Page 121 - Green - Maritime Archaeology: A Technical Handbook. 2nd ed

100 Maritime Archaeology: A Technical Handbook, Second Edition
Y2 Y1
y2
(x,y)
y1
X1 0x2 X2
q
Where x1 = x2Cosq + y2Sinq and y1 = y2Cos q - x2Sinq
x1
Figure 4.6 Coordinate rotation showing how a coordinate system X2, Y2 is rotated to coor- dinate system X1, Y1.
surement, although the calculated position will be incorrect, the surveyor will have no obvious indication of this other than that the plotted position may seem rather unusual. In order to overcome this, three reference points and three tapes are often used. Thus if there is an error, when the arcs are drawn it will show up because the three arcs will not intersect. This is known, because of its shape, as a cocked hat. The larger the cocked hat, the larger the error. This system has a great advantage over the two-tape system because it tells the surveyor when there is an error. It does not, however, indicate which measurement is at fault, so all that can be done is to discard the measurement or treat it with caution. The three-tape technique is more difficult to use under water with the added confusion of yet another tape, but it is worth considering on shallow water sites where there is more time available. As will be discussed in the next section, three-tape trilateration is unsuitable for recording the third dimension, if this is small in relation to the distances measured. Three-tape trilateration can only be used if one of the reference points is elevated in the Z-axis, or if the component of Z is comparable with the other two axes. In other words, it cannot be used to measure small height differences.
III. THREE-DIMENSIONAL SURVEY TECHNIQUES A. GENERAL
On some sites, where there is an extensive vertical component in the topography, some form of three-dimensional measurement is required. This occurs because the object being surveyed is required in three dimensions,