Military Triangulation & Coordinate Solver

Input Parameters

Station 3 (Known)

Easting (m)

Northing (m)

Azimuths (in mils)

S3 to S1

S3 to S2

S2 to S1

S1 to S2

S1 to Sub-base

S2 to Sub-base

Measurements

Dist. S2 to Sub (m)

Mil Constant

Reference Formulas

1. Mils to Degrees Conversion:

2. Sine Rule (Dragon Formula):

3. Grid Coordinates Change:

Station 3 (Known) -

Station 1 (Target) -

Station 2 (Calculated) -

Sub-base (SUSHI) -

Mathematical Solution Breakdown

1 Solve Triangle S1-S2-Subbase (SUSHI)

Determine interior angles at Station 1 and Station 2 to find the distance between Station 2 and Station 1 ($D_{12}$).

Using the Sine Rule (Dragon Formula), compute the unknown side opposite to the Sub-base angle:

2 Solve Primary Triangle S1-S2-S3

Determine the interior angles of the larger triangle formed by the three stations ($\triangle(\text{S1-S2-S3})$) to calculate the distance between Station 3 and Station 1 ($D_{31}$).

Apply the Sine Rule to calculate the length of the unknown side $D_{31}$ opposite to the angle at Station 2:

3 Calculate Coordinates for Station 1

Compute grid deltas ($dE, dN$) from Station 3 to Station 1 using the solved distance and the given azimuth $A_{31}$.

Apply changes to the Easting and Northing of Station 3 to yield Station 1's coordinates: