A COMPUTATIONAL ANALYSIS OF DOUBLE MERIDIAN DISTANCE FOR A CLOSED TRAVERSE AREA TOWARDS DEVELOPING A CONTOUR MAP AND LAND TITLE FOR A PROPOSE GYMNASIUM IN QASSIM UNIVERSITY
A Graduation Design Project Presented to the Faculty of the
Bachelor of Science in Civil Engineering Qassim University Buraidah, KSA
In Partial Fulfillment of the Requirements for the Degree
BACHELOR OF SCIENCE IN CIVIL ENGINEERING
By ABDUL AZIZ ALNASSER ANAS ALKHALIFAH BANDER MOIED ALGAHTANI SALMAN AL-MANSSOR Safar 1432
APPROVAL SHEET In partial fulfillment of the requirements for the degree, Bachelor of Science in Civil Engineering, this project design project entitled “A COMPUTATIONAL ANALYSIS OF DOUBLE MERIDIAN DISTANCE FOR A CLOSED TRAVERSE AREA TOWARDS DEVELOPING A CONTOUR MAP AND LAND TITLE FOR A PROPOSE GYMNASIUM IN QASSIM UNIVERSITY”, has been prepared and submitted by ABDUL AZIZ ALNASSER, ANAS ALKHALIFAH, BANDER MOIED ALGAHTANI and SALMAN AL-MANSSOR, are hereby recommended for Oral Examination. ________________________________ Assoc Prof. Dr. Tomas Ucol-Ganiron Jr Adviser
Approved by the Committee on Oral Examination with a grade of _____
________________________________________ Chairman _______________________ PROF.
Accepted and approved in partial fulfillment of the requirements for the Degree of BACHELOR OF SCIENCE IN CIVIL ENGINEERING
________________________________ PROF. Dr. Sulaiman Al-Alyahya CE DEPARTMENT HEAD
The authors wish to express their sincere gratitude and deep appreciation to the following individuals to whom they are greatly indebted for the completion of this study; Dr. Sulaiman Al-Alyahya, our Dean of the College of Engineering and Civil Engineering Department Head; Dr. Tomas-Ucol- Ganiron Jr., our adviser, for his untiring guidance, inspiring encouragement and sincere concern for the completion of the research; The members of the panel of the Oral Examination Committee, for their intellectual comments and suggestions towards the improvement of the manuscript; The civil engineering instructors for helping us using the surveying instruments and plot the contour lines using corel draw. Professors, classmates, friends and family for moral support and encouragement; Above all Allah, for his wisdom, strength, guidance and blessings in writing this manuscript.
ABDUL AZIZ ALNASSER ANAS ALKHALIFAH BANDER MOIED ALGAHTANI SALMAN AL-MANSSOR
This manuscript is dedicated to Allah and our parents who are the only sources of wisdom, knowledge in all our research and development works. To you Allah, we give back all the Glory, honor, thanksgiving and all the credit for this after all undertaking and made known to this research.
â€œA COMPUTATIONAL ANALYSIS OF DOUBLE MERIDIAN DISTANCE FOR A CLOSED TRAVERSE AREA TOWARDS DEVELOPING A CONTOUR MAP AND LAND TITLE FOR A PROPOSE GYMNASIUM IN QASSIM UNIVERSITYâ€?
Abdulaziz AL Nasser
Anas Al-Khalifa Bander Moied Algahtani Salman Al-Mansor Adviser
Dr. Tomas U. Ganiron Jr.
Qassim University Buraidah, Qassim
No. of Pages :
Bachelor of Science in Civil Engineering
This research aimed to analyze double meridian distance for a closed traverse area in developing a land title for a propose gymnasium in Qassim University. Theodolite, leveling rod and steel tape plays an important role in measuring elevations, bearings and distances of the boundaries of a lot. Contour map is necessary to determine the traces of level surfaces of successive elevation. This will enable to identify the type of contour map and type of contour lines necessary for this project. A Corel Draw software is used to draw contour map and guide to interpret the significance of the variables. It is essential to check the error of closure for interior angles and for both latitude and departure before applying the Double Meridian Distance (DMD) method to obtain the total area of the lot. Technical descriptions of the land such as distance, bearing, boundaries and area are necessary to visualize the shape & exact location of the land. Developing a land title will be obtained using the technical descriptions of the lot in preparation for the type of gymnasium necessary for Qassim University.
Table of Contents Title page Approval sheet Copyright Page Acknowledgement Dedication Abstract Table of contents
i ii iii iv v vi
THE PROBLEM AND ITS BACKGROUND Introduction Background of the Study Statement of the Problem Significance of the study Scope and Delimitation
CONCEPTUAL FRAMEWORK Review of Related literature Research Paradigm Definition of Terms Acronyms
RESEARCH DESIGN Setting up the Theodolite Levelling the Theodolite. Zero the scales Traversing with theodolite and steel tape Adjustment of angular error of closure Traverse Adjustment Measurement of the area by DMD Drawing Contour Map using Corel Draw
PRESENTATION, ANALYSIS AND INTERPRETATION OF DATA
SUMMARY OF FINDINGS, CONCLUSION AND RECOMMENDATION Summary of Findings Conclusion Recommendation
PROPOSE GYMNASIUM IN QASSIM UNIVERSITY
CHAPTER 1: THE PROBLEM AND ITS BACKGROUND 1.1 Introduction We deal with a lot of important issues in our lives but the three that seem most timeless and universal are our families, our health, and our rights to our land. Our welfare is directly affected by our ability to define our space. That‟s one of the land surveyor‟s most important jobs, to mark, describe, and map property ownership. His or her work creates a stable framework on which we can build our homes and communities, and generate the wealth necessary to sustain those communities. If we don‟t know the location of the boundaries of our land we can‟t enjoy any unique use of it. We could not buy, sell, mortgage or develop land in an orderly and predictable fashion. The land surveyor provides that knowledge. Although the rules of land surveying may vary depending on whether you practice in the states of the original 13 colonies, or in the Public Land Survey System (everything else), There‟s one fundamental principle that governs our work. In the words of Justice Cooley of the Michigan Supreme Court, “No man loses title to his land or any part of it merely because the evidence of where it once was becomes uncertain.” The perpetuation of property rights and title is tied to the land. Land surveyors use computers, precise measuring tools, and mapping systems to gather and analyze data (evidence) in the field. They then interpret that data to establish the most probable location for property corners. Their opinions are formed from knowledge of common law, rules of evidence, state and federal laws, and local standards of practice. In many ways it is much an art as it is science. Another important part of the land surveyor‟s professional activity involves understanding and “decrypting” the often-confusing language in legal descriptions. Just what did the author of the deed mean to convey? If you really want to get a land surveyor talking, ask him to describe how many different ways there are to go “North.” The list is probably similar to the number of words for snow in the Inuit language. Despite the fact that there are a lot of flashy new tools available now to make expert measurers out of novices, we will never really know the true location of boundary lines if we don‟t understand the value of what is being measured. That is the expertise of the land surveyor, and one of the reasons that you may see someone carrying a red and white pole (with something that looks like a Frisbee on top of it) peeking under the sod in your front yard.
As in many professions, Land Surveyors have seen many changes through time. History has always demonstrated that the skills of the Land Surveyor have always been an important part of civilization. People have shared, owned, sold, development, fought over, given away, coveted, told stories of, imagined, photographed, fenced, studied, mapped, described and been thankful for that which remains constant for all of us, namely our land. According to Ganiron Jr (2007) that a land surveying is the technique and science of accurately determining the terrestrial or three-dimensional position of points and the distances and angles between them. These points are usually on the surface of the Earth, and they are often used to establish land maps and boundaries for ownership or governmental purposes. To accomplish their objective, surveyors use elements of geometry, engineering, trigonometry, mathematics, physics, and law .An alternative definition, per the American Congress on Surveying and Mapping (ACSM), is the science and art of making all essential measurements to determine the relative position of points and/or physical and cultural details above, on, or beneath the surface of the Earth, and to depict them in a usable form, or to establish the position of points and/or details. Furthermore, as alluded to above, a particular type of surveying known as "land surveying" (also per ACSM) is the detailed study or inspection, as by gathering information through observations, measurements in the field, questionnaires, or research of legal instruments, and data analysis in the support of planning, designing, and establishing of property boundaries. It involves the reestablishment of cadastral surveys and land boundaries based on documents of record and historical evidence, as well as certifying surveys (as required by statute or local ordinance) of subdivision plats/maps, registered land surveys, judicial surveys, and space delineation. Land surveying can include associated services such as mapping and related data accumulation, construction layout surveys, precision measurements of length, angle, elevation, area, and volume, as well as horizontal and vertical control surveys, and the analysis and utilization of land survey data. Accuracy is one of the most important factors of land surveys. The purpose of a land survey is to accurately map and designate land boundaries. Any inaccuracies can lead to potential legal issues down the track. Some types of land surveys require even more accuracy than others as they are used to help establish where to construct buildings by taking into account topographic and hydrological features such as sewage systems and trees. Any inaccuracies could cause difficulties in the building process.
The accuracy of land surveys is particularly important when they are used for map making as the wider community relies on the accuracy of maps and assumes that they are precise documents. The 2005 version of ALTA specifications, â€œALTAâ€? stands for American Land Title Association, states a Positional Accuracy of 0.07 feet or 20mm in new money, plus 50 parts per million. Many of the modern instruments used by a Land Surveyor have an accuracy of distance measurements to within 2mm +/- 2 ppm but that alone does not assure compliance with the ALTA standards. The ALTA Standards require that these conditions are taken into account: The Relative Positional Accuracy may be tested by either: comparing the relative location of points in a survey as measured by an independent survey of higher accuracy or; In other words the survey would required to be a traverse ending at its point of origin, beginning and ending on two different points of higher order. These higher orders can be monuments can be NGS monuments, or monuments established on an older survey where the location was determined in accordance with condition 2 as here or the results of a minimally constrained correctly weighted least square adjustment of the survey. The surveyor needs to apply a squares adjustment program. Therefore the surveyor needs to know the accuracy standards of their equipment and surveying techniques. This means they must know the distance and angular measurement specifications of their instrument and an estimate of such things as centering tolerance. One of the most important elements that affects the accuracy of land surveys are the tools that the land surveyors use. According to Rivera (2009) in Jubail University, the following findings were gathered: obesity levels rose by 70% in adults between 2003 and 2009, About one third of the men in the KSA are predicted to be obese by 2011, About 22% of girls under 15 and 19% of boys under 15 will be obese by 2011and about 9,000 deaths a year are caused by obesity in the KSA. Most of their projections have come true. It's safe to say though, that these numbers have only become worse since then. The researchers proposed a gymnasium in Qassim University that will helps the students to control weight, reduces blood pressure in the body, raises HDL (good cholesterol levels) in the body, reduces the risk of diabetes, cancer and other diseases and t gives one more confidence, and also builds one's self esteem through proper exercises. Moreover, the researchers made this study to, draw the contour map using corel draw software and identify the type of contour map and type of contour line necessary for this project, analyze the computation of double meridian distance , enumerate the technical description of the proposed land, and develop a Torrens title for Gymnasium in Qassim University.
1.2 Background of the study In order to resolve the deficiencies of the common law and deeds registration system, Robert Torrens introduced the new title system in 1858, after a boom in land speculation and a haphazard grant system resulted in the loss of over 75% of the 40,000 land grants issued in the colony (now state) of South Australia. He established a system based around a central registry of all the land in the jurisdiction of South Australia, embodied in the Real Property Act 1886 (SA). All transfers of land are recorded in the register. Most importantly, the owner of the land is established by virtue of his name being recorded in the government's register. The Torrens title also records easements and the creation and discharge of mortgages The Torrens title system operates on the principle of "title by registration" (i.e. the indefeasibility of a registered interest) rather than "registration of title." The system does away with the need for a chain of title (i.e. tracing title through a series of documents). The State guarantees title and is usually supported by a compensation scheme for those who lose their title due to the State's operation. There are other parcels of land which are still unregistered. The Certificate of Title shows: the present owners, easements such as underground pipes that may require access for storm water or sewage, and 'right of carriageway' for neighbours get access to their property, covenants such as building restrictions, caveats such as a requirement for someone's approval before transfer of ownership and mortgages The measure of land is its area. But area itself is not measured. It is calculated. The calculation of the area of a piece of land is easy enough when it has a regular shape. A regularly shaped piece of land, of course, has many practical advantages. Towns, cities, counties and large portions of this country are laid out in a grid, not merely for aesthetic reasons or for ease of laying them out, but because a grid allows for an eminently efficient use of the land. But for surveyors and assessors, the advantage of the regular shape, especially of small lots, is that it makes area calculations a matter of simple multiplication. Unfortunately, parcels of land are seldom regular in shape. Often, especially in colonial days, they were occupied long before they were surveyed. Inhabitation followed the terrain, an invariable feature of which is its irregularity. The resulting pieces of ground usually had straight lines between corners, but indeterminate shapes. Calculating the area of such a form has been known since Euclid. The trick is to break up the irregular shape into manageable components, and then perform
the appropriate multiplications and sums. By colonial times, the mathematics involved was greatly facilitated by the invention of logarithms and trigonometric function tables. Given these, and reasonably accurate field measurements, any colonial surveyor could calculate its area with a pencil - "more or less". The colonial surveyors were using a standardized method called "DMD", the abbreviation for double mean distance or double meridian distance. Once transits were used, the first step in the DMD method was to balance the angles. They could be interior or exterior. The field check was to add up the number of sides to the figure, either less by two (interior) or more by two (exterior), times 180 degrees. That sum could be compared to the sum of the angles turned for an initial check. The angles were not always adjusted for balance, but if they were, the error was most likely distributed proportionately among all the angles. The second step was to calculate the latitudes and longitudes. This required looking up the cosines and sines for the directions of the property lines with respect to north and south. (This is the rationale for quadrants in the first place). These functions were generally carried to eight places after the decimal point, and then multiplied by the lengths of the lines. The results were arranged in columns: N, S, E, and W. North and East were positive, and South and West were negative. The third step was to balance these columns. Theoretically, the sum of the latitudes and the sums of the departures must equal zero, for the figure to close. Since measurements are inherently imprecise, they never really equaled zero, and were mildly suspect when they did. From the difference in the starting and ending latitudes and departures, the direction and length of the closing line were calculated. The error of closure was most easily eliminated by placing it in the line(s) whose direction most nearly mimicked the closing line. The error could also be distributed in other ways. The most methodical way was to distribute the error proportionately, the correction in each line being determined by the closing line multiplied by the ratio of a line length to the total perimeter length. However the error was reapportioned, the latitudes and departures would then be recalculated. The next step was to calculate a series of areas, one corresponding to each of the parcel lines. A longitudinal line was drawn, at least hypothetically, through the westerly-most corner of the parcel plat, and latitudinal lines drawn from the corners to that line. The result was a series of areas, the first and last of which were triangular and the rest trapezoidal in shape. At this point, the procedure was to add the two departures of each area and multiply the sum by the longitudinal divergence of the line. The result was not an absolute number for each area, but a number with a positive or negative sign, derived from the signs ascribed in step two.
The last step was to add all these areas and divide the sum by two. By simply adding the two sides of each trapezoidal area, a rectangular area double the size of the trapezoid was calculated, thus requiring the division by two. There are several ways of indicating elevation and relief on maps. The most common way is by contour lines. A contour line is a line representing an imaginary line on the ground along which all points are at the same elevation. Contour lines indicate a vertical distance above or below a datum plane. Starting at sea level, normally the zero contours, and each contour line represents an elevation above sea level. The vertical distance between adjacent contour lines is known as the contour interval. The amount of the contour interval is given in the marginal information. On most maps, the contour lines are printed in brown. Starting at zero elevation, every fifth contour line is drawn with a heavier line. These are known as index contours. Someplace along each index contour, the line is broken and its elevation is given. The contour lines falling between index contours are called intermediate contours. They are drawn with a finer line than the index contours and, usually, do not have their elevations given. Corel draw software is used to draw contour maps in 2D. Qassim University is a public university in the Al-Qassim Province of Saudi Arabia. It was established in 2004 jointly between King Saud University and Imam Muhammad ibn Saud Islamic University, each of which used it as its Qassim campus. Subsequently, its constituent colleges became a part of Qassim University. The main campus of Qassim University covers about eight square kilometers and is situated between Buraidah and Unaizah in the heart of the region. There are campuses in different cities in Al-Qassim Province. During 2008, enrollment at Qassim University was 40,000 students. Faculty and staff totaled 3,500. Colleges at Qassim University include Sharia College; the College of Arabic Language and Social Sciences; the College of Agricultural and Veterinary Sciences; a College of Economics; a College of Science; a College of Medicine; a College of Engineering; a College of Computer Science; a College of Applied Medical Sciences; a College of Dentistry and a College of Pharmacy. There is also a Science College in Zelfy, community colleges and women's colleges. In the KSA it is estimated that 70% of the student population can be classed as physically inactive. Moreover, 60% of students do not participate in the recommended level of physical activity & 25% are not active at all. In Qatar , 33% of the population are said to be so inactive that they gain no health benefits at all & the risk to the community from their physical inactivity, and therefore lack of fitness, is great. For thousands of yearâ€&#x;s physical activity and the level of fitness
have been linked to good health. Due to the advance of science in this day & age this link can be proven, with overwhelming evidence those students who lead active lifestyles are less likely to die early or to experience major illnesses such as heart disease, diabetes & colon cancer. Fitness is therefore a major, if not the major, factor in the type of health . This lead to construct a new gymnasium in Qassim University. Open gyms are an integral part of the ability to compete with teams that may have more tradition or more talent or more size. Open gyms allow teaching students how to play in semi-chaotic situations like basketball, tennis and badminton
1.3 Statement of the Problem This research aims to analyze double meridian distance for a closed traverse area in developing a contour map and land title for a propose gymnasium in Qassim University. The researchers of this study seek to answer the following questions: 1. What are the characteristics of the elevation measured in a lot? 2. Is there any linear error of closure for angles and both latitude and departure. If so, what adjustment is necessary to close this traverse? 3. What is the technical descriptions of the lot in terms of: 3.1 Distance 3.2 Bearing 3.3 Boundaries 3.4 Area 3.5 Elevations 4. Based in No. 3, what contour mapping and contour lines are suitable for this project? 5. What model of land title is appropriate for this project? 6. Based in the findings of the study, what typical gymnasium is necessary for Qassim University?
1.4 Significance of the Study The civil engineering students and students of other fields could be provided with a reference and can give them knowledge about computational analysis of double meridian distance towards developing a contour map and land title for proposed gymnasium in Qassim University. This study will encourage them to focus the significance of such variables such as distance, bearing, latitude and departure for technical description of the lot. Moreover, students will enable to use critical thinking and creativity in developing a land title, constructing contour map and choose a type of gymnasium appropriate in Qassim University. The University will be aware the level of fitness of students that have been linked to good health through the construction of propose gymnasium. The home builders will be provided with knowledge and information about technical description of the lot. The owners of the lot will solve the problems of uncertainty, complexity and cost associated with old-system title, which depended on proof of an unbroken chain of title back to a good root of title. 1.5 Scope and Delimitation of the Study The study focuses on the computational analysis of double meridian distance for area of propose gymnasium lot of Qassim University . Technical descriptions such as distance, bearing, latitude ,departure and elevation are variables essentials in developing a contour map and land title of the lot. The research concentrates on the type of contour map and contour lines based on the technical descriptions of land title. It will also cover the type of gymnasium that is applicable in this study. In addition, the study is delimited to double prime distance, trapezoidal rule, simsonâ€&#x;s one third rule and coordinates . These four methods of area computation for a tract of land which will entail too much time to determine
CHAPTER 2 CONCEPTUAL FRAMEWORK This chapter presents the review of related literature on the computational analysis of double meridian distance towards developing a land title for propose gymnasium in Qassim University. It also covers the following: research paradigm, definition of terms and acronyms. 2.1 Review of Related Literature In order to resolve the deficiencies of the common law and deeds registration system, Robert Torrens introduced the new title system in 1858, after a boom in land speculation and a haphazard grant system resulted in the loss of over 75% of the 40,000 land grants issued in the colony (now state) of South Australia. He established a system based around a central registry of all the land in the jurisdiction of South Australia, embodied in the Real Property Act 1886 (SA). All transfers of land are recorded in the register. Most importantly, the owner of the land is established by virtue of his name being recorded in the government's register. The Torrens title also records easements and the creation and discharge of mortgages. For convenience, it is customary to use double meridian distance (DMD) rather than meridian distance in calculations. When the meridian distance of the initial traverse line in a closed traverse equals one half of the departure of the line, the DMD of this line equals its departure. Again, from the rule for meridian distance of the next line, the DMD of that line equals the DMD of the preceding line, plus the departure of the preceding line, plus the departure of the line itself. It can be shown geometrically that the area contained within a straight-sided closed traverse equals the sum of the areas obtained by multiplying the meridian distance of each traverse line by the latitude of that line. Again the result is the algebraic sum. If you multiply a positive meridian distance (when the reference meridian runs through the most westerly station, all meridian distances are positive) by a plus or north latitude, you get a plus result that you add. If you multiply a positive meridian distance by a minus or south latitude, however, you get a minus result that you subtract. Therefore, if you multiply for each traverse line the double meridian distance by latitude instead of meridian distance by latitude, the sum of the results will equal twice the area, or the double area. To get the area, you simply divide the double area by 2
The construction of gymnasium offers a legitimate energy outlet, which may be especially important for every university. Those who actually practice the lifestyle of why is gym important tend to avoid fights with other students and may be more apt to share toys and equipment. In addition, students have a lot of excess energy which they can run off in gym class. This helps prevent behavior problems in the classroom and at home from boredom and lack of sustainable activity. 2.2 Research Paradigm The Project Management handouts of Prof. Sulaiman & Prof. Eltoumi (2009) ,concluded that a design project is a response to the problem. Therefore, a project always starts with a problem and the value created by project is the product. The strategic value delivered by product is the output. The lectures of Prof. Ganiron Jr (2010) in Project Management & Design presents the importance of research paradigm as a framework within which theories are built, determines the researchers perspective, and understanding of how things are connected. One way of presenting a research paradigm is by the use of Input-Output-Process(IPO)model. The input is the information, ideas and resources used, the process is the actions taken upon/using input or stored material and output is the results of the processing that then exit the system. The two components of a traverse line are latitude and departure. According to Hipolito (2009), latitude is the vertical component of a traverse line wherein the distance is multiplied by the cosine of the bearing angle of the line whereas the departure is the horizontal component of a traverse line wherein the distance is multiplied by the sine of the bearing angle of the line. Moreover, the technical descriptions of a land contain distance, bearing, boundaries and area. This will measured by theodolite and a steel tape to determine the distance, horizontal & vertical angles. The azimuth will be converted to bearing whereas, distance should be measured in meter. It is important to check the interior angles and the components of a traverse line if there are adjustments in the data. The area of the land is computed by means of double meridian distance (DMD) .This is done by setting the first line equal to the departure of line itself. The DMD of the succeeding line is equal to the DMD of preceding line plus the departure of the line itself, the DMD of the last line is equal to the departure of the line but opposite in sign and multiply the DMD of the line by its latitude and add algebraically all the product and divide it by two to get the area. The use of corel draw software will be use to plot the successive elevations. Through the use of this process, developing a contour map ,land title and type of gymnasium will be the output of the study.
Theodolite, Leveling rod & steel tape
Distance Bearing Area Elevation
Adjustment Error of Closure Double Meridian Distance
CONTOUR MAP LAND TITLE TYPE OF GYMNASIUM
2.3 Definition of Terms For better understanding and appreciations of the study, the following terms are operationally defined. Area by double meridian distance..The meridian distance of a Traverse line is equal to the length of a line running east to west from the Midpoint of the traverse line to a reference meridian. The reference Meridian is the meridian that passes through the most westerly traverse Station. Bearing. The direction of a line given by the acute Angle between the Line and a meridian. Measured clockwise or counterclockwise from the North or south end of a meridian .It is always accompanied by letters NE, SE, SW and NW). Departure. It is the horizontal component of a traverse line wherein the Distance is multiplied by the sine of the bearing angle of the line.
Distance. It is a numerical description of how far apart objects are. Gymnasium. It is a training facility for competitors in public games. It was also a place for socializing and engaging in intellectual pursuits. Land Title. The legal document conveying title to a property Latitude. It is the vertical component of a traverse line wherein the distance is multiplied by the cosine of the bearing angle of the line. Torrens title. It is a system of land title where a register of land holdings maintained by the state guarantees an indefeasible title to those included in the register.
2.4 Acronyms BM
Double Meridian Distance
Input Process Output
CHAPTER 3 RESEARCH DESIGN This chapter discusses the research methodology, project design, and evaluation procedure. This chapter also includes figures and tables for the easy understanding of the topics. ` 3.1 Setting up the Theodolite. A) The Theodolite is mounted on a tripod. B) Extend the tripod legs, splay them fully and push the ends firmly into the ground C) Look at the Theodolite mounting platform. This should be reasonably level and not too high nor too low for the users. D) Adjust the leg lengths until it is right then screw the theodolite onto the platform. E) Set the theodolite up over a reference point on the ground by using the sight on the front of the instrument to view the point F) Adjust the theodoliteâ€&#x;s position by slightly unscrewing the mounting screw and moving the theodolite sideways. G) Ask a helper to push a nail or peg into the ground under your guidance to fix a new reference point. 3.2 Leveling the Theodolite. A).
B). C) D)
Know the 3 leveling screws (labeled A, B and C) at the base of the instrument. (These should be used with the round spirit level to obtain a coarse adjustment.) Line the long spirit level with 2 of the leveling screws and make the first fine adjustment. Turn the theodolite through 90 degrees so the long spirit level is Pointing at the 3rd leveling screw and adjust that until it is level. Recheck the fine adjustment if necessary. (If there is not enough adjustment in the leveling screws, then the theodolite table is not level enough and you will have to adjust the leg heights until it is.)
Zero the scales A). B)
Release clamps D and E. Align the red mark on the upper part of the theodolite with the white mark on the black ring and lock the upper horizontal clamp (E). (This roughly sets the theodolite optics to zero on the horizontal scale. )
Open the mirror (H) and adjust until you see a bright patch of light falling on the window underneath it. (Now if you look through the small eyepiece, you will see some illuminated scales. )
Traversing with theodolite and steel tape by azimuth method and finding the area by DMD method A. Drive the 8 hubs with nails (min) at 8 different points and designate them as stations, 1, 2, 3, 4, 5, 6, 7 and 8. B. Follow the procedures in leveling the theodolite. C. Measure with steel tape the distance 1-2 with the aid of theodolite for alignment D. Loosen lower clamp. Transfer to and set the theodolite at point 2. E. Backsight point 2 with telescope at inverted position. Tighten lower clamp. F. Plunge the telescope to normal; loosen upper clamp and sight point 3. Tighten upper clamp and record the reading found in small eyepiece. G. Measure with steel tape the distance 2-3 with the aid of theodolite for alignment. H. Loosen lower clamp. Transfer to and set the theodolite at point 3. I. Repeat the same procedure as that at point 3 J. At point 4, 5, 6, 7 and 8, repeat also the same procedure. K Compute the error of closure and make the necessary adjustment for the azimuth (if necessary). L. Compute the magnetic bearings of the line. M. Compute the latitudes and departures and balance them. N. Compute the area of the traverse using DMD method.
Adjustment of angular error of closure in a closed loop traverse A). Determine the difference between forward and back azimuth of the last line and compare it to 180 deg. .The difference from 180 a degree of the computed value is the actual angular error. B)
Compare actual angular error to the allowable angular error. (If beyond the following allowable angular error. Repeat the traverse). Tertiary Traverse; = 30‟‟square root of n Secondary Traverse; = 10‟‟ square root of n Primary Traverse; = 2.5‟‟square root of n
Adjust the azimuth using the following method a) No of group (g) = a + 1 b) No. per group (npg) = n/g where a n g npg
= actual angular error of closure in minutes =no. of station =no. of group =no per group
Correction per group First Group = No. of correction Second Group= 0 deg. 01‟ Third Group= 0 deg. 02‟
Transit Rule Transit rule states that the correction to the latitude (or departure) of a line is equal to the total error in latitude ( or departure) times the latitude of the line divided by the sum of all the positive and negative latitude (or departure) CL n-m = Latitude n-m
eTL Sum of (+lat) + (-lat)
CD n-m = Departuren-m
eTL Sum of (+dep) + (-dep)
Measurement of the area by double meridian distance technique
3.7.1. Rules for determining double meridian distance A. For the initial traverse line in a closed traverse, the meridian distance equals one half of the departure. B. For each subsequent traverse line, the meridian distance equals the meridian distance of the preceding course line, plus one half of the departure of the preceding line, plus one half of the departure of the line itself. If the rules have been followed correctly, the DMD of the last course will be equal to departure of the last course with its sign changed. The altitude is the latitude of the course, and the average of the bases of the several courses is equal to the perpendicular distance to each course of the meridian. 3.7.2 Methodology (Equipment Required): One theodolite with a tripod, Stadia Rod, and Data Collection forms shown in Table 1. Table 1 Design Technical Description Line Distance Bearing Elevation Latitude Departure DMD Double (meter) Area N S E W (+) (-) (+) (-) 1-2 2-3 3-4 4-5 5-6 6-7 7-8
3.7.3 Measurements The Theodolite operator will be assisted by one individual to position the Stadia Rod under the command of the Theodolite Operator. The Theodolite will measure the range and bearing of the points. It is envisioned that a minimum of ten readings from each side will be taken. Table 1 illustrates the necessary data elements that must be recorded during the survey. Columns #1is the station number, Column #2 is the slant range, Column #3 bearing angle, and Column #4 the elevation angle. Columns #5 thru #10 are the elements of data calculated from the recorded measurements. The analytical results will be calculated before the measurements. The algorithm has been tested and verified . 3.7.4 Calculations: Table 2 illustrates the series of calculations based on the following measurements: Distance, Bearing, and Altitude. For this project, it is assumed to be in two dimensions excluding the topography and elevation or altitude considerations. The recorded measurements are used to calculate the latitude, departure, double meridian distance, and double areas. At the end of the calculations, the DMD of the last course should be the same or approximated to the departure of the last course except a different sign. If they are not the same, a truncation error must have occurred. A test case has been used to define the area in distances and bearing to calculate the latitude and longitude of each course line. In essence, the table data elements are the basis to determine the acreage of the land. A table of the liner measure and area measure standards are provided for information only.
The following is a summary of the formulas used to calculate the area of the St = Slant Distance in yards. Bo = The azimuth angle to the course line referenced to North. Latitude = (St)*Sine Bo (Theta). Departure = (St)* cosine Bo (Theta). DMD of the first course = Departure of the first course. DMD (1) = (DMD of the first course) + (departure of the preceding point) + (the departure of the current point) Note 1. Double Areas = (Latitude) * (DMD) - Multiply the latitude of the course line by the DMD of the course line. The results will be either positive or negative.
3.8 Drawing Contour Map using Corel Draw 1.First, find the point data map we will use in this lab (it's at the bottom of this page), and save it to the computer hard drive or your disk or drive. Save it as you did the scanned map . Start Corel Draw, and open your file for Drawing Lab 1. Add a contour layer to that existing base map. It's a good idea, right now before you have an accident with it, to go to 'File - save as' and save this file as 'Lab 4'. That way Lab 1 is retained in case you need it again. Make a NEW LAYER underneath everything in your old map. Lock the other layers (turn off 'edit across layers' in the Object Manager layers menu). While in the new layer, use 'File - import' to put the contour point data file in your new layer. Adjust its size to fit exactly under your map . This is easiest if you remove all the shading from the earlier map... select all the polygons and make them transparent. Adjust the size and position of
the point data map to match up the coastline on the new scan to the coast on your map. This new image consists of dots with numbers (similar to the picture below). These values are fictitious, but designed to be similar in nature to the real ones for this data. Your job is to draw isolines among the points. Draw them in another NEW LAYER above the layer with the point data. Then get rid of the point data layer. WARNING!!! If you don't work in a new layer it will be more difficult to get rid of the background point data map, and impossible to separate the contours from everything else.
Figure 1. Example of spot height (or point data) file. The values can be measurements other than elevation - e.g. temperature, pollution concentration. The dots are the actual points at which the measurements were made. 2. Create the new layer you will draw contours in, if you have not done so already. Start by drawing a new internal box to contain the isoline map itself. This will exactly duplicate the internal box from the map you draw in the previous lab (in fact you can copy and paste it.) This internal box will contain nothing but the isoline map. Usually in our maps the internal box and the isolines will be drawn in VERY narrow lines. Sometimes in an isoline map we will specify that the isolines be drawn over a background map (e.g. temperature isolines over a background of lakes, provincial borders etc.) To help keep the two types of line (background map and isolines) separate, the background map is drawn very thin and the isolines
slightly thicker. In this case you should use the same thicker line for the internal box. You might find it easier to plan your contours if you print the file now (save it first). You can draw contours on the print to figure out where they should be, then draw them on screen with your drawing as a guide. Draw your isolines (contours) as discussed in class. Draw isolines as polygons, so they can hold shading (next lab). Each contour must be a polygon so it can contain shading!!! If it touches the side of the box, draw a line along the box to the other end of the line to close the polygon. Remember that contours cannot normally cross or even touch (they would touch only in the special case of a vertical cliff.) Draw with the polyline tool, not freehand, but add enough points that the curves are quite smooth. It is often useful to draw the shape quickly with very few points just to decide where it will go. Then you can go back and edit, adding other points to smooth out the line to make it look natural. Arrange menu to move things up and down until they are visible. It's often easier to start with the outermost contour and work inwards, and to make every contour transparent so they do not cover each other at first, then add shading and rearrange the order as needed.
Figure 2. A contour is drawn to represent the 300 m level. Since there are two patches of higher land there are two separate contours. See how all the points over 300 are inside the contours, all points below 300 are outside. Use that as a check to make sure your contours are correct. You can see at once how much uncertainty there is in the exact locations of the lines.
Figure 3. Another contour is added at the 250 m level. Check the points - nothing below 250 should be inside the contour. 3. Finish the set of contours, and edit to make them smooth curves. Last, delete the point data map. Your finished map will have contours and (if it's a topographic map) shorelines on it, but NOT the original points and numbers.
Figure 4. The full set of contours is finished. Note those which touch the edge of the map box. The straight edge of the box is PART OF THE POLYGON. The layer with the numbers is not deleted yet but that would be the next step.
CHAPTER 4 PRESENTATION AND ANALYSIS OF DATA This chapter discusses the analysis and interpretation of data which resulted from the fieldworks performed for this study. For the purpose of understanding the presentation easily, tables and figures are used in the presentation. 1
Characteristics of the elevations Table 4.1 Technical Description Line
S 43° 15ˊ W
S 58° 53ˊ W
N 80° 10ˊ W
N 21° 45ˊ W
N 31° 15ˊ E
N 50° 31ˊ E
S 85° 02ˊ E
S 05° 17ˊ W
S 50° 25ˊ E
S 71° 28ˊ E
Table 4-1 shows the technical descriptions of the lot with the use of theodolite, leveling rod and steel tape. The highest elevation is 21.5 m along line 45 with a distance of 257.50 m , bearing of N 21 deg. 45‟W and 5-6 with a distance of 665.20 m, bearing of N 31 deg. 15‟E. However, the lowest elevation is 2.3 m, bearing S 05 deg. 17‟W. This means that the elevations show a uniform, steep slope will be evenly closed to each other
Linear Error of Closure for Interior angles , latitude and departure Table 4.2: Computed Latitude And Departure : Latitude
S 43° 15ˊ W
S 58° 53ˊ W
N 80° 10ˊ W
N 21° 45ˊ W
N 31° 15ˊ E
N 50° 31ˊ E
S 85° 02ˊ E
S 05° 17ˊ W
S 50° 25ˊ E
S 71° 28ˊ E
998.63 1090.3 1090.41 1058.39 2088.93 eL = -91.67
eD = 32.02
e interior angle= 0.00 Table 4-2 shows the computed latitude and departure by applying the trigonometry functions of an angle. This also shows that there is no error in interior angles (see Appendix A for computation). However, Latitudes in the north direction has a sum of 998.63 meters . Latitudes in the south direction has a sum of 1090.30 meters. This means that the error in latitude is 91.67 meters .Departures in the east direction has a sum of 1095.41meters . Departures in the west direction has a sum of 1058.39 meters. This means that the error in departure is 37.02 meters (see Appendix A for both
computation).The adjustment necessary to close the components of a traverse line is use the transit rule. 3 Line
S 43° 15ˊ W
S 58° 53ˊ W
N 80° 10ˊ W
N 21° 45ˊ W
N 31° 15ˊ E
N 50° 31ˊ E
S 85° 02ˊ E
S 05° 17ˊ W
S 50° 25ˊ E
S 71° 28ˊ E
S 181.66 7.97 173.69 150.38 6.60 143.78
85.22 3.74 88.96 239.17 10.50 249.67 568.69 24.96 593.65 105.55 4.63 110.18 21.66 0.95 20.71 554.63 24.34 530.29 95.39 4.19 91.20 86.58 3.79 82.79
Departure E W 170.88 2.94 173.82 249.13 4.28 253.41 491.67 8.45 500.12 95.42 1.64 97.06 345.09 5.93 339.16 128.12 2.20 125.92 248.56 4.27 244.29 51.29 0.89 52.18 115.37 1.98 113.39 258.27 4.44 253.83
Double Area + -
Table 4.3 Adjusted Latitude and Departure
This table 4-3 shows the adjusted technical descriptions of a lot . The sum of latitude for both north and south is zero. Moreover, the sum of the departure for both east and west direction is zero. This means that the traverse is closed. Beginning at a point marked “1” S 43deg. 15‟ W ; 249.70 m. , thence S 58 deg.53‟ W, 291.00 m to point 2; thence N 80 deg. 10‟ W, 499.00 m to point 3; thence N 21 deg. 45‟ W, 257.50 m to point 4; thence N 31deg. 15 „E, 665.20 m; thence 50 deg. 31‟ E, 665.20 m to point 5, thence N 50 deg. 31‟ E , 166.00 m to point 6; thence S 85 deg. 02‟E , 249.50 m to point 7; thence S 5 deg. 17‟ W, 557.00 m to point 8; thence S 50 deg. 25‟E, 149.70 m to point 9 , thence S 71 deg. 28‟ E, 272.70m to point 10 containing an area of 592, 849.45 square meter (see appendix A for computation).
Contour Map Figure 1 Contour Map
Figure 1 shows a profile of elevations using contour map. Core Draw is used to plot the elevations. This topographic contour map shows the horizontal and vertical positions of the terrain .The intermediate contour line was used to represents a line of equal elevation.
CHAPTER 5 SUMMARY OF FINDINGS, CONCLUSION AND RECOMMENDATIONS This chapter presents the summary of findings, conclusions and recommendations of this study which are based on the data gathered from the performed field works . Specifically, this study is required to answer the questions from the statement of the problem. This study used the fieldworks method of research and identifying the magnitude of known variables as the main data-gathering instrument. The procedures of the field works performed were based from the Engineering Surveying Manual By the Committee on Engineering Surveying of the Surveying Engineering Division of the American Society of Civil Engineers. The results were gathered and values were used to enable researchers give appropriate responses to the statement of the problem. 1. What is the characteristics of the elevation measured in a lot? 2. Is there any linear error of closure for angles and both latitude and departure. If so, what adjustment is necessary to close this traverse? 3. What is the technical descriptions of the land in terms of: 3.1 Distance 3.2 Bearing 3.3 Boundaries 3.4 Area 4. Based in No. 3, what contour mapping and contour lines are suitable for this project 5. What model of land title is appropriate for this project? 6. Based in the findings of the study, what typical gymnasium is necessary for Qassim University?
5.1 Summary of findings After fieldworks and gathering of data, the following findings are made available:
Characteristics of elevation The elevations show a uniform and are spaced close to each other representing a steep slope.
Linear Error of Closure 2.1 Interior Angles The computed total interior angles of the land is 1440 degrees whereas the allowable interior angles for 10 sides is 1440 degrees. This means that there is no error in the interior angles. 2.2
Latitudes Latitudes in the north direction has a sum of 998.63 meters . Latitudes in the south direction has a sum of 1090.30 meters. This means that the error in latitude is 91.67 meters .
Departures Departures in the east direction has a sum of 1095.41meters . Departures in the west direction has a sum of 1058.39 meters. This means that the error in departure is 37.02 meters .
The adjustment necessary to close the components of a traverse line is use the transit rule.
Technical Descriptions of the land A parcel of land situated in Qassim University, Province of Buraidah, beginning at a point marked “1” S 43deg. 15‟ W ; 249.70 m. , thence S 58 deg. 53‟ W, 291.00 m to point 2; thence N 80 deg. 10‟ W, 499.00 m to point 3 ; thence N 21 deg. 45‟ W, 257.50 m to point 4; thence N 31deg. 15 „E, 665.20 m; thence 50 deg. 31‟ E, 665.20 m to point 5, thence N 50 deg. 31‟ E , 166.00 m to point 6; thence S 85 deg. 02‟E , 249.50 m to point 7; thence S 5 deg. 17‟ W, 557.00 m to point 8; thence S 50 deg. 25‟E, 149.70 m to point 9, thence S 71 deg. 28‟ E, 272.70m to point 10 containing an area of 592, 849.45 square meter.
Contour Map Topographic contour map is necessary to shows the horizontal and vertical positions of the terrain . Moreover, intermediate contour line is used to represents a line of equal elevation.
Land Title This title contains the land description surveyed by Geodetic Engineer including the lot plan , rights of ownership and attest by concern authorities.
Type of Gymnasium The single most important characteristic of gymnasium design is the concept of openness. The gym is most likely the largest space in a typical center and there‟s no design rule that requires it be treated as just another room at the end of a corridor. Because of its size and ceiling height, the gymnasium has the potential to lend a feeling of spaciousness and openness to any of the spaces surrounding it, but not if it‟s completely walled off from its surroundings
5.2 Conclusions After evaluating the results of the foregoing findings, the following conclusions were drawn: 1. The variables necessary for technical descriptions of the land are distance, bearing, boundaries, elevations and area . 2. The (n-2)180 deg. is the allowable interior angle for a close loop traverse. 3. There is an adjustment of angular error of closure in a close traverse if the sum of interior angles of the land is not equal to (n-2)180deg. 4. The transit rule is a method for traverse adjustment. 5. The components of a traverse line are latitude and departure. 6. There is an adjustment of traverse line if the sum of positive latitude (or departure) is not equal to the sum of negative latitude (or departure). 7. The Double Meridian Distance of the last line is equal to the departure of the last line but opposite in sign. 8. The product of the latitude and double meridian distance is called double area. 9. The quotient of the sum of double area and two (2) is called total area of the land..
10. Intermediate contour line is use to determine the elevation of a feature or location. It is a brown line on a topographic map and represents a line of equal elevation. 11.Topographic Contour map is use to shows both the horizontal and vertical positions of the terrain. Contour lines, symbols, labels and colors are used to portray shapes and locations of mountains, rivers, lakes and other natural features of the land. 12. Corel Draw is a software use to plot elevations of a lot.
Recommendation Based on stated conclusion, the researchers proposed the following recommendations. 1. The researchers recommend integrating more fieldworks related to electronic distance measurement with high precision total station , land subdivision and route surveying in CE 464 (Project Surveying). 2. Encourage Civil Engineering Students to enroll CE 464 (Project Surveying) as an elective course. The department should introduce students to role models in industry and show them the importance of surveying in construction industry.
CHAPTER 6 LAND TITLE CERTIFICATE OF TITLE No. _____ It is HEREBY CERTIFIED that certain land situated in the ________________ ________bounded and described as follows: Lot 1 ,Block 1 Psd 53740 A parcel of land situated in Qassim University, Province of Buraidah , beginning at a point marked “1” S 43deg. 15‟ W ; 249.70 m. , thence S 58 deg. 53‟ W, 291.00 m to point 2; thence N 80 deg. 10‟ W, 499.00 m to point 3 ; thence N 21 deg. 45‟ W, 257.50 m to point 4; thence N 31deg. 15 „E, 665.20 m; thence 50 deg. 31‟ E, 665.20 m to point 5, thence N 50 deg. 31‟ E , 166.00 m to point 6; thence S 85 deg. 02‟E , 249.50 m to point 7; thence S 5 deg. 17‟ W, 557.00 m to point 8; thence S 50 deg. 25‟E, 149.70 m to point 9 , thence S 71 deg. 28‟ E, 272.70m to point 10 containing an area of 592, 849.45 square meter. is registered in accordance with the provisions of the Property Registration Degree in the name of _______________________as owner thereof in fee simple , subject to such of the encumbrances and maybe subsisting. Entered at _____________________ on the_______day of ________
in the year of ______at ______ Attest _____________________ (Owner)
Figure 2- Lot Plan
CHAPTER 7 PROPOSE GYMNASIUM IN QASSIM UNIVERSITY It‟s important to visualize this urban mix of student‟s players, playerobservers, observers and passersby, and to appreciate the richness of the resulting social experience, because this is the conceptual model for a new generation of gymnasiums in the multi-sport recreation centers and clubs of the coming decade. This model applies to any member-supported facility that‟s sustained by a sense of community among users or members. In some respects, this gymnasium can be viewed as the town square of these communities where people come to participate and large dedicated spectator seating areas are not needed. The single most important characteristic of gymnasium design is the concept of openness. The gym is most likely the largest space in a typical center and there‟s no design rule that requires it be treated as just another room at the end of a corridor. Because of its size and ceiling height, the gymnasium has the potential to lend a feeling of spaciousness and openness to any of the spaces surrounding it, but not if it‟s completely walled off from its surroundings. For example, by locating an aerobics room off a narrow corridor you create a closed-in room and a restricted corridor. Locate an aerobics room open to and adjacent to a gymnasium, however, and see that the corridor disappears and the feeling of spaciousness in both areas is enhanced.
An athletic facility is subject to peak use periods that can result in crowded and congested conditions. It‟s not always possible to maintain high ceiling heights in exercise rooms that will be filled with active people. By locating these rooms adjacent to and open to the gymnasium, it‟s possible to “borrow” the perception of space from the larger volume and enhance the apparent spaciousness of the smaller room.
Other benefits of open gymnasium planning include economy, acoustics, ease of orientation and opportunities for day lighting. The case for economy can be made by the reduction in wall construction that can be realized in an open plan approach, although some of these savings may be offset by increased use of tempered glass partitions. Acoustically, the benefits also seem to point toward open planning. The problem of the gymnasium as an echo chamber is alleviated by creating an irregular and largely open perimeter that allows gym noise to be dissipated rather than reflected. The matter of unwanted gym noise intruding on certain perimeter uses must be addressed, however, and this is there glass partitions come in. For the purposes of recreation or light competition, the researcherâ€&#x;s conclusions are that a 40-footby- 50-foot court will prove functionally adequate for a single full-court recreational basketball game with three or four players per team, or two half-court games. Another possibility is a half-court gymnasium that is suitable for half-court basketball (45 by 35 feet of clear 20-foot-high ceiling is adequate for this use). Creating a gymnasium with suitable dimensions for volleyball can be a bid asset for a small club facility with limited opportunities for recreational programming. Adhering to regulation dimensions is more important for volleyball than it is for basketball, although a compromise of 2 or 3 feet in curt length is possible without jeopardizing the enjoyment of the game. However, it may be better to preserve the regulation volleyball court dimensions (29 feet,6 inches by 59 feet) and eliminate the buffer/safety zone normally provided outside the court boundaries and provide instead a completely cushioned wall just outside the end lines. With respect to ceiling heights, 18 feet is a practical minimum clear height in which to enjoy recreational basketball or volleyball. At this dimension, all lights must be fully recessed. It must be emphasized that while these off-size minigyms are less than ideal, the owners and operators of such facilities report a high level of member satisfaction with the unexpected opportunity for basketball play in what would otherwise be a small, fitness-only facility
REFERENCES A. BOOKS Fajardo, , M. (2009), Elements of Roads and Highways. Manila: Goodwill Bookstore Fajardo., M. (2010), Project Construction Management. Manila: Goodwill Bookstore Kavanagh, B. (2010), Surveying with Computer Applications. Essex: Pearson Education La Putt, J. (2007), Higher Surveying . Quezon City: National Bookstore Moffitt, F. (1987), Surveying, New York: Harper & Row Publishers.
B. MANUALS/HANDOUTS Al-Alyahya, S. & Eltoumi A. (2009) Handouts in Project Management, Qassim University Architectural Design Publication Magazine of the Architectural and Engineering Planner.(2004). Washington, DC ASEP Engineering Surveying Manual(2008), Washington, D.C. Dimaunahan, P. (1999), Studentâ€&#x;s Fieldwork Manual in Elementary Surveying. Caloocan City: University of the East. Estanero, R. (1988), Field Manual in Higher Surveying. Manila : Dela Salle University Ganiron, T. (2010). Handouts in Project Management, Qassim University Ganiron, T. (2010), Handouts in Basic Survey , Qassim University Hipolito, J. (1989), A Review Manual Surveying . Manila: Rex Bookstore Kebbieh, Y. (2009), Handouts in Basic Survey, Qassim University. .
C. UNPUBLISHED MATERIAL
Al-Maziad, M., Al-Harbi, M. & Mostafa, M. (2010). Investigation and Design of Foundation System of a Multistorey Building at Qassim University. Unpublished Design Project. Qassim University
APPENDIX A COMPUTATIONS
( I ) Checking the Interior Angle : 1. L1 = 180° - (43° 15ˊ+ 71° 28ˊ ) L1 = 65° 17ˊ 2. L2 = 43° 15ˊ + 180° - 58°53ˊ L2 = 164°22ˊ 3. L3 = 58°53ˊ + 80°10ˊ L3 = 139°03ˊ
4. L4 = 21°45ˊ + 180° - 80° L4 = 121°35ˊ 5. L5 = 180° - (31°15ˊ + 21°45ˊ ) L5 = 127°00ˊ 6. L6 = 31°15ˊ + 180° - 50°31ˊ L6 = 160°44ˊ 7. L7 = 50°31ˊ + 85°02ˊ L7 = 135°33ˊ 8. L8 = 180° - 85°02ˊ - 5°17ˊ L8 = 89°41ˊ 9. L9 = 180° + 5°17ˊ + 50°25ˊ L9 = 235°42ˊ 10. L10 = 180° - 50°25ˊ + 71°28ˊ L10 = 201°03ˊ ( II ) Computation of transverse components: A. Latitude 1. L1-2 = cos 43° 15ˊ (249.70) L1-2 = 181.66 m 2. L2-3 = cos 58° 53ˊ (291.00) L2-3 = 150.38 m
3. L3-4 = cos 80° 10ˊ (499.00) L3-4 = 85.22 m 4. L4-5 = cos 21° 45ˊ (257.50) L4-5 = 239.17 m 5. L5-6 = cos 31° 15ˊ (665.70) L5-6 = 568.69 m 6. L6-7 = cos 50° 31ˊ (166.00) L6-7 = 105.55 m 7. L7-8 = cos 85° 02ˊ (249.50) L7-8 = 21.66 m 8. L8-9 = cos 5° 17ˊ (557.00) L8-9 = 554.63 m 9. L9-10 = cos 50° 25ˊ (149.70) L9-10 = 95.39 m 10. L10-1 = cos 71° 28ˊ (272.40) L10-1 = 86.58 m B. Departure 1. D1-2 = sin 43° 15ˊ (249.70) D1-2 = 170.88 m 2. D2-3 = sin 58° 53ˊ (291.00) D2-3 = 249.13 m 3. D3-4 = sin 80° 10ˊ (499.00) D3-4 = 491.67 m
4. D4-5 = sin 21° 45ˊ (257.50) D4-5 = 95.42 m 5. D5-6 = sin 31° 15ˊ (665.70) D5-6 = 345.09 m 6. D6-7 = sin 50° 31ˊ (166.00) D6-7 = 128.12 m 7. D7-8 = sin 85° 02ˊ (249.50) D7-8 = 248.56 m 8. D8-9 = sin 5° 17ˊ (557.00) D8-9 = 52.18 m 9. D9-10 = sin 50° 25ˊ (149.70) D9-10 = 115.37 m 10. D10-1 = sin 71° 28ˊ (272.40) D10-1 = 258.27 m
- Error in Latitude
= 998.63 – 1090.30 = 91.67
- Error in Departure =1095.41 – 1058.39 = 37.02
(III) Traverse Adjustment by Transit Rule: Correction for Latitude :
Correction for Departure :
CL 1-2 = 181.66 *
CD 1-2 = 170.88 *
CL 1-2 = 7.97
CD 1-2 = 2.94
CL 2-3 = 150.38 *
CD 2-3 = 249.13 *
CL 2-3 = 6.60
CD 2-3 = 4.28
CL 3-4 = 85.22 *
CD 3-4 = 491.67 *
CL 3-4 = 3.74
CD 3-4 = 8.45
CL 4-5 = 239.17 *
CD 4-5 = 95.42 *
CL 4-5 = 10.50
CD 4-5 = 1.64
CL 5-6 = 568.69 *
CD 5-6 = 345.09 *
CL 5-6 = 24.96
CD 5-6 = 5.93
CL 6-7 = 105.55 *
CD 6-7 = 128.12 *
CL 6-7 = 4.63
CD 6-7 = 2.20
CL 7-8 = 21.66 *
CD 7-8 = 248.56 *
CL 7-8 = 0.95
CD 7-8 = 4.27
CL 8-9 = 554.63 *
CD 8-9 = 51.29 *
CL 8-9 = 24.34
CD 8-9 =0.89
CL 9-10 = 95.39 *
CD 9-10 = 115.37 *
CL 9-10 = 4.19
CD 9-10 = 1.98
CL 10-1 = 86.58 *
CD 10-1 = 258.27 *
CL 10-1 = 3.79
CD 10-1 = 4.44
(IV) Double Meridian Distance : DMD1-2 = -173.82 DMD2-3 = -173.82 - 173.82 – 253.41 = -601.05 DMD3-4 = -605.05 – 253.41 – 500.12 = -1354.58 DMD4-5 = -1354.58 – 500.12 – 97.06 = -1951.76 DMD5-6 = -1951.76 – 97.06 + 339.16 = - 1709.66 DMD6-7 = - 1709.66 + 339.16 + 125.92 = - 1244.58 DMD7-8 = - 1244.58 + 125.92 + 244.29 = - 874.37 DMD8-9 = - 874.37 + 244.29 + 52.18 = - 682.26 DMD9-10 = - 682.26 - 52.18 + 113.39 = -621.05 DMD10-1 = -621.05 + 113.39 + 253.83 = - 253.83
(V) Area by Double Meridian Distance : + 2A = 574 167 .98
A = ( + 2A - 2A )
- 2A = 1 759 866 .90
A = (574 167 .98 - 1 759 866 .90) A = 592 849 .45