_______ is the correct formula to determine the elevation difference (dz) between two points on the ground using a total station. (VD = Vertical difference, HI = Instrument height and HR = Reflector height)
- Adz = VD - (HI + HR)
- Bdz = VD + (HI - HR)Correct
- Cdz = VD(HI + HR)
- Ddz = VD(HI - HR)
Solution
Concept
Elevation difference = vertical difference measured by the total station + instrument height - reflector (prism) height.
Formula
dz = VD + HI - HR
Step-by-step solution
1. The instrument axis is HI above the station point. 2. The total station measures VD from its axis to the prism. 3. The prism is HR above the target point. 4. So the ground difference is dz = HI + VD - HR = VD + (HI - HR).
Explanation
The total station measures height from its own axis to the prism centre. To get the height difference between the two ground points, add the instrument height and subtract the reflector height. This gives option B.
Why the other options are wrong
A: HR must be subtracted but HI must be added, not subtracted. C and D: heights are added or subtracted, never multiplied.
Shortcut
Ground to ground: go up by HI, then by VD, then down by HR.
Common mistake
Mixing up the signs of HI and HR.
Correct answer: B) dz = VD + (HI - HR)