Embedded Files
LEC: Solve for distances, elevations and areas from a provided set of survey data.
LAB: Conduct fieldwork exercises to measure distances and angles/direction leading towards the determination of areas and elevations and report the results in an organized manner.
MODULE 2: AREA COMPUTATION
OVERVIEW
This module starts with the measurement of direction and angles which leads to balancing the traverse and area computation. Some of the methods for area computation that will be discussed are the use of triangles and coordinates, DMD and DPD Methods, trapezoidal rule, Simpson’s one-third rule and many more.
This module starts with the measurement of direction and angles which leads to balancing the traverse and area computation. Some of the methods for area computation that will be discussed are the use of triangles and coordinates, DMD and DPD Methods, trapezoidal rule, Simpson’s one-third rule and many more.
LEARNING ACTIVITIES:
The topics to be discussed below are:1. Measurement of Directions and Angles2. Bearing and Azimuth3. Magnetic Declination
The topics to be discussed below are:1. Measurement of Directions and Angles2. Bearing and Azimuth3. Magnetic Declination
1.1 MEASUREMENT OF DIRECTIONS AND ANGLES
TYPES OF MEASURED ANGLES
Interior angles are angles that are enclosed by sides of a closed traverse while exterior angles are the angles that are not enclosed by sides of a closed traverse. Note that they can be measured either clockwise or counterclockwise direction. Angle to the right is the clockwise angle between the preceding line and the next line of a traverse while angle to the left is the counterclockwise angle between the preceding line and the next line of a traverse. Deflection angle is the angle between the preceding line and the present one. If the deflection angle is turned to the right or in clockwise direction, it is called deflection right. If the deflection angle is turned to the left or in counterclockwise direction, it is called deflection left. For better understanding of these definitions, I decided to insert the picture on the left which was screen captured from our study guide.
TYPES OF MEASURED ANGLES
Interior angles are angles that are enclosed by sides of a closed traverse while exterior angles are the angles that are not enclosed by sides of a closed traverse. Note that they can be measured either clockwise or counterclockwise direction. Angle to the right is the clockwise angle between the preceding line and the next line of a traverse while angle to the left is the counterclockwise angle between the preceding line and the next line of a traverse. Deflection angle is the angle between the preceding line and the present one. If the deflection angle is turned to the right or in clockwise direction, it is called deflection right. If the deflection angle is turned to the left or in counterclockwise direction, it is called deflection left. For better understanding of these definitions, I decided to insert the picture on the left which was screen captured from our study guide.
1.2 BEARINGS AND AZIMUTHS
AZIMUTH
The azimuth of a line is defined as the clockwise angle from the north end or south end of the reference meridian. Usually, it is measured from the north end of the meridian. Shown on the right are the lines B, C, D, and E with their corresponding azimuths. Notice that the azimuth are simply the angle the lines make with the north line as the reference meridian. The azimuth of a line in the direction in which a survey is progressing is called forward azimuth, while the azimuth of a line in the direction opposite to that of progress is called the back azimuth.
AZIMUTH
The azimuth of a line is defined as the clockwise angle from the north end or south end of the reference meridian. Usually, it is measured from the north end of the meridian. Shown on the right are the lines B, C, D, and E with their corresponding azimuths. Notice that the azimuth are simply the angle the lines make with the north line as the reference meridian. The azimuth of a line in the direction in which a survey is progressing is called forward azimuth, while the azimuth of a line in the direction opposite to that of progress is called the back azimuth.
BEARING
The bearing of a line is defined as the smallest angle which that line makes with the reference meridian. A bearing cannot be greater than 90 degrees. In other words, it is always an acute horizontal angle. It is measured in relation to the north end or south end of the of the meridian such as north of the east (NE), north of the west (NW), south of the east (SE), and south of the west (SW). The bearing of a line in the direction in which a survey is progressing is called forward bearing, while the azimuth of a line in the direction opposite to that of progress is called the back bearing.
The bearing of a line is defined as the smallest angle which that line makes with the reference meridian. A bearing cannot be greater than 90 degrees. In other words, it is always an acute horizontal angle. It is measured in relation to the north end or south end of the of the meridian such as north of the east (NE), north of the west (NW), south of the east (SE), and south of the west (SW). The bearing of a line in the direction in which a survey is progressing is called forward bearing, while the azimuth of a line in the direction opposite to that of progress is called the back bearing.
1.3 MAGNETIC DECLINATION
Compass needles point nearly north over a large portion of the surface of the Earth. However, there are few locations where a compass needle would point precisely north due to the complex nature of the Earth's magnetic field. Magnetic north is the direction in which a compass aligns with the horizontal component of the magnetic field. On the other hand, true north is the direction that leads from a certain location to the north geographic pole. The angle between the true north and the magnetic north is called the magnetic declination.
Compass needles point nearly north over a large portion of the surface of the Earth. However, there are few locations where a compass needle would point precisely north due to the complex nature of the Earth's magnetic field. Magnetic north is the direction in which a compass aligns with the horizontal component of the magnetic field. On the other hand, true north is the direction that leads from a certain location to the north geographic pole. The angle between the true north and the magnetic north is called the magnetic declination.
MERIDIAN
Meridians are imaginary lines of longitude on the earth that extend from the North to South Pole. A principal meridian is one which is used as a reference line to survey a large area. There are mainly four types of meridian, namely, the true meridian, the magnetic meridian, the grid meridian, and the assumed meridian. The true meridian is known as the astronomic or geographic meridian which passes the geographic north and south poles of the earth and the observer's position. The magnetic meridian is the fixed reference line which lies parallel with the magnetic lines of force of the earth. Furthermore, the grid meridian is a fixed reference line parallel to the central meridian of the system of plane rectangular coordinates, whereas, assumed meridian is an arbitrary fixed reference line which is taken for convenience.
Meridians are imaginary lines of longitude on the earth that extend from the North to South Pole. A principal meridian is one which is used as a reference line to survey a large area. There are mainly four types of meridian, namely, the true meridian, the magnetic meridian, the grid meridian, and the assumed meridian. The true meridian is known as the astronomic or geographic meridian which passes the geographic north and south poles of the earth and the observer's position. The magnetic meridian is the fixed reference line which lies parallel with the magnetic lines of force of the earth. Furthermore, the grid meridian is a fixed reference line parallel to the central meridian of the system of plane rectangular coordinates, whereas, assumed meridian is an arbitrary fixed reference line which is taken for convenience.
DESIGNATION OF NORTH POINTS
The true meridian's north point is known as the True North. It is always depicted along a vertical line in maps and illustrations, pointing in the general direction of where the geographic north pole of the earth actually resides. The north point that is determined by a magnetized compass needle when there are no nearby attractions that would change it is known as Magnetic North. The direction of the magnetic lines of force traveling through a given spot on the earth's surface at a specific moment serves as a clue as to its orientation. True north can be found either east or west of magnetic north. Furthermore, Grid North is the northernmost point on a map that is constructed by lines that are perpendicular to a particular central meridian. It might line up with the lines pointing in the real north. The location of any arbitrarily selected north point is known as Assumed North.
The true meridian's north point is known as the True North. It is always depicted along a vertical line in maps and illustrations, pointing in the general direction of where the geographic north pole of the earth actually resides. The north point that is determined by a magnetized compass needle when there are no nearby attractions that would change it is known as Magnetic North. The direction of the magnetic lines of force traveling through a given spot on the earth's surface at a specific moment serves as a clue as to its orientation. True north can be found either east or west of magnetic north. Furthermore, Grid North is the northernmost point on a map that is constructed by lines that are perpendicular to a particular central meridian. It might line up with the lines pointing in the real north. The location of any arbitrarily selected north point is known as Assumed North.
TRAVERSE COMPUTATIONS
A traverse is a series of distances and angles, or distances and bearings, or distances and azimuths, connecting successive points. Note that if the bearing or azimuth of one side of a traverse has been determined and the angles between the sides have been measured, the bearings, or azimuths of the other sides can be computed. In the sample computation shown on the left, the given quantities are the bearing of line AB which is N 30° 35' E and the bearing of line BC which is S 54° 39' E. From the given bearings, we can compute the interior angle of B by adding them and obtained 85° 14'. Then, compute the deflection angle of line BC by subtracting 85° 14' from 180° and obtained 94° 46'. Finally, to compute for the azimuth of line BC, just add the bearing of line AB and the deflection angle previously computed and obtained 125° 21'.
A traverse is a series of distances and angles, or distances and bearings, or distances and azimuths, connecting successive points. Note that if the bearing or azimuth of one side of a traverse has been determined and the angles between the sides have been measured, the bearings, or azimuths of the other sides can be computed. In the sample computation shown on the left, the given quantities are the bearing of line AB which is N 30° 35' E and the bearing of line BC which is S 54° 39' E. From the given bearings, we can compute the interior angle of B by adding them and obtained 85° 14'. Then, compute the deflection angle of line BC by subtracting 85° 14' from 180° and obtained 94° 46'. Finally, to compute for the azimuth of line BC, just add the bearing of line AB and the deflection angle previously computed and obtained 125° 21'.
Salazar_BSCE_2B_Lec_CA#3.pdfLec_CA#3
CLOSING ERROR
Before the area of a piece of land can be computed, it is necessary to have a closed traverse. While plotting a closed traverse, it is required that the end point coincides exactly with the starting point to say that the measurements and computations made are precise and accurate. However, there are times that that the end point is not the starting point and that is because of errors obtained during the field measurements of angles and distances. The distance by which the end point of a survey fails to meet with the starting one is called the closing error or error of closure.
Before the area of a piece of land can be computed, it is necessary to have a closed traverse. While plotting a closed traverse, it is required that the end point coincides exactly with the starting point to say that the measurements and computations made are precise and accurate. However, there are times that that the end point is not the starting point and that is because of errors obtained during the field measurements of angles and distances. The distance by which the end point of a survey fails to meet with the starting one is called the closing error or error of closure.
LATITUDES AND DEPARTURES
The closure of a traverse can be computed using the closure in latitudes and closure in departures. Latitude is the projection of a line onto a reference meridian or North-South line while departure is the projection onto a reference parallel or East-West line. Just like the Cartesian plane, the latitude on the north is positive and on the south is negative. Likewise, the departude on the east is positive and on the west is negative. The latitude of any line can be computed using the formula: lat = d cos θ where d is the length or distance of the line while θ is the bearing of the line. Further, the departure of any line can be computed using the formula: dep = d sin θ where d is the distance of the line and θ is the bearing.
The closure of a traverse can be computed using the closure in latitudes and closure in departures. Latitude is the projection of a line onto a reference meridian or North-South line while departure is the projection onto a reference parallel or East-West line. Just like the Cartesian plane, the latitude on the north is positive and on the south is negative. Likewise, the departude on the east is positive and on the west is negative. The latitude of any line can be computed using the formula: lat = d cos θ where d is the length or distance of the line while θ is the bearing of the line. Further, the departure of any line can be computed using the formula: dep = d sin θ where d is the distance of the line and θ is the bearing.
LINEAR ERROR OF CLOSURE
Linear error of closure is a short line of unknown length and direction connecting the initial and final station of the traverse. It is approximately determined by plotting the traverse to scale, or more exactly by computing hypotenuse of a right triangle whose sides are the closure in latitudes and closure in departures respectively. Shown on the right is the formula to determine the LEC and its bearing which is basically the θ. Note that the CL or closure in latitude is simply the algebraic sum of North and South latitudes while the CD or closure in departure is basically the algebraic sum of the East and West departures. Further, the relative precision (RP) or sometimes called relative error of closure (REC) can be computed by dividing the LEC by the total length or the perimeter of the traverse. I provided an example below.
Linear error of closure is a short line of unknown length and direction connecting the initial and final station of the traverse. It is approximately determined by plotting the traverse to scale, or more exactly by computing hypotenuse of a right triangle whose sides are the closure in latitudes and closure in departures respectively. Shown on the right is the formula to determine the LEC and its bearing which is basically the θ. Note that the CL or closure in latitude is simply the algebraic sum of North and South latitudes while the CD or closure in departure is basically the algebraic sum of the East and West departures. Further, the relative precision (RP) or sometimes called relative error of closure (REC) can be computed by dividing the LEC by the total length or the perimeter of the traverse. I provided an example below.
TRAVERSE ADJUSTMENTS
Adjusting a traverse (also known as balancing a traverse) is used to distribute the closure error back into the angle and distance measurements.
1. COMPASS RULE
Compass Rule is also known as the Bowditch rule as it was named after the American navigator Nathaniel Bowditch. The rule applies the proportion of the closure error to each line. It is also based on the assumptions that all lengths are measured with equal care, all angles are taken with approximately the same precision, errors are accidental, and the total error in any side is directly proportional to the length of the traverse. Shown below are some of my notes on how compass rule works.
2. TRANSIT RULE
Transit Rule. The method of adjusting a traverse by the transit rule is similar to the method using the compass rule. The main difference is that with the transit rule the latitude and departure corrections depend on the length of the latitude and departure of the course respectively instead of both depending on the length of the course. It is based on the assumptions that angular measurements are more precise than linear measurements, and that errors in traversing are accidental. Shown below are some of my notes on how transit rule works.
Adjusting a traverse (also known as balancing a traverse) is used to distribute the closure error back into the angle and distance measurements.
1. COMPASS RULE
Compass Rule is also known as the Bowditch rule as it was named after the American navigator Nathaniel Bowditch. The rule applies the proportion of the closure error to each line. It is also based on the assumptions that all lengths are measured with equal care, all angles are taken with approximately the same precision, errors are accidental, and the total error in any side is directly proportional to the length of the traverse. Shown below are some of my notes on how compass rule works.
2. TRANSIT RULE
Transit Rule. The method of adjusting a traverse by the transit rule is similar to the method using the compass rule. The main difference is that with the transit rule the latitude and departure corrections depend on the length of the latitude and departure of the course respectively instead of both depending on the length of the course. It is based on the assumptions that angular measurements are more precise than linear measurements, and that errors in traversing are accidental. Shown below are some of my notes on how transit rule works.
CALCULATING TRAVERSE AREA
1. DMD (DOUBLE MERIDIAN DISTANCE)
The best known procedure for calculating land areas is the double meridian distance (DMD) method. The meridian distance of a line is the east-west distance from the midpoint of the line to the reference meridian. The meridian distance is positive (+) to the east and negative (-) to the west. The rules of the DMD method include the following:Rule 1: The DMD of the first course is equal to the departure of the course.Rule 2: The DMD of any other course is equal to the DMD of the preceding course, plus the departure of the course itself.Rule 3: The DMD of the last course is numerically equal to the departure of that course but with the opposite sign.
In the sample problem on the left, notice that I applied the double area. The sum of the products of each point, DMD and latitude, equal twice the area, or the double area. For instance, the double area of line AB equals the DMD of the line AB times the adjusted latitude of the line AB.
1. DMD (DOUBLE MERIDIAN DISTANCE)
The best known procedure for calculating land areas is the double meridian distance (DMD) method. The meridian distance of a line is the east-west distance from the midpoint of the line to the reference meridian. The meridian distance is positive (+) to the east and negative (-) to the west. The rules of the DMD method include the following:Rule 1: The DMD of the first course is equal to the departure of the course.Rule 2: The DMD of any other course is equal to the DMD of the preceding course, plus the departure of the course itself.Rule 3: The DMD of the last course is numerically equal to the departure of that course but with the opposite sign.
In the sample problem on the left, notice that I applied the double area. The sum of the products of each point, DMD and latitude, equal twice the area, or the double area. For instance, the double area of line AB equals the DMD of the line AB times the adjusted latitude of the line AB.
2. DPD (DOUBLE PARALLEL DISTANCE)
The DPD method follows the same procedure as the DMD except that it is focused on the latitudes of the lines to obtain the DPD value. The parallel distance of a line is the distance from the midpoint of the line to the reference parallel or east-west line. The rules of the DPD method include the following:Rule 1: The DPD of the first course is equal to the latitude of the course.Rule 2: The DPD of any other course is equal to the DPD of the preceding course, plus the latitude of the course itself.Rule 3: The DPD of the last course is numerically equal to the latitude of the course but with opposite sign.
In the sample problem on the right, notice that I applied the double area. The sum of the products of each point, DPD and departure, equal twice the area, or the double area. For instance, the double area of line AB equals the DPD of the line AB times the adjusted departure of the line AB.
The DPD method follows the same procedure as the DMD except that it is focused on the latitudes of the lines to obtain the DPD value. The parallel distance of a line is the distance from the midpoint of the line to the reference parallel or east-west line. The rules of the DPD method include the following:Rule 1: The DPD of the first course is equal to the latitude of the course.Rule 2: The DPD of any other course is equal to the DPD of the preceding course, plus the latitude of the course itself.Rule 3: The DPD of the last course is numerically equal to the latitude of the course but with opposite sign.
In the sample problem on the right, notice that I applied the double area. The sum of the products of each point, DPD and departure, equal twice the area, or the double area. For instance, the double area of line AB equals the DPD of the line AB times the adjusted departure of the line AB.
CHAPTER 2: TAPING AND PACE FACTOR DETERMINATION
OVERVIEW
This chapter talks about the two commonly employed methods of linear measurement which are pacing and taping over level and sloping grounds. The students are expected to execute their first field works properly. The accurate determination of the distance between two points on any surface is one of the basic operations of Plane Surveying.
This chapter talks about the two commonly employed methods of linear measurement which are pacing and taping over level and sloping grounds. The students are expected to execute their first field works properly. The accurate determination of the distance between two points on any surface is one of the basic operations of Plane Surveying.
LEARNING OBJECTIVES:
At the end of this module, you should be able to: 1. Determine individual Pace Factor; 2. Measure distance by pacing; 3. Determine the horizontal length of a line over smooth and level ground with the tape supported throughout its length; and 4. Determine the horizontal length of a line over uneven and sloping ground by the method of breaking tape.
At the end of this module, you should be able to: 1. Determine individual Pace Factor; 2. Measure distance by pacing; 3. Determine the horizontal length of a line over smooth and level ground with the tape supported throughout its length; and 4. Determine the horizontal length of a line over uneven and sloping ground by the method of breaking tape.
FIELD WORK #1: PACING ON LEVEL GROUND
Salazar_BSCE2B_Field Work #1.pdfA pace is defined as the length of a single step while the double step or two paces is called a stride. To pace is to count the number of steps in a required distance. In surveying, pacing is useful especially in measuring distances. Pacing is the simplest and easiest way of measuring distances. Simply, pacing is defines as the practice of measuring how many "paces" it takes to walk a certain distance. The distance is obtained by multiplying the number of steps taken between two points by one's pace factor. Finding a person's pace factor involves pacing (walking) a distance, typically 300 to 500 feet, multiple times and determining the average length of step. In other words, pace factor is determined by dividing the measured or known length of a line by the mean number of paces taken to walk or traverse a line. These are the things we did in the first field work
It was actually conducted in the school premises since the school is a level ground. The first part of the field work is determining our own's pace factor. What we did first is measured a 90m-distanced line and designated its end points as A and B. Then, we walked over that line individually and at a natural pace while counting the number of paces we walked over that course. I did it for 6 trials and computed my mean number of paces which is equal to 125.617 paces. Finally, I was able to determine my pace factor by dividing the measured distance of course AB by the computed mean number of paces which is 0.716m per pace. The second part of the field work is measuring distance by pacing. In this part, we first established end points, A and B, whose length is unknown. Then, just like in the first part, I walked over the said course at a natural pace, and counted the number of paces for six trials. I once again computed for the mean number of paces which is 50.316 paces. Then, by multiplying this mean by the pace factor in the first part, I obtained the paced distance which is equal to 36.230m. When we measured the course, it was actually 36m. Finally, I calculated the relative precision by dividing the difference between the taped distance and paced distance by the taped distance or (TD - PD) / TD and I obtained 1/156.522 which is acceptable.
It was actually conducted in the school premises since the school is a level ground. The first part of the field work is determining our own's pace factor. What we did first is measured a 90m-distanced line and designated its end points as A and B. Then, we walked over that line individually and at a natural pace while counting the number of paces we walked over that course. I did it for 6 trials and computed my mean number of paces which is equal to 125.617 paces. Finally, I was able to determine my pace factor by dividing the measured distance of course AB by the computed mean number of paces which is 0.716m per pace. The second part of the field work is measuring distance by pacing. In this part, we first established end points, A and B, whose length is unknown. Then, just like in the first part, I walked over the said course at a natural pace, and counted the number of paces for six trials. I once again computed for the mean number of paces which is 50.316 paces. Then, by multiplying this mean by the pace factor in the first part, I obtained the paced distance which is equal to 36.230m. When we measured the course, it was actually 36m. Finally, I calculated the relative precision by dividing the difference between the taped distance and paced distance by the taped distance or (TD - PD) / TD and I obtained 1/156.522 which is acceptable.
Taping is simply the process of measuring the length of a line or course through the use of a tape. When it comes to precision, the data obtained by taping is undoubtedly more precise and accurate than the measurement obtained by pacing. That is why the acceptable precision for taping should be at least 1/1000. Note that only minimal effort is required to measure and tape a distance between two points when the ground is relatively smooth and the ground cover vegetation is light and low. For instance, it only requires the surveyor to lay the tape on the ground and measure. The only factor that can cause inaccuracy of the results is the alignment of the tape, henceforth, the field party should make sure that the measuring tape is correctly aligned and both ends of the tape are at the same elevation.
The procedure of this field work was easy. As a group, we first designated two points A and B which is approximately 150m to 300m. Then, using the measuring tape, we measured the course twice, from A to B, and from B to A. I computed the difference as well as the mean of the two measurements to be used in calculating the relative precision. For instance, the lengths we obtained are 190.45m and 190.30m. Their difference is equal to 0.15m and their mean is 190.375m. To calculate for the relative precision, divide the discrepancy by the mean length. 0.15m divided by 190.45m is equal to 1/1269.17. This relative precision is acceptable since the acceptable precision should be at least 1/1000.
The procedure of this field work was easy. As a group, we first designated two points A and B which is approximately 150m to 300m. Then, using the measuring tape, we measured the course twice, from A to B, and from B to A. I computed the difference as well as the mean of the two measurements to be used in calculating the relative precision. For instance, the lengths we obtained are 190.45m and 190.30m. Their difference is equal to 0.15m and their mean is 190.375m. To calculate for the relative precision, divide the discrepancy by the mean length. 0.15m divided by 190.45m is equal to 1/1269.17. This relative precision is acceptable since the acceptable precision should be at least 1/1000.
FIELD WORK #2: TAPING OVER SMOOTH AND LEVEL GROUND
Salazar_BSCE2B_Field Work #2.pdfFIELD WORK #3: TAPING OVER UNEVEN AND SLOPING GROUND
Salazar_BSCE2B_Field Work #3.pdfTaping is the process of measuring how long a line or course is through the use of a tape. Unlike the previous field work, titled "taping over smooth and level ground" that only requires the surveyors to lay the tape on the ground and measure, “taping over uneven and sloping ground” demands an extra effort to align the tape horizontally with one or both tape men using plumb bobs. Aligning the tape horizontally is removing the obstacles or slopes that hinder the correct measurement of a distance. Further, in times of large elevation which makes impossible the use of a full tape length, the “breaking tape” method is used. This method is simply breaking the whole distance into shorter distances as long as it is possible to keep the tape horizontal and accumulating these distances to total a full tape length. In other words, “if the slope is too great to allow an entire tape length to be employed, shorter increments are measured until all the required distance has been measured”.
This field work was conducted at the Monte Cielo Subdivision, Cocepcion Pequeña. As stated, the area has slopes that forced us to break the tabe by 10 or 20m. The process we did was almost the same with the previous field work except that this was extra challenging because of the large slopes. For instance, we designated points A and B and measured it twice from A to B and from B to A. We obtained the data 204.70m and 204.55m. Their difference is 0.15m and their mean length is 204.625m. We got 1/1400 relative precision which is very much acceptable
Measuring a field is a complex and tiring task since fields seldom have the simple geometrical shapes such as a triangle, square, rectangle, etc. The sides are often curved and the shape can be complicated. But in the majority of cases, the shape of a field can be roughly represented by a simple figure; curved lines can be roughly approximated by straight ones, and the field can be divided into triangles and rectangles, all of which can be measured and used to determine the field's area. Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. In this field work, we are tasked to determine the area of a rectilinear field. Rectilinear means straight so when we say ‘rectilinear field’, it is pertaining to a field whose shape is made up of straight lines.
It is convenient to divide the field into a series of connected triangles and determine the area of each triangle to get the total area of the field. First, we measured the lengths of each side of the triangle connected to the center and computed the included angles through the chord distance. Use the formula θ=sin-1 ((d/2)/L)×2, where d is the measured chord distance and L is the length of the shorter side of each triangle. Then, SAS formula will be utilized in determining the area of each triangle since two sides and an included angle are given in every triangle in the field. The formula is A=1/2 absinC, where a and b are the two measured sides of the triangle and C is the included angle. The total area of the rectilinear field is obviously the sum of the computed areas of the series of connected triangles into which the field is subdivided. We obtained a total area of 1031.79m2.
FIELD WORK #4: DETERMINING AREA OF A RECTILINEAR FIELD BY TAPE
Salazar_BSCE2B_Field Work #4.pdfCENG101_MidtermExam_Oct15_2022.pdfMIDTERM EXAM
REFLECTION
LEC: This module covered a lot of computations starting from the traverse computation, computing the linear error of closure, the compass and transit rule, calculating traverse area through the DMD and DPD methods, and lastly incorporating the double area theorem to determine the area of the traverse. I found the traverse computation to be the easiest of the topics since it only requires understanding of the angles which was already discussed since elementary. Note that, a sketch is very helpful in finding the missing quantities in a traverse. Further, in the computation of linear error of closure, I made again mnemonics to easily familiarize some of the terms. One of the mnemonic is cos-y-lat which is read is cosylat. This means that the latitude is the vertical projection of the line which is represented by the y; and the cos is simply used in the formula to find latitude which is basically distance times the cosine of the bearing. Another mnemonic is sine-x-dep which is read as sinexdep. This means that the departure is the horizontal projection of the line which is represented by x; and the sine is again used in the formula to find departure which is distance times the sine of the bearing. Moreover, I found the last topics which are used in traverse adjustments to be time-consuming since a lot of process is needed before arriving to the required traverse area. Nonetheless, I was able to understand them all especially on how the computation works.
LAB: This course learning outcome allowed us to perform four field works which are the pacing on level ground, taping over smooth and level ground, taping over uneven and sloping ground, and determining area of a rectilinear field by tape. The first field work taught me that it is possible to measure large distances even without the use of a measuring equipment. Once the pace factor of an individual is determined, he or she can approximately determine the measurement of a line or course. Further, when it comes to precision, taping is more precise and accurate than pacing because of the fact that it uses a surveyor's tape to determine the measurement of a liner or course. Taping over smooth and level ground needs only minimal effort since it only requires the tape to be laid out on the ground compared to the taping over uneven and sloping ground which requires the tape to be suspended or aligned horizontally to remove the slope, thus the need to use plumb bobs and make sure that the tape does not sag or whatsoever to ensure the accuracy of the measurements. Furthermore, in the field work #4, I had realized the importance of the SAS theorem since it was used to ultimately determine the area of the rectilinear field. By the way, when we say, rectilinear, it means straight so when we rectilinear field, it is a field whose sides are straight lines. Also, I had learned that the chord distance could be used in computing the included angle of a triangle. I just familiarized this formula: θ=sin-1 ((d/2)/L)×2 where d is the chord distance and L is the length of the shorter side.
LEC: This module covered a lot of computations starting from the traverse computation, computing the linear error of closure, the compass and transit rule, calculating traverse area through the DMD and DPD methods, and lastly incorporating the double area theorem to determine the area of the traverse. I found the traverse computation to be the easiest of the topics since it only requires understanding of the angles which was already discussed since elementary. Note that, a sketch is very helpful in finding the missing quantities in a traverse. Further, in the computation of linear error of closure, I made again mnemonics to easily familiarize some of the terms. One of the mnemonic is cos-y-lat which is read is cosylat. This means that the latitude is the vertical projection of the line which is represented by the y; and the cos is simply used in the formula to find latitude which is basically distance times the cosine of the bearing. Another mnemonic is sine-x-dep which is read as sinexdep. This means that the departure is the horizontal projection of the line which is represented by x; and the sine is again used in the formula to find departure which is distance times the sine of the bearing. Moreover, I found the last topics which are used in traverse adjustments to be time-consuming since a lot of process is needed before arriving to the required traverse area. Nonetheless, I was able to understand them all especially on how the computation works.
LAB: This course learning outcome allowed us to perform four field works which are the pacing on level ground, taping over smooth and level ground, taping over uneven and sloping ground, and determining area of a rectilinear field by tape. The first field work taught me that it is possible to measure large distances even without the use of a measuring equipment. Once the pace factor of an individual is determined, he or she can approximately determine the measurement of a line or course. Further, when it comes to precision, taping is more precise and accurate than pacing because of the fact that it uses a surveyor's tape to determine the measurement of a liner or course. Taping over smooth and level ground needs only minimal effort since it only requires the tape to be laid out on the ground compared to the taping over uneven and sloping ground which requires the tape to be suspended or aligned horizontally to remove the slope, thus the need to use plumb bobs and make sure that the tape does not sag or whatsoever to ensure the accuracy of the measurements. Furthermore, in the field work #4, I had realized the importance of the SAS theorem since it was used to ultimately determine the area of the rectilinear field. By the way, when we say, rectilinear, it means straight so when we rectilinear field, it is a field whose sides are straight lines. Also, I had learned that the chord distance could be used in computing the included angle of a triangle. I just familiarized this formula: θ=sin-1 ((d/2)/L)×2 where d is the chord distance and L is the length of the shorter side.
REFERENCES:
https://dawood.net/wp-content/uploads/2019/03/0-3.jpghttps://jerrymahun.com/images/open_access/trav_comps/directions/c-04.gifhttps://jerrymahun.com/images/open_access/trav_comps/directions/c-06.gifhttps://www.geomag.nrcan.gc.ca/mag_fld/magdec-en.phphttps://1.bp.blogspot.com/-wK1QIOu4jkU/YQTahb2Q4tI/AAAAAAAADvo/sFvRuVMnX_EF5A2UCI6KrmJDtQVXkKBqACLcBGAsYHQ/s578/declination%2Band%2Bdip.JPGhttps://www.sidwellco.com/company/resources/principal-meridians-base-lines/#:~:text=Meridians%20are%20imaginary%20lines%20of,to%20survey%20a%20large%20area.https://readcivil.com/types-of-meridian-in-surveying-surveying-in-civil-engineering/https://www.studocu.com/ph/document/cebu-institute-of-technology-university/general-surveying/topic-3-measurement-of-angles-and-directions/33762245https://images.squarespace-cdn.com/content/v1/5f872a1e0559c85d25404ef9/1611851488374-OVYF98TLDBQWQPTP99HA/arrows.jpghttp://www.ce.memphis.edu/1112/notes/project_3/traverse/Surveying_traverse.pdfhttps://www.engineeringenotes.com/surveying/theodolite-surveying/adjustment-of-a-closed-traverse-theodolite-surveying-surveying/14172https://gs-blog-images.grdp.co/gate-exam/wp-content/uploads/2016/12/02123727/image0051.jpghttps://sites.google.com/site/civilengineeringwebsite/our-pastorshttps://breakthelight.files.wordpress.com/2012/11/ge-11-lecture-6-traverse-computations-and-adjustments-1.pdfhttps://sites.google.com/site/civilengineeringwebsite/what-we-believehttps://www.progressivegardening.com/agricultural-engineering-2/pacing.htmlhttps://images4.alphacoders.com/652/thumb-1920-652737.jpghttps://www.survey-solutions.co.uk/wp-content/uploads/2020/07/Project-17-Bishops-Lydeyard.jpghttps://t4.ftcdn.net/jpg/02/98/68/73/360_F_298687332_D0GAA6fAgr70NWtF8UKXPyLx0mTGug0x.jpghttps://i.pinimg.com/originals/ff/cf/d1/ffcfd1e82699b5b51e2f20438a9d8ccc.jpghttps://i.pinimg.com/originals/32/96/9c/32969c8d097e908ffa28514c98253454.jpghttps://wallpaperaccess.com/full/4149226.jpghttps://i.pinimg.com/originals/5c/ad/e6/5cade6da6c5e0eed3bc7f59e03c36c42.jpghttps://cutewallpaper.org/cdn-cgi/mirage/dd19f2d06ebc24f541f142b37b4289ffa7de722a7607e39984c5c6dd4ce8defd/1280/27x/1vzl6pojd/142661618.jpg
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