The correction for slope in chaining is proportional to

🎯 Understanding Slope Correction

When measuring a distance on sloped ground, the measured length (L) is always greater than the true horizontal distance. The slope correction (C_s) is the value that must be subtracted from the measured length to find the true horizontal distance. This correction is always negative.

🔬 Mathematical Proportionality

The approximate but widely used formula for slope correction, when the difference in elevation (h) between the two ends of the chain (L) is known, is:

C_s ≈ h² / 2L

In this formula:

• C_s is the slope correction.
• h is the vertical distance (difference in elevation).
• L is the length measured along the slope.

Since the measured length L is constant for a given chain length, the formula clearly shows that the correction C_s is directly proportional to the square of the vertical distance (h²).

💡 Alternative Formula (Using Angle)

It's also important to remember the exact formula for slope correction when the slope angle (θ) is known:

C_s = L(1 - cosθ)

While this formula is exact, the proportionality to h² is derived from the approximation, which is very accurate for the small angles typically encountered in surveying.