The correction to be applied to each 30 m chain for a line measurement along a slope of θ is

🎯 Understanding Slope Correction

When you measure a distance along a slope, this measured length (the hypotenuse) is always longer than the true horizontal distance (the base of the triangle). To get the correct horizontal measurement, a slope correction (C_s) must be calculated and subtracted. Therefore, the correction is always negative.

🔬 Derivation of the Formula

The relationship between the sloped distance (L), the horizontal distance (H), and the slope angle (θ) is based on basic trigonometry.

• The horizontal distance is given by: H = L cos(θ)
• The slope correction (C_s) is the difference between the measured slope length and the true horizontal length: C_s = L - H
• Substituting the first equation into the second gives: C_s = L - L cos(θ)
• Factoring out L, we get the general formula: C_s = L(1 - cosθ)

For a 30 m chain length, where L = 30 m, the formula becomes: C_s = 30(1 - cosθ).

🖼️ Visualizing the Derivation

The diagram below illustrates the relationship between the sloped length (L), the horizontal length (H), and the angle (θ), forming a right-angled triangle.

💡 Alternative Formula

It's also useful to know the alternative formula for slope correction when the difference in elevation (h) between the two ends of the measured line (L) is known:

C_s ≈ h² / 2L

This is a very common and practical approximation used in the field.