CONSTRUCTION SLOPE · FIELD TOOL
Elevation difference = horizontal distance × tan(vertical angle) + instrument height − target height. Sighting a point 50 m away at +5°, with instrument and target both 1.5 m high, the point is 4.374 m higher: RL 104.374 from a station at 100.000, 50.19 m away along the slope.
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| Level of target point (RL) | 104.374 m |
| Slope distance | 50.19 m |
| Ground gradient between points | 8.75 % |
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Δh = HD × tan(α) + HI − HT
Target level = station level + Δh
Slope distance = HD ÷ cos(α)Horizontal distance 50 m, vertical angle +5°, instrument 1.5 m, target 1.5 m, station RL 100.000:
| Vertical angle | Δh per 100 m |
|---|---|
| 1° | 1.746 m |
| 2° | 3.492 m |
| 5° | 8.749 m |
| 10° | 17.633 m |
| 15° | 26.795 m |
Δh = HD × tan(α) + HI − HT, where HD is the horizontal distance, α the vertical angle above or below horizontal, HI the instrument height and HT the target (prism) height.
Convert it to a vertical angle first: vertical angle = 90° − zenith angle. A zenith reading of 85° is +5°.
Over long sights, roughly beyond 300 m. The combined correction is about 0.0675 × d² metres with d in kilometres: 6.75 mm at 316 m, 67.5 mm at 1 km.