Differential Leveling Closure in Windy Conditions
A two-person crew is running a differential level loop to establish a temporary benchmark near a construction site. The loop starts and ends on a known benchmark (elevation 100.000 ft). They use a 25-ft rod and a level with a 32x telescope. The wind is gusting to 25 mph, and the rod is held without a rod level. The loop consists of 8 setups, each with backsight and foresight distances averaging 150 ft. The recorded elevation difference is +0.048 ft after completing the loop. The allowable closure for this project is 0.05 ft * sqrt(miles). The total loop length is 0.6 miles. The crew chief wants to accept the loop because the misclosure is only 0.048 ft, which is less than 0.05 ft. However, the instrument was not shielded from the wind, and the rod was not plumbed with a level. What should the crew chief do?
1. Calculate the allowable misclosure for the loop and determine if the observed misclosure is within tolerance.
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Allowable misclosure = 0.05 ft * sqrt(0.6 miles) = 0.05 * 0.7746 = 0.0387 ft. The observed misclosure is 0.048 ft, which exceeds the allowable 0.0387 ft. Therefore, the loop does not meet the project tolerance. Even though 0.048 ft is less than 0.05 ft, the tolerance is scaled by the square root of the distance, not a fixed 0.05 ft. The crew chief must not accept the loop as is.
2. Identify the sources of error in the setup that could contribute to the misclosure and recommend corrective actions.
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Sources of error: (1) Wind causing the level to vibrate and the rod to sway, leading to reading errors. (2) Rod not plumb: without a rod level, the rod may be tilted, causing the reading to be too high (if tilted away) or too low (if tilted toward the instrument). (3) Unequal backsight and foresight distances: although average 150 ft, if not balanced per setup, earth curvature and refraction errors may not cancel. (4) Instrument not shielded: wind can cause the compensator to oscillate. Corrective actions: Re-observe the loop with proper shielding (windbreak) and use a rod level to ensure plumb. Balance backsight and foresight distances per setup. If wind persists, use a more stable instrument or wait for calmer conditions. Re-run the loop and check misclosure again.