tensions for tapes supported at only the ends as
For 100-ft tapes, from 20 to 30 lb
angle, A, or the difference in elevation h between
the taped stations.
When the vertical angle is used, the formula
for slope correction is as follows:
For 150-ft tapes, from 25 to 30 lb
For 200-ft tapes, from 30 to 40 lb
Generally, for a heavy 100-ft tape weighing
about 3 lb that was standardized, whether
supported throughout or at the ends only, the
systematic error per tape length caused by sag is
10-lb tension = 0.37 ft
20-lb tension = 0.09 ft
30-lb tension = 0.04 ft
For the Engineering Aids survey work,
measurements are normally in the lower order of
precision. The correction for sag varies with the
cube of the unsupported length; for short spans,
it is often negligible.
CORRECTING FOR SLOPE. When you
take a measurement with a tape along an inclined
plane (along the natural slope of the ground),
obviously, the taped distance is greater than the
horizontal distance. This taped distance is
represented by s in figure 12-15.
The difference between the slope distance and
the horizontal distance (s d) is called the slope
correction. This correction is always subtracted
from the slope distance. To compute for the slope
correction, you should know either the vertical
Figure 12-15.-Correction for slope distance.
When the difference in elevation is used, the
approximate formula derived by Pythagorean
theorem of a right triangle (fig. 12-15) for the
slope correction is as follows:
But for a small slope, d is approximately equal
to s; therefore,
For slopes greater than 5 percent, a closer
approximation of Ch can be determined by
expanding the above formula to this form.