d. Compute the position of the survey vessel at each fix. The 

 program control cards provide the California Lambert Coordinates of the 

 shore beacon, and the data input tapes provide the beacon ranges. By the 

 cosine law this can be translated into distance in terms of a rectangular 

 coordinate system: 



DX 



= (DB 2 + q\ - D2)/(2- 



DB) 



DY n = (D z - DXf) 

 1 1 1 



Where D^ = the distance of survey vessel from the upcoast radar beacon 

 D = the distance from the downcoast beacon 



DB = the distance between the two beacons 



DX-i = the distance of the fix position of survey vessel from 

 the upcoast beacon in a direction parallel to a line 

 intersecting the two beacons 



DYi = the distance of the fix from an upcoast beacon in a 



direction normal to a line intersecting the two beacons. 



These distances may be translated and rotated to give the Lambert 

 Coordinates for each fix 



NORTH f = DX, sine + DY 1 cos 6 + NORTH b 



EAST f = DX 2 cos6 - DYj sine + EAST b 



Where 6 = the angle of rotation of the coordinate system 



NORTH, and EAST, = the Lambert coordinates of the upcoast 

 b b , , 



radar beacon 



NORTH f and EAST f = the coordinates of the fix. 



