Measuring vertical distances

Vertical distances are perpendicular to the ground or earth surface. We talk usually about height or altitude. Most common methods used are listed below.

Rough methods for vertical leveling

Most surveyors now use levels or transits. Since these instruments are costly and rarely available in rural communities of developing countries, other alternatives may be useful.


The Roman surveyors used chorobates. This level-transit can be made using locally available materials, wood.

Chorobates (improvised level)

Plastic tube leveling

If plastic tube is available, it will be faster than chorobates. Tubing about 6 mm diameter is probably best and normally available. The difference in elevation between of about 25 to 30 m apart can be measured.

Levelling with plastic tube

Differential leveling using level

Level instrument with rods is more precise equipment to find heights difference. Differential leveling assumes that we know the altitude of the starting point A:

Benchmark points (BP)

are stable points of known elevation.
Some BP may typically belong to BP network maintained by the government agency. Their purpose is to provide elevation with high precision and are usually located along road. From there measurements with lower precise can continue.
A system of benchmarks is in demand for further measurements through the whole lifetime of the project.
Benchmarks points

It is not given that near surveyed site any benchmark point is to be found. In that case network of benchmarks will be established by surveyor. Because BP can suffer from damage, at least 3 BPs have to be established. In case of damage, based on two others, the damaged point can be re-established. Benchmarks should be established before leveling is required. Almost any fixed or permanent object can serve as BP. Sometimes nail in tree, wooden stake or clearly identified position on the pavement.

Basic leveling operation with level instrument

Operation with level equipment

The figure above describes the idea of working with equipment called level. General idea should be obvious from the picture. Level instrument is set to horizontal position and has telescopic sight to make a reading of both rods.

BS and FS reading

Positioning the instrument

The exact location of level is not subject of a measurement and in general could be left unknown. However two rules are a common practice:

There are several kinds of instruments.

Spirit bubble

Instrument is leveled into a horizontal position by means of spirit bubble. Spirit bubble is in a transparent container filled with a low viscosity liquid, e.g. alcohol or ether. The precision of bubble depends on the radius of curvature.

In general larger radius will enable better precision. If the precision is to high, bubble becomes too sensitive to any move, and it can be very time consuming to establish horizontal position and high precision might be sometimes unpractical.

Spirit bubble circle

For self-leveling and digital instruments, circular bubble is built-in. Circular container is of lower precision than tubular vial, but lower precision is compensated by other internal optical components of the instrument.

Tripod legs have to be laid solidly, and once the instrument is leveled, we have to avoid further touching
(until the instrument is being taken to a next setup). We use carefully instrument's telescopic sight (optic) only for reading values

Focusing telescopic sight

Running levels

When moving over long distances, we need to move instrument and rods continuously according to points measured. We talk about turning points (TP) then. We turn the instrument over TP to the next setup.

Let's have an example: we need to take level of station B and we know coordinates of benchmark point BM A. The characteristic of terrain doesn't allow us to make a mere one setup to read BS to BM A and FS to B to find out the level of B. We have to use path around, through Setup 1 + Setup 2.

BM A is given. Station B is given and its altitude is to be found. We need a temporary station at TP: either a new station can be established at TP or it can be just a temporary position without any station.

Station BS HI FS Elevation
BM A 3.00 23.00 20.00
TP 1.50 22.50 2.00 21.00
B 0.50 22.00
Sum 4.50 2.50 Δ = 2.00

The sum, which was found to be 2.00 m, serves to check computations above: 2.00 m has to comply with start and end point level difference.

Reciprocal leveling

It was said that setting the instrument should be done nearby center of points being measured. In that case, errors from BS and FS almost cancels each other.

Sometimes requirement of instrument's placement into middle can not be fulfilled because of obstacle, e.g. river. Reading may lead to improper evaluation of the level then.

It is desired to establish control setup ("Setup 2" on the picture) in the situation depicted below. We have to conduct a measurement from each side and average the results in order to avoid exaggeration of some of the errors (see the red color below). It will not cancel errors of improper adjustment of instrument into the horizontal plane. But errors caused by effect of Earth curvature, refraction and some imperfections of optics within the instrument will be almost eliminated.
Reciprocal leveling

Closing the level circuit


Then check of measurement can be made. Otherwise, without closing the level circuit, there is no way to detect or prevent errors and blunders. It is much less expensive to find and correct blunder in the field by closing the loop.

When the circuit is completed, there is usually error of closure detected. Measured levels have to be fixed for error found.

Closing the circuit

In the example above it was planned to establish BM1 to BM4. Point TP serves only to close the loop, because, in such case, we have confidence no blunder was made.
Value +20.000 m in BM1 is given and it was found that error on closure is 14 mm. This error will be divided into whole path:
Segment DistanceFixElev.Elev. fixed
BM1-BM2 2.20 km-0.002 m+20.671 m+20.669 m
BM1-BM3 4.50 km-0.005 m+20.997 m+20.992 m
BM1-BM4 6.71 km-0.007 m+21.331 m+21.324 m
BM1-TP 9.74 km-0.011 m+21.003 m+20.992 m
BM1-BM1 12.66 km-0.014 m+20.014 m+20.000 m

High precision leveling

Better precision can be achieved using more advanced equipment and procedure.

Procedure called three-wire leveling has long been applied for precise work. The improvement stands in crosshair, which is built into telescopic sight. Instead of the cross, there are 2 additional stadia hairs. Surveying engineer reads central value together with lower and upper. The average computed provides more accurate reading. It provides great protection against blunders as well.

The more up-to-date method is level instrument equipped with optical micrometer, which is able to move its vertical sight. The crosshair can be accurately aligned to mark on the rod then and correction from micrometer is added to the reading.

Ordinary level rods are not used for precision leveling. Instead, a precise level rod is used. It is constructed to enforce holding in a vertical position.

  • Three-wire leveling
  • Level instrument equipped with optical micrometer
  • Used together with precise level rod
Cross hair for three-wire leveling; micrometer

Rod shots

Sometimes it is desirable to collect high density coverage of many points, respective their elevations. It can be processed as rod shots. Running the levels is conducted as usually. And from each setup we collect, in addition, reading from surrounding points of interest.
Each rod shot is written onto separate line in the field book.
Leveling with rod shots

Measuring distances using level instrument

It is common that the optics in telescope is calibrated to use reading of upper and lower wire of crosshair to evaluate distance from instrument.
For example, upper wire reading is 1.235 m and lower wire reading is 1.000 m. Then the distance of rod from instrument is 0.235 × 100 = 23.5 m.
The multiplier—in this case 100—might differ and have to be found in manual of used equipment.

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