Checking for precision

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Adjusting a chain of quadrilaterals

Intermediate Engineering

Location of points

CHECKING FOR PRECISION

Early in this chapter the fact was stated that the precision of a triangulation survey may be classified according to (1) the average triangle closure and (2) the discrepancy between the measured length of a base line and its length as computed through the system from an adjacent base line.

Average Triangle Closure

The check for average triangle closure is made after the station adjustment. Suppose that, for the quadrilateral shown in figure 15-28, the values of the as follows:

. The sum of the angles that make up each of the overlapping triangles within the quadrilateral is as follows:

The sum of the closing errors for the four triangles is (09 + 01 + 07 + 01), or 18 seconds. The average triangle closure for the four triangles, then, is 18/4, or 04.5 seconds. For third-order triangulation, the maximum average triangle closure is 05 seconds; therefore, for the third-order work this closure would be acceptable.

Base Line Discrepancy

If AD is the base line in figure 15-28, then BC would be the adjacent baseline. assume that the baseline AD measures 700.00 feet and compute the length of BC on the basis of the angles we have adjusted. These angles now measure as follows:

The natural sine of each of these angles is as follows:

You can compute the length of BC by (1) solving triangle ABD for AB and triangle ABC for BC and (2) ACD for DC and triangle DBC for BC. Using the law of sines and solving triangle ABD for AB, we have

Solving triangle ABC for side BC, we have

Solving triangle ACD for side CD, we have

Solving triangle DBC for side BC, we have

Figure 15-29.-Bearing and distances of a quadrilateral.

Thus we have, by computation of two routes, values for BC of 433.322 feet and 433.315 feet. There is a BC would be taken to be the average between the two, or (to the nearest 0.01 foot) 433.32 feet.

Suppose, now, that the precision requirements for the base line check are 1/5,000. This means that the ratio between the difference in lengths of the measured and computed base line must not exceed 1/5,000. You measure the base line BC and discover that it measures 433.25 feet. For a ratio of error of 1/5,000, the maximum allowable error (discrepancy between computed and measured value of base line) is 433.25/5,000, or 0.08 feet. The error here is (433.32 433.25), or 0.07 foot, which is within the allowable limit.