The Use and Calibration of the Kern ME5000 Mekometer - SLAC ...

ME5000 Data Reductions
a) Major-Axis: a, the semimajor axis of the reference ellipsoid, in meters. The reference figure
used at SLAC is Clarke’s ellipsoid of 1866, defined by its semimajor a and semiminor b axes,*
Fig. 4.
FIGURE 4. Ellipsoid
semimajor axis: a = 6378206.4 m
semiminor axis: b = 6356583.8 m
b) Eccentricity: e*, the square of the first eccentricity,
a* - P
first eccentricity: e* = 7 (26)
c) Latitude: $, the latitude of the site, in degrees.
These first three parameters are used to calculate the earth’s radius of curvature at the site. Since
the reference surface is a spheroid not a sphere, the radius of curvature varies with both latitude
and azimuth. At a given latitude the curvature is usually expressed in the form of the two
. principal radii of curvature, p (referred to as M in some of the literature) the radius of curvature
in the meridian, and v (or N in some of the literature) the radius of curvature in the prime
vertical, perpendicular to the meridian (27-28). SLAC is a sufftciently small site that it is
adequate to ignore the azimuth of the line, taking instead the mean radius R, which is the
geometric mean of the two principal radii, (29).
P
V
a (l-e*)
= (l-e* sin* $)“I
a
= (l-e* sin&$)”
R, = pv
d-
The latitude given in the example file above is for the origin of the SLAC coordinate system,
station 100 at the east end of the linac.
latitude: $ = 37.4168’
mean radius: R, = 6372508.16 m
d) Refheight: the reference height to which reduced ellipsoidal distances are projected. This is the
normal height, in metres, above the ellipsoid.
* Ch. 8 SLC Alignment Handbook, in SLC Design Handbook, 1984, p. 8-31.
34
(27)
(28)
(2%