SAR Fundamentals/Navigation/Map/Triangulation/Samples

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

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

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