 Welcome to Caltrans LSIT LS exam preparation course. One aid in your preparation for California licensure examinations. A word of caution. Don't use this course as your only preparation. Devise and follow a regular schedule of study which begins months before the test. Work many problems in each area, not just those in this course's workbook, but problems from other sources as well. This course is funded by Caltrans, but you and I owe a profound thanks to others, the courses instructors from the academic community, the private sector, other public agencies, and from Caltrans as well. We wish you well in your study toward becoming a member of California's professional land surveying community. Hi, my name is Les Carter. I'm an associate land surveyor for the city of San Diego, and I've been a licensed land surveyor in the state of California for the past two years. This section of the Caltrans LSIT LS review preparation video course covers the basic principles of traversing. This video and the accompanying workbook will provide you with an overview of the subject of performing survey traverses, and will help you identify further areas of study. Traversing is an integral part of every aspect of land surveying, whether you are surveying for sectionalized lands or to establish horizontal control for construction project staking. Before viewing the videotape, I recommend that you take the time to read the course outline. Your surveying experience will dictate at what point in the video you will want to begin. Our review of traversing will include obtaining and adjusting angle and distance measurements, performing field and office computations, and a final adjustment of the data. After viewing the video and working the self-test portion of the workbook, you should have a working knowledge of the following topics related to traversing. The key terms used in traversing, the various purposes and applications for the traverse, the different types of traverses, angle and distance measurements, basis of bearings, the different reference datums for California coordinate Lambert's coordinates, the standards of accuracy used to determine the order of classifications for the work being completed. I want to emphasize that this exam preparation will provide you with an opportunity to review your personal knowledge related to traversing and help you identify areas of further study. I recommend that you take the time to familiarize yourself with the key terms and general topics that will be covered. I also recommend that after viewing the video, you should complete each of the problems in the sample tests question section of the workbook. If there are problems in the workbook that you have difficulty in solving, continue to study that topic using one or more of the recommended references at the end of the workbook. There is no substitute for thoroughly studying the material and working practice problems. If you make the commitment to a disciplined, well-organized comprehensive schedule of self-study, you will be successful. We need to begin our review by forming a definition of traversing. Webster's dictionary lists many definitions for the term traverse. The one most familiar is simply a line surveyed across a plot of ground. This definition may be adequate for the layperson, but leaves out many aspects for the surveyor. We will use the following definition. Traversing is a method of surveying in which the lengths and directions of lines between points on the earth are obtained by field measurements and used in determining points, the positions of the points. By performing the traverse in related computations, the surveyor determines the relative positions of the traverse points and when the points are referenced to control stations on a specified datum, the positions can be referred to that datum. Examples of this are geographic coordinates, NAD 27 or NAD 83 coordinates. Survey traverses are classified in a variety of ways. According to methods used as in transit and EDM traverse, according to the quality of results as in second order class one traverse, and according to the purpose served as in aerial controlled traverse for photogrammetry. Traverse surveys can be defined in the following way. Surveys are based on the historical record and depending on the purpose of the traverse, the survey may require the actual field measurements are performed or the traverse may be a mathematical survey based solely on the record data. In either case, the survey data is related mathematically to a commonly defined horizontal datum, well-established surveying procedures and legal rules are used to analyze evidence uncovered by the survey and relate it to the historical record. Each survey is checked mathematically to discover and eliminate blunders and distribute random errors. Results of surveys are incorporated into the historical record in the form of field notes, record maps, legal descriptions, and the survey monuments that mark the locations of property corners and rights of way incident to the above record documents. As surveyors, it is your primary responsibility to keep this in mind when performing the survey. Your work will become part of that historical record. During this video presentation, we will review various traverse activities and discuss the definitions of many key words and phrases related to performing the traverse. Both the student and the practicing surveyor must be familiar with the vernacular of surveying. Some examples are closed figure traverse, radial traverse, zenith angle, instrument collimation, precision and accuracy, basis of bearings, grid distance, combination factor. Some of these terms may be new to you. Like you, whenever I encountered new words or phrases, I am compelled to pursue an understanding of their meaning and usage. If you hear words or terms that are not familiar to you, I recommend that you note them and review the references in the bibliography. The manual of surveying terms and definitions published by the American Congress of Surveying and Mapping is an excellent reference. Traverses are performed for many reasons and simply stated, the primary purpose of traversing is to calculate, search for, establish, and or extend survey control to determine the position of points on the surface of the earth. These points may be horizontal control points that are part of a high precision geodetic network or they may be construction stakes that mark the location of the improvements in a subdivision. However, traverses may also be purely mathematical. That is, traverse calculations based solely on record data. Traversing is and will remain a convenient, efficient method of establishing control points for a variety of surveying activity. Examples of this are establishing survey control for construction projects, aerial surveys, hydrographic surveys, and boundary or ordered control surveys. Also, the calculation of declosures, improvement plan checks, subdivisions, parcel maps, records of survey, and rights-of-way drawings. Another example of survey traverse is the establishment of control for construction staking. On these types of surveys, the random control points or traverse stations are usually located on or near the area in locations that provide safety and convenience for the surveyor. The majority of mapping done today is accomplished by aerial photogrammetry. When photogrammetric methods require the establishment of registration points, which are more commonly referred to as aerial control points, these ground control points have coordinate and elevation values and provide the reference data for the photogrammetrist. This enables the photogrammetrist to generate horizontal and vertical coordinate values on any topographic feature within the stereo model. The foundation for the relative accuracy of the photogrammetrist's digital mapping files is the horizontal and vertical control established by the surveyor in the field. It is essential that the surveyor identify the appropriate accuracy for the survey and adhere to accepted standards when performing the work. The surveyor is responsible for determining the appropriate accuracy to satisfy the requirements of the survey and balance these needs with the economic realities of the project. As we discussed earlier, the primary purpose of each type of survey is to establish, extend, or perpetuate the survey control for the project in question. It is therefore essential that the character, that is the description of the monuments, be clear and adequately documented. This will ensure that future surveyors are able to identify any found monuments and thereby continue the chain of history of how they were set. In completing our review of the various purposes and applications of traverses, we can observe the following advantages. Traversing provides a flexible, efficient method for establishing survey control for a wide range of surveying activity. It requires a minimum of reconnaissance in planning the survey and is easily adaptable to varying field conditions. In our review of the various purposes of traverses, we noted that each survey must satisfy the specific needs for establishing control in the given project area. And given the specific project requirements, constraints for time, and the availability of personnel and equipment, the surveyor must determine the best type of traverse to accomplish this. The various types of traverses are the closed figure traverse, the closed linear traverse, the open or continuous traverse, and radial surveys. For each type of traverse, it is presumed that the control stations are compatible. That is that the points are established on the same datum. The closed figure traverse starts and ends at the same point. The benefits of the closed figure traverse are angle and distance measurements are easily adjusted by computations to minimize the effect of random errors. Also, mistakes and blunders can be readily detected by review of the raw data, computations, and resultant values. It is important to note that systematic errors should have been minimized prior to performing the field survey by checking and adjusting the instruments. Random errors can be distributed by adjustment. The closed linear traverse starts and ends at different points of known value, and normally includes a closed station asthma mark for angular closure. When no asthma mark is available, the determining factor to the accuracy of the survey is the positional error of closure. The open or continuous traverse starts at known or assumed coordinates, but does not close on a known value. Open traverses do not provide checks for blunders or the opportunity to distribute errors in the fieldwork, and for this reason are not recommended for most survey projects. An open traverse can be useful when it is not necessary to generate accurate coordinates of the points being located. And even though the open traverse is not recommended, when the surveyor follows standard guidelines, that is turning sets of angles to the traverse stations, checking the observed distances, he or she can be assured results commensurate with the precision of the equipment being used and of the relative accuracy suitable for the project. The radial traverse is something of an oxymoron in that making radial ties to eccentric points is not of itself traversing. The following is an example of a radial traverse. A set of field observations obtained from a single traverse station which locates the eccentric traverse stations is used often referred to as a radial traverse. In the example we observed that two found monuments are used for the basis of bearings and coordinates. Station A1 was set from station A and the remaining radial ties and azimuth checks are made. It is important to note that field ties performed in this manner are subject to blunders that might not be caught. And it is essential to incorporate azimuth and distance checks whenever possible. This method is most helpful when used where the surrounding area is open with few restrictions to the line of sight. The radial survey method of locating points is also referred to as side shooting and is used frequently in performing topographic surveys. Any boundary ties made in this manner must be checked against the record data and their relationship to other located or calculated points. The positions of control points located from radial surveys cannot be adjusted unless field ties are made from two traverse stations. In the following example, we can see that when radial survey is performed, additional cross ties for angle and or distance can be added to strengthen the correlation of the measurements and facilitate adjustment of random errors. This is referred to as building a survey network. Cross ties and additional measurements made in a network, like the one shown, provide the redundancy needed for least squares adjustments. In completing our review of the various types of traverses, it is apparent that for each survey, there are many options for the types of traverses and or combinations of traverses the surveyor can choose from. Our next topic is angle and distance measurement. The precision of modern surveying instruments makes it possible to obtain consistently precise field measurements. However, it is often taken for granted that the instruments are in proper adjustment. Whether you are using a theodolite and EDM or total station, it is essential that you regularly check for calibration and collimation adjustment. This should also include all equipment that affects the observation data, such as prism poles, tribracks and optical plummets. There are several methods for determining traverse angles. Angles can be read by deflection. In determining deflection angles to the right or left, the instrument operator will orient the horizontal circle on the backside, plunge or flop the scope and then observe and record the right or left deflection angle. In the example, you will note that the instrument orientation is the direction from point A to point B. More commonly, angles are measured directly to the right or left, either with the repeating method or the direction method. The repeating method utilizes the horizontal circle to collect the summation of repeated angle measurements. The observed angle is the mean of the several readings. For observing the right or left direction angles, the horizontal circle of the instrument is set to approximate zero on the backside. This backside orientation is recorded and the scope is then turned to the foresight and a direct reading taken and recorded. The scope is plunged and a reverse reading is taken on the backside and the foresight. The observed angle is the average of the difference between the foresight and backside readings for both the direct and reverse position of the scope. In traversing, we must determine our angular error of closure. To facilitate this in a closed figure traverse, the sum of the angles is checked for mathematical closure. Depending on the surveyor's preference, the angles can be turned and recorded as internal or external angles. Normally, the traverse angles are observed as angles right and the procedures for observing and recording direct angles are used. Angles may also be in the form of direct azimus. The horizontal circle is oriented on the backside with the record or calculated azimus between the instrument station and the backside station. Any direct readings from the horizontal circle are then direct azimus. A method of determining direction that is seldom used today but may be useful is determining the direction of a line by magnetic bearing. There are numerous types of surveying equipment available today that enable the surveyor to determine highly accurate angle and distance measurements. For the majority of control traverses performed today, an EDM is used. Errors that can adversely affect EDM distances, such as incorrect parts per million corrections, incorrect prism constants, and instrument setup or optical plummet errors can be eliminated by the use of standard procedures for instrument setup. There are many references available for the student who wishes to develop his or her personal background of the various surveying equipment for observing and recording angle and distance information. The Caltrans Surveys Manual, chapter five, sections one and two, provides an excellent reference for further study in this area. It is also important for the student and practicing surveyor to be aware of the need for being proficient in calculations in feet and meters. Our next section is basis of bearings. For every survey, the surveyor must establish or assume a meridian. This is a quote from Evidence and Procedure by Brown, Robillard, and Wilson. By this brief statement, the authors have acknowledged the significance of the basis of bearing as the primary reference for the survey. The basis of bearings can be either a reference to a previously recorded map derived from direct astronomical observation obtained from calculations based on published geodetic or state plane coordinate values or when appropriate determined by magnetic observation. In either case, the surveyor must place an appropriate note on the plat to explain how the basis of bearing was determined. For the majority of field surveys, a record bearing between found monuments, which were set per a subdivision map, parcel map, or a record of survey is the most commonly used basis of bearing. In the following example, we see that two found points of record are required. However, when control stations are not within the immediate project area, determining a basis of bearings by astronomical observation should always be considered a viable option. The two monuments could represent a NAD-83 station for the instrument setup, and the azimuth mark could be the sun. If the survey covers a large area, many record maps and adjacent deeds may be involved that can have different basis of bearings. In this case, it is necessary to reconcile these differences. The principle that must be applied is to maintain the record angular relationships that is the record geometry between the various record map boundaries. In our example, the boundary of track one, two, three differs from track four, five, six by 15 minutes. The reason for this is that the maps had different basis of bearings. To hold our basis of bearings per track one, two, three, we must rotate the bearings of track four, five, six clockwise by 15 minutes. By doing this, we will generate compatible bearings and maintain the record angular relationships within map four, five, six. If an inverse from coordinates of published control points is used to generate a basis of bearings for the survey, the surveyor must show the datum, that is, whether this is NAD 27 or NAD 83, and how the survey was tied to the coordinate basis. Also, the surveyor must show the mapping or convergence angle. Today it is simple for the practicing surveyor to determine the true azimuth from observations on the sun or stars. The calculations are based on plane and spherical trigonometry and utilize tables and formula published annually in ephemeris available from various firms specifically for surveying applications. While magnetic bearing orientation is not often used, it is an excellent tool for approximating directions. One example of this is for site reconnaissance in remote locations. Another would be to follow in the footsteps of the original surveyor when retracing government notes. Our discussion of coordinates will be a brief review of the general differences in coordinate datums and will focus primarily on computation of NAD 83 station coordinates of traverse points. Lambert coordinate computations are covered in depth in another module of the training video. The North American datum of 1927 was established by the U.S. Coast and Geodetic Survey and was based on the Clarks Feroard of 1866. The point of origin was Point Meads Ranch, Kansas, NAD 27. The North American datum of 1983 has been established by the National Geodetic Survey and is based on the center of ellipsoid of the earth as established by the geodetic reference system of 1980. Per section 8801 of the Public Resources Code of the State of California, after January 1st, 1995, all state plane coordinates generated after this date must be referenced to the NAD 83 datum. Our next topics are precision and accuracy. These two topics are the subject of much misunderstanding in the surveying community. And our review will probably generate further discussion. It is important to note that while the error of closure of a traverse may indicate a high measure of precision, it may have little if any relationship to the accuracy of the survey. This is because the accuracy of your survey is attained at all points along the traverse. The term precision is traditionally applied to methods and equipment used in attaining results of a high order of accuracy. An example of this would be that many optical and digital theodolites are capable of displaying readings to the second. But these instruments have varying precision tolerances. While some are rated at plus or minus one second, others are rated at plus or minus five seconds. This is because the seconds are doubtful to within the range of precision specified. All surveys must be performed with a degree of precision which ensures that the required accuracy is attained. In addition to conforming to the applicable standards of precision and accuracy, field surveys which are to be classified as ordered must use field procedures that meet or exceed the requirements for the specified classification. Measurements and results should be stated in terms that reflect the precision used to attain the results. A logical but not always valid assumption is that with modern surveying technology, angle and distance measurements are made with the same precision. In the following example, we see a graphic representation of precision. Precision refers to the closeness to one another of a set of repeated observations. Precision is observed when a set of measurements are very closely grouped. However, as shown in our example, while meeting prescribed standards of precision, these closely grouped observations may not reflect an accurate value of the quantity being observed. Precision can also be described as the quality and consistency that is the refinement of the methods and the equipment used to obtain the raw field data. Accuracy, while precision is defined as a measure of the closeness of a set of repeated measurements to each other, accuracy is the nearness of a given observation to the true value. Examples of accuracy standards are an exact value such as the sum of three angles of a plane triangle equals 180 degrees or an established value for a unit of measure such as one mile contains exactly 5,280 feet. A value that has been determined by established procedures and thereby observed to be of suitable accuracy to be used as control for comparison of subsequently computed values is also a standard of accuracy. In the following example, we can see that the measurements are closely grouped and are also very near the true value. Many factors affect accuracy. These include instrument precision, field procedures, and environmental factors. Earlier, we reviewed how poor instrument adjustment also adversely affects the accuracy of field data. When equipment of the necessary precision is used and appropriate procedures are adhered to, the results of the field survey traverses can be consistently achieved at the desired levels of accuracy. Accuracy can be further defined as the measure of quality of the results obtained when performing field traverses. The two primary observable quantities that determine accuracy of a traverse are the angle and distance closures. While the advances in technology of today's surveying equipment make it possible to obtain consistently precise distance measurements far exceeding those of 20 years ago, it is important to understand that without adhering to sound surveying procedure, you may have a very precise data and very inaccurate results. The following slide, which is a table of allowable horizontal and angular error by order of survey is an example of this. In the example, we can see that if you want to achieve first order accuracy, you must follow the specified procedure and use an instrument that is able to redirect to two-tenths of a second. You must turn 16 cents of horizontal angles. Also, the standard specify a rejection limit of four seconds. This means that no one set of angles can exceed four seconds of angular deviation from the mean of the angles for the set. The manual of surveying terms and definitions published by the American Congress of Surveying and Mapping is an excellent reference for the student in practicing surveyor and should be viewed as an essential reference. Our next topic will be the types of errors in traversing. Systematic errors. Given the same set of conditions, systematic errors occur as a constant quantity, follow a definable pattern, and have the same algebraic sign. Systematic errors can be minimized by following sound surveying procedures. And once detected, systematic errors can be applied as an adjustment to a given set of measurements. Systematic errors occur, and once detected, systematic errors can be applied as an adjustment to the given set of measurements. Systematic errors can be caused by the observer as in the case of the instrument operator not setting the correct parts per million or prism constants. Subsequent measurements would be affected consistently by the incorrect settings. Or by the equipment, as in the case of a theodolite tribrac, an optical plummet that is out of adjustment. In this case, each instrument setup is subject to have a position error equal to the radius of the plummet error, which will be dependent on the height of the instrument. The instrument collimation error is another type of systematic error and is normally accounted for by the averaging of direct and reverse observations of horizontal and vertical angles. Detecting and minimizing systematic errors can be extremely difficult. It is therefore essential that the surveyor be able to recognize deficiencies in the field procedures and or equipment that may cause these errors to ensure confidence that your results will be consistent. A good rule of thumb is to verify and document instrument adjustment at least every three months. Accidental and random errors do not always follow a fixed pattern in response to the conditions or circumstances of performing the survey. Examples of this are small compensating errors such as estimating between the marks on a tape or not setting up exactly over the point. It is important to understand that these errors can be minimized but never completely eliminated. Blunders are human mistakes and as such are not defined as errors unless the erroneous data becomes a part of the historical record and is subsequently used for reference or in computations. Examples of blunders include transposition of numbers, neglecting to level the instrument, misunderstanding another survey crew member and writing down the wrong number. Blunders are a surveyor's worst enemy but they can be detected and eliminated by following sound procedures. By this I'm simply referring to being alert, making checks on the observation and measurement data and where possible reviewing the work of other crew members. Our previous review of the types of errors and traversing focused primarily on the angle and distance data necessary to perform the traverse computations. Another area of potential error and one particularly pertinent to taking the LSIT or LS exam is the reference material that may be used to supplement the field data such as record maps, rights of way drawings and or deed documents. I should include in this other surveyor's notes. As surveyors and professionals we refer to the work of other surveyors but we may not want to rely on it without evaluating its correctness. For the exam and for your surveying career in general you will always want to review the data that you have provided and attempt to identify any obvious conditions that will affect your computations. If you are given a map, deed or other parcel description you should form the habit of reviewing the data from an analytical perspective and by this I mean that you should subject any information you receive to a certain critical analysis. By following this approach in all phases of research and calculations you will ensure that your solution will be based on correct information. We have reviewed topics relative to generating the raw field data. The remaining portion of the video will focus on the areas of computations and traverse adjustments. There are three primary areas of activity related to performing traverse computations. These are generating the raw field data, processing the raw data to adjust for systematic errors such as incorrect tape corrections, incorrect temperature corrections when taping. Another example is to distribute random error and identify blunders. And finally performing coordinate computations to determine final traverse stations positions. We have reviewed the first two topics. As Lambert coordinate computations are covered in depth in another module of the training video we will not review these at length. However, because the calculations of coordinates is an essential aspect of performing the traverse we will review the basic concepts used in calculating coordinates. On the exam you will be required to know how to determine the following. Grid or geodetic azimuth, the convergence or mapping angle, reduction to sea level or elevation factor, and the combination factor which is a sea level factor times the scale factor. I recommend that you devote adequate study time to each of these areas. They are an integral part of performing the traverse and associated calculations. The first step in traverse calculations is to balance the field angles. You must adjust the angles proportionately to eliminate the angular area of closure. This is part of the standard methodology of calculating traverse station coordinates and traverse closure using in our example the compass adjustment method. The following conditions equations apply to closed figure traverses. The sum of interior angles of a traverse must equal the number of sides minus two times 180 degrees. Or when the exterior angles have been observed the formula is in plus two times 180 degrees. An example of this would be what is the sum of the interior angles in a traverse of five sides? The answer would be 540 degrees. In the case of a closed linear traverse the observed angular misclose as determined by the computed check azimuth on the closed station foresight or azimuth mark would be proportioned equally to each of the traverse station angles. We will begin our review of distance measurements by acknowledging that presently the United States uses the foot standard for measurements. The future trend is towards the meter standard. It is therefore essential that the student in practicing land surveyor develop proficiency in foot and meter conversions. The following formulas reflect the basic conversion factors used to convert US survey feet to meters and or meters to feet. To obtain a relationship between meters and feet we observe the relationship in inches and compute the following constant. To convert US survey feet to meters multiply the distance in feet by the derived constant. To convert meters to US survey feet multiply the distance in meters by the derived constant. Presently NGS publishes all California coordinate NAT 83 control station data in meters. And the state plane coordinate system of NAT 83 is defined in meters. It is likely that you will see a problem on the exam that will require you be proficient at making the conversion. When calculating coordinates the distance must be grid distance. To obtain grid distances it is necessary to apply the C level, reduction to C level and the projection scale factor to horizontal distances before using the distances and calculations of Lambert coordinates. Normally these adjustments are expressed in a single term known as the combination factor. Currently the computation of latitudes and departures is seldom required for surveying applications. However, there are instances where being able to compute station coordinates using this method may prove beneficial. You should be familiar with the following formulas. The latitude of a line is equal to the cosine of the bearing times the length of the course. The departure of a line is equal to the sine of the bearing times the length of the course. It is also necessary to keep track of the algebraic sine of the quadrant the bearing is in. The tangent of the bearing is the departure divided by the latitude which can also be stated as the tangent of the bearing equals the difference in eastings divided by the difference in northings. The length of a line can then be determined by the following formula. The length of a line equals the square root of the difference of the eastings squared plus the difference in the northings squared. Developing and maintaining a sound understanding of these fundamental concepts will provide you with a better foundation for passing the exam. It is important to note that while a calculator at PC will provide an answer and will certainly do so very quickly to as many decimal places as you can display, it will be your knowledge of fundamental geometric relationships and trigonometric functions that will enable you to observe whether your answer appears correct. That is, is the value in the correct quadrant? As a surveyor, you must develop an analytical perspective that will enable you to always be on guard for results that simply don't look right. With the use of programmable handheld calculators to generate coordinates, there would seem to be no need for being proficient at longhand computations to generate coordinates. Even so, there are times when being able to perform these computations is helpful if not necessary. While there is little likelihood of your being required to do longhand latitude and departure computations in practice, for the exam, the possibility does exist. And certainly it is better to be prepared. The following is an example of a straightforward cookbook method of calculating and adjusting a traverse using latitudes and departures. In the following example, we observe a closed linear traverse with three sides. You can presume that all angles shown have been reviewed and correctly represent the field observations but have not been adjusted. And all distances shown have been reduced to grid distances. Note that at point one, the closing angle was turned from point three back into point 11. This provides a check on the angular closure for the traverse and is necessary for the angles to be correctly adjusted. Often, in the interest of time, position closure is calculated while the instrument is at station three. And if the calculated position closure is satisfactory, the party chief may decide to not observe a closing angle. While this is a common practice, it does leave room for errors that could be readily identified and eliminated by performing the angular closure. The first step in the computation of traverse station coordinates is balancing the angles. The formula for determining angular error closure when the external angles have been observed is, as we reviewed, the number of sides in the figure plus two times 180 degrees. The sum of the external angles in our example should be 900 degrees. From the field data, we observe that the angular error closure is 6.3 seconds. Since technically, we have three angles external to the figure, each of the external angles would be increased by 2.1 seconds. In the following example, we can see that the initial and closing angles turned at point one would receive a proportionate amount of the correction. Notice that by observing the proportionate relationships, the amount of adjustment that the independent angles at point one receive is readily computed. Once the angles have been adjusted, it is possible to compute the bearings of the traverse lines. In the following example, we have created a table of the adjusted angles and bearings. The initial backside bearing from point one to point 11 was north 49 degrees, 59 minutes, 53.5 seconds west. In the example, we see the adjusted angles and subsequent bearings and that the adjusted angles of our traverse mathematically close back on the basis of bearings. It is essential that the surveyor incorporate ways to identify angle errors, such as checking some of interior angles in the case of a closed-figure traverse or observing an azimuth mark as a check when performing a linear traverse. Incorporating checks for angle and distance closures into the standard methodology of performing the survey is essential. Without these checks, the possibility of errors cannot be avoided. After the angles have been adjusted, any slope distances must be reduced to horizontal distances. Normally, when the slope distance is measured, the zenith angle will be observed. The formulas that apply are shown in the following example. Where vertical angles are observed, the horizontal distance equals the slope distance times the cosine of the vertical angle. Where the zenith angles are observed, the horizontal distance equals the slope distance times the sine of the zenith angle. Previously, we observed that for computation of Lambert coordinates, it is necessary to calculate the elevation factor, scale factor, and apply these corrections in the form of the combination factor to the observed ground distances to obtain grid distances. It is important to keep in mind that this is necessary calculation and that the combination factor be applied prior to calculating latitudes and departures for traverse courses when generating Lambert coordinates. Latitudes and departures are expressed as values associated with a rectangular coordinate system. Latitude is the value that reflects the magnitude of change in position along the north-south axis and is computed by multiplying the cosine of the bearing times the length of the traverse course. Departure is the change in position along the east-west axis and is computed by multiplying the sine of the bearing times the length of the traverse course. In the following example, we have computed the latitudes and departures of our traverse. We observed that the sine of the functions of the bearings have given the latitudes and departures a plus or minus value. In the next example, we have calculated the values needed to compute our traverse closure. These are the summation of horizontal traverse distance, the latitude and departure misclosures, the linear misclosure, which equals the square root of the sum of squares of the latitude and departure misclosures, and the traverse closure accuracy ratio, which is equal to one over the quotient of the summation of horizontal traverse distances divided by the linear misclosure. The computation of latitudes and departures may seem extraneous in an age of handheld calculators that make calculating and adjusting coordinates seem almost effortless. But if you periodically review these fundamental calculations, you'll be assured to never be cut off guard with your batteries down. To begin our review of the various types of adjustments for traverse closures, it is important for the student and the practicing surveyor to understand that an observed linear closure, such as a mathematical traverse closure of 1 in 100,000, by itself is relatively meaningless. At best, it is only an indication of the precision of the survey and may have little if any relationship to how accurate the survey truly is. Measurements are not exact, and due to instrument and human error, traverses do not close exactly. In the case of the compass adjustment, the linear area of closure is simply distributed throughout the traverse. It is important to keep in mind that only when the appropriate procedural standards have been adhered to is the surveyor able to have confidence that the observed linear closure is representative of the accuracy of the survey. The various types of traverse adjustments are the arbitrary method, the transit rule method, the Crandall rule method, compass rule, and least squares method. The arbitrary method of traverse adjustment has no set of fixed rules and no standard equations apply. The surveyor uses his or her logical assessment of the field conditions to form a professional opinion of where the closure errors are most likely to have occurred. If there were extremely short traverse legs, the party chief could choose to apply a larger angle correction at that instrument station. This method is simple to perform and is based solely on the individual surveyors' personal judgment. The transit rule method of traverse adjustment presumes that angles are more accurate than distances. The Crandall rule method also is based on the assumption of higher angle accuracy but is a more rigorous calculation. Neither the transit rule or Crandall rule method of adjustment are used frequently today. However, it is important to understand these basic concepts and keep in mind that either method of adjustment might be viable given a certain set of conditions. The compass rule method of adjustment was developed on the basis that the precision of the angles and distances in the traverse is the same. Each leg of the traverse receives a proportionate correction to the latitudes and departures for that leg of the traverse. The correction that is applied to the latitude and departure for each leg of the traverse is the ratio of the length of each leg to the summation of distances for the perimeter of the traverse. The most comprehensive method for traverse adjustment is the least squares method. The least squares method of adjustment can be expressed as a method of placing the errors where they are statistically most likely to have occurred. The least squares method of adjustment uses the error residual as a means of measuring the relative accuracy of the observations. The error residual is equal to the best value, which is the arithmetic mean of a series of observations minus the observed value. The more complex the field data, that is, when we have multiple control stations, independent angle or distance ties, the more complex the task of correlating all the data and maintaining the correct geometric conditions within the survey while conducting the adjustment. In the example, we can see that by using a least squares adjustment method to distribute random errors and identify and eliminate blunders, the surveyor achieves a true best fit adjustment of the survey control network that reconciles the error of closure and also minimizes the adjustments to the original field data. As we reviewed previously, it is necessary to adjust observed angles to correct for angular misclose of the travers. The basic rule for balancing angles is to adjust each angular measurement equally to eliminate the angular error of closure. This is based on the theory that the accuracy of the angular measurements is the same for each angle and that there is no basis for presuming that any one of the angles contains more or less of the total angular error than any other angle. The following steps are required for balancing the survey using a compass adjustment. Computing the angular error of closure and adjusting each field angle, computing the bearings of each leg of the traverse, and computing the latitudes and departures. Also, we must compute the error of closure and ratio of error, compute the latitude and departure corrections, adjust the latitudes and departures, and calculate final station coordinates. We have completed our review of the first three topics and will now review the topics related to adjustments. The actual error within each traverse leg cannot be determined. However, the total error of closure and ratio of error are readily computed. The compass rule method of traverse adjustment proportions this misclosure throughout the traverse. This is referred to as balancing the traverse. In balancing the traverse, we determine and apply the appropriate corrections to the latitudes and departures of each traverse course. In the following example, the latitude correction for traverse line one two is shown. The adjustment in latitude to traverse leg point one to point two divided by the traverse misclosure in latitudes is proportional to the length of leg point one point two divided by the total length of the traverse. And we can note that it is important to keep track of the algebraic sign of the functions you are using. Once you have calculated the latitude and departure corrections, you would apply these corrections to each leg of the traverse by applying the latitude and departure values to your start point coordinates. You will compute the individual traverse station coordinates. In the following example, the corrections to latitude and departure and final station coordinates of point two are shown. It is important to apply the corrections algebraically. The adjusted latitude and departure for line one is added to the beginning coordinate of point one to obtain the final station coordinates for point two. Once the adjustment to latitude and departure have been applied to each traverse leg, the station coordinates have been calculated and the bearings and distances of the traverse courses must be recalculated. Periodic review of this relatively simple procedure will ensure that you are never caught off guard should your calculator blow a fuse. We have observed that when we perform subsequent traverse computations, we are able to find and correct blunders, adjust for systematic errors, and distribute random error. The question I want to pose to each of you is how are we as a group, and my reference is to all surveyors, whether you work for a municipal agency or the private sector, how are we as a group able to provide consistently accurate survey data for the specific surveying applications in question? The answer is simply that we must adhere to standard procedural methodologies that will ensure the desired results. The surveyor must strive to establish the personal habit of conducting a comprehensive analysis of all the related components of performing the traverse. These include the condition of the field equipment, the completeness of the reference data, and field conditions that will affect traverse results. In every aspect of our profession, we are continually made aware that we must conform to varying standards of accuracy. As a profession, we accomplish this by adhering to standard procedures and methods. When we think of this in terms of performing the individual activities related to traversing, the term methodology takes on a much less abstract meaning. When you establish work habits, such as regularly checking the optical plummet, or rod bubble, or when you perform specific computations such as balancing angles, reduction of slope distance, or calculation of the combination factor, you are employing a procedural methodology. And whether you are in the field or the office, time-consuming mistakes can be easily avoided by establishing personal work habits which incorporate making a reasonable number of checks while the work is progressing. Some of the activities that make up a procedural methodology are project planning and liaison to define the specific project requirements, verifying instrument adjustment and calibration, assembling and reviewing all pertinent references for the survey, performing a field reconnaissance, and incorporating checks on angle and distance data. When you perform reductions of the adjustment and adjustment of the angle and distance measurements, you want to be sure to balance your angles, apply temperature corrections, apply parts per million corrections. This will allow, these procedures allow you to calculate your error of closure, perform traverse adjustments, and calculate your final Lambert coordinates. In planning for our traverse, we must define a basis of bearing for the survey. We noted that this could be based on a variety of reference points, that is, record map bearing between two fond monuments or astronomical observation. An effective field procedure to ensure consistency of results is to lay out the traverse so that the traverse legs are balanced. That is of approximate equal length between instrument setup stations. This will minimize the effect of siding and instrument adjustment errors. When conducting reference research, and certainly during the exam, verifying your reference documentation will be an area for primary consideration. You'll be required to analyze the information you are presented with, state all pertinent factors affecting their survey, and that were used in determining a valid solution. Prior to performing any calculations, all available survey references for the project area must be compiled. And as I stated earlier, when performing a survey, the surveyor relies on the historical record. It is important to note that each surveyor must also determine if the historical record is correct prior to utilizing this information in the current survey. I feel this topic cannot be overemphasized as you prepare to take the exam. It should be one of your most important areas for study and must be applied in problem solving and in practice. By establishing personal policies of following consistent problem solving procedures, that is, develop a standard format and sequence for doing the calculations and identifying the specific requirements of the survey, you will ensure that your results will be correct. We have completed our review of the traverse, and I would like to take the opportunity to offer my personal perspective on the future of land surveying relative to the need for performing field survey traverses and related computations. In the past few years, the profession has seen many developments being made in the area of GPS applications, and there are those who feel that GPS will ultimately replace conventional surveying in its entirety. GPS is, without question, a very efficient method for establishing high accuracy survey control, and while there are different schools of thought as to the ultimate future of land surveying, conventional field survey traverses offer certain advantages. Because of the versatility and relative convenience of performing the conventional field traverse and relative computations and ease of relative computations, the traverse will continue to remain a fundamental aspect of surveying and an area of knowledge and skill that the land surveyor must possess, and it certainly will remain an essential topic of study for those of you preparing for the LSIT and LS exam. Regardless of the development of technology, traversing is and will continue to remain the heart of the surveying profession. Good luck on the exam and your career in land surveying.