Temperature Error in Chaining

How Temperature Affects Measurement

A surveying chain or tape is calibrated at a specific standard temperature. If the temperature during the measurement is different from this standard temperature, the actual length of the chain or tape will change:

• If the field temperature is higher than the standard temperature, the chain/tape expands and becomes longer.
• If the field temperature is lower than the standard temperature, the chain/tape contracts and becomes shorter.

Understanding Temperature Error

This change in the instrument's length leads to an error in the measured distance:

• When the chain/tape is longer (due to higher temperature), it means the marked length (e.g., 20m) covers a greater true distance. When measuring a line, you will use fewer applications of the tape than you should, resulting in the measured distance being shorter than the actual distance (a negative error).
• When the chain/tape is shorter (due to lower temperature), the marked length covers a smaller true distance. You will use more applications of the tape, resulting in the measured distance being longer than the actual distance (a positive error).

The magnitude of this error depends on the difference between the field temperature and the standard temperature, the coefficient of thermal expansion of the material, and the total length being measured.

Why the Error is Cumulative

In chaining or taping a line, the entire length is measured by applying the chain or tape multiple times end-to-end. The temperature condition is generally consistent over the length of the line being measured. Therefore, the error introduced in each application of the chain or tape (whether positive or negative) adds up over the entire length. Errors that accumulate in this manner are called cumulative errors.

Since the error can be either negative (when temperature is high) or positive (when temperature is low), the error due to temperature in chaining is a cumulative + or - error.

Cumulative vs. Compensating Errors

• Cumulative errors: These errors tend to accumulate and become larger as the measurement process is repeated over a longer distance or more observations are made. They are usually caused by factors that systematically affect the measurement in the same direction (like temperature or incorrect chain length).
• Compensating errors: These errors are random and tend to cancel each other out over a series of measurements. They are often caused by factors that are equally likely to cause a positive or negative error (like errors in marking the ends of the chain).

Temperature error is not random; it consistently affects the length of the tape/chain in one direction (either making it longer or shorter) for a given temperature difference, causing the error to add up. Therefore, it is a cumulative error.

Based on the effect of temperature on the length of the measuring instrument and how this error adds up over the total measured distance, the error due to temperature in chaining is a cumulative error that can be either positive or negative.