Which corrections are needed when a measuring tape is used for precise surveying?

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surveying Figure 1: Photogrammetric photographs from two short, overlapping flight strips arranged for supplying mapping details. Photo-control points are shown on only one photograph; shading indicates a typical terrain feature such as a lake (see text).

When using a measuring tape for precise surveying, several physical factors can introduce errors that must be accounted for to ensure accuracy. To maintain precision, especially in geodetic work where errors must be limited to one part in 1,000,000, the following corrections are required if conditions differ from the tape's standardized values:1

Sag: When a tape is suspended between two points (such as tripods) rather than laid flat on the ground, it naturally hangs in a curve. A correction for this sag must be applied to determine the true horizontal distance.1
Tension: The amount of pull applied to the tape affects its length. If the tension differs from the force used during the tape's standardization, a correction is necessary to account for the resulting elastic stretch.1
Temperature: Metal tapes expand or contract with changes in temperature. If the field temperature deviates from the temperature at which the tape was calibrated, a correction must be calculated to adjust for the thermal expansion or contraction of the material.1

Additionally, the slope of the measured line must always be accounted for to reduce the measurement to the horizontal plane.1