Tape Corrections in Surveying

In surveying, tape corrections are adjustments made to measured distances using a surveyor's tape due to various factors such as temperature, tension, slope, and sag. These corrections are crucial for achieving accurate measurements in land surveying projects. There are several types of tape corrections, each addressing different sources of error. Here's an overview of the common tape corrections along with solved examples:

1. Correction for Absolute Length: This correction compensates for any deviation in the actual length of the tape from its nominal length due to manufacturing errors. It is usually provided by the tape manufacturer.

   Example:
   If the nominal length of the tape is 30 meters, but the actual measured length is found to be 30.02 meters, the correction for absolute length would be -0.02 meters.

2. Correction for Pulling or Tension: When the tape is stretched under tension during measurement, it elongates slightly, leading to an overestimation of distance. This correction accounts for the elongation of the tape.

   Example:
   If the measured distance with a tension of 20 N is 100 meters, and the tape has a pulling correction factor of 0.1 mm/N, the correction would be 20 N * 0.1 mm/N = 2 mm. Hence, the corrected distance is 100 meters - 0.002 meters = 99.998 meters.

3. Correction for Temperature: Changes in temperature cause the tape to expand or contract, affecting its length. This correction compensates for temperature-induced errors.

   Example:
   If the temperature during measurement is 25°C, but the standard temperature is 20°C, and the coefficient of thermal expansion for the tape material is 12 x 10^-6 per degree Celsius, the correction can be calculated as follows:
   Correction = (25°C - 20°C) * 12 x 10^-6 * measured distance.
   If the measured distance is 200 meters, the correction would be (25 - 20) * 12 x 10^-6 * 200 = 1.2 meters.

4. Correction for Slope or Inclination: When measuring on sloping terrain, the tape is not horizontal, leading to an error in distance measurement. This correction accounts for the effect of slope on the measured distance.

   Example:
   If the slope angle is 5 degrees uphill, and the measured distance along the slope is 150 meters, the correction can be calculated using trigonometry. If 'd' is the horizontal distance, then d = measured distance * cos(slope angle).
   d = 150 * cos(5°) ≈ 150 * 0.9962 ≈ 149.43 meters.

5. Correction for Sag: When the tape sags due to its own weight, it causes an error in distance measurement. This correction accounts for the effect of sag on the measured distance.

   Example:
   If the tape sags by 0.02 meters over a measured distance of 100 meters, the correction for sag would be -0.02 meters.

After calculating these corrections, they are applied to the measured distances to obtain corrected distances, ensuring greater accuracy in surveying measurements.