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Curvature and Refraction

h_{c + r} = 0.0239 D^{2} (D in thousands of ft, h in ft)

Level surfaces follow the geoid, so a horizontal telescope line lies above the level surface by about 0.667 M² ft (M in miles) from curvature alone. Refraction bends the ray down (~14% of curvature). Combined handbook values: 0.0239 D² (often listed as curvature; 0.0206 D² combined) with D in thousands of feet. SI combined ≈ 0.0675 K² metres (K in kilometres). Subtract from the rod reading on long sights.

h_{c + r}

(ft)

Combined correction (rod too high)

D

Sight distance in thousands of feet

M

Sight distance in miles (alt. form)

K

Sight distance in kilometres (SI)

Step-by-step solved example

A 4000 ft sight. Using h = 0.0239 D² (D in thousands of feet), find the combined correction.

Level line vs curved earth — the same instrument-and-rods figure.

1. D
4000 ft = 4 thousand feet, so D = 4.
$D = 4$
2. Correction
h = 0.0239 × 16 = 0.382 ft (apparent rod reading too large; subtract).
$h = 0.382 ft$

Answer: h = 0.382 ft (subtract from rod)

10 practice questions

0/10 correct

1.For D = 2 (2000 ft sight), 0.0239 D² is nearest

2.Curvature alone (M in miles) is about

3.Refraction makes the line of sight

4.1 km sight, SI combined 0.0675 K². h ≈

5.On a long foresight the uncorrected rod reading is too

6.Balanced BS and FS distances cause C+R errors to

7.0.0206 D² (D in thousands of ft) is commonly the

8.A 3-mile sight, curvature 0.667 M², is nearest

9.For ordinary construction leveling of 150 ft sights, C+R is

10.Earth radius R ≈ 3959 mi enters h = D²/(2R), which is why h grows