Attaining Precision with a Maximum
Angular
Error of Closure You know that the sum of the interior angles
of
a closed traverse should theoretically equal the product
of 180° (n – 2), n being the number of sides
in the polygon described by the traverse. A prescribed
MAXIMUM ANGULAR ERROR OF CLOSURE is
stated in terms of the product of a
given angular value times the square root of the number
of interior angles in the traverse. Again,
if we use the traverse shown in figure 1327
as an example, the prescribed maximum angular
error of closure in minutes is 01 fi because
the figure has three interior angles. The sum
of the interior angles should be 180°. If the sum
of the angles as actually measured and recorded
is 179°57´, the angular error of closure is
03´. The maximum permissible error of closure is
the product of 01´ times the square root of 3,
or about 1.73´. The prescribed maximum angular
error of closure has therefore been exceeded.
Meeting Precision Specifications
The following specifications are intended to give
you only a general idea of the typical precision
requirements for various types of transittape surveys.
When linear and angular errors of closure
are specified, it is understood that a closed
traverse is involved.
For many types of preliminary surveys and for land
surveys, typical precision specifications may read
as follows:
l Transit angles to nearest minute, measured once.
Sights on range poles plumbed by eye. Tape leveled
by eye, and standard tension estimated. No
temperature or sag corrections. Slopes under 3
percent disregarded. Slopes over 3 percent measured
by breaking chain or by chaining slope distance
and applying calculated correction. Maximum
angular error of closure in minutes is 1.5
. Maximum ratio linear error of closure,
1/1000. Pins or stakes set to nearest 0.1
ft. For most land surveys and
highway location surveys, typical
precision specifications may read as
follows:
l Transit angles to nearest minute, measured once.
Sights on range poles, plumbed carefully. Tape
leveled by hand level, with standard tension by
tensionometer or sag correction applied. Temperature
correction applied if air temperature more
than 15° different from standard (68°F). Slopes
under 2 percent disregarded. Slopes over 2
percent measured by breaking chain or by applying
approximate slope correction to slope distance.
Pins or stakes set to nearest 0.05 ft. Maximum
angular error of closure in minutes is
]. Maximum ratio linear error of closure,
1/3,000.
For important boundary surveys and extensive topographical
surveys, typical precision specifications may
read as follows:
. Transit angles by 1rein transit, repeated four
times. Sights taken on plumb lines or on range
poles carefully plumbed. Temperature and slope
corrections applied; tape leveled by level. Pins
set to nearest 0.05 ft. Maximum angular error
of closure in minutes is 0.5. Maximum ratio
linear error of closure is 1/5,000.
Note that in the first two
specifications, onetime angular
measurement is considered sufficiently
precise. Many surveyors, however, use twoline
angular measurement customarily to maintain
a constant check on mistakes.
Measuring Angles vs. Measuring Distances
It is usually the case on a transittape survey that
the equipment for measuring angles is considerably
more precise than the equipment for measuring
linear distances. This fact leads many surveyors
into a tendency to measure angles with great
precision, while overlooking important errors
in linear distance measurements.
Making the precision of angular measurement greater
than that of linear measurement is useless because
your angles are only as good as your linear
distances. Suppose that you are running traverse
line BC at a right deflection angle of 63°45´
from AB, 180.00 ft to station C. You set up
at B, orient the telescope to AB extended, and turn
exactly 63°45´00´´ to the right. But instead of
measuring off 180.00 ft, you measure off 179.96
ft. Regardless of how precisely you turn all
of the other angles in the traverse, every station
will be dislocated because of the error in the
linear measurement of BC.
Remember that angles and linear distances must
be measured with the same precision.
IDENTIFYING ERRORS AND
MISTAKES
IN TRANSIT WORK
In transit work, errors are grouped into three
general
categories; namely, INSTRUMENTAL, NATURAL,
and PERSONAL errors. First, we will
discuss these errors, and then, later, we will explain
the common mistakes in transit work.
