# Military

## TRAVERSE

In survey, traverse is defined as the field operation of measuring the lengths and directions of a series of straight lines connecting a series of points on the earth. Each of these straight lines is called a traverse leg, and each point is called a traverse station.

### METHODS AND PROCEDURES

Traverse legs are measured by using electronic devices, a 30-meter steel tape, or trig-traverse procedures. At each traverse station, a horizontal angle is measured and used to determine the azimuth of the next traverse leg. These measurements are used to compute the relative horizontal position of each unknown traverse station on some system of coordinates, such as the UTM grid system. A vertical angle is also measured at each station and is used to determine the height above or below vertical datum of each of the unknown traverse stations. In FA surveys, the angular measurements may be made with one of two instruments, depending on the accuracy required and the echelon at which the traverse is conducted. These instruments are the T16 and T2 theodolites.

#### 5-1. FIELDWORK

In a traverse, three stations are considered to be of immediate significance. (See Figure 5-1.) These stations are referred to as the rear station, the occupied station, and the forward station. The rear station is that station from which the persons performing the traverse have just moved or a point to which the azimuth is known. The occupied station is the station at which the angle-measuring instrument is set up. The forward station is the next station in succession and is the immediate destination of the party. During the traverse (Figure 5-2), the horizontal angles, vertical angles, and distances are measured.  a. Horizontal Angles. Horizontal angles are determined from instrument readings made at the occupied station by sighting the instrument on the rear station and turning the instrument clockwise to the forward station. When measuring horizontal angles, the instrument is always sighted at the lowest visible point of the station markers designated the rear and forward stations. Horizontal angles are used in determining azimuths.

b. Vertical Angles. Vertical angles are determined from instrument readings made at the occupied station to the height of instrument on the station marker (usually a range pole) at the forward station. When the distance between two successive stations in a traverse exceeds 1,000 meters, the vertical angle must be measured reciprocally (measured from each end of that particular traverse leg). This reciprocal measurement procedure is used to eliminate errors caused by curvature and reflection. Vertical angles are used in determining the difference in height between stations.

c. Distance. The distance between the occupied station and the forward station is measured by using electronic devices, horizontal taping, or trig-traverse procedures (see Section IV). The distance is used in conjunction with the horizontal and vertical angles to determine coordinates and height.

#### 5-2. STARTING CONTROL (TRAVERSE REQUIREMENTS)

The purpose of traverse is to locate the unknown points relative to each other and to locate all points within the traverse relative to a common grid. Three elements of starting data are needed. They are the coordinates and height of a starting point and an azimuth to a visible azimuth mark. (See Figure 5-3.) Starting data may be obtained from existing control data or maps or may be assumed. a. Known Control. Known survey control data may be acquired from trig lists, local or national survey agencies, or supporting survey elements of a higher HQ. An azimuth to an azimuth mark (starting direction) may be obtained by use of a SIAGL, by astronomic observation, by computation from known coordinates, by reference to an existing trig list, and by PADS.

b. Maps. If no known control is available, a careful map inspection may be used to determine starting coordinates and height. For survey purposes, data scaled from a map are considered to be assumed data. If possible, a starting azimuth should be determined by using a SIAGL astronomic observation, simultaneous observation, or PADS. If the situation is such that none of these methods can be used, then a starting azimuth may be obtained by carefully scaling from a large-scale map or by using a declinated compass.

c. Assumed. When neither known control nor maps are available, the coordinates and height for the starting station may be assumed. Starting direction will be determined by the most accurate means available. Assumed data must be converted as soon as more accurate starting control becomes available.

#### 5-3. TYPES OF TRAVERSE

There are three types of traverse used in FA survey. These are open traverse, closed traverse, and directional traverse.

a. Open Traverse. An open traverse begins at a point of known control and ends at a station whose relative position is known only by computations. The open traverse is considered to be the least desirable type of traverse, because it provides no check on the accuracy of the starting control or the accuracy of the fieldwork. For this reason, traverse is never deliberately left open. Open traverse is used only when time or enemy situation does not permit closure on a known point.

b. Closed Traverse. This traverse starts and ends at stations of known control. There are two types of closed traverse--closed on the starting point and closed on a second known point.

(1) Closed on the starting point. This type of closed traverse begins at a point of known control, moves through the various required unknown points, and returns to the same point. This type of closed traverse is considered to be the second best and is used when both time for survey and limited survey control are considerations. It provides checks on fieldwork and computations and provides a basis for comparison to determine the accuracy of the work performed. This type of traverse does not provide a check on the accuracy of the starting data or ensure detection of any systematic errors. If a conventional survey team uses a PADS SCP, they must close on the same point because of the PADS circular error probable (CEP) and errors in determining assumed data.

(2) Closed on a second known point. This type of closed traverse begins from a point of known control, moves through the various required unknown points, and then ends at a second point of known control. The point on which the survey is closed must be a point established to an equal or higher order of accuracy than that of the starting point. This is the preferred type of traverse. It provides checks on fieldwork, computations, and starting control. It also provides a basis for comparison to determine the accuracy of the work performed.

c. Directional Traverse. Directional traverse is a type of traverse that extends directional control (azimuth) only. This type of traverse can be either open or closed. If open, the traverse should be closed at the earliest opportunity. It can be closed on either the starting azimuth or another known azimuth of equal or higher order of accuracy. It also can be closed by comparison to an astronomic azimuth, gyroscopic azimuth, or a PADS azimuth. Since direction is the most critical element of FA survey and time is frequently an important consideration it is sometimes necessary at lower echelons to map-spot battery locations and extend direction only.

#### 5-4. TRAVERSE STATIONS

a. Selection of Stations. In FA survey, sites for traverse stations normally are selected as the traverse progresses. Stations must be located so that at any one station both the rear and forward stations are visible. Some brush cutting may be required to clear lines of sight between stations. If the distance is to be measured with a tape, the line between stations must be free of obstacles for the taping team. Electronic lines of sight must also be free of obstructions if electronic equipment is to be used. The number of stations in a traverse should be kept to a minimum to reduce the accumulation of instrumental errors and the amount of computation required. Short traverse legs require the establishment and use of more stations and may cause excessive errors in azimuth because small errors in instrument centering and pointings will be magnified and reflected in the azimuth closure.

*b. Station Markers. Traverse station markers are usually 1-inch by 1-inch wooden stakes, 6 inches or more in length. These stakes, called hubs, are driven flush with the ground. The center of the top of the hub is marked with a surveyor's tack or with an X to designate the exact point of reference for angular and linear measurements. To help in recovering principal stations such as the OS, EOL, and north reference point and its azimuth mark (Patriot unit), a reference (witness) stake is driven into the ground so that it slopes toward the station. (See Figure 5-4.) The identification of the station is written on the reference stake with a lumber crayon or china-marking pencil or on a tag attached to the stake. Signal cloth may also be tied to the reference stake to further help in identifying or recovering the station (unit standing operating procedure [SOP]). During phases of survey expansion, more permanent types of markers may be used, such as shell casings or concrete monuments. c. Station Signals. Signals must be erected over survey stations to provide sighting points for the instrument operator and to serve as a reference for tape alignment by the taping team. Permanent tripods or similar signals have been erected over some primary survey control stations so that the stations can be occupied without disturbing the signal. In artillery survey, most of the station sites are selected and marked as the fieldwork progresses. Temporary signals must be erected at the stations as they are needed. The equipment used for station signals is discussed below.

(1) Range poles. Range poles are made of tubular steel, and each consists of two interlocking sections. The assembled pole is 6.5 feet long, and one end is tapered to a point. The pole is painted in 1-foot sections with alternate colors of red and white. For storage, the pole is disassembled and placed in a canvas case. To use the range pole, place the tapered point on the station mark and use a rod level to make the pole vertical for observations. Place the angular portion of the level against the pole, with the circular level vial facing upward. Then move the top of the pole until the bubble in the vial is centered. Check the verticality of the range pole by verifying that the bubble remains centered at other points on the range pole. Maintain the range pole in a vertical position throughout the observing period, normally by using a range pole tripod. To prevent the measurement of angles to the wrong point, place the range pole in a vertical position only when it is being used to mark a survey station. Cloth flags of various colors may be attached to the top of the range pole to help identify the station.

(2) Target set, surveying. To mark survey stations, artillery missile batteries that have special accuracy requirements for the azimuth of the orienting line use the target set. (See Figure 5-5.) The target set may also be issued to FA survey elements that are required to perform survey to fourth-order accuracy. The target is mounted on the same tripod that is used with the T2 and T16 theodolites. The tripod is set up, leveled, and plumbed in the same manner as the theodolite tripod. After setup, the target is oriented so that it can be seen directly by the instrument that is sighting on it. The target can be illuminated for night use. Greater accuracy is obtained on short traverse legs by using the target rather than range poles. When the telescope is sighted on the target, the telescope cross hairs should bisect the triangles of the target. Flexibility can be obtained by interchanging and leapfrogging theodolites and targets. This reduces setup time by leaving tripods and tribrachs in place. The target level and optical plumb on the target must be adjusted in the same manner as for the T2 theodolite. #### 5-5. ORGANIZATION OF CONVENTIONAL TRAVERSE PARTIES

The number of personnel authorized to perform survey will depend on the unit TOE. The organization of these persons into a traverse party and the duties assigned to each member will depend on the unit SOP. The organization and duties of traverse party members and modifications proposed for reduced-strength parties (a through d below) are based on the functional requirements of a traverse. See Chapter 1 for a detailed description of individual duties.

a. Fifth-Order Traverse Party.

(1) Chief of party. The chief of party plans the traverse, selects and marks the locations of the traverse stations, and supervises the work of the other members of the party. When directed, he helps the survey officer or chief surveyor in the reconnaissance and planning of the survey.

(2) Instrument operator. The instrument operator measures the horizontal and vertical angles at each traverse station. He measures distances with the SEDME-MR. He also operates the azimuth gyro and is responsible for the care and cleaning of those instruments.

(3) Computer-recorder. The computer-recorder keeps the field notes for the party in a field notebook. He records the angles measured by the instrument operator, the distances measured with the SEDME or measured by the tapemen, and all other data pertaining to the survey. He also checks the length of each taped traverse leg by pacing (fifth order). Also, he computes the grid coordinates and height of each traverse station as the traverse progresses and checks his results with the computer.

(4) Computer. The computer computes the grid coordinates, height, and azimuth of each traverse station as the survey progresses. The computer and the computer-recorder work independently and check their results with each other.

(5) Rodman-tapeman. The rodman-tapeman helps in setting up and marking stations. He erects the SEDME reflector and helps the instrument operator care for the instruments. When the 30-meter steel tape is used, the rodman-tapeman and an individual designated by the chief of party measure the distance from one traverse station to the next. Each keeps a record of the distance taped. They compare their recorded distances before reporting the measured distance to the recorder. The rodman-tapeman maintains all taping equipment.

b. Fourth-Order SEDME Traverse Party. The fourth-order SEDME traverse party is equipped with two T2 theodolites and one SEDME-MR. The personnel are one chief of party, two instrument operators, two computer-recorders, and one rodman. Party deployment and measuring operations are shown in Figure 5-6. Measuring Section (MS) 1 occupies the survey control point, measures Angle 1 (A1), and sets up a set of infrared reflectors (IRRs) before moving to TS 2. Measuring Section 2 occupies TS 1, measures A2 and distances 1 and 2 (D1 and D2), and moves to TS 3 to repeat the cycle. The recon section plans the survey, establishes forward stations, and recovers the IRRs and range poles, as required. c. Fourth-Order Taped Traverse Party. Duties for a fourth-order taped traverse are the same as in a above with the exceptions discussed below.

(1) The computer-recorder is not required to check the length of a taped traverse leg by pacing.

(2) In artillery fourth-order taped traverse, all distances are double taped to a comparative accuracy of 1:5,000. The recorder helps the rodman-tapeman with the taping operation.

(3) There are two instrument operators and two T2 theodolites in each fourth-order party.

d. Reduced-Strength Party. Often, enough personnel are not available for a full traverse party. In such circumstances, members of the survey party may be required to do more than one job. Shortages in personnel will never affect the jobs of the instrument operator or tapemen, since these two jobs must be done if a traverse is to be conducted. Shortages will, therefore, be apparent in the duties of rodman, computer, and computer-recorder. If the party is short one rodman, the chief of party will perform, in addition to his own duties, the duties of the rodman. If three or more members are absent from the party, the fieldwork is completed and the computations are performed later by designated personnel. The organization of a reduced-strength party is not bound by strict rules. However, for a party to function when personnel shortages exist, each party member must be trained to perform all duties.

#### 5-6. NIGHT TRAVERSE

At times, the FA surveyor will be required to survey at night to accomplish his mission. Night traverse can be done by modifying daylight techniques and organization. However, night traverses require more work, more training, more personnel, and more coordination.

a. Equipment. The same equipment used for performing daylight traverse is also used to perform night traverse with the addition of night-lighting equipment. This lighting equipment includes flashlights for all personnel and two signal lights for each range pole. If signal lights are not available, two flashlights for each range pole will suffice. All lighting devices should be equipped with filters of some type to ensure greater light security and to prevent undue glare in the telescope of the observing instrument when it is pointed at a station. The observing instrument should be equipped with its integral lighting equipment.

b. Personnel. The standard traverse party must be supplemented with additional personnel to enable it to function properly at night. Three additional men who are light holders go with and help the tapemen.

c. Station Marking. At night, the traverse stations are marked the same as in daylight except for the lighting devices required at the rear and forward stations. Two signal lights should be placed on each range pole that will be observed from a traverse station. Usually, this will include two range poles-both the rear and the forward stations. One of these lights should be placed on the pole at the height of the instrument and the other at the lowest point visible from the instrument. Both lights should be pointed directly at the observing instrument. If signal lights are not available, flashlights may be taped or securely strapped to the pole in the same manner prescribed for the target lights. To ensure that the lights are placed and pointed properly, the chief of party will designate one man to remain with the range poles and coordinate the placement and pointing of the lights with the instrument operator.

d. Angle Measuring and Recording.

(1) Angle measuring. There is no difference between measuring angles at night and measuring angles during daylight, except at night the instrument must be equipped with a night-lighting device. The chief of party should coordinate with the instrument operator to ensure that the lights at the rear and forward stations are placed and pointed properly and are moved to the next station when the observation is completed.

(2) Recording. The same recording procedures used for recording during daylight hours are used for night recording except that the recorder must have a flashlight so he can see to record. He should record in the remarks section of the field notes anything that may affect the survey, such as burnt-out lights or only one light on the forward station.

e. Distance Measurement at Night.

(1) Taping. For information on taping at night, see paragraph 2-18.

(2) SEDME. Use the same procedures at night as for daylight measurements. Lighting devices are required to orient the SEDME and reflector assembly. After the SEDME is oriented and before measurements are taken, lights at or behind the reflector assembly must be turned off. Communication between stations must be maintained.

f. Communication. Communication during a night traverse should be by radio. However, radio is not always convenient or available, and at times, the survey party must resort to light signals. These light signals should be prearranged and simple. For example, the instrument operator may have to signal the rodman to raise or lower the bottom light on a range pole or inform him to move to the next station. In arranging signals, the survey party should avoid waving lights, since a waving light may easily attract the enemy's attention. Every precaution should be taken in sending light signals to avoid detection by the enemy.

#### 5-7. TRAVERSE FIELD NOTES

For correct procedures and examples of field notes on traverse, see paragraphs 4-1 through 4-5 and Figures 4-6 and 4-7.

### TRIGONOMETRY OF TRAVERSE

The distance and azimuth between points can be used to form and compute a right triangle. The distance between points serves as the hypotenuse, and the azimuth can be used to determine an angle. Three right triangles must be solved for each leg. Three trigonometric functions are used to compute a traverse. These functions are the sine, cosine, and tangent. The sine and cosine functions are used to compute the differences in easting and northing coordinates. The tangent is used to compute the difference in height.

#### 5-8. AZIMUTH DETERMINATION

An azimuth to an azimuth mark (starting direction) may be obtained by use of the following:

• SIAGL.
• Astronomic observation.
• Computation from known coordinates.
• Reference to an existing trig list.

As the last effort, the azimuth may be scaled from a map, but an accurate azimuth must be obtained as soon as possible.

#### 5-9. EXTENDING AZIMUTH

In artillery survey, direction may be defined as the angular measurement between a specific reference line and a given line. Azimuth is the term used in artillery survey to describe direction and is the horizontal clockwise angle from a reference line (grid north [GN]) to a given line. Every line has two azimuths (a forward azimuth and a back-azimuth), depending on the observer's position on the line. In Figure 5-7, a survey is progressing from Station A toward Station B. Angle a is the forward azimuth for the line from A to B. To designate the azimuth from B to A, the Angle b is used. This is known as the back-azimuth of the line. For artillery survey purposes, the forward azimuth and the back-azimuth of a line differ by 3,200 mils (forward azimuth ±3,2000 mils = back-azimuth). To compute a traverse, an azimuth to the forward station must be determined for each leg of the traverse. This is done by adding the value of the station angle to the azimuth to the rear station. Figure 5-8 and the following example illustrate this procedure. It should be noted that on occupation of each successive station, the first step is to compute the back-azimuth of the preceding traverse leg.   #### 5-10. AZIMUTH AND DISTANCE COMPUTATIONS

In survey operations, the azimuth and distance between two stations of known coordinates must be determined. Some examples of such a requirement are the computation of the following:

• Azimuth and length of a target area base.
• Base of a triangulation scheme.
• Azimuth and distance between critical points in converting an assumed grid to a common grid.
• A starting azimuth for a control point when the coordinates of the two intervisible points are known.

#### 5-11. DA FORM 5590-R

DA Form 5590-R (Computation of Azimuth and/or Distance From Coordinates (BUCS)) (Figure 5-9) is used to record the computation of the grid azimuth and distance between two points of known coordinates. The form is designed to help the operator perform the computations. The form has five sections as discussed below. a. At the top of the form, right below the form title, you will notice six blocks. These blocks are for recording administrative information. Each block is labeled for the information required for each block. When conducting field survey operations, all required information must be entered.

b. On the left side of the form under the six administrative blocks, are the instructions for using the BUCS. These instructions consist of three columns--STEP, PROMPT, and PROCEDURE. These columns are used to compute the azimuth and distance.

(1) The STEP column specifies the sequence in which the computations must be performed.

(2) The PROMPT column indicates the display that should appear on the BUCS at each step.

(3) The PROCEDURE column lists the actions that the operator must take at each step.

c. Immediately below the INSTRUCTION section is the REMARKS: section. The REMARKS: section is used for recording any information that will help clarify the computations or survey.

d. On the right side of the form under the administrative section, is a block containing notes. The purpose of these notes is to help the operator use the form and the BUCS to compute the survey.

e. On the right side of the form under the notes is the DATA RECORD section. The blocks in the DATA RECORD section are used for recording the field data, known data and station names. This is where the known coordinates of the occupied station and the azimuth mark, the name of the occupied station and the azimuth mark, and the results of the BUCS computations are recorded. (See Table 5-1 for instructions on computing DA Form 5590-R.) (1) The blocks marked with a filled-in arrow are for recording the known coordinates. Blocks that are not marked with the filled-in arrow are for recording the computed azimuth and distance. The remaining blocks are for recording the station names.

(2) There are spaces on the form to record the results of four individual sets of azimuth and distance computations.

#### 5-12. AZIMUTH AND BEARING ANGLE RELATIONSHIP

a. An azimuth is required in traverse to permit determination of a bearing angle. The bearing angle of a traverse leg and not the azimuth is used in traverse computations to determine differences in coordinates. The bearing angle of a line is the acute angle formed by the intersection of that line with a grid north-south line. Figure 5-10 illustrates the relationship between the azimuth of a line and its bearing angle. b. In artillery survey, the horizontal plane (or circle) is divided into four quarters. Each quarter circle contains 1,600 mils and is called a quadrant. The four quadrants are numbered in a clockwise direction, since azimuths are measured in a clockwise direction. Numbering begins at grid north and proceeds around the circle, using roman numerals I through IV. (See Figure 5-10.)

#### 5-13. DETERMINATION OF BEARING ANGLE

The manner in which the bearing angle is computed from a given azimuth depends on the quadrant in which that azimuth lies. (See Figure 5-11.) a. When the azimuth is in the first quadrant (0 to 1,600 mils), the bearing angle equals the azimuth.

b. When the azimuth is in the second quadrant (1,600 to 3,200 mils), the bearing angle equals 3,200 mils minus the azimuth.

c. When the azimuth is in the third quadrant (3,200 to 4,600 mils), the bearing angle equals the azimuth minus 3,200 mils.

d. When the azimuth is in the fourth quadrant (4,600 to 6,400 mils), the bearing angle equals 6,400 mils minus the azimuth.

#### 5-14. TRIGONOMETRY AND THE TRAVERSE LEG

a. If the coordinates of a point are known and the azimuth and distance from that point to a second point are known, the coordinates of the second point can be determined. In Figure 5-12, the coordinates of Station A are known and the coordinate of TS 1 are to be determined. The azimuth and distance from Station A to TS 1 have been determined by turning the horizontal angle at Station A from the azimuth mark to TS 1 and by measuring the horizontal distance from Station A to TS 1. b. Determining the coordinates of TS 1 requires the solution of a right triangle. The intersection of the north-south line through Station A and the east-west line through TS 1 forms a right angle (1,600 mils or 90°). The known side (A to TS 1) (measured distance) becomes the hypotenuse, and the bearing angle at Station A is determined from the azimuth of Station A to TS 1. Thus, a right triangle is formed.

#### 5-15. COORDINATE COMPUTATIONS

The two unknown sides of this right triangle are designated as the difference in easting (dE) and the difference in northing (dN). To compute the length of sides dE and dN, use two of the trigonometric functions of a right triangle. To determine dE, use the following formula: Note. When using a BUCS or a calculator capable of performing logarithms, enter the formula as follows: Distance (Hypotenuse) x SIN (bearing angle x .05625) END LINE = dE

To determine dN, use the following formula: Note. When using a BUCS or a calculator capable of performing logarithms, enter the formula as follows: Distance (Hypotenuse) x COS (bearing angle x .05625) END LINE = dN

To determine the coodinates of the unknown point (TS 1), algebraically add the difference in easting to the easting coordinate of the known point (Station A) and the difference in northing to the northing coordinate of the known point (Station A). In Figure 5-13, for the traverse leg appearing in the first quadrant, the dE and dN must be added to the easting and northing coordinates of Station A. For the traverse legs in the other quadrants, the signs of the dE and dN change. In all instances, the quadrant in which the traverse leg lies determines if dE and dN are added to or subtracted from coordinates of Station A. (See Figure 5-13.) #### 5-16. DETERMINATION OF dH

a. In a traverse, the FA surveyor must determine the height of each of the unknown stations in relation to the height of the starting (known) station. He does this by computing the difference in height (dH) between the occupied station and the forward station. Through the solution of a right triangle, the vertical angle at the occupied station and the measured horizontal distance to the forward station are used to determine the difference in height between the two stations. This difference is then added to or subtracted from the known height at the occupied station.

b. In Figure 5-14, the measured distance is the horizontal distance from Station A to Station B. The vertical angle at Station A is measured to the height of instrument at Station B (AA is the height of instrument at Station A, and BB is the height of instrument at Station B). Both of the heights are the distance from the known ground elevation at Station A to the horizontal axis of the telescope of the instrument being used. AA' is equal to BB'. The height of instrument must be determined and marked on the range pole at the forward station. The difference in height between the two stations is side CB of the right triangle. Determine dH as follows : Note. When using a BUCS or a calculator capable of performing logarithms, enter the formula as follows: Distance (Hypotenuse) x TAN (vertical angle x .05625) END LINE = dH The dH computed is actually the difference in height at ground level between the two stations. The computed dH is added to or subtracted from the height of the known station according to the sign of the measured vertical angle.

#### 5-17. UNIVERSAL TRANSVERSE MERCATOR GRID

The grid coordinates used most often in survey computations are coordinates based on the UTM grid system. These coordinates differ from the military grid reference system in that the grid reference of a point has a grid zone designator and a 100,000-meter square identification. The grid zone designator and 100,000-meter identification replace the false easting and northing digits of UTM grid coordinates. In the lower margin of military maps, the grid reference box shows the grid zone designator and 100,000-meter identification for that map sheet. For a detailed discussion of map reading, see FM 21-26, Chapter 4, page 4-17, Figure 4-14, and paragraph 4-4c(1).

### TRAVERSE COMPUTATIONS

Survey computations can be performed in any mathematical sequence that will produce the correct solution. However, for the purpose of simplicity and uniformity, Department of the Army has devised standardized forms for use in performing survey computations. Accurate and timely computations are the key to a successful survey. Computations performed on a standard form are easily checked, adjusted, and filed when necessary.

#### 5-18. COMPUTING THE TRAVERSE LEG

a. To determine the coordinates of the unknown point, the azimuth and distance from the known point to the first unknown station are used.

b. Determining the coordinates of the first unknown point requires the use of DA Form 5591-R. (See Figures 5-15 and 5-16.)  #### 5-19. DETERMINATION OF HEIGHT

In a traverse, the FA surveyor must determine the height of each of the unknown stations in relation to the height of the starting (known) station. The vertical angle at the occupied station and the measured horizontal distance to the forward station are used to determine the height of the unknown station.

#### 5-20. DA FORM 5591-R

a. DA Form 5591-R is the form on which traverse computations are recorded. It is used in conjunction with Program 2 (BUCS, SURVEY REV1) to determine coordinates and height from azimuth, distance, and vertical angle of main scheme traverse stations. The program also converts slope distance to horizontal distance and computes the total traverse length, total azimuth and height corrections, radial error of closure, accuracy ratio, and traverse adjustment.

b. Entries on the form are discussed below. (Instructions for completing the front and reverse sides of DA Form 5591-R are in Tables 5-2 and 5-3.)    (1) The known data of the starting and closing stations and the traverse field data are required by the BUCS. The known starting and closing data consist of the coordinates and height of the starting and closing stations and a line of known azimuth at each of the stations. The traverse field data consist of horizontal and vertical angles measured at each station and the distance between the traverse stations.

(2) The user must enter the known starting station data and then the traverse field data. The traverse field data must be entered in the same sequence that the traverse stations were encountered in the field operations.

(3) The operator must enter the known closing station data to allow computation of the following:

• Total traverse distance.
• Total azimuth and height corrections.
• Traverse accuracy ratio.

(See Figure 5-16.)

(4) The basic design of DA Form 5591-R is the same as DA Form 5590-R. In the DATA RECORD section, there are spaces for recording the starting data, the field data for four traverse stations, and the computed data for three traverse stations. The computed data for the fourth station must be recorded on another form. Additional forms are used as required. Closure and adjustment data are recorded on the reverse side of the form.

(5) The administrative information is entered in the six spaces provided on the top of each form. When a survey operation is conducted, all information must be recorded.

(6) The names of the stations are entered in the blocks on the left side of the DATA RECORD section. Start with the REAR STATION: block, and then complete the STATION NAME: blocks for the forward and known stations. Number the known station 1. Each station name in a traverse must be written and numbered.

(7) The coordinates of the known point are recorded in the EASTING: and NORTHING: blocks of the DATA RECORD section.

(8) The height of the known point is recorded in the HEIGHT (METERS): block, The height is obtained from a trig list of local survey control.

(9) The azimuth from the known point to an azimuth mark is recorded in the AZIMUTH TO REAR (MILS): block.

(10) The next information recorded on the form is the measured field data--horizontal angles, vertical angles (with sign and whether reciprocal or nonreciprocal noted), and the distances (whether horizontal or slope noted). The field data must be obtained from the recorder. The recorder also provides the station names. Enter the data in the blocks with the black triangle.

c. The computer is now ready to compute the first leg of the traverse.

d. The reverse side of DA Form 5591-R is used to record the closing data for the survey just computed. The format of the front and reverse sides of the form is similar. The DATA RECORD section has spaces for recording the known closing data, the measured closing horizontal angle, the computed closing data, and the adjusted data for four stations. Fifth-order surveys are not adjusted.

 Note. If the response in step 17 is Y; END LINE, the steps in e and f below are followed.

e. If the computer wishes to compute closure data, he must record the known data of the closing station on the reverse side of the form. He records these data as discussed below.

(1) Record the closing horizontal angle in the CLOSING ANGLE (MILS): block. The angle is obtained from the recorder.

(2) Record the known closing azimuth in the KNOWN AZIMUTH FORWARD (MILS): block. This azimuth may be determined from a trig list, by using an azimuth gyro, by astronomic observation, by computation, or by PADS.

(3) Record the known height in the KNOWN HEIGHT (METERS): block the known easting in the KNOWN EASTING: block, and the known northing in the KNOWN NORTHING: block. These data may be obtained from a trig list, or they could be provided by the supporting survey element.

f. The computer ensures the BUCS is still displaying the prompt CLOSURE (Y/N): The actions required to compute the closing data are to press the Y key and then the END LINE key. The BUCS now starts computing the closing data for the survey.

#### 5-21. RECIPROCAL MEASUREMENT OF VERTICAL ANGLES

The effects of the curvature of the earth and atmospheric refraction must be considered for traverse legs in excess of 1,000 meters. Vertical angles at each end of such a leg are measured to compensate for these effects. When vertical angles are measured reciprocally, the vertical angle at each end of the leg should be measured to the same height above the station (normally the HI).

#### 5-22. ACCURACY RATIO

a. Certain minimum accuracy requirements are prescribed for survey fieldwork and computations. These accuracies are based on the requirements of installations to be surveyed (howitzer position or molar position). To determine whether this accuracy requirement has been met for a closed traverse, an accuracy ratio is computed. If the accuracy requirement is not met and the errors cannot be determined, the traverse must be performed again.

b. An accuracy ratio is expressed as a ratio between the radial error of closure and the total length of the traverse (for example, 1:3,000, 1:1,000). It may also be expressed as a fraction with a numerator of 1 (for example, 1/3000, 1/1000). The radial error of closure is the linear distance between the known coordinates of the closing point and the computed coordinates of the closing point as determined from the survey. The total length of the traverse is the sum of the lengths of all traverse legs (excluding distances to offset stations). The numerator of the accuracy ratio is 1; the denominator is equal to the total length of the traverse divided by the radial error of closure. The equation for the accuracy ratio is as follows: c. After the accuracy ratio has been computed, the denominator of the fraction is always reduced to the next lower hundred (for example, 1/3879 becomes 1/3800).

#### 5-23. RADIAL ERROR OF CLOSURE

a. The radial error of closure is determined by comparing the correct coordinates of the closing point with the computed coordinates of that point and determining the differences. The difference between the two eastings of the closing point, or error in easting (eE), forms one side of a right triangle. The difference between the two northings of the closing point, or error in northing (eN), forms the second side of the triangle. The hypotenuse of this right triangle is the radial error of closure. (See Figure 5-17.) It is computed by using DA Form 5590-R or the Pythagorean theorem. From the Pythagorean theorem, it is derived that the radial error of closure is equal to the square root of the sum of the square of the error in easting and the square of the error in northing. The equation for computing the radial error is as follows:   If computed by using the BUCS, the equation is computed as follows:

SQR(.56^2 + .72^2) END LINE = .91

b. The maximum allowable error in position closure for a fourth-order traverse generally is expressed as 1:3,000, or 1 unit of radial error for each 3,000 similar units of traverse. A maximum allowable radial error for a fourth-order survey is determined in one of two ways. If the traverse is less than 9,000 meters in length, the maximum allowable radial error is determined by dividing the total length of the traverse by 3,000. For example, in a 3,469.91-meter fourth-order traverse, the maximum allowable radial error by the 1:3,000 evaluation is 1.15 meters (3,469.91 ÷ 3,000). When the traverse length exceeds 9,000 meters (9 km), the accuracy achieved may be within 1:3,000 yet the radial error will be excessive. Therefore, the maximum allowable radial error (AE) is determined by the following formula: in which AE = allowable radial error and K = total (main scheme) length of the traverse to the nearest 0.1 km.

For example, using the 1:3,000 evaluation in a traverse 37.3 km in length would allow a maximum radial error of 12.4 meters (37,300 ÷ 3,000). Whereas, would allow a maximum radial error of 6.1 meters . The result of the method used will then be compared with the radial error computed for the traverse to determine if the traverse radial error meets the requirement. The traverse must be rerun when the radial error exceeds the computed maximum allowable radial error and no error can be determined. #### 5-24. CLOSING AZIMUTH ERROR

The closing azimuth error is determined by comparing the known closing azimuth with the closing azimuth determined by the traverse. The difference between the two is the closing azimuth error. The error is considered to be within tolerance if it does not exceed 0.1 mil per main scheme angle for fifth-order traverse. Fourth-order traverses are evaluated for azimuth closure in two ways. If the number of main scheme angles is six or less, multiply the number of main scheme angles by 0.04. For traverses of seven or more main scheme angles, multiply the square root of the number of main scheme angles by 0.1 (Appendix B).

#### 5-25. ACCURACIES, SPECIFICATIONS, AND TECHNIQUES

The overall accuracy of a traverse depends on the equipment and methods used in the measurements, the accuracy achieved during the fieldwork, and the accuracy of the starting and closing data.

a. Fourth-Order Accuracy. Normally, fourth-order surveys are performed by the div arty survey platoon and the TAB survey platoon to extend survey control to using units. The maximum allowable error in position closure for an artillery fourth-order traverse generally is expressed as 1:3,000, or 1 unit of radial error for each 3,000 similar units of traverse executed. A fourth-order traverse starting from existing survey control must start and close on stations established to fourth-order accuracy or higher. If survey control of the required accuracy is not available, the fieldwork and computations can be computed and the traverse evaluated for accuracy (accuracy ratio determined) by using assumed starting data, provided the traverse is ended at the starting station. The T2 theodolite is used to measure the angles. Horizontal angles are measured as one-position angles (1 D/R). Vertical readings are taken once with the telescope in the direct position and once in the reverse position (1 D/R). The vertical angle is then computed. If traverse legs are greater than 1,000 meters in length, vertical readings must be observed reciprocally. Distances are double taped with the 30-meter steel tape to a comparative accuracy of 1:5,000. When the SEDME is used, three readings must be taken to determine the distance.

(1) Position accuracy. The procedure used to evaluate the position accuracy of a fourth-order traverse depends on the length of the main scheme of the traverse. Traverses of less than 9,000 meters in main scheme length are evaluated by determining accuracy ratios as explained in paragraph 5-23b. However, when the traverse length exceeds 9,000 meters, the accuracy achieved may be excessive. Therefore, when the main scheme length of the traverse exceeds 9,000 meters (9 km), the maximum allowable radial error is computed by the formula , in which K is the total length of the traverse to the nearest 0.1 km. Therefore, in this example, 3.85 meters is the maximum allowable radial error for the traverse length. If the radial error of the traverse exceeds 3.85 meters and no errors are determined, the traverse must be rerun.

(2) Azimuth closure. The allowable error in azimuth closure depends on the number of main scheme angles used in carrying the azimuth through the traverse. If the traverse exceeds 25 main scheme angles, then azimuth must be checked by comparing the computed azimuth with an astronomic azimuth, gyroscopic azimuth, a preestablished azimuth or a PADS azimuth. The allowable azimuth error in mils for a traverse having no more than six main scheme angles is computed by the formula AE = 0.04 x N, in which N is the number of main scheme angles used to carry azimuth. If there are more than six main scheme angles in the traverse, the allowable azimuth error is computed by the formula (3) Height accuracy. The allowable error in meters for the height closure of a traverse of any length performed to fourth-order accuracy is also computed by the formula .

b. Fifth-Order Accuracy. Normally, FA battalions perform fifth-order survey to establish survey control for the firing units of the battalion. A fifth-order traverse starting from existing control must start and close on stations established to fifth-order accuracy or greater. When survey control of the required accuracy is not available, the fieldwork and computations can be completed and the traverse evaluated for accuracy (accuracy ratio) by using assumed starting data, provided the traverse is closed on the starting station. The T16 theodolite is used to measure the angles. Horizontal angles are turned one position with the T16 theodolite. Vertical readings are taken once with the telescope in the direct position and once with the telescope in the reverse position (1 D/R), The vertical angle is then computed. Distances, when measured with the 30-meter steel tape, are single taped and checked for gross errors by pacing. When distances are measured with the SEDME, three readings will be taken.

(1) Position accuracy. The maximum allowable error in position closure is expressed by the accuracy ratio of 1:1,000, or 1 unit of error for each 1,000 similar units of traverse executed.

(2) Azimuth closure. The allowable error in azimuth closure is computed by the formula AE = 0.1 mil x N, in which N is the number of main scheme angles in the traverse. After 20 main scheme angles, azimuth must be checked by comparing the computed azimuth with an astronomic azimuth gyroscopic azimuth, a preestablished azimuth, or a PADS azimuth.

(3) Height accuracy. The maximum allowable error in height closure is 2 meters for traverses of less than 4,000 meters. For traverses over 4,000 meters, use the formula
AE = to compute allowable error.

### TRIG TRAVERSE

When a traverse is conducted in the field, it may be impossible to tape or electronically measure a traverse leg because of the terrain, electrical interference, or equipment failure. If this occurs, a method known as trig traverse may be used. When properly executed, this method is adequate for accomplishing fourth- and fifth-order traverse requirements. The trig traverse method uses the triangular figure, the base of which is carefully measured.

#### 5-26. METHOD

In the trig traverse method, the base of the triangle need not be established perpendicular to the required side of the triangle but may be established at an angle more convenient for measurement. When possible, however, it should be placed perpendicular to the required side by using the theodolite to place the base ends at right angles to the desired side. If it is not possible to make the base perpendicular, the angle formed by the base and the desired side must be measured. The base must be long enough to minimize the effects of instrumental error on the distance to be measured. To do this, the base must be longer than one-twentieth and preferably about one-tenth of the distance to be determined. In Figure 5-18, the length to be determined is the line AB. Two independent bases are measured to offset the slight inaccuracy that will prevail in the base measurement and to provide a check on the work. The bases are shown by the lines BC1 and BC2. The shortest base should not be less than one-twentieth of the required distance. #### 5-27. BASE ACCURACY

The accuracy of the base measurement is the key to a successful trig traverse. When the base length is one-twentieth of the required side and an error of 0.01 meter was made in determining the length of the base, the result is an error of 0.20 meter in determining the computed length of the base. Each base should be double taped separately within a comparative accuracy of 1:7,000 for fourth order and 1:3,000 for fifth order. The distance C1 to C2 is also measured to provide a check. Reasonable control over the accuracy of the distance measurements can be exercised by limiting the ratio of the length of the base to the length to be computed.

#### 5-28. ANGLES

a. In fourth-order survey, the T2 theodolite is used for angle measurement. Two-position horizontal angles are measured. If the two measured values for any angle differ by more than 0.050 mil, these angles will be rejected and remeasured.

b. In fifth-order survey, the T16 theodolite is used for angle measurement. One-position horizontal angles are measured.

#### 5-29. TARGETS

Because of the very short distance to the end of the base, the targets must be designed for accurate pointings. The string of a suspended plumb bob or a sharpened pencil point may be sighted on. On longer bases, a range pole may be used, provided the range pole is very carefully plumbed over the point. If available, a tripod-mounted target may also be used. It also must be carefully leveled and plumbed over the point.

#### 5-30. DISTANCE COMPUTATION

Two independent lengths (AB1 and AB2) are computed, one from each base. The mean of the two computed lengths is the required distance. A comparative accuracy is computed to determine the reliability of the computed distance. For fourth-order survey, the required side accuracy must be at least 1:5,000; and for fifth-order survey, at least 1:1,000. Computations for perpendicular and non-perpendicular bases without the use of DA forms are described below.

AB1 = cot Q1 x BC1

AB2 = cot Q2 x BC2

b. Nonperpendicular Base. When the base is not perpendicular, the distance is computed by using the following formulas: Y is the angle formed by the base and the required side. See the nonperpendicular base in Figure 5-18.

#### 5-31. DA FORM 5603-R

Trig traverse is computed with the BUCS and by using DA Form 5603-R (Computation of Trig Traverse/Subtense (BUCS)). (A reproducible copy of this form is included in the Blank Forms section.) This form follows the same basic format of the BUCS forms used in computing the traverse.

a. The top of the form is for recording administrative data. Data in this area include the following:

• Computer.
• Name of the individual who checks the computations (checker).
• Area in which survey was performed.
• Notebook reference.
• Date computations were performed.
• Identification of the sheet number.

b. The next part of the form provides notes for the specific operations of the program and other notes needed to complete the form.

c. The next part of the form is divided into two major sections. The section on the left provides instructions for the operator to complete the program.

(1) The right section is for recording data--both field and computed. Two trig traverses may be computed on each form.

(2) The left section is divided in three columns--STEP, PROMPT, and PROCEDURE. The STEP column is the numerical sequence the operator uses as he proceeds down the form. The PROMPT column tells the operator what will appear on the BUCS display at each particular step. The PROCEDURE column tells the operator what action he should take at each particular step or prompt.  ### LOCATION OF TRAVERSE ERRORS

A good survey plan executed by a well-trained party provides for numerous checks in both computations and fieldwork. However, these checks do not always eliminate errors. On the contrary, errors made both in fieldwork and in computations often are not discovered until the survey has been completed. The FA surveyor must, therefore, be able to isolate these errors and determine their causes. Often, a critical analysis of both the fieldwork and the computations of a survey in error will save additional hours of repetitious labor and computation.

#### 5-32. ANALYSIS OF TRAVERSE FOR ERRORS

To rapidly analyze a survey, a wel1-trained chief of survey party will maintain a sketch of the fieldwork, to scale, of each survey as it is being conducted. If a reliable map is available, it will allow him to check errors that may occur in either the fieldwork or the computations. If, upon completion of the survey, an error is apparent, then the following assumptions can be made. To isolate an error in a traverse, an assumption must be made that only one error exists. If more than one error exists, isolation of the error may not be possible. Under some conditions, when there is more than one error in a traverse, an apparent solution will exist; however, an investigation of the error isolated may show that both fieldwork and computations are correct for the station in question. When this condition exists, no effort should be made to continue an analysis. Instead, provisions should be made to perform the entire traverse again. Table 5-5 lists the error indicators and the type of error for a traverse closed on the starting point and closed on a second known point. This table assumes that only one error is made. #### 5-33. ISOLATION OF DISTANCE ERRORS

a. A distance error is indicated when the azimuth for the traverse closes within tolerance but coordinate closure is in error beyond the limits allowed for the prescribed accuracy.

b. Compare the known coordinates of the point on which the survey was closed to the computed coordinates determined by the survey. From this comparison, determine the error in easting and the error in northing. Note the sign of each error, and compute the azimuth from the known coordinates of the closing station to the computed coordinates of the closing station on DA Form 5590-R. The traverse leg containing the distance error will have the same azimuth (or back-azimuth) as the azimuth computed. (See Figure 5-20.) The distance computed will be the radial error. In analyzing an error of this nature, some tolerance and judgement must be used to determine the traverse leg in error. This is because in both angular and distance measurements, minor errors occur that are too small to affect the overall accuracy but are large enough to make error analysis difficult. Under some circumstances, several legs with azimuths approximating the azimuths of the radial error could contain the distance error. Check computations for each suspected leg. If there is no error in computations, then each suspected leg must be remeasured until the leg containing the error is found. #### 5-34. ISOLATION OF AZIMUTH ERRORS

a. Indication of Azimuth Error. An azimuth error is indicated when the azimuth does not close within required tolerance and coordinate closure is in error beyond the limits allowed for the prescribed accuracy.

b. Isolation Procedure. Compare the computed azimuth to the known azimuth of the closing point, and determine the azimuth error. Compare the computed coordinates of the closing station to the known coordinates, and determine the error in easting and the error in northing. Compute the distance (RE) and azimuth of the radial error by using DA Form 5590-R, the known coordinates of the closing station, and the computed coordinates of the closing station. Using a scaled sketch of the traverse, construct a line perpendicular to, and at the midpoint of, the plotted radial error line. Extend this line in the appropriate direction through the area in which the fieldwork was executed. (See Figure 5-21.) The suspect station at which the angle error was made will be on or very near the extended line. c. Corrective Procedure. After the suspect station is located, a check should be made of computations at the station to include the angular values in the field notes recorded for that station. If there was no error in meaning of angles, the angle for the station should be remeasured and compared with the recorded angle measured as a part of the original survey. This procedure will reveal the error, if one exists. If the remeasured angle compares favorably with the recorded angle, a multiple error exists in the survey and a solution is not possible. When this situation occurs, the survey should be rerun to determine the location of the errors.

d. Alternate Solution. The tria1-and-error method is another method that may be used to determine the location of the angular error when a graphical plot of the survey is not available or the perpendicular method does not isolate one station. To determine suspect stations (stations where the error may exist) by this method, first compute the distance between the correct coordinates of the closing station and the computed coordinates of the closing station. Second, determine the amount the azimuth is in error by comparing the closing azimuth with the correct grid azimuth at the closing station. Third, substitute the distance error and the azimuth error into the mil relation formula (w/r = m), and determine the approximate distance (in kilometers) from the closing station to the station in error. By this procedure, one or more suspect stations may be determined. Then use the trial-and-error method and systematic elimination to locate the suspect station in error. Using the coordinates of the suspect station and the known coordinates of the closing station, compute the azimuth and distance between the two. Using the coordinates of the suspect station and the computed coordinate of the closing station, compute an additional azimuth and distance between these two. Compare the results with the azimuth and distance first determined. If the error is at the suspect station, the azimuth should vary by the amount of the azimuth error of closure and distances should agree relatively closely. If the error is not at the suspect station, the azimuth will disagree but not by an amount equivalent to the azimuth closure error. (See Figure 5-22.)  #### 5-35. ISOLATION OF MULTIPLE ERRORS

Multiple errors are errors in both azimuth and distance or more than one error in either azimuth or distance. When there are multiple errors in a traverse, the indications will be the same as for an azimuth error. It is possible that in the procedure for azimuth error determination, definite suspect stations will be located but an analysis of the fieldwork and computations at these stations will not produce the error. When this occurs, the entire traverse should be performed again to locate the errors that were made.

### Section VI

 Note. The BUCS will perform these adjustments if required.

#### 5-36. SOURCES OF ERRORS

The errors for which traverse adjustment compensates are not those errors commonly known as mistakes or blunders but are errors that fall into one of the classes discussed below.

b. Personnel Errors. These are errors that arise from the limitations of the human senses of sight and touch. For example, an error might be made in estimating the tension applied to a steel tape or in plumbing a plumb bob over a point.

c. Natural Errors. Natural errors arise from variation in the phenomena of nature, such as temperature, humidity, wind, gravity, and refraction. For example, the length of a tape varies directly with the temperature. The tape becomes longer as the temperature increases and shorter as the temperature decreases.

a. Determining Azimuth Correction. Since the computation of position depends partly on azimuth, the first step in adjusting a traverse is to determine the azimuth error and adjust the azimuth. The azimuth error is obtained by determining the difference between the azimuth established by traverse (computed) and the known azimuth at the closing point. The azimuth correction is the azimuth error with the proper sign affixed so that the computed azimuth with the azimuth correction applied will equal the known azimuth.

 EXAMPLE A traverse is performed from Point A to Point B. The azimuth from Point B to an azimuth mark is known to be 4,794.529 mils and was used as the closing azimuth. However, the azimuth to the same point from point B derived from the traverse (computed azimuth) was 4,794.459 mils. Therefore, the azimuth error for this traverse was 0.070 mil (4,794.529 - 4,794.459).

b. Application of Azimuth Correction. Since traverse adjustment is based on the assumption that errors present have accumulated gradually and systematically throughout the traverse, the azimuth correction is applied accordingly. The correction is distributed equally among the angles of the traverse with any remainder distributed to the larger angles. For example, assume that the traverse for which the azimuth correction was determined consisted of three traverse legs and four angles. The azimuth correction is divided by the total number of angles. In this case, +0.070 mil ÷ 4 = 0.017 mil per angle with a remainder of 0.002 mil. Each of the four angles will be adjusted by 0.017 mil, and the two largest angles will be adjusted by an additional 0.001 mil each to compensate for the remaining 0.002 mil. c. Action After Adjustment. After the angles have been adjusted, the adjusted azimuth of each leg of the traverse should be recomputed by using the starting azimuth and adjusted angles at each traverse station. These computations should be performed on clean copies of DA Form 5591-R, not on the forms used for the original computations. The adjusted azimuth should be computed throughout the entire traverse and checked against the correct azimuth to the closing azimuth mark before adjusting the coordinates After the azimuth of each traverse leg has been adjusted, the coordinates of the stations in the traverse must be adjusted. The first step in adjusting the coordinates is to recompute the coordinates of all stations in the traverse, using the adjusted azimuths. It is now assumed that all azimuth error has been eliminated. Any remaining error is assumed to be a distance error. a. Determining Easting and Northing Corrections. The easting and northing corrections for the traverse are determined by algebraically subtracting the coordinates of the closing station (as recomputed with the adjusted azimuth) from the known coordinates of the closing station.

b. Application of Easting and Northing Corrections. The corrections determined in a above are for an entire traverse. It is assumed that these corrections are based on errors proportionately accumulated throughout the traverse. Therefore, the corrections must be distributed proportionately throughout the traverse. The amount of easting or northing correction to be applied to the coordinates of each station is computed by multiplying the total correction (easting or northing) by the total length of all the traverse legs up to that station and dividing the result by the total length of all of the legs in the traverse. For example, using the total easting and northing corrections previously determined, assume the total length of the traverse is 22,216.89 meters and the total length of the traverse legs up to TS 4 is 3,846.35 meters. a. Height adjustment is based on the assumption that the error of closure of height is accumulated throughout the traverse in equal amounts at each traverse station and not proportionately to the length of the traverse legs. Errors caused by this assumption have no effect for FA purposes.

b. The height correction is the error in height with the sign reversed. It is determined by comparing the height of the closing point established by the traverse with the known height of the closing point and applying a sign (±) that will cause the established height, with the algebraic correction applied, to equal the known height. For example, if the known height is 478.3 meters and the computed height (established by traverse) is 477.5 meters, the height correction would be 0.8 meter (478.3 - 477.5). For the height determined by traverse to equal the correct height, 0.8 meter would have to be added to the height of the closing station determined by traverse.

c. The height correction is distributed equally among the stations of the traverse with any remainder distributed to those stations computed from the longest legs. Assume that the traverse for which the height correction was determined consists of four stations. To distribute the height correction throughout the traverse, divide the height correction by the total number of stations in the traverse excluding the starting station (a known height). In this case, 0.8 meter ÷ 3 stations = 0.2 meter with a remainder of 0.2 meter to be divided and applied equally to those stations computed from the longest legs. The adjustment would be as shown in the example below. The adjustment is an accumulation of the correction, since the correction is applied to the differences in height between the stations and not directly to the station heights. The height adjustment can be made on the same form and at the same time that coordinate adjustments are being made. 