![Tide station leveling](https://upload.wikimedia.org/wikipedia/commons/1/1a/Tide_station_leveling.jpg)
Levelling or leveling (
American English
American English, sometimes called United States English or U.S. English, is the set of variety (linguistics), varieties of the English language native to the United States. English is the Languages of the United States, most widely spoken lan ...
;
see spelling differences) is a branch of
surveying
Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is ca ...
, the object of which is to establish or verify or measure the
height
Height is measure of vertical distance, either vertical extent (how "tall" something or someone is) or vertical position (how "high" a point is).
For example, "The height of that building is 50 m" or "The height of an airplane in-flight is abou ...
of specified points relative to a datum. It is widely used in
geodesy
Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equivale ...
and
cartography
Cartography (; from grc, χάρτης , "papyrus, sheet of paper, map"; and , "write") is the study and practice of making and using maps. Combining science, aesthetics and technique, cartography builds on the premise that reality (or an im ...
to measure
vertical position
Vertical position or vertical location, also known as vertical level or simply level, is a position along a vertical direction above or below a given vertical datum (reference level).
Vertical distance or vertical separation is the distance betwee ...
with respect to a
vertical datum
In geodesy, surveying, hydrography and navigation, vertical datum or altimetric datum, is a reference coordinate surface used for vertical positions, such as the elevations of Earth-bound features (terrain, bathymetry, water level, and built stru ...
, and in
construction
Construction is a general term meaning the art and science to form objects, systems, or organizations,"Construction" def. 1.a. 1.b. and 1.c. ''Oxford English Dictionary'' Second Edition on CD-ROM (v. 4.0) Oxford University Press 2009 and com ...
to measure height differences of construction artifacts.
Optical levelling
Optical levelling, also known as spirit levelling and differential levelling, employs an ''
optical level
A level is an optical instrument used to establish or verify points in the same horizontal plane in a process known as levelling, and is used in conjunction with a levelling staff to establish the relative height levels of objects or marks. It is ...
'', which consists of a precision telescope with
crosshair
A reticle, or reticule also known as a graticule, is a pattern of fine lines or markings built into the eyepiece of an optical device such as a telescopic sight, spotting scope, theodolite, optical microscope or the screen of an oscilloscope ...
s and
stadia marks. The cross hairs are used to establish the level point on the target, and the stadia allow range-finding; stadia are usually at ratios of 100:1, in which case one metre between the stadia marks on the levelling staff represents 100metres from the target.
The complete unit is normally mounted on a
tripod
A tripod is a portable three-legged frame or stand, used as a platform for supporting the weight and maintaining the stability of some other object. The three-legged (triangular stance) design provides good stability against gravitational loads ...
, and the telescope can freely rotate 360° in a horizontal plane. The surveyor adjusts the instrument's level by coarse adjustment of the tripod legs and fine adjustment using three precision levelling screws on the instrument to make the rotational plane horizontal. The surveyor does this with the use of a
bull's eye level
A bull's eye level is a type of spirit level that allows for the leveling of planes in two dimensions — both the 'pitch' and 'roll' in nautical terms. Standard tubular levels only consider one dimension. Bull's eye levels are used prim ...
built into the instrument mount.
The surveyor looks through the eyepiece of telescope while an assistant holds a vertical
level staff {{short description, Graduated rod used to measure differences between heights
A level staff, also called levelling rod, is a graduated wooden or aluminium rod, used with a levelling instrument to determine the difference in height between points ...
which is graduated in inches or centimeters. The level staff is placed vertically using a level, with its foot on the point for which the level measurement is required. The telescope is rotated and focused until the level staff is plainly visible in the crosshairs. In the case of a high accuracy manual level, the fine level adjustment is made by an altitude screw, using a high accuracy bubble level fixed to the telescope. This can be viewed by a mirror whilst adjusting or the ends of the bubble can be displayed within the telescope, which also allows assurance of the accurate level of the telescope whilst the sight is being taken. However, in the case of an automatic level, altitude adjustment is done automatically by a suspended prism due to gravity, as long as the coarse levelling is accurate within certain limits. When level, the staff graduation reading at the crosshairs is recorded, and an identifying mark or marker placed where the level staff rested on the object or position being surveyed.
Procedure
![NivellementExample](https://upload.wikimedia.org/wikipedia/commons/9/97/NivellementExample.svg)
A typical procedure for a linear track of levels from a known datum is as follows. Set up the instrument within of a point of known or assumed elevation. A rod or staff is held vertical on that point and the instrument is used manually or automatically to read the rod scale. This gives the height of the instrument above the starting (backsight) point and allows the height of the instrument (H.I.) above the datum to be computed.
The rod is then held on an unknown point and a reading is taken in the same manner, allowing the elevation of the new (foresight) point to be computed. The difference between these two readings equals the change in elevation, which is why this method is also called ''differential levelling''. The procedure is repeated until the destination point is reached. It is usual practice to perform either a complete loop back to the starting point or else close the traverse on a second point whose elevation is already known. The closure check guards against blunders in the operation, and allows residual error to be distributed in the most likely manner among the stations.
Some instruments provide three crosshairs which allow
stadia
Stadia may refer to:
* One of the plurals of stadium, along with "stadiums"
* The plural of stadion, an ancient Greek unit of distance, which equals to 600 Greek feet (''podes'').
* Stadia (Caria), a town of ancient Caria, now in Turkey
* Stadi ...
measurement of the foresight and backsight distances. These also allow use of the average of the three readings (3-wire leveling) as a check against blunders and for averaging out the error of interpolation between marks on the rod scale.
The two main types of levelling are single-levelling as already described, and double-levelling (double-rodding). In double-levelling, a surveyor takes two foresights and two backsights and makes sure the difference between the foresights and the difference between the backsights are equal, thereby reducing the amount of error. Double-levelling costs twice as much as single-levelling.
Turning a level
When using an optical level, the endpoint may be out of the effective range of the instrument. There may be obstructions or large changes of elevation between the endpoints. In these situations, extra setups are needed. Turning is a term used when referring to moving the level to take an elevation shot from a different location.
To "turn" the level, one must first take a reading and record the elevation of the point the rod is located on. While the rod is being kept in exactly the same location, the level is moved to a new location where the rod is still visible. A reading is taken from the new location of the level and the height difference is used to find the new elevation of the level gun. This is repeated until the series of measurements is completed.
The level must be horizontal to get a valid measurement. Because of this, if the horizontal crosshair of the instrument is lower than the base of the rod, the surveyor will not be able to sight the rod and get a reading. The rod can usually be raised up to 25 feet high, allowing the level to be set much higher than the base of the rod.
Trigonometric levelling
The other standard method of levelling in construction and surveying is called trigonometric levelling, which is preferred when levelling "out" to a number of points from one stationary point. This is done by using a
total station
A total station (TS) or total station theodolite (TST) is an electronic/optical instrument used for surveying and building construction. It is an electronic transit theodolite integrated with electronic distance measurement (EDM) to measure b ...
, or any other instrument to read the
vertical, or zenith angle to the rod, and the change in elevation is calculated using
trigonometric functions
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all ...
(see example below). At greater distances (typically 1,000
feet
The foot ( : feet) is an anatomical structure found in many vertebrates. It is the terminal portion of a limb which bears weight and allows locomotion. In many animals with feet, the foot is a separate organ at the terminal part of the leg made ...
and greater), the
curvature of the Earth
Spherical Earth or Earth's curvature refers to the approximation of figure of the Earth as a sphere.
The earliest documented mention of the concept dates from around the 5th century BC, when it appears in the writings of Greek philosophers. I ...
, and the
refraction
In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomeno ...
of the instrument
wave
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (res ...
through the
air
The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing f ...
must be taken into account in the measurements as well (see section below).
Ex: an instrument at Point A reading to a rod at Point B a zenith angle of < 88°15'22" (degrees,
minutes, seconds of arc) and a slope distance of 305.50 feet not factoring rod or instrument height would be calculated thus:
: cos(88°15'22")(305.5)≈ 9.30 ft.,
meaning an elevation change of approximately 9.30 feet in elevation between Points A and B. So if Point A is at 1,000 feet of elevation, then Point B would be at approximately 1,009.30 feet of elevation, as the reference line (0°) for zenith angles is straight up going clockwise one complete revolution, and so an angle reading of less than 90 degrees (horizontal or flat) would be looking uphill and not down (and opposite for angles greater than 90 degrees), and so would gain elevation.
Refraction and curvature
The curvature of the earth means that a line of sight that is horizontal at the instrument will be higher and higher above a spheroid at greater distances. The effect may be insignificant for some work at distances under 100 meters.
The line of sight is horizontal at the instrument, but is not a straight line because of
atmospheric refraction
Atmospheric refraction is the deviation of light or other electromagnetic wave from a straight line as it passes through the atmosphere due to the variation in air density as a function of height. This refraction is due to the velocity of light t ...
. The change of air density with elevation causes the line of sight to bend toward the earth.
The combined correction for refraction and curvature is approximately:
:
or
For precise work these effects need to be calculated and corrections applied. For most work it is sufficient to keep the foresight and backsight distances approximately equal so that the refraction and curvature effects cancel out. Refraction is generally the greatest source of error in leveling. For short level lines the effects of temperature and pressure are generally insignificant, but the effect of the temperature gradient ''dT / dh'' can lead to errors.
Levelling loops and gravity variations
Assuming error-free measurements, if the Earth's gravity field were completely regular and gravity constant, leveling loops would always close precisely:
:
around a loop. In the real gravity field of the Earth, this happens only approximately; on small loops typical of engineering projects, the loop closure is negligible, but on larger loops covering regions or continents it is not.
Instead of height differences, ''
geopotential
Geopotential is the potential of the Earth's gravity field. For convenience it is often defined as the ''negative'' of the potential energy per unit mass, so that the gravity vector is obtained as the gradient of this potential, without the negati ...
differences'' do close around loops:
:
where
stands for gravity at the leveling interval ''i''. For precise leveling networks on a national scale, the latter formula should always be used.
:
should be used in all computations, producing geopotential values
for the
benchmark
Benchmark may refer to:
Business and economics
* Benchmarking, evaluating performance within organizations
* Benchmark price
* Benchmark (crude oil), oil-specific practices
Science and technology
* Benchmark (surveying), a point of known elevati ...
s of the network.
Instruments
Classical instruments
The
dumpy level
A level is an optical instrument used to establish or verify points in the same horizontal plane in a process known as levelling, and is used in conjunction with a levelling staff to establish the relative height levels of objects or marks. It i ...
was developed by English civil engineer
William Gravatt
William Gravatt FRS (14 July 1806 – 30 May 1866), was a noted English civil engineer and scientific instrument maker.
Apprenticed as a mechanical engineer in London from aged 15, after interview he worked with Sir Marc Isambard Brunel on t ...
, while surveying the route of a proposed railway line from London to Dover. More compact and hence both more robust and easier to transport, it is commonly believed that dumpy levelling is less accurate than other types of levelling, but such is not the case. Dumpy levelling requires shorter and therefore more numerous sights, but this fault is compensated by the practice of making foresights and backsights equal.
Precise level designs were often used for large leveling projects where utmost accuracy was required. They differ from other levels in having a very precise spirit level tube and a micrometer adjustment to raise or lower the line of sight so that the crosshair can be made to coincide with a line on the rod scale and no interpolation is required.
Automatic level
Automatic levels make use of a ''compensator'' that ensures that the line of sight remains horizontal once the operator has roughly leveled the instrument (to within maybe 0.05 degree). The surveyor sets the instrument up quickly and does not have to relevel it carefully each time he sights on a rod on another point. It also reduces the effect of minor settling of the tripod to the actual amount of motion instead of leveraging the tilt over the sight distance. Three level screws are used to level the instrument.
Laser level
Laser levels
project a beam which is visible and/or detectable by a sensor on the leveling rod. This style is widely used in construction work but not for more precise control work. An advantage is that one person can perform the levelling independently, whereas other types require one person at the instrument and one holding the rod.
The sensor can be mounted on earth-moving machinery to allow automated
grading.
See also
*
Astrogeodetic levelling
Geodetic astronomy or astronomical geodesy (astro-geodesy) is the application of astronomical methods into geodetic networks and other technical projects of geodesy.
Applications
The most important applications are:
* Establishment of geodetic da ...
*
Glossary of levelling terms
This is a glossary of levelling terms. Levelling is a surveying method used to find relative height, one use of which is to ensure ground is level during construction, for example, when excavating to prepare for laying a foundation for a house.
L ...
*
Survey camp
Survey Camp is an army tradition that was discontinued in the later part of twentieth century but was reinstated in 2002 across the universities of the world with a whole new structure. It is the civil engineering training course for two weeks usu ...
*
Land levelling
Grading in civil engineering and landscape architectural construction is the work of ensuring a level base, or one with a specified slope, for a construction work such as a foundation, the base course for a road or a railway, or landscape and ga ...
*
Orthometric height
The orthometric height is the vertical distance ''H'' along the plumb line from a point of interest to a reference surface known as the ''geoid'', the vertical datum that approximates mean sea level. Orthometric height is one of the scientific fo ...
*
Dynamic height Dynamic height is a way of specifying the vertical position of a point above a vertical datum; it is an alternative for orthometric height or normal height.
It can be computed dividing the location's geopotential number by the normal gravity at 4 ...
*
Physical geodesy
Physical may refer to:
*Physical examination
In a physical examination, medical examination, or clinical examination, a medical practitioner examines a patient for any possible medical signs or symptoms of a medical condition. It generally co ...
References
External links
USALandSurveyorDifferential leveling video tutorials
E-Learning-site with online-exercise for differential levellingDifferential levelling online calculation
{{Authority control
Civil engineering
Geomatics engineering
Surveying
Vertical position