Civil Engineering Reference
In-Depth Information
the ground has an effect on the distortion, and the higher the elevation, the greater
the distortion. In fact, because the zone size of a state plane system is limited, in
mountainous areas the elevation of the ground can have a greater effect on dis-
tortion than the state plane/ellipsoid distortion. It is important to understand that
when we speak of distortion we are talking about distances which are measured
on the ground between points. Distances measured on the flat state plane grid will
be different than distances measured along the surface of the earth. This is the pri-
mary issue faced by surveyors when working with state plane coordinates.
Based on Figs.
12.5
and
12.6
, we can conclude that in order to convert from
state plane distances to ground distances, we need to know how far the points are
from the central meridian and we also need to know the elevation of the ground
where we are performing our survey. In practice, a factor called a grid factor, also
known as a combined grid factor or combined factor is used to convert ground
dimensions to grid dimensions and the other way around. A combined factor is
a number that can be multiplied by a distance in one system in order to convert
the distance to the other system. The combined factor takes into consideration
the distortion between the ellipsoid and the state plane grid and the elevation of
the ground where the survey is located. At the point where the state plane grid
crosses the ellipsoid surface, the combined factor will be 1 (for an elevation of
zero). As we already discussed, there is no distortion at this point. At other points
on the state plane grid, the combined factors will typically be close to 1, such as
0.999777 or 1.000215. We can see from Fig.
12.6
that, from the central meridian
to the point where the state plane grid crosses the ellipsoid, the combined factor is
less than one and it increases as the distance increased from the central meridian.
If we multiply the combined factor times the ground distance, we will have the
distance on the state plane grid. For example, if we measure a survey line on the
ground that is 1,000.00 feet long and we have a scale factor of 0.999777 the dis-
tance on the state plane grid would be 999.78. In our example, the difference is
0.22 feet. If our survey were a small house lot with a boundary length of 100.00
feet the distance on the state plane grid would be 99.98 feet, a difference of only
0.02 feet. As our example demonstrates, unless the survey is very large, or if it is
at a very high elevation, the difference between ground distances and state plane
distances will not be large, but the differences will still be enough that they will
need to be corrected—at least when the survey requires high accuracy, such as
when establishing boundaries. For survey work in which accuracy standards are
less demanding, correction may be less important. Surveying software running on
a personal computer or in a data collector will usually have scale factor conversion
built in so that a user can easily switch from one coordinate system to the other.
When working with conversions between ground coordinates and state plane
coordinates, it is important to realize that the coordinates themselves are not dis-
torted. If we have a grid of one foot squares on the state plane grid and a grid
of one foot squares on the ground surface where we are performing a boundary
survey, the squares on both surfaces will measure exactly one foot. However, the
distances between points projected from the ground grid to the state plane grid
will have different lengths. Mistakes have been made in the past by applying
