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<o:Author>Kevin Trott</o:Author>
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<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
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margin-bottom:.0001pt;text-align:justify'><a name=geocentric></a><b>Description
129
of Geocentric Coordinates</b></p>
131
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
132
margin-bottom:.0001pt;text-align:justify'>Geocentric coordinates are Cartesian
133
coordinates (X, Y, <span class=GramE>Z</span>) that define the position of a
134
point with respect to the center of mass of the earth. The origin of the coordinate
135
system is at the center of the reference ellipsoid. The coordinate system is a
136
right-handed system, with the positive X axis emerging from the ellipsoid at
137
the equator on the prime meridian, and the positive Z axis emerging from the
138
ellipsoid at the <span class=GramE>north pole</span>.</p>
140
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
141
margin-bottom:.0001pt;text-align:justify'><a name=loccart></a><b>Description of
142
Local Cartesian Coordinates</b></p>
144
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
145
margin-bottom:.0001pt;text-align:justify'>A local Cartesian coordinate system
146
is primarily defined by the location of its origin, in geodetic coordinates. If
147
the specified origin height is zero, the local XY plane is tangent to the
148
surface of the reference ellipsoid at the specified origin. If the origin
149
height is non-zero, the local XY plane is shifted up or down accordingly. If
150
the specified orientation angle is zero, the local positive Y axis points
151
north, while the local positive X axis points east, and the local positive Z
152
axis points "up", perpendicular to the ellipsoid surface at the
153
origin. If the orientation angle is not zero, then the local Cartesian
154
coordinate system is rotated clockwise about the Z axis by the specified
155
amount. For example, if the orientation angle is 90�, the local positive Y axis
156
will point east, while the local positive X axis points south.</p>
158
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
159
margin-bottom:.0001pt;text-align:justify'><a name=geodetic></a><b>Description
160
of Geodetic Coordinates</b></p>
162
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
163
margin-bottom:.0001pt;text-align:justify'>Geodetic coordinates consist of
164
geodetic latitude (f), geodetic longitude (l), and geodetic height (h) which
165
define the position of a point on, or near, the surface of the earth with
166
respect to a reference ellipsoid. Their relationship to the reference ellipsoid
167
is shown in the figure below. The angle between the normal SP and the equatorial
168
(X-Y) plane is called the geodetic latitude (f) of point P. The meridian plane
169
containing point P is defined as the half-plane containing the Z-axis and point
170
P. The angle between the prime meridian (X-Z) plane and the meridian containing
171
point P is the geodetic longitude (l) of point P. Geodetic longitude is not
172
defined when P lies on the Z-axis. The distance from Q to P is called the
173
geodetic or ellipsoidal height (h).</p>
175
<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
176
margin-left:0in;margin-bottom:.0001pt;text-align:center'><img width=657
177
height=654 id="_x0000_i1025" src=geodetic.gif></p>
179
<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
180
margin-left:0in;margin-bottom:.0001pt;text-align:center'>Relationship <span
181
class=GramE>Between</span> Geocentric and Geodetic Coordinates</p>
183
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
184
margin-bottom:.0001pt;text-align:justify'>Latitude limits:</p>
186
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:.5in;
187
margin-bottom:.0001pt;text-align:justify'>-90� (90�S) to +90� (90�<span
188
class=GramE>N )</span></p>
190
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
191
margin-bottom:.0001pt;text-align:justify'>Longitude limits:</p>
193
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:.5in;
194
margin-bottom:.0001pt;text-align:justify'>0� to 360� or -180� (180�W) to +180�
197
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
198
margin-bottom:.0001pt;text-align:justify'><a name=GEOREF></a><strong>Description
199
of GEOREF Coordinates</strong></p>
201
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
202
margin-bottom:.0001pt;text-align:justify'>The World Geographic Reference System
203
(GEOREF) is an alpha-numeric system for reporting positions for air defense and
204
strategic air operations. It is based upon geodetic coordinates. The first two
205
letters in a GEOREF coordinate string identify a 15� quadrangle, as shown
206
below. The next two letters define a 1� cell within that quadrangle, also as
207
shown below. The remaining digits define the location within the cell in terms
208
of decimal minutes of longitude and latitude, with a maximum resolution of
209
0.001 minutes (approximately 2 meters).</p>
211
<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
212
margin-left:0in;margin-bottom:.0001pt;text-align:center'><img width=659
213
height=490 id="_x0000_i1026" src=georef1.gif></p>
215
<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
216
margin-left:0in;margin-bottom:.0001pt;text-align:center'>GEOREF 15� Quadrangles</p>
218
<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
219
margin-left:0in;margin-bottom:.0001pt;text-align:center'><img width=613
220
height=606 id="_x0000_i1027" src=georef2.gif></p>
222
<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
223
margin-left:0in;margin-bottom:.0001pt;text-align:center'>GEOREF 1� Cells within
226
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
227
margin-bottom:.0001pt;text-align:justify'><a name=GARS></a><strong>Description
228
of GARS Coordinates</strong></p>
230
<p class=MsoNormal>The Global Area Reference System (GARS) is an alpha-numeric
231
system which divides the world into 30 minute cells using quadrant/keypad
232
tiling. The first three numbers identify the 30 minute east/west quadrangle,
233
ranging from 1 to 720.<span style='mso-spacerun:yes'>� </span>The next two
234
letters identify the 30 minute north/south quadrangle, ranging from AA to QZ,
235
omitting <span class=GramE>I</span> and O. The next number identifies a 15
236
minute cell within that quadrangle. This value ranges from 1 to 4, arranged
237
left to right, top to bottom. The last number identifies a 5 minute cell within
238
the 15 minute cell. This value ranges from 1 to 9, arranged as a keypad left to
239
right, top to bottom. </p>
241
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<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
271
margin-left:0in;margin-bottom:.0001pt;text-align:center'>GARS Quadrant/Keypad
274
<p class=MsoNormal align=center style='text-align:center'><o:p> </o:p></p>
276
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
277
margin-bottom:.0001pt;text-align:justify'><a name=MGRS></a><strong>Description
278
of MGRS Coordinates</strong></p>
280
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
281
margin-bottom:.0001pt;text-align:justify'>The Military Grid Reference System
282
(MGRS) is an alpha-numeric system, based upon the UTM and UPS map projections,
283
for identifying positions. An MGRS coordinate consists of a zone designation, alphabetic
284
100,000-meter grid square designator, and numeric coordinates within the
285
100,000 meter grid square. <span class=GramE>MGRS</span> coordinates are
286
defined for the primary UTM and UPS areas, but not for the overlap areas.</p>
288
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
289
margin-bottom:.0001pt;text-align:justify'>In the UTM area, MGRS coordinates are
290
based on the ellipsoid, geodetic latitude, UTM zone, Easting and Northing as
293
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
294
margin-bottom:.0001pt;text-align:justify'>a. The first two characters of the
295
MGRS coordinate are the two digits of the numeric UTM zone. Leading zeros must
296
be included. The figure below shows the layout of the zones, including the
297
irregular zones in the <st1:place w:st="on">North Atlantic</st1:place>.</p>
299
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
300
margin-bottom:.0001pt;text-align:justify'>b. The third character of the MGRS
301
coordinate is a letter representing a band of geodetic latitude. Beginning at
302
80�S and <span class=GramE>proceeding</span> northward, the 20 bands are
303
lettered C through X, omitting I and O. The bands are all 8� high except band X
304
(72�N to 84�N), which is 12� high. The figure below shows the layout of these
307
<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
308
margin-left:0in;margin-bottom:.0001pt;text-align:center'><img width=1000
309
height=556 id="_x0000_i1029" src="mgrs_zones.gif"></p>
311
<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
312
margin-left:0in;margin-bottom:.0001pt;text-align:center'>MGRS Zones and Bands</p>
314
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
315
margin-bottom:.0001pt;text-align:justify'>c. The fourth and fifth characters of
316
the MGRS coordinate are a pair of letters representing the 100,000-meter grid
317
square. Two different patterns of two-letter designations are used, depending
318
on the ellipsoid associated with the current datum. The first diagram below
319
shows the pattern of 100,000 meter square designations used with the Clarke
320
1866, Clarke 1880, Bessel 1841 and Bessel 1841 <st1:country-region w:st="on"><st1:place
321
w:st="on">Namibia</st1:place></st1:country-region> ellipsoids. The second
322
diagram shows the pattern used with all other ellipsoids. The patterns are
323
repeated every six zones.</p>
325
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
326
margin-bottom:.0001pt;text-align:justify'>Note: The alphabetic method of
327
designating 100,000-meter grid squares has changed over time. Older products
328
may have different grid square designations.</p>
330
<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
331
margin-left:0in;margin-bottom:.0001pt;text-align:center'><img width=1001
332
height=667 id="_x0000_i1030" src="mgrs_al.gif"></p>
334
<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
335
margin-left:0in;margin-bottom:.0001pt;text-align:center'>MGRS 100,000m Square
336
Designations (AL Pattern)</p>
338
<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
339
margin-left:0in;margin-bottom:.0001pt;text-align:center'><img width=1000
340
height=667 id="_x0000_i1031" src="mgrs_aa.gif"></p>
342
<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
343
margin-left:0in;margin-bottom:.0001pt;text-align:center'>MGRS 100,000m Square
344
Designations (AA Pattern)</p>
346
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
347
margin-bottom:.0001pt;text-align:justify'>d. The remainder of the MGRS
348
coordinate string consists of the numeric Easting and Northing values within
349
the 100,000-meter grid square. The left half of the digit sequence is the
350
Easting value, which is read to the right from the left edge of the
351
100,000-meter grid square. The right half of the digit sequence is the Northing
352
value, which is read northward from the bottom edge of the 100,000-meter grid
353
square. Both the Easting and Northing values are within the range from 0 to
354
100,000 meters. Both Easting and Northing values must have the same resolution
355
and must include leading zeros.</p>
357
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
358
margin-bottom:.0001pt;text-align:justify'>In the UPS area, MGRS coordinates are
359
based on the ellipsoid, geodetic latitude and longitude, Easting, and Northing
362
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
363
margin-bottom:.0001pt;text-align:justify'>a. The first character of the MGRS
366
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:.5in;
367
margin-bottom:.0001pt;text-align:justify'>A in the Southern and Western
370
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:.5in;
371
margin-bottom:.0001pt;text-align:justify'>B in the Southern and Eastern
374
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:.5in;
375
margin-bottom:.0001pt;text-align:justify'>Y in the Northern and Western
378
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:.5in;
379
margin-bottom:.0001pt;text-align:justify'><span class=GramE>Z in the Northern
380
and Eastern Hemispheres.</span></p>
382
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
383
margin-bottom:.0001pt;text-align:justify'>b. The second and third characters of
384
the MGRS coordinate are letters representing a 100,000 meter grid square. The
385
diagrams below show the layout of the 100,000 meter squares in the north and
386
south polar zones.</p>
388
<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
389
margin-left:0in;margin-bottom:.0001pt;text-align:center'><img width=964
390
height=709 id="_x0000_i1032" src="mgrs_n.gif"></p>
392
<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
393
margin-left:0in;margin-bottom:.0001pt;text-align:center'>MGRS 100,000m Square Designations
394
for North Polar Zone</p>
396
<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
397
margin-left:0in;margin-bottom:.0001pt;text-align:center'><img width=914
398
height=709 id="_x0000_i1033" src="mgrs_s.gif"></p>
400
<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
401
margin-left:0in;margin-bottom:.0001pt;text-align:center'>MGRS 100,000m Square
402
Designations for South Polar Zone</p>
404
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
405
margin-bottom:.0001pt;text-align:justify'>c. The method for calculating the
406
remainder of the MGRS coordinate is the same as in d (above).</p>
408
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
409
margin-bottom:.0001pt;text-align:justify'><a name=F16GRS></a><strong>Description
410
of F-16 GRS Coordinates</strong></p>
412
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
413
margin-bottom:.0001pt'>The F-16 Grid Reference System (F-16 GRS) is a variant
414
of MGRS that is intended to be compatible with the navigation system of the
415
F-16 fighter aircraft.<span style='mso-spacerun:yes'>� </span>All other users should
416
use standard MGRS coordinates.</p>
418
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
419
margin-bottom:.0001pt'>At 100,000m precision, an F-16 GRS coordinate string
420
includes two trailing zeros, following the zone number, the zone letter, and
421
the two-letter 100,000m square designation.<span style='mso-spacerun:yes'>�
422
</span>In a standard MGRS coordinate string, the presence of these zeros would
423
imply 10,000m precision.<span style='mso-spacerun:yes'>� </span>However, due to
424
a quirk in the F-16 navigation system, strings of this form are used to
425
designate a 100,000m square.<span style='mso-spacerun:yes'>� </span>Except for
426
this quirk, F-16 GRS coordinates are identical to MGRS coordinates.</p>
428
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
429
margin-bottom:.0001pt;text-align:justify'><a name=USNG></a><strong>Description
430
of USNG Coordinates</strong></p>
432
<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
433
margin-bottom:.0001pt;text-align:justify'>The United States National Grid
434
(USNG) is an alpha-numeric system, based upon the UTM and UPS map projections,
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for identifying positions. An USNG coordinate consists of a zone designation,
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alphabetic 100,000-meter grid square designator, and numeric coordinates within
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the 100,000 meter grid square. USNG coordinates are defined for the primary UTM
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and UPS areas, but not for the overlap areas. USNG coordinates are identical to
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MGRS coordinates, except that USNG coordinates use a single pattern of
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100,000-meter grid square designators (the AA pattern), regardless of the
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<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
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margin-bottom:.0001pt;text-align:justify'>In the UTM area, USNG coordinates are
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based on the ellipsoid, geodetic latitude, UTM zone, Easting and Northing as
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<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
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margin-bottom:.0001pt;text-align:justify'>a. The first two characters of the
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USNG coordinate are the two digits of the numeric UTM zone. Leading zeros must
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be included. The figure below shows the layout of the zones, including the
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irregular zones in the <st1:place w:st="on">North Atlantic</st1:place>.</p>
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<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
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margin-bottom:.0001pt;text-align:justify'>b. The third character of the USNG
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coordinate is a letter representing a band of geodetic latitude. Beginning at
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80�S and <span class=GramE>proceeding</span> northward, the 20 bands are
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lettered C through X, omitting I and O. The bands are all 8� high except band X
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(72�N to 84�N), which is 12� high. The figure below shows the layout of these
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<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
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margin-left:0in;margin-bottom:.0001pt;text-align:center'><img width=1000
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height=556 id="_x0000_i1034" src="mgrs_zones.gif"></p>
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<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
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margin-left:0in;margin-bottom:.0001pt;text-align:center'>USNG Zones and Bands</p>
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<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
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margin-bottom:.0001pt;text-align:justify'>c. The fourth and fifth characters of
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the USNG coordinate are a pair of letters representing the 100,000-meter grid
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square. The diagram below shows the pattern of 100,000 meter square. The
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patterns are repeated every six zones.</p>
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<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
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margin-bottom:.0001pt;text-align:justify'>Note: The alphabetic method of
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designating 100,000-meter grid squares has changed over time. Older products
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may have different grid square designations.</p>
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<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
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margin-left:0in;margin-bottom:.0001pt;text-align:center'><o:p> </o:p></p>
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<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
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margin-left:0in;margin-bottom:.0001pt;text-align:center'><img width=1000
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height=667 id="_x0000_i1035" src="mgrs_aa.gif"></p>
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<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
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margin-left:0in;margin-bottom:.0001pt;text-align:center'>USNG 100,000m Square
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Designations (AA Pattern)</p>
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<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
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margin-bottom:.0001pt;text-align:justify'>d. The remainder of the USNG
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coordinate string consists of the numeric Easting and Northing values within
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the 100,000-meter grid square. The left half of the digit sequence is the
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Easting value, which is read to the right from the left edge of the
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100,000-meter grid square. The right half of the digit sequence is the Northing
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value, which is read northward from the bottom edge of the 100,000-meter grid
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square. Both the Easting and Northing values are within the range from 0 to
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100,000 meters. Both Easting and Northing values must have the same resolution
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and must include leading zeros.</p>
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<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
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margin-bottom:.0001pt;text-align:justify'>In the UPS area, USNG coordinates are
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based on the ellipsoid, geodetic latitude and longitude, Easting, and Northing
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<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
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margin-bottom:.0001pt;text-align:justify'>a. The first character of the USNG
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<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:.5in;
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margin-bottom:.0001pt;text-align:justify'>A in the Southern and Western
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<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:.5in;
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margin-bottom:.0001pt;text-align:justify'>B in the Southern and Eastern
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<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:.5in;
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margin-bottom:.0001pt;text-align:justify'>Y in the Northern and Western
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<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:.5in;
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margin-bottom:.0001pt;text-align:justify'><span class=GramE>Z in the Northern
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and Eastern Hemispheres.</span></p>
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<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
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margin-bottom:.0001pt;text-align:justify'>b. The second and third characters of
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the USNG coordinate are letters representing a 100,000 meter grid square. The
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diagrams below show the layout of the 100,000 meter squares in the north and
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south polar zones.</p>
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<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
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margin-left:0in;margin-bottom:.0001pt;text-align:center'><img width=964
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height=709 id="_x0000_i1036" src="mgrs_n.gif"></p>
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<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
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margin-left:0in;margin-bottom:.0001pt;text-align:center'>USNG 100,000m Square
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Designations for North Polar Zone</p>
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<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
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margin-left:0in;margin-bottom:.0001pt;text-align:center'><img width=914
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height=709 id="_x0000_i1037" src="mgrs_s.gif"></p>
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<p align=center style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;
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margin-left:0in;margin-bottom:.0001pt;text-align:center'>USNG 100,000m Square
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Designations for South Polar Zone</p>
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<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
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margin-bottom:.0001pt;text-align:justify'>c. The method for calculating the
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remainder of the USNG coordinate is the same as in d (above).</p>
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<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
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margin-bottom:.0001pt;text-align:justify'><o:p> </o:p></p>
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<p style='margin-top:6.0pt;margin-right:0in;margin-bottom:0in;margin-left:0in;
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margin-bottom:.0001pt;text-align:justify'><o:p> </o:p></p>
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geotrans2/help/coordDescriptions.htm
