SURVEYING: ERROR SOURCES IN
TOTAL STATION
Total Station Error Sources
All theodolites
measure angles with some degree of imperfection. These imperfections result
from the fact that no mechanical device can be manufactured with zero error. In
the past very specific measuring techniques were taught and employed by
surveyors to compensate for minor mechanical imperfections in theodolites. With
the advent of electronic theodolites, the mechanical errors still exist but are
related to in a different way. One must now do more than memorize techniques
that compensate for errors. One must clearly understand the concepts behind the
techniques and the adjustments for errors that electronic theodolites now make.
The following paragraphs provide the major sources of error when using a
theodolite and also the particular method employed to compensate for that
error.
a) Circle eccentricity
Circle eccentricity
exists when the theoretical center of the mechanical axis of the theodolite
does not coincide exactly with the center of the measuring circle. The amount
of error corresponds to the degree of eccentricity and the part of the circle
being read. When represented graphically circle eccentricity appears as a sine
wave. Circle eccentricity in the horizontal circle can always be compensated
for by measuring in both faces (opposite sides of the circle) and using the
mean as a result. Vertical circle eccentricity cannot be compensated for in
this manner since the circle moves with the telescope. More sophisticated
techniques are required.
(1) Some theodolites are individually tested to determine the
sine curve for the circle error in that particular instrument. Then a
correction factor is stored in ROM that adds or subtracts from each angle
reading so that a corrected measurement is displayed.
(2) Other instruments employ an angle-measuring system
consisting of rotating glass circles that make a complete revolution for every
angle measurement. These are scanned by fixed and moving light sensors. The
glass circles are divided into equally spaced intervals which are diametrically
scanned by the sensors. The amount of time it takes to input a reading into the
processor is equal to one interval, thus only every alternate graduation is
scanned. As a result, measurements are made and averaged for each circle
measurement. This eliminates scale graduation and circle eccentricity error.
b) Horizontal collimation error
Horizontal collimation
error exists when the optical axis of the theodolite is not exactly perpendicular
to the telescope axis. To test for horizontal collimation error, point to a
target in face one then point back to the same target in face two; the
difference in horizontal circle readings should be 180 degrees. Horizontal
collimation error can always be corrected for by meaning the face one and face
two pointings of the instrument.
(1) Most electronic
theodolites have a method to provide a field adjustment for horizontal
collimation error. Again, the manual for each instrument provides detailed
instruction on the use of this correction.
(2) In some
instruments, the correction stored for horizontal collimation error can affect
only measurements on one side of the circle at a time. Therefore when the
telescope is passed through zenith (the other side of the circle is being
read), the horizontal circle reading will change by twice the collimation
error. These instruments are functioning exactly as designed when this happens.
(3) When prolonging a
line with an electronic theodolite, the instrument operator should either turn
a 180-degree angle or plunge the telescope and turn the horizontal tangent so
that the horizontal circle reading is the same as it was before plunging the
telescope.
c) Height of standards error:
In order for the
telescope to plunge through a truly vertical plane the telescope axis must be
perpendicular to the standing axis. As stated before there is no such thing as
perfection in the physical world. All theodolites have a certain degree of
error caused by imperfect positioning of the telescope axis. Generally,
determination of this error should be accomplished by a qualified technician
because horizontal collimation and height of standards errors interrelate and
can magnify or offset one another. Horizontal collimation error is usually eliminated
before checking for height of standards. Height of standards error is checked
by pointing to a scale the same zenith angle above a 90-degree zenith in
"face-one" and "face-two." The scales should read the same
in face one as in face two.
d) Circle graduation error
In the past, circle
graduation error was considered a major problem. For precise measurements
surveyors advanced their circle on each successive set of angles so that circle
graduation errors were “meaned out.” Current technology eliminates the problem
of graduation errors. This is accomplished by photo-etching the graduations
onto the glass circles and making a precise master circle and photographing it.
An emulsion is then applied to the circle and a photo-reduced image of the
master is projected onto the circle. The emulsion is removed and the glass
circle has been etched with very precise graduations.
e) Vertical circle error
It is important to
check the vertical circle indexing adjustment on surveying instruments on a
routine basis. When direct and indirect zenith angles are measured to the same
point, the sum of the two angles should equal 360°. Over time, the sum of these
two angles may diverge from 360° and consequently cause errors in vertical
angle measurements. While averaging the direct and indirect zenith angles
easily eliminates this error, on many jobs it may not be cost effective to make
two readings. Acceptable accuracy may still be maintained for many applications
with only a direct reading; however, as long as the index error is kept to a
minimum by periodically performing a vertical adjustment, such as TOPCON’s
"Vertical Angle 0 Datum Adjustment." Most total stations are provided
with some type of electronic adjustment to correct the vertical circle indexing
error. This adjustment takes just a few seconds and will insure that you get
good vertical angle readings with just one measurement. Consult the
manufacturer’s manual for instructions on making this adjustment.
f) Pointing errors:
Pointing errors are
due to both human ability to point the instrument and environmental conditions
limiting clear vision of the observed target. The best way to minimize pointing
errors is to repeat the observation several times and use the average as the
result.
g) Uneven heating of the
instrument.
Direct sunlight can
heat one side of the instrument enough to cause small errors. For the highest
accuracy, utilize an umbrella or pick a shaded spot for the instrument.
h) Vibrations
Avoid instrument
locations that vibrate. Vibrations can cause the compensator to be unstable.
i) Collimation errors
When sighting points a
single time (e.g., direct position only) for elevations, check the instrument
regularly for collimation errors.
j) Vertical angles and
elevations
When using total
stations to measure precise elevations, the adjustment of the electronic tilt
sensor and the reticule of the telescope becomes very important. An easy way to
check the adjustment of these components is to set a baseline. A line close to
the office with a large difference in elevation will provide the best
results. The baseline should be as long as the longest distance that will be
measured to determine elevations with intermediate points at 100- to 200-ft
intervals. Precise elevations of the points along the baseline should be measured
by differential leveling. Set up the total station at one end of the baseline
and measure the elevation of each point. Comparing the two sets of elevations
provides a check on the accuracy and adjustment of the instrument. Accuracy
requirements may dictate that more than one set of angles and distances is
measured to each point. Some examples are distances over 600 feet, adverse
weather conditions, and steep observations.
k) Atmospheric corrections
Meteorological data
corrections to observed EDM slope distances may be significant over longer
distances. Usually for most topographic surveying over short distances, nominal
(estimated) temperature and pressure data is acceptable for input into the data
collector. Instruments used to measure atmospheric temperature and pressure
must be periodically calibrated. This would include psychrometers and
barometers.
l) Optical plummet errors
The optical plummet or
tribrachs must be periodically checked for misalignment. This would include
total stations with laser plummets.
m) Adjustment of prism poles
When using prism
poles, precautions should be taken to ensure accurate measurements. A common
problem encountered when using prism poles is the adjustment of the leveling
bubble. Bubbles can be examined by establishing a check station under a doorway
in the office. First, mark a point on the top of the doorway. Using a plumb
bob, establish a point under the point on the doorway. If possible, use a
center punch to make a dent or hole in both the upper and lower marks. The
prism pole can now be placed into the check station and easily adjusted.
n) Recording errors
The two most common
errors are reading an angle incorrectly and/or entering incorrect information
into the field book. Another common (and potentially disastrous) error is an
incorrect instrument or rod height. Although electronic data collection has all
but eliminated these errors, it is still possible for the surveyor to identify
an object incorrectly, make a shot to the wrong spot, or input a bad target height
(HR) or HI. For example, if the surveyor normally shoots a fire hydrant at the
ground level, but for some reason shoots it on top of the operating nut,
erroneous contours would result if the program recognized the fire hydrant as a
ground shot and was not notified of this change in field procedure.
o) Angles
As a rule, a surveyor
will turn a doubled angle for move-ahead, traverse points, property corners, or
other objects that require greater accuracy. On the other hand, single angles
are all that are required for topographic shots. Refer to the total station
operating instructions for repeating angle methods where required.
p) Slope to grid and sea level
EDM corrections
Slope distances will
be reduced to horizontal distances in the data collector, and then reduced to a
grid distance if a grid scale factor (or combined scale sea level factor) is
input into the data collector. For most topographic survey applications
involving short side shots, the grid scale factor is ignored (e.g., 1.000 is
used). This would not be correct for control traverses covering larger
distances. Scale factors can be obtained directly in CORPSCON.
q) EDM calibration
All EDM instruments
should be periodically (at least annually) checked over a NGS Calibration
Baseline or a baseline established by local state surveying societies.
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