trapeziumsGeometric method giving good to very good estimates

Trapezoidal ruleGeometric method giving good to very good estimates Suitable for curved boundary

.When you need to measure areas directly in the field, divide the tract of land intoregular geometrical figures,such as triangles, rectangles or trapeziums. Then take all the necessary measurements, and calculate the areas according tomathematical formulas. If a plan or map of the area is available, you can draw these geometrical figures on it, and find their dimensions by using the reduction scale.

You can easily calculate the area ofany trianglewhen you know the dimensions

Another method is using a base line to subdivide land areas.When the shape of the land ispolygonal*,you should usually subdivide the total area you need to measureinto a series of regular geometrical figures(1-7 in the example)from a common base line AD. You will lay out offsets from the other summits of thepolygon*which are perpendicular to this base line to formright triangles1, 3, 4 and 7, andtrapeziums2, 5 and 6. Calculate each area of the right triangle and the trapezoid. Getting the sum of the following will get the area of the polygon.

But because of technology now a days there are applications that can easily give you the area of certain field. One of these is GPS Field Area Measure for android phones and Kuraves-K for computers.

Conclusion

The area of a certain land can be determined in many ways. Since some fields do not have the same length or rectangle in shape it is hard for us to measure its area. In this fieldwork we learned on how to use triangles in getting the area. Dividing the field in triangles and by getting the individual area of the triangles using the base and altitude, length of the two sides and the intruded angle and finally the length of each side of the triangle. Getting their individual we can get their summation to get the area of the field we want. Applying also the lessons we have learned especially in pacing, we can determine the area without any tools because we only need to know our pace factor.

It is important to use the plumb bobs in getting the plumb bob because the surface itself is not really in horizontal state. You will be measuring a longer or shorter horizontal distance if you will only plot the tape measure on the ground. As much as possible reduce the sagging of the tape measure to make sure you can get more accurate results. In the first part of the fieldwork, in order to get an accurate measure of the altitude of the triangle you can use protractor to help you or an L-square to make sure it is perpendicular to the line. It is difficult to assume the angle on the ground. For the second part, it is easier to measure shorter distance for the semi triangle needed for the data.It is important to remember that what we data we got is not their true actual value because if we remember there are also factors that change the length of the tape measure and of one that is the tape measure, especially if you measure on a very hot day. If possible the manual should also add additional polygon not only a pentagon so that we can also try this method to other polygons.