Correcting for slope

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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.

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:

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.