Editing SAR Fundamentals/Navigation/Map/Triangulation/Samples

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<pre>
Material Covered:
  * triangulation

Prerequisites:

Objective: 
    Students w

Duration: 45 minutes

Aids:

Plan:

LE = local east 
LN = local north
L1B = bearing to remote 1
L2B = bearing to remote 2
R1E = remote 1 east
R1N = remote 1 north
R1B = bearing from remote 1
R2E = remote 2 east
R2N = remote 2 north
R2B = bearing from remote 2

R1B = L1B - 180
R2B = L2B - 180
(LE-R1E)/(LN-R1N) = tan(R1B)
(LE-R2E)/(LN-R2N) = tan(R2B)

LE-R1E            = tan(R1B)*LN - tan(R1B)*R1N
LE-R2E            = tan(R2B)*LN - tan(R2B)*R1N

LE                = tan(R1B)*LN - tan(R1B)*R1N + R1E
LE                = tan(R2B)*LN - tan(R2B)*R2N + R2E

tan(R1B)*LN - tan(R1B)*R1N + R1E = tan(R2B)*LN - tan(R2B)*R2N + R2E
tan(R1B)*LN                      = tan(R2B)*LN - tan(R2B)*R2N + R2E + tan(R1B)*R1N - R1E 
tan(R1B)*LN - tan(R2B)*LN        = - tan(R2B)*R2N + R2E + tan(R1B)*R1N - R1E 
(tan(R1B) - tan(R2B)) * LN       = - tan(R2B)*R2N + R2E + tan(R1B)*R1N - R1E 
LN = (- tan(R2B)*R2N + R2E + tan(R1B)*R1N - R1E)/(tan(R1B) - tan(R2B))
LN = (tan(R1B)*R1N - tan(R2B)*R2N + R2E  - R1E)/(tan(R1B) - tan(R2B))

On a line with a bearing to a remote point
Line,RemoteUTM,TNBearingToRemote,LocalUTM
Cutline 929760 893792    ,915786, 90,900785
Cutline 929760 893792    ,915786, 76,903783
Cutline 929760 893792    ,915786, 45,908779
Cutline 929760 893792    ,915786,  0,916772
Cutline 929760 893792    ,915786,336,927762
Left Bank of Castle River,915786,320,936763
Left Bank of Castle River,915786,270,938787
Left Bank of Castle River,915786,250,940793

Cutline 103766 078767    ,086757,226,095766
Right Bank of West Castle,897680,187,900718

82G/8 Zone 11, Grid North is 2deg 5min east of TN
Remote1UTM,TNBearingToRemote1,Remote2UTM,TNBearingToRemote2,LocalUTM
915786  56 866784 316 886765 
915786  67 866784 344 872766
086757 148 045776 272 073776
086757 130 045776 229 053783
016628 283 013665 187 026626   !! degrees backwards
=915786  70 866784 295 888775   harder to be accurate b/c of relative angle
915786  70 866784 296 887775
915786  60 866784 304 889770 !!890768

* Can generate more samples,
  but make sure points are visible on the map.
wuth@errant$ utm-triangulate 915786  70 866784 295 2 5
888775
wuth@errant$

Fancy thing about the utm-triangulate calculation is that you can get
either or both bearings 180 degrees backwards and you still get the same
answer.

Accuracy   Sources of Error:
UTM rounding:
	UTMs are only to nearest 100m, can be out by sqrt(2*50m^2)=71m

Measuring angles on the map:
        When points close together UTM rounding is exagerated.
	want the points to be far apart.
	But if actually moving to the point, close point is not necessary.

User Error:
	* misreading compass
	* metal objects

Compass Inaccuracies:
	* gradients only ever 2 degress -> estimate difference
	* needle not exactly magnetic north -> learn calibration of compass

Environment
	* local variants in declination
	* shifting magnetic pole
		* progressive
		* daily  100 km elipse

Geometry
	* Parallax -> sight on close by objects when point to angle
			sight on object close to destination when angle to point
	* Earth's curvature
		West is not a straight line
		remembered: 1 degree / 100 mi at 49 degrees N

Triangulate with 3 bearings
	get a triangle of results

1 degree error in 1km is 17m left/right
2 degree error in 1km is 35m left/right
5 degree error in 1km is 87m left/right
10 degree error in 1km is 176m left/right

</pre>

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@@ Line 1: / Line 1: @@
 <pre>
+Material Covered:
+  * triangulation
+Prerequisites:
+Objective:
+    Students w
+Duration: 45 minutes
+Aids:
+Plan:
 LE = local east
 LN = local north
@@ Line 28: / Line 45: @@
 LN = (- tan(R2B)*R2N + R2E + tan(R1B)*R1N - R1E)/(tan(R1B) - tan(R2B))
 LN = (tan(R1B)*R1N - tan(R2B)*R2N + R2E  - R1E)/(tan(R1B) - tan(R2B))
-</pre>
-<pre>
 On a line with a bearing to a remote point
 Line,RemoteUTM,TNBearingToRemote,LocalUTM
@@ Line 55: / Line 70: @@
 70 866784 296 887775
 60 866784 304 889770 !!890768
-</pre>
-* Can generate more samples, but make sure points are visible on the map.
+* Can generate more samples,
-<pre>
+  but make sure points are visible on the map.
 wuth@errant$ utm-triangulate 915786  70 866784 295 2 5
 wuth@errant$
-</pre>
@@ Line 70: / Line 84: @@
 answer.
-<pre>
 Accuracy   Sources of Error:
 UTM rounding:
@@ Line 109: / Line 123: @@
 degree error in 1km is 87m left/right
 degree error in 1km is 176m left/right
 </pre>