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LEC: Compute for the missing data from an incomplete traverse data.
LAB: Utilize modern surveying equipment such as the total station and handheld GPS in obtaining vertical and horizontal distances, angles and coordinates.
MODULE 4: COMPUTATION FOR MISSING DATA
OVERVIEW
Sometimes it is not possible or practical to determine by field observation the length or direction of a line (or lines) withina closed traverse. These missing quantities may be determined analytically to obtain a complete set of notes for thetraverse as long as they do not exceed two in number.
Sometimes it is not possible or practical to determine by field observation the length or direction of a line (or lines) withina closed traverse. These missing quantities may be determined analytically to obtain a complete set of notes for thetraverse as long as they do not exceed two in number.
COMMON REASONS FOR MISSING DATA
Surveyors may experience missing data because of various reasons. First is obstruction in the area. For example, the line or course you are about to measure is in a bushy forest or rugged terrain or is enclosed by a private property. Another is the landowner does not permit surveying. In case that an area to be surveyed is part of a private property, the surveyors need to ask permission from the owner of the property and their fate will depend on the owner. Third is limited time. Surveying is easier said than done. It takes a lot of courage, time, and patience to be able to obtain all the required data. Last reason is division of lands. If a large area is subdivided into several tract of lands, the dividing line will be a missing data.
Surveyors may experience missing data because of various reasons. First is obstruction in the area. For example, the line or course you are about to measure is in a bushy forest or rugged terrain or is enclosed by a private property. Another is the landowner does not permit surveying. In case that an area to be surveyed is part of a private property, the surveyors need to ask permission from the owner of the property and their fate will depend on the owner. Third is limited time. Surveying is easier said than done. It takes a lot of courage, time, and patience to be able to obtain all the required data. Last reason is division of lands. If a large area is subdivided into several tract of lands, the dividing line will be a missing data.
The following are some of the more common types of omitted measurements:
1. Omitted measurements are in one sideCase 1: Length and bearing of one side unknown2. Omitted measurements involving two adjoining sidesCase 1: Length of One Side and Bearing of another Side UnknownCase 2: Lengths of Two Sides UnknownCase 3: Bearings of Two Sides Unknown3. Omitted Measurements Involving Two Non-Adjoining SidesCase 1: Length of One Side and Bearing of another Side UnknownCase 2: Lengths of Two Sides UnknownCase 3: Bearings of Two Sides Unknown
1. Omitted measurements are in one sideCase 1: Length and bearing of one side unknown2. Omitted measurements involving two adjoining sidesCase 1: Length of One Side and Bearing of another Side UnknownCase 2: Lengths of Two Sides UnknownCase 3: Bearings of Two Sides Unknown3. Omitted Measurements Involving Two Non-Adjoining SidesCase 1: Length of One Side and Bearing of another Side UnknownCase 2: Lengths of Two Sides UnknownCase 3: Bearings of Two Sides Unknown
HOW DO YOU COMPUTE FOR MISSING DATA?
Computation for missing data is a bit time-consuming. It is advisable to first sketch the given quantities to have a full grasp of your strategy on solving the missing quantities. The sketch must be as accurate as possible in a way that the angles complement well with the drawing. Personally, I am using a ruler and a protractor in solving every problem on missing data. Then, the strategy will depend on the number of missing quantities in the sketch. Usually, assigning division lines will help in determining the missing quantities.
Dividing the traverse allow the formation of triangle which then permits the usage of the sine law and the cosine law. To solve a triangle is to find the lengths of each of its sides and all its angles. Note that sine law is used when the given quantities on the triangle are AAS or two angles and one side and SSA or two sides and a non-included angle. The law sine law or the sine rule states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides. The law is shown on the right. Further, cosine law is used when the given quantities are SSS or three sides and SAS or two sides and an included angle. In trigonometry, the cosine law or cosine rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them. Shown on the right are the formulas of the cosine law.
Computation for missing data is a bit time-consuming. It is advisable to first sketch the given quantities to have a full grasp of your strategy on solving the missing quantities. The sketch must be as accurate as possible in a way that the angles complement well with the drawing. Personally, I am using a ruler and a protractor in solving every problem on missing data. Then, the strategy will depend on the number of missing quantities in the sketch. Usually, assigning division lines will help in determining the missing quantities.
Dividing the traverse allow the formation of triangle which then permits the usage of the sine law and the cosine law. To solve a triangle is to find the lengths of each of its sides and all its angles. Note that sine law is used when the given quantities on the triangle are AAS or two angles and one side and SSA or two sides and a non-included angle. The law sine law or the sine rule states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides. The law is shown on the right. Further, cosine law is used when the given quantities are SSS or three sides and SAS or two sides and an included angle. In trigonometry, the cosine law or cosine rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them. Shown on the right are the formulas of the cosine law.
SAMPLE PROBLEM #1 (USING SINE LAW)
This sample problem was taken from my notes. Notice that the missing quantities are one length and one bearing. I first sketched the given measurements and decided to create a division line from point A to point D. Then by using the latitudes of lines AB, BC, and CD, I was able to determine the length of line AD and its bearing. Notice that a triangle was created and it was ΔAED. Using the sum of the bearing of line DE and the bearing of AD, I was able to identify the angle of D in the triangle. Now, the given quantities of the triangle are two sides and a non-included angle. Henceforth, I utilized the sine law to determine the bearing of line EA and the length of line DE. Note that I only chose one equality from the sine rule. It is imperative to choose the equality with only one missing quantity while considering that the missing quantity is exactly the missing measurement in the problem. It only needs algebraic manipulation such as cross-multiplication and division to determine the missing data. Furthermore, the latitudes and the departures of the lines DE and EA are also missing but I was not able to include them in my solution.
This sample problem was taken from my notes. Notice that the missing quantities are one length and one bearing. I first sketched the given measurements and decided to create a division line from point A to point D. Then by using the latitudes of lines AB, BC, and CD, I was able to determine the length of line AD and its bearing. Notice that a triangle was created and it was ΔAED. Using the sum of the bearing of line DE and the bearing of AD, I was able to identify the angle of D in the triangle. Now, the given quantities of the triangle are two sides and a non-included angle. Henceforth, I utilized the sine law to determine the bearing of line EA and the length of line DE. Note that I only chose one equality from the sine rule. It is imperative to choose the equality with only one missing quantity while considering that the missing quantity is exactly the missing measurement in the problem. It only needs algebraic manipulation such as cross-multiplication and division to determine the missing data. Furthermore, the latitudes and the departures of the lines DE and EA are also missing but I was not able to include them in my solution.
Nonetheless, we can use formulas to solve them. For the latitude, use the formula Lcosθ or simply the length of the line times the cosine of the bearing. For instance, the latitude of the line DE is 2423.87 x cos (28° 39') = 2127.10. The latitude of the line EA is 1738.96 x cos (84° 51' 17.66'') = 155.95. Furthermore, for the departure, use the formula Lsinθ or simply the length of the line times the sine of the bearing. For instance, the departure of the line DE is 2423.87 x sin (28° 39') = 1162.14. The departure of the line EA is 1738.96 x sin (84° 51' 17.66'') = 1731.95.
SAMPLE PROBLEM #2 (USING COSINE LAW)
This problem was again taken from my notes. Just like what I did in the first problem, I first sketched the data from the table and decided to create a division line from points A to D. Then, using the latitudes and departures of lines AB, BC, and CD, I computed for the length and bearing of the line AD. From here, I noticed that the given quantities of the created triangle (ΔAED) are three sides. Henceforth, I utilized the cosine rule to solve the missing quantities. Note that the missing data are the bearings of lines DE and EA as well as their latitudes and departures. Computing for the bearings is simply algebraic manipulation and derivation of the formula. While for the latitudes and departures, use the formulas Lsinθ and Lcosθ where L is the length of the line θ is the bearing of the line. The data in the table was already updated with the computed latitudes and departures.
This problem was again taken from my notes. Just like what I did in the first problem, I first sketched the data from the table and decided to create a division line from points A to D. Then, using the latitudes and departures of lines AB, BC, and CD, I computed for the length and bearing of the line AD. From here, I noticed that the given quantities of the created triangle (ΔAED) are three sides. Henceforth, I utilized the cosine rule to solve the missing quantities. Note that the missing data are the bearings of lines DE and EA as well as their latitudes and departures. Computing for the bearings is simply algebraic manipulation and derivation of the formula. While for the latitudes and departures, use the formulas Lsinθ and Lcosθ where L is the length of the line θ is the bearing of the line. The data in the table was already updated with the computed latitudes and departures.
Salazar_BSCE2B_Lec_CW#4.pdfLec_CW#4
A traverse is a series of straight lines connecting successive points whose lengths and directions have been determined from field observation. When a sequence of connected lines extends along a general direction and doesn’t return to the starting point, it is known as open traverse or unclosed traverse. Open traverse is advisable for the survey of roads, rivers and coastlines. The act of measuring the directions and lengths of a traverse is called traversing. Note that there are several methods of traversing, depending on the instruments used in determining the relative directions of the traverse lines. Meanwhile, this particular field work is focused in “compass traversing” where the magnetic bearings of the traverse legs are measured by a compass and the lengths of these lines are measured with a tape. Then the observed bearings are verified and necessary corrections for local attraction are applied.
This field work was conducted in the school campus with the objectives of determining the magnetic bearings of each line of an open compass traverse and to learn how to adjust an open compass traverse. Magnetic bearings are affected by the occurrence of local attraction or the proximity of steel, iron, magnetic ores, and direct electric current. Thus, errors in readings of the compass may arise. That is why necessary corrections are applied. In adjusting the observed bearings, it must be taken in consideration that bearings should be an acute angle or less than 90 degrees angle. Therefore, the forward and back bearings of a single traverse line should be of the same angle but different direction. If the forward bearing is north of the west, the back bearing should be south of the east. Likewise, if the forward bearing is north of the east, the back bearing should be south of the west. Necessary calculations are already obvious once the sketch has been drawn. Hence, the sketch should be as accurate as possible.
This field work was conducted in the school campus with the objectives of determining the magnetic bearings of each line of an open compass traverse and to learn how to adjust an open compass traverse. Magnetic bearings are affected by the occurrence of local attraction or the proximity of steel, iron, magnetic ores, and direct electric current. Thus, errors in readings of the compass may arise. That is why necessary corrections are applied. In adjusting the observed bearings, it must be taken in consideration that bearings should be an acute angle or less than 90 degrees angle. Therefore, the forward and back bearings of a single traverse line should be of the same angle but different direction. If the forward bearing is north of the west, the back bearing should be south of the east. Likewise, if the forward bearing is north of the east, the back bearing should be south of the west. Necessary calculations are already obvious once the sketch has been drawn. Hence, the sketch should be as accurate as possible.
FIELD WORK #6: OPEN COMPASS TRAVERSE
Salazar_BSCE2B_Field Work #6.pdfFIELD WORK #7: CLOSED COMPASS TRAVERSE
Salazar_BSCE2B_Field Work #7.pdfThis field work follows the same procedure as the previous one except that this field work aims to determine the magnetic bearings as well as the included angles of a closed traverse. When the lines form a circuit which ends at the starting point, it is known as closed traverse. Closed traverse is convenient for surveying of boundaries of ponds, sports grounds, and forests. Just like field work #6, this field work used compass traversing where the magnetic bearings of the traverse legs are measured by a compass and the lengths of these lines are measured with a tape. Then the observed bearings are verified and necessary corrections for local attraction are applied.
Magnetic bearings are affected by the occurrence of local attraction or the proximity of steel, iron, magnetic ores, and direct electric current. Thus, errors in readings of the compass may arise. That is why necessary corrections are applied. In adjusting the observed bearings, it must be taken in consideration that bearings should be an acute angle or less than 90 degrees angle. Therefore, the forward and back bearings of a single traverse line should be of the same angle but different direction. If the forward bearing is north of the west, the back bearing should be south of the east. Likewise, if the forward bearing is north of the east, the back bearing should be south of the west. Necessary calculations are already obvious once the sketch has been drawn. Furthermore, computing the interior angles of a closed traverse is easy especially if the sketch has been drawn accurately. Necessary calculations will become obvious once the data has been sketched. The angular error of closure can be determined by subtracting the sum of the computed interior angles of the traverse from (n – 2)180° where n is the number of sides in the traverse. In this field work, we obtained a zero angular error of closure which gives us no correction and which means that the computed interior angles are accurate.
Magnetic bearings are affected by the occurrence of local attraction or the proximity of steel, iron, magnetic ores, and direct electric current. Thus, errors in readings of the compass may arise. That is why necessary corrections are applied. In adjusting the observed bearings, it must be taken in consideration that bearings should be an acute angle or less than 90 degrees angle. Therefore, the forward and back bearings of a single traverse line should be of the same angle but different direction. If the forward bearing is north of the west, the back bearing should be south of the east. Likewise, if the forward bearing is north of the east, the back bearing should be south of the west. Necessary calculations are already obvious once the sketch has been drawn. Furthermore, computing the interior angles of a closed traverse is easy especially if the sketch has been drawn accurately. Necessary calculations will become obvious once the data has been sketched. The angular error of closure can be determined by subtracting the sum of the computed interior angles of the traverse from (n – 2)180° where n is the number of sides in the traverse. In this field work, we obtained a zero angular error of closure which gives us no correction and which means that the computed interior angles are accurate.
REFLECTION
LEC: This module allowed me to realize that surveying is easier said than done. It takes a lot of courage, time, and patience to be able to gather all the required data in one operation. The fact there is a method for the computation of missing data says it all. The course itself anticipated any untoward incident that may happen during field work operations. In case that there is an obstruction of the surveying area, the landowner does not permit surveying, limited time, or there is a division of lands, various strategies can be used to calculate the missing data thus eliminating the hindrances encountered during the surveying process. Furthermore, this module is a review of the trigonometric topics such as the sine law and the cosine law which was previously discussed in the subject Higher Mathematics for Engineers/Engineering Technologists. In computing the missing data, the first thing to do is to sketch the given data to get a full grasp of the traverse and eventually get an idea on how to solve it. Dividing the traverse creates triangles which then permits the use of the sine law and cosine law. Though the process is time-consuming, I kind of enjoy solving for the missing data since it involves trigonometry.
LAB: This module involves the last two laboratory field works for the course. Both field works aim to determine the magnetic bearings of a traverse or a series of straight lines connecting successive points using the compass traversing method. The only difference is that the first one is an open traverse while the second one is a closed traverse. Open compass traverse is a bit easier than the closed compass traverse since it wan only conducted in school plus the traverse lines were a bit shorter. The closed compass traverse field work was conducted at the Monte Cielo Subdivision in Concepcion Pequeña. It was a bit tiring since we did not bring our own lunch and we were forced to finish the computations before leaving. In short, we were able to take our lunch at about 4 in the afternoon. Nonetheless, it was unforgettable since I was the chief of party of the group and did my best to fill that position. We encountered a bit of problem in the computation but thanks to our computer for having solved that. About the topic, I learned that the forward and back bearings should have the same angle but different direction and that the adjustment of these bearings would be easier by sketching first the obtained data.
LEC: This module allowed me to realize that surveying is easier said than done. It takes a lot of courage, time, and patience to be able to gather all the required data in one operation. The fact there is a method for the computation of missing data says it all. The course itself anticipated any untoward incident that may happen during field work operations. In case that there is an obstruction of the surveying area, the landowner does not permit surveying, limited time, or there is a division of lands, various strategies can be used to calculate the missing data thus eliminating the hindrances encountered during the surveying process. Furthermore, this module is a review of the trigonometric topics such as the sine law and the cosine law which was previously discussed in the subject Higher Mathematics for Engineers/Engineering Technologists. In computing the missing data, the first thing to do is to sketch the given data to get a full grasp of the traverse and eventually get an idea on how to solve it. Dividing the traverse creates triangles which then permits the use of the sine law and cosine law. Though the process is time-consuming, I kind of enjoy solving for the missing data since it involves trigonometry.
LAB: This module involves the last two laboratory field works for the course. Both field works aim to determine the magnetic bearings of a traverse or a series of straight lines connecting successive points using the compass traversing method. The only difference is that the first one is an open traverse while the second one is a closed traverse. Open compass traverse is a bit easier than the closed compass traverse since it wan only conducted in school plus the traverse lines were a bit shorter. The closed compass traverse field work was conducted at the Monte Cielo Subdivision in Concepcion Pequeña. It was a bit tiring since we did not bring our own lunch and we were forced to finish the computations before leaving. In short, we were able to take our lunch at about 4 in the afternoon. Nonetheless, it was unforgettable since I was the chief of party of the group and did my best to fill that position. We encountered a bit of problem in the computation but thanks to our computer for having solved that. About the topic, I learned that the forward and back bearings should have the same angle but different direction and that the adjustment of these bearings would be easier by sketching first the obtained data.
REFERENCES:
https://www.survey-solutions.co.uk/wp-content/uploads/2020/07/Project-10-Kirkcudbright.jpghttps://www.studocu.com/ph/document/baguio-central-university/civil-engineering/gefs-omitted-measurements-or-missing-data-compress/39627865https://i.ytimg.com/vi/Nm0_ITZKDrM/maxresdefault.jpghttps://www.mathcentre.ac.uk/resources/Engineering%20maths%20first%20aid%20kit/latexsource%20and%20diagrams/4_6.pdfhttps://www.onlinemathlearning.com/image-files/law-of-sines.pnghttps://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/cosine-rule-formula-1613465537.pnghttps://byjus.com/maths/law-of-sines/#:~:text=The%20law%20of%20sine%20or,known%20as%20the%20sine%20rule.https://byjus.com/maths/cosine-rule/#:~:text=In%20trigonometry%2C%20the%20Cosine%20Rule,of%20angle%20included%20between%20them.
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https://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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