FM 6-2 Chptr 11 Conversion and Transformation

CHAPTER 11 CONVERSION AND TRANSFORMATION

Universal transverse mercator grid zones are 6° wide. There are 60 such zones surrounding the earth. At the equator, each of these zones is about 360 nautical miles wide. When moving north or south from the equator, each zone decreases in width. In the UTM grid system, there are overlap areas east and west of zone junctions. It is very possible that survey operations will take place at the junctions of these zones. It is also probable that missiles and longer-range field artillery will be required to fire from one zone to another. Since FA operations will span such large areas, survey personnel may have to transform coordinates and/or azimuth from one zone to another. They may have to convert geographic coordinates to UTM grid coordinates in areas where existing survey is available only in geographic coordinates. Survey personnel may also need to convert UTM coordinates to geographic coordinates for the purpose of computing astro observations.

Section I

CONVERTING GEOGRAPHIC COORDINATES TO UTM COORDINATES AND UTM COORDINATES TO GEOGRAPHIC COORDINATES

Conversion computations depend on the method of computation and the spheroid that is used for a particular locality. To determine the spheroid for a particular locality, refer to local trig lists, maps, or higher HQ.

11-1. CONVERSION OF GEOGRAPHIC COORDINATES TO UTM COORDINATES COMPUTATION

The BUCS is the primary means of conversion computations. DA Form 5600-R (Computation--Conversion of Geographic Coordinates to UTM Coordinates (BUCS)) is used for computations of conversion. (See Figure 11-1). (A reproducible copy of this form is indcluded in the Blank Forms section of this book.)The correct spheroid must be determined.

a. DA Form 5600-R follows the same basic format of the other BUCS forms. The top of the form is for recording administrative data. Data in this area include the following:

Computer's name.

Checker's name.

Area in which the survey was performed.

Notebook reference.

Date the computations were performed.

Block to identify the sheet number.

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

c. The next part of the form is divided into two major columns. The column on the left provides instructions for the computer to use the program. The right column is for recording data. Two conversions can be computed on each form.

d. The left column is divided into three smaller columns--STEP, PROMPT, and PROCEDURE. The STEP column is the numerical sequence the computer uses as he proceeds down the form. The PROMPT column tells the computer what will appear on the BUCS display at each particular step. The PROCEDURE column tells the computer the action he will take at each particular step or prompt.

e. The procedures for computing DA Form 5600-R are shown in Table 11-1.

11-2. CONVERSION OF UTM COORDINATES TO GEOGRAPHIC COORDINATES COMPUTATIONS

a. Geographic coordinates are required for the computation of certain methods of astro observation. Often UTM coordinates will be the only data available. In these situations, the surveyor must convert the UTM grid coordinates to geographic coordinates.

b. The computation of conversion from UTM coordinates to geographic coordinates is performed on DA Form 5601-R (Computation--Conversion of UTM Coordinates to Geographic Coordinates (BUCS)) by using the BUCS. (See Figure 11-2.) The procedures for computing DA Form 5601-R are shown in Table 11-2.

Section II

ZONE-TO-ZONE TRANSFORMATIONS

When a combat area includes more than one grid zone, transformation may be required. In the UTM grid system, there are overlap areas east and west of zone junctions; however, transformation is not restricted to these overlap areas. Grid coordinates and azimuths can be transformed from any point in one zone into terms of an adjacent zone.

11-3. TRANSFORMATION OF COORDINATES AND AZIMUTH

a. The point of origin for northing coordinates is the equator. The point of origin for easting coordinates is the central meridian (CM) of each grid zone. The CM is given a false value of 500,000. Easting coordinates increase as you move east and decrease as you move west.

b. Figure 11-3 shows two adjacent UTM zones--14 and 15. Visualize Point P located in zone 14. The coordinates shown for Point P are (800,000 and 3,700,000). If the coordinates of Point P were to be transformed to the adjacent grid (zone 15), the action taken would be equivalent to superimposing grid zone 15 over grid zone 14 as indicated in Figure 11-3. Actually, the transformation of coordinates involves only the mathematical continuation of the adjacent grid to the grid being used and the subsequent corrections for location caused by the change in grid north reference. In Figure 11-3, although the location of Point P on the ground is unchanged, the values of the coordinates will change with transformation. The values in terms of zone 15 would be less than 100,000 meters in easting and greater than 3,700,000 meters in northing. From this figure, it is obvious that in the transformation of coordinates, the easting coordinates will change appreciably because of the coordinate numbering system of each zone and the change in grid north reference. There will be only a small change in northing coordinates based only on the difference in the grid north reference.

11-4. TRANSFORMATION COMPUTATIONS

The BUCS is the primary means of computing transformation. DA Form 5602-R (Computation--Zone-to-Zone Transformation--UTM Grid Coordinates and UTM Grid Azimuth (BUCS)) is used for computations. (See Figure 11-4.) (A reproducible copy of this form is included in the Blank Forms section of this book.) This form follows the same basic format of the BUCS forms previously discussed. Table 11-3 shows the instructions for computing DA Form 5602-R.

Section III

DATUM-TO-DATUM TRANSFORMATIONS

Maps, trig lists, and other survey information are prepared and published on the basis of a specific datum. As new products with new datums are developed by DMA, a variety of conflicting maps and survey information may exist that cover identical areas. Some of these products may be based on the old datum and others on the current (preferred) datum. To operate on a common grid, all fire support systems must use the same datum. Survey elements, fire direction centers, and target-detecting systems must be able to perform datum-to-datum coordinate transformations (DDCT).

11-5. ELLIPSOIDS AND DATUMS

a. The earth is not a sphere, but an ellipsoid (or spheroid), flattened slightly at the poles and bulging somewhat at the equator. An ellipsoid is a mathematical figure generated by the revolution of an ellipse about one of its axis. (See Figure 11-5.) The ellipsoid is used as a surface of reference for the mathematical reduction of geodetic and cartographic data.

b. A datum is any numerical or geometrical set of quantities specifying the reference coordinate system used for geodetic control in the calculation of coordinates of points on the earth. Datums may be either global or local in extent. A local datum defines a coordinate system that is used only over a region of limited extent. A global datum specifies the center of the reference ellipsoid to be located at the earth's center of mass.

c. The Defense Mapping Agency (DMA) TM 8358.1 identifies five preferred ellipsoids for the purpose of new map production. The DMA has identified 21 preferred geodetic datums within the various ellipsoids. At present, there are over 1,000 datums in use worldwide. Currently, TM 5-241-1 is being used to determine spheroids and datums; however, DMA TM 8358.1 replaces it.

d. The coordinates of a point based on one datum will show a difference when compared to the same point based on another datum. In extreme cases, the difference will exceed 1,000 meters radial error. Figure 11-6 shows an example of the difference between datums for the same map area.

e. The problem of transforming survey information between datums exists because each of the ellipsoids assumes a slightly different dimension for the earth (the semimajor axis, semiminor axis, and the flattening of the ellipsoid). This problem is further compounded by the datums within each of the ellipsoids. Each datum has its own point of origin on which the major survey network throughout an area is adjusted.

11-6. BUCS DDCT MODULE

The BUCS DDCT module has three programs--Program 14 (listed datums), Program 15 (Gauss-Kruger), and Program 16 (user-defined).

a. Program 14--Listed Datums. Transforms UTM and/or geographic (gee) coordinates between datums listed in DMA TR 8350.2. The program also performs zone-to-zone transformations when selected.

b. Program 15--Gauss-Kruger. Transforms Gauss-Kruger (GK) coordinates (UTM and/or geo) to UTM coordinates. The GK datums are used primarily in Warsaw Pact countries.

c. Program 16--User-Defined. Transforms UTM and/or geo coordinates between a user-defined datum and listed datums or another user-defined datum. The DMA or a higher HQ will disseminate user-defined datum parameters when needed.

Note. Datum shifts performed between WGS-72 and any other datum by using Program 14 or 15 do not produce the same solutions as Program 16 when inputting the transformation parameters as user defined datums. This occurs because a more accurate formula for WGS-72 is used in Programs 14 and 15. Program 16 uses the abridged Molodensky formulas and datum shifts for WGS-72. Program 16 is used for datum transformations only when directed by a higher HQ and specific parameters are provided.

11-7. BUCS DDCT APPLICATION

Note. The DDCT program prints a blank form for each program when attached to the BUCS printer.

The primary function of the BUCS DDCT module is the computation of coordinate transformations between datums designated by the user. The programs use the abridged Molodensky method to transform local geodetic datums to WGS-72 and to WGS-84.

11-8. BACKUP, TOP OF FILE, ERROR CORRECTION, AND ABORT CAPABILITIES

The BACKUP, TOP OF FILE, ERROR CORRECTION, and ABORT capabilities used in the survey module are also in the DDCT module. (See Chapter 12.) These functions are identical with one exception. The operator cannot back up to the prompt MODULE DESIRED: ## and select a different module. If a different module is desired, use the ABORT function.

11-9. ERROR WARNING MESSAGES

The BUCS DDCT programs use the error or warning messages shown in Table 11-4.

11-10. DDCT PROGRAMS

The BUCS DDCT programs are designed to be user friendly. The user is guided through each program by a series of prompts that are simple and understandable. The prompts encountered in the display must be followed step by step to determine the correct data or solution in that program. DDCT data and computations may be recorded on the appropriate computation forms developed for use with the BUCS or recorded directly by the printer when using the BUCS Special. The prompt abbreviations are explained in the program instructions where they occur.

a. Follow the steps in Table 11-5 to run the DDCT programs when the module number is known.

b. To run the DDCT programs when the module number is unknown, follow the procedure in Table 11-6.

Note. When running the DDCT programs, BUCS prompts MODULE DESIRED: 00. What the BUCS is requesting is the program number.

11-11. PROGRAM 14--LISTED DATUMS

a. Purpose. This program transforms coordinates between any two datums whose ellipsoid and abridged Molodensky transformation parameters are stored permanently in the BUCS DDCT ROM. A list of these datums appears in Appendix E. The program has four separate functions available for coordinate transformations.

(1) UTM to UTM. This function converts UTM coordinates from one datum into UTM coordinates in the same or another datum. Zone-to-zone transformations may be included as part of a UTM-to-UTM transformation. In such cases, the grid zone designated for the output datum must be adjacent to the grid zone designated for the input datum.

(2) UTM to GEO. This function converts UTM coordinates in one datum into geographic coordinates in the same or another datum.

(3) GEO to UTM. This function converts geographic coordinates in one datum into UTM coordinates in the same or another datum.

(4) GEO to GEO. This function converts geographic coordinates in one datum into geographic coordinates in the same or another datum.

b. Capabilities. This program will convert coordinates from one datum into the same or another datum. The input and output coordinates may be any combination of UTM and geographic coordinates. In addition, this program may be used to compute zone-to-zone transformations when both the input and output coordinates are given in UTM grid. The grid zone designated in the output datum must be adjacent to the grid zone designated in the input datum. See the grid zone chart in Appendix F to determine adjacent grid zones. When performing zone-to-zone transformations, several error or warning conditions exist.

(1) Zone-to-zone coordinate transformations may produce negative eastings. If the transformation is to a grid zone to the west and the point is too far west of the zone boundary, a negative easting is produced. The distances that cause negative eastings are a function of latitude (north or south) and are listed in Table 11-7.

(2) Zone-to-zone coordinate transformations may produce the IMAGE OVFL error warning message for easting coordinates. If the transformation is to a grid zone to the west and the point is too far east of the zone boundary, an IMAGE OVFL error or warning message is displayed. The error message is displayed if the easting coordinate exceeds or equals the legal limit of one million meters. The distances that cause the error or warning message are a function of latitude (north or south) and are listed in Table 11-8.

(3) BUCS DDCT does not recognize the abnormal-sized grid zones 31, 33, 35, and 37 between 72° and 84° north latitude. Additionally, it does not recognize the absence of grid zones 32, 34, and 36 between the same latitudes. There are no major land masses in this region with the exception of the Norwegian island group of Svalbard.

Note. When the coordinate to be transformed is near the equator, a negative northing or an IMAGE OVFL error message may be displayed. This occurs when the datum shift places the coordinate in a different hemisphere; for example, the equator shifts from north to south of the point and vice versa. For grid zones north of the equator, the equator has a value of zero. If the transformation datum shift causes the coordinate point north of the equator to end up south of the equator, subtract one million from the input northing coordinate. After the transformation has been computed, add 1 million back to the northing coordinate and subtract 10 million if the sum is greater than 10 million. The point is now in the Northern Hemisphere.

c. Required data. See Table 11-9 for the data required to use Program 14.

d. Instructions for Program 14--Listed Datums and DA Form 7287-R. Instructions for using Program 14 to compute DA Form 7287-R (Computation of Datum-to-Datum Coordinate Transformation (Program 14--Listed Datums) (BUCS)) (Figures 11-7 to 11-11) are discussed in Table 11-10.

11-12. PROGRAM 15--GAUSS-KRUGER

a. Purpose. This program transforms coordinates between GK and UTM datums whose ellipsoid and abridged Molodensky transformation parameters are in the BUCS-DDCT module. A list of these datums appears in Appendix E. The program has four separate functions available for coordinate transformations.

(1) Krassovsky to UTM. This function converts GK coordinates in a Krassovsky-based datum to UTM coordinates.

(2) UTM to Krassovsky. This function converts UTM coordinates to GK coordinates in a Krassovsky-based datum.

(3) Bessel to UTM. This function converts GK coordinates in a Bessel-based datum to UTM coordinates.

(4) UTM to Bessel. This function converts UTM coordinates to GK coordinates in a Bessel-based datum.

b. Capabilities. This program converts coordinates from GK datums to UTM datums and vice versa. The input and output coordinates may be any of the above combinations of GK and UTM coordinate datums.

WARNING

Program 15 incorrectly computes Gauss-Kruger coordinate transformations in the Southern Hemisphere. Add 4,000 meters to the northing coordinate when computing UTM to GK and GK to UTM transformations. The only country using the GK projection that is affected is Somalia.

c. Required Data. See Table 11-11 for the data required to use Program 15.

d. Instructions for program 15 and DA Form 7288-R. The instructions for computing DA Form 7288-R (Computation of Datum-to-Datum Coordinate Transformation (Program 15--Gauss-Kruger [GK]) (BUCS)) (Figures 11-12 through 11-15) are discussed in Table 11-12. (A reproducible copy of this form is included in the Blank Forms section of this book.)

11-13. PROGRAM 16--USER-DEFINED

a. Purpose. This program transforms coordinates between two user-defined datums, between a user-defined datum and a listed datum, and between a listed datum and a user-defined datum. See Appendix E for the listed datums. The DMA or a higher HQ will disseminate user-defined datum parameters when needed.

(1) User-Defined Datum to User-Defined Datum. This function converts UTM coordinates from one user-defined datum into UTM coordinates in the same or another user-defined datum.

(2) User-Defined Datum to Listed Datum. This function converts UTM coordinates from a user-defined datum into UTM coordinates in a listed datum.

(3) Listed Datum to User-Defined Datum. This function converts UTM coordinates from a listed datum into UTM coordinates in a user-defined datum.

Note. The Adindan datum (code 1) transformation parameters have been updated by the Defense Mapping Agency. To perform transformations involving the Adindan datum, use the updated parameters in Table 11-13.

Note. Datum shifts performed between WGS-72 and any other datum by using Program 14 or 15 do not produce the same solutions as Program 16 when inputting the transformation parameters as user-defined datums. This occurs because a more accurate formula for WGS-72 is used in Programs 14 and 15. Program 16 relies on the abridged Molodensky formulas and datum shifts for WGS-72. Use Program 16 for datum transformations only when directed by a higher HQ and when specific parameters are provided. Zone-to-zone transformations may be included in any of the above transformations. In such cases, the grid zones must be adjacent. See the grid zone chart in Appendix F.

b. Capabilities. This program converts coordinates between user-defined datums or between a user-defined datum and a listed datum and also computes zone-to-zone transformations.

Note. The semimajor axis and the semiminor axis cannot both be 6360000.000, or the program may abort.

c. Required data. See Table 11-14 for the data required to use Program 16.

d. Instructions for Program 16 and DA Form 7289-R. The instructions for using Program 16 to compute DA Form 7289-R (Computation of Datum-to-Datum Coordinate Transformation (Program 16--User-Defined) (BUCS) (Figures 11-16 through 11-18) are discussed in Table 11-15. (A reproducible copy of this form is included in the Blank Forms section of this book.)