OFFSHORE LOCATION BY TRIANGULATION

For piles located farther offshore, the triangulation method of location is preferred. A pile location diagram is shown in figure 10-30. It is presumed that the piles in section X will be located by the method just described, while those in section Y will be located by triangulation from the two control stations shown.

The base line measures (1,038.83 – 433.27), or 595.56 feet, from control station to control station. The middle line of piles runs from station 7 + 41.05, making an angle of 84° with the base line. The piles

in each bent are 10 feet apart; bents are identified by letters; and piles, by numbers. The distance between adjacent transit setups in the base line is 10/sin 84°, or 10.05 feet.

You can determine the angle you turn, at a control station, from the base line to any pile location by triangle solution. Consider pile No. 61, for example. This pile is located 240 + 72.10, or 312.10 feet, from station 7 + 61.15 on the base line. Station 7 + 61.15 is located 1,038.83 – 761.15, or 277.68 feet, from control station 10 + 38.83. The angle between the line from station 7 + 61.15 through pile No. 61 and the base line measures 180°- 84°, or 96°. Therefore, you are dealing with the triangle ABC shown in figure 10-31. You want to know the size of angle A. First solve for b by the law of cosines, in which b² = a² + c² - 2ac cos B, as follows:

b² = 312.102 + 277.68² - 2(312.10)(277.68) cos 96° 

b = 438.89 feet

Knowing the length of b, you can now determine the size of angle A by the law of sines. Sin A = 312.10 sin 96°/438.89, or 0.70722. This means that angle A measures, to the nearest minutes, 45°00´.

To determine the direction of this pile from control station 4 + 43.27, you would solve the triangle DBC shown in figure 10-31. You do this in the same manner as described above. First solve for b using the law of cosines and then solve for angle D using the law of sines. After doing this, you find that angle D equals 47°26´.

It would probably be necessary to locate in this fashion only the two outside piles in each bent; the piles between these two could be located by measuring off the prescribed spacing on a tape stretched be-tween the two. For the direction from control station 10 + 38.83 to pile No. 65 (the other outside pile in bent M), you would solve the triangle shown in figure 10-32. Again, you solve for b using the law of cosines and then use the law of sines to solve for angle A. For each control station, a pile location sheet like the one shown in figure 10-33 would be made up. If desired, the direction angles for the piles between No. 61 and No. 65 could be computed and inserted in the intervening spaces.