In this section we provide information on procedures used in making level and traverse computations. We also discuss methods of differential leveling, including steps to follow in checking level notes. Coverage includes information on adjusting intermediate bench marks as well as a level net. In addition, we describe several methods of plotting horizontal control that may be used in determining the bearing of the traverses. These methods include plotting angles by protractor and scale, plotting angles from tangents, and plotting by coordinates. We point out some of the common types of mistakes that the EA may encounter in making or checking computations, and we provide some information about locating mistakes.

Before computations are started, a close check on the field data for completeness and accuracy is required. This includes checking the field notes to ensure that they accurately reflect what was actually measured; for example, a deflection-angle note 7901'R must be checked to be sure that the angle actually measured 7901' (by ascertaining that the sum of the angle and the closing angle is 360 or within allowable differences) and to ensure that the angle was actually turned to the right.

A field measurement may itself require transformation (called reduction) before it can be applied as a value in computations; for example, field notes may show plate readings for two-, four-, or

Figure 7-4.Differential-level circuit and notes for differential leveling.

In a closed traverse you must attain a ratio of linear error of closure and a ratio of angular error of closure that are within the maximums specified for, or implied from, the nature of the survey.

An error that is within the maximum allowable is eliminated by adjustment. "Adjustment" means the equal distribution of a sum total of allowable error over the separate values that contribute to the total. Suppose, for example, that for a triangular closed traverse with interior angles about equal in size, the sum of the measured interior angles comes to 17957. The angular error of closure is 03. Because there are three interior angles about equal in size, 01 would be added to the measured value of each angle.

In making level computations, be sure to check the notes for a level run by verifying the beginning bench mark (BM); that is, by determining that the correct BM was used and its correct elevation was duly recorded. Then check the arithmetical accuracy with which you added backlights and subtracted foresights. The difference between the sum of the foresights taken on BMs or turning points (TPs) and the sum of the backlights taken on BMs or TPs should equal the difference in elevation between the initial BM or TP and the final BM or TP. This fact is shown in figure 7-4. You must remember that this checks the arithmetic only. It does not indicate anything about how accurately you made the vertical distance measurements.

Adjusting Intermediate Bench Mark Elevations

Level lines that begin and end on points that have fixed elevations, such as benchmarks, are often called level circuits. When leveling is accomplished between two previously established bench marks or over a loop that closes back on the starting point, the elevation determined for the final bench mark is seldom equal to its previously established elevation. The difference between these two elevations for the same bench mark is known as the error of closure. The REMARKS column of figure 7-4 indicates that the actual elevation of BM 19 is known to be circuit is 136.457 136.442 = 0.015 ft.

Assume that errors have occurred progressively along the line over which the leveling was accomplished. You make adjustments for these errors by distributing them proportionally along the line as shown by the following example. If you refer to figure 7-4, you will notice that the total distance between BM 35 and BM 19, over which the line of levels was run, is 2,140 ft. The elevation on the closing BM 19 is found to be 0.015 ft greater than its known elevation. You must therefore adjust the elevations found for the intermediate BMs 16, 17, and 18.

The amount of correction is calculated as follows:  

BM 16 is 440 ft from the starting BM. The total length distance between the starting and closing BMs is 2,140 ft. The error of closure is 0.015 ft. By substituting these values into the above formula, the correction is as follows:

Since the observed elevation of the closing BM is greater than its known elevation, the adjustments are subtracted from the intermediate BMs. Therefore, for BM 16, the adjusted elevation is 134.851 0.003 = 134.848. The adjustments for inter-mediate BMs 17 and 18 are made in a similar manner.

The error of closure that can be allowed depends on the precision required (first, second, or third order). The allowable error of closure in leveling is expressed in terms of a coefficient times the square root of the horizontal length of the actual route over which the leveling was accomplished

Most differential leveling (plane surveying) is third-order work. In third-order leveling, the closure is usually made on surveys of higher accuracy without doubling back to the benchmark at the original starting point of the level circuit. The length of the level circuit, therefore, is the actual distance leveled. For third-order leveling, the allowable error is

Refer again to figure 7-4. By adding the sight distances in the sixth and seventh columns of the figure, you will find that the length of the level circuit is 2,140 ft (or 0.405 miles). The allowable error of closure, then, is

 Since the actual error is only 0.015 ft, the results are sufficiently accurate for third-order precision.

First-order leveling is even more precise. The allowable error cannot be greater than