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Levelling: height from backsight and foresight

Which altitude has point and how much must I raise or lower?

Answer: With the levelling instrument you sight first back at a point with known height (backsight) and then forward at the point you want to know (foresight). Known height plus backsight gives the sight height, i.e. the height of the instrument's line of sight. Sight height minus foresight gives the point's height. The calculator also shows what the staff should show when the point is exactly at the design height, and how many mm you are too high or too low.

Formula

Sigtekote = kendt kote + bagsigt

Punktets kote = sigtekote − forsigt

Aflæsning ved projekteret kote = sigtekote − projekteret kote

Afvigelse = (punktets kote − projekteret kote) × 1000 mm. Positiv: punktet ligger for højt og skal sænkes. Negativ: det skal hæves

Symbols and units in the formula
SymbolMeaningUnit
fikskoteKnown elevation (fixed point or spot height)m
bagsigtBack sight (reading on the known point)m
forsigtForesight (reading at the point)m
projekteretDesign height in the pointm
=Point's heightm
=Sight elevation (instrument height)m
=Reading when the point is at the projected elevationm
=Afvigelse fra projekteret kote (+ = for højt)mm

Validity and source

Source
Nivellement: kote = kendt kote + bagsigt − forsigt

Does not apply when

  • If you move the instrument you get a new sight altitude: take a new backsight on a point with known altitude. Finish a levelling line at a known point so you can see the closing error. The staff must be vertical: an angled staff always shows too much.

Worked example

The calculator's own default values inserted. The figures are calculated with exactly the formula the tool uses.

Substituted

  • Known elevation (fixed point or spot height)12.35 m
  • Back sight (reading on the known point)1.43 m
  • Foresight (reading at the point)1.81 m
  • Design height in the point11.95 m

Giver

  • Point's height11.965 m
  • Sight elevation (instrument height)13.775 m
  • Reading when the point is at the projected elevation1.825 m
  • Afvigelse fra projekteret kote (+ = for højt)15 mm

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Sådan bruger du den

Med nivelleringsinstrumentet finder du koter og afsætter højder. Beregneren giver punktets kote, sigtekoten og den aflæsning, der giver projekteret kote.

Step by step

  1. Stil instrumentet op, og tag bagsigt på et punkt med kendt kote.
  2. Tag forsigt på punktet.
  3. Skriv den projekterede kote.
  4. Læs afvigelsen, og ret op.

Typical errors

  • At bytte om på bag- og forsigt.
  • At holde stadiet skævt.
  • At flytte instrumentet uden nyt bagsigt.

Examples from everyday life

Afretning af sættelag

Kotepælen har 12,350. Bagsigt 1,425 og forsigt 1,810. Projekteret kote er 11,950.

Known elevation (fixed point or spot height)
12.35 m
Back sight (reading on the known point)
1.425 m
Foresight (reading at the point)
1.81 m
Design height in the point
11.95 m

It means: Punktet ligger i 11.965 m, sigtekoten er 13.775 m, og afvigelsen er 15 mm, altså for højt. Stadiet skal vise 1.825 m, når punktet er rigtigt.

Bund af rørgrav

Fikspunktet har 24,800. Bagsigt 0,982 og forsigt 1,554. Bunden skal ligge i 24,250.

Known elevation (fixed point or spot height)
24.8 m
Back sight (reading on the known point)
0.982 m
Foresight (reading at the point)
1.554 m
Design height in the point
24.25 m

It means: Bunden ligger i 24.228 m, og afvigelsen er -22 mm, altså for lavt. Fyld op og komprimer, til stadiet viser 1.532 m.

Rule of thumb

Større aflæsning betyder lavere punkt.

How to check the answer

Kendt kote plus bagsigt minus forsigt: 12,350 + 1,425 − 1,810 = 11,965.