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Varied Forces
Affect Surveying on the Surface
Reprint from Texas Surveyor
NovJDec. 1985
by David Moore, RPS 2040
NOTE: The following is not written
as a treatis on geodetic science but
to familiarize surveyors with the
forces, concepts and relationships
that exist in the physical and
mathematical conditions that affect
surveying results.
The surveyor, his surveying, and
his resulting data, are directly affected
by certain forces and conditions
that in most cases are not
physically evident and may be
changed by varying the conditions
mathematically. Each of these
forces and conditions may be
visuahzed as a surface and then expressed
in numerical terms.
The obvious surface is that of the
earth or some part thereof, upon, or
near, where we actually make our
measurements. This topographic
surface controls location of the
survey lines and the slope of the
lines of sight, but in and of itself,
and other than in slope, has little
physical affect on the
measurements.
The surface with the greatest
physical affect on the
measurements is that of gravity.
Although we seldom consider gravity
as having a surface, such a concept
allows us to visualize a surface
in which the force of gravity is the
same at all points on that surface —
an equipotential surface. The
equipotential surface which has
been adopted for the earth is called
the geoid.
Of course we can adopt various
potentials and each will be of a different
size, but they will have the
same shape. Because of the mixed
density of the earth, the geoid is not
uniform in shape. The surface undulates,
and one might look at it as
a potato.
Another visualization would be to
cut friction-free channels across the
land masses and fill them with
water, so as not to dimish the
volume in the oceans. Then, having
eliminated the effects of wind, air
pressure, and luni-solar tides, the
resulting water surface would be the
surface of the geoid.
At each point there is a line
perpendicular to the geoidal surface,
called the vertical or the direction of
the force of gravity; and it is the vertical
to which the axis of a survey instrument
is oriented.
Because the geoid is non-uniform
in shape and its surface has no
uniformly variable distance from
The surface with
the greatest
physical affect on
the measurements is
that of gravity.
Tangent Cylinder
>./- -+-;-^l
Figure 1
some fixed point, it offers a very
undesirable surface upon which to
compute.
Another surface, one that is mathematically
expressable, therefore, is
substituted. This surface is usually
an oblate eUipsoid revolved on its
minor axis to provide a soHd form.
(Continued on page 25)
Tangent Cone
The California Surveyor — Summer, 1986 Page 23