In a chain surveying work of a traverse, it is necessary to apply the correction due to sag for the tape. The correction is

⚖️ Core Concept: Understanding Sag

When a survey tape or chain is stretched between two supports, it does not form a perfectly straight line. Due to its own weight, it hangs downwards in a curve known as a catenary. This means the actual measured length along the curved tape is always longer than the true, straight-line horizontal distance between the two support points.

Because the measured distance is always too long, this introduces a positive error into the measurement. To get the correct distance, a correction must be applied, and this correction must therefore be always negative (subtractive).

🔬 Formula for Sag Correction

The magnitude of the sag correction ( \(C_s\) ) depends on the weight of the tape, the length of the span, and the tension applied. The formula is:

$$ C_s = \frac{w^2 L^3}{24 P^2} = \frac{W^2 L}{24 P^2} $$

• \(C_s\) = The sag correction (always negative)
• \(L\) = The length of the tape suspended between supports
• \(P\) = The pull or tension applied to the tape
• \(w\) = The weight of the tape per unit length
• \(W\) = The total weight of the tape between the supports (W = wL)

As you can see from the physics, sag will always occur unless the tape is fully supported, so the correction will always be required and will always be negative.

📊 Summary of Errors and Corrections

It's helpful to remember the nature of different errors in chain surveying: