by Juan Chow, Maureen Kennedy,
Rebecca Tedford and Carrie Walker.
SOKKIA Set 6F theodolite projects a laser beam to a prism target and returns
a 3-D coordinate set in the form of N, E, and Z.
Juan and Rebecca
theodolite requires a coordinate set as its starting position.
We choose due north as our Yo
coordinate, due east as our Xo coordinate, and Zo to be the vertical direction;
Xo, Yo, and Zo are all zeros at the theodolite measuring station.
Fig. 1. a = Azimuth
angle. Angle on the horizontal plane that diverges from Xo (in our case,
North). from the vertical above the theodolite to the line that defines
the slope distance S.
|Ih is the height
of the theodolite. Th is the height of the prism target; because these
two heights are not equal and are not on the surface of the land, they
must be taken into account when calculating Z.
Fig. 2. b = Zenith angle. Angle
measured from above the theodolite down to the line that defines the slope
distance S. (See Fig. 3.)
Fig. 3. S = Slope distance. The
direct distance from the theodolite to the prism target. Z = Height difference
between Zo and the height of the land at the prism target.
S = N / cosa sinb = E / sina
Z = Zo + Ih + S (cosb) ñ
Th (for our purposes, Zo = 0)
Fig. 4. Plan view of the relationship
among N, E, and a (azimuth angle).
N = Distance from the theodolite
to a point along the Yo axis that is perpendicular to the target.
= Yo + ( S sinb cosa)
E = Distance from the theodolite
to a point along the Xo axis that is perpendicular to the target
= Xo + ( S sinb sina)
Maureen and Carrie