Which of the following is a reason for negative error in chaining?
📝 Detailed Explanation: Understanding Negative Error
In surveying, an error is defined as the Measured Value minus the True Value. A negative error occurs when the measured length is shorter than the true length (Measured Value < True Value).
Effect of Temperature on Measurement
When the ambient temperature rises above the standard temperature at which a tape was calibrated, the metal tape expands due to thermal expansion. This makes the tape physically longer than its stated length. When you use this elongated tape to measure a distance, you are essentially using a longer-than-expected "ruler," which leads to an under-measurement of the distance. For example, the tape might read 100 m when the true distance is actually 100.1 m. This results in a measured value that is less than the true value, hence a negative error.
Temperature Correction Formula
The correction for temperature is calculated using the formula:
Ct = L × α × (Tm - T0)
Where:
- Ct = Correction for temperature
- L = Measured distance
- α = Coefficient of thermal expansion of the tape material
- Tm = Average temperature in the field during measurement
- T0 = Standardization temperature of the tape
When there is a rise in temperature (Tm > T0), the correction (Ct) is positive, which means the error is negative.
Analysis of Other Options (Positive Errors)
The other options provided all result in a positive error (Measured Value > True Value):
- Sag in chain: The tape hangs in a curve (catenary), which is a longer path than the straight horizontal distance.
- Wrong ranging / Not being straight: The tape follows a crooked path, which is longer than the direct straight line between the two points.