Page 120 - Green - Maritime Archaeology: A Technical Handbook. 2nd ed

Chapter 4: Conventional Survey 99
on the correct side of the baseline and not the mirror image). The main crit- icism of this method of plotting is that it produces a mass of unsightly arc intersections on the plan, and on large-scale plans the distances involved may be beyond the length of conventional beam compasses. A more effi- cient means is a programmable hand-held calculator or a small computer to convert the trilateration data to rectangular coordinates. The program requires that the X and Y coordinates of the two reference points be known. With this information, it is possible to link the survey with the grid or coor- dinate system of the whole site. If this is not required, the X and Y coordi- nates of the two points A and B (Figure 4.5) will be A = (0,0) and B = (c,0) with c being the measured distance between the two points. Take the complex case of A = Xa,Ya, B = Xb,Yb, and C is the point at which the X, Y coordinates are required (Xp,Yp).
Then if AC = b, BC = a, and AB = c.
Assuming first that A = (0,0) and B = (c,0) then:
X3 = b cosA and Y3 = b sinA.
Now rotate and translate the coordinate system so that
B = Xb,Yb and A = Xa,Ya.
The angle of rotation b is given by
and coordinates of C are Xc = X3cosb + Y3sinb and Yc = Y3cosb - X3 sin b (see Figure 4.6).
These equations can be set up quite simply in a programmable calcula- tor or a computer such that the entry of X3 and Y3 will give the values Xc and Yc. This method of plotting is much faster and more reliable than the double arc system. These data can be presented on printout paper so that with suitable programming, one can obtain a listing of the measured dis- tances and the coordinates. Alternatively, with a computer, these data can be imported into a plotting program and the results accurately scaled and plotted onto paper.
The two-tape system has some inherent problems that need to be con- sidered. Because only two distances are measured, there can be only one solution (ignoring the trivial mirror image solution). In the case of one of the measurements being wrongly recorded or some inaccuracy in the mea-
Êc2 +b2 -a2ˆ cosA = ÁË 2bc ˜¯
Tanb = Ê Xb - Xa ˆ ËYb-Ya ¯