Plane Surveying

Height of Instrument

The backsight reading is added to the known or assumed elevation of the initial benchmark (or turning point TP) to determine the height of the instrument.

𝐻𝐼 = 𝐸𝑙𝑒𝑣 𝐵𝑀𝑎 + 𝐵𝑆 or 𝐻𝐼 = 𝐸𝑙𝑒𝑣 𝑇𝑃𝑛 + 𝐵?

Elevation of Turning Point and Benchmark

The foresight reading is subtracted to the height of the instrument to determine the elevation of the turning point or the next benchmark

𝐸𝑙𝑒𝑣 𝑇𝑃 = 𝐻𝐼 − 𝐹𝑆 or 𝐸𝑙𝑒𝑣 𝐵𝑀2 = 𝐻𝐼 − 𝐹𝑆

Double Rodded Differential Leveling

• method of determining differences in elevation between two points by employing two level routes simultaneously.

• two turning points are established such that at each set up of the level instrument, two sets of independent backsights and foresights are taken

• one advantage of this method is that it provides a continuous check while the work is in progress.

Three-wire levelling

• more precise method

• determines the elevation and difference in elevation of points wherein, three horizontal hairs are read and recorded rather than a single horizontal hair reading

Profile leveling

• process of determining differences in

  elevation along a fixed line at designated short measured intervals.

• provides data from which a vertical section of the ground surface can be plotted.

• profile is necessary for the design and construction of bridges, roads, canals, culverts, and etc.

Profile

A curve line which graphically portrays the intersection of a vertical plane with the surface of the earth. It depicts ground elevations of selected critical points along a surveyed line and the horizontal distances between these points.

Stationing

A numerical designation given in terms of horizontal distance any point along a profile is from the starting point. Each stake is marked with its station and plus.

It is used to indicate the distance of any ground stake from the beginning point of the level route.

Intermediate foresights

Also known as ground rod readings, are sights taken along the centerline of the proposed project to provide an accurate representation of the ground surface. They are observed at regular intervals and at points where sudden change in elevation occur.

Full stations

Are points which are established along the profile level route at uniformly measured distances. These points are usually made in multiples of 100, 50, 30, 20 or 10 meters.

Plus Stations

Any other intermediate points established along a profile level route which is not designated as a full station

Vertical Exaggeration

The process of drawing the vertical scale for a profile much larger than the horizontal scale in order to accentuate the differences in elevation.

Procedures of Profile Leveling

1. A transit and tape survey is undertaken starting at the beginning of the line which is designated as 0+00. The length of the level route is measured and stakes are set at each full station to define the path to be followed.

2. The instrument is set up at a convenient location and a backsight is taken on a reference bench mark near the initial point to determine the elevation of the height of instrument.

3. A series of intermediate foresights are taken along the centerline to determine the elevation of ground points. This is done without transferring the instrument. By the time it is no longer possible to continue with the foresights, a turning point is established. This permits the instrument to be moved to a new location which will allow additional foresights to be taken forward.

Plotting Profiles

• should give an accurate and useful representation of the existing ground configurations. It is plotted on a linear scale which shows the correct length of the surveyed line.

• the profile is plotted as a

  curve in which the distance of each station from the initial point is shown

  in the abscissa and the elevation of each station is plotted on the

  ordinate.

Curvature and Refraction

• The effects of earth’s curvature and atmospheric refraction are taken into account in leveling work since the measurements are

  made in vertical planes and these effects all occur in the same plane.

0.0785 minus 0.0110/0.0675 m

Telescope line of sight minus coefficient of refraction.

Reciprocal Leveling

• employed to determine the difference in

  elevation between two points when it is difficult or impossible to keep backsights and foresights short and equal.

• done when the leveling line crosses a body of water, ravines or places when it is impossible to conduct differential leveling.

Trigonometric leveling

• defined as the determination of differences in elevation from observed vertical angles and either horizontal or inclined distances.

• is used when undertaking a survey over rugged or rolling terrain since it provides rapid means of determining vertical distances and elevation of points.

Barometric Leveling

• differences in elevation of points are determined by observations of the prevailing atmospheric pressure.

• is based on the principle that the pressure caused by the weight of the column of air above the observer decreases (or increases) as the observer goes higher (or lower) in elevation.

Mercury Barometers

This type of barometer measures atmospheric pressure by the height of the column of mercury supported by the atmosphere in an evacuated glass.

Aneroid Barometers

The instrument functions by using an airtight metal box which responds to changes in air pressure.

Altimeter Surveys

The elevation difference is computed based on the ratio of the differences in elevation and the altimeter readings on the base stations.

True Meridians

Sometimes known as the geographic meridian. It is generally adapted reference line in surveying practice. This line passes through the geographic north and south poles of the earth and the observer’s position

Magnetic meridian

A fixed line of reference which lies parallel with the magnetic line of forces of the earth. Its direction is defined by a freely suspended magnetic needle of a compass held at the observer’s position. This lines converge at the magnetic poles of the earth.

Assumed Meridians

An arbitrarily chosen fixed line of reference which is taken for convenience. This meridian is usually the direction of from a survey station to an adjoining station or some well-defined and permanent point.

Degree

The sexagesimal system is used in which the circumference of a circle is divided into 360 parts or degrees.

(symbols ° , ‘, “ , respectively)

Grad

The grad unit is the unit of measure in the centesimal system. In this system, the circumference of the a circle is divided into 400 parts called grads.

(symbols, 𝑔 , 𝑐 , 𝑐𝑐 , respectively)

Mil

The circumference of a circle is divided into 6400 parts called mils, or 1600 mils is equal to 90 degrees. It is commonly used in military operations as in fire directions of artillery units.

Radian

• defined as the angle subtended at the center of the circle by an arc length equal to the radius of the circle.

• equals 180/π or 57.2958 degrees.

• It is sometimes referred to as the natural unit of angle because there is no arbitrary number in its definition

True North

is the north point of the true meridian. It is portrayed in the direction of the actual location of the earth’s geographic north pole and is always shown along a vertical line.

Magnetic North

a north point established by means of a magnetized compass needle when there are no local attractions affecting it. It usually points to the earth’s magnetic north pole.

Assumed North

is used to portray the location of any arbitrary chosen north point.

Direction of Lines

Defined as the horizontal angle the line makes with an established line of reference. There are various kinds of angles which can be used to describe the direction of lines: interior angles, deflection angles, bearings, and azimuths.

Interior angles

the angle between two adjacent lines in a closed polygon is an interior angle.

Deflection angles

the angle between a line and the prolongation of the preceding line is called a deflection angle. It may be turned to the right (clockwise) or left (counterclockwise) and it is always necessary to append the letters R and L.

Bearings

The bearing of a line is the acute horizontal angle between the reference meridian and the line. A quadrantal system is used to specify bearings such that a line may fall under one of the following quadrants: NE, SE, SW, and NW.

Forward Bearing

is obtained when the end of a line is observed in the direction of the survey. If the bearing is viewed in the opposite direction it is called back bearings.

Azimuths

The azimuth of a line is its direction as given by the angle between the meridian and the line measured in a clockwise direction from either the north or south branch of the meridian.

Traverse

A traverse is a series of lines connecting successive points whose lengths and directions have been determined from field measurements.

Traversing

The process of measuring the lengths and directions of the lines of a traverse for the purpose of locating the position of certain points.

Traverse Station

Any temporary or permanent point of reference over which the instrument is set up. Traverse stations are sometimes called the angle points because an angle is usually measured at stations.

Traverse Lines

Lines connecting traverse stations and whose lengths and directions are determined.

Interior Angle Traverse

The interior angle traverse is used principally in land surveying. The angles formed between the adjacent sides of the closed figure shown are known as interior angles. These are the angles at stations A, B, C, D, E and F.

Deflection Angle Traverse

The deflection angle traverse is used frequently for the location survey of roads, railroad, canals, transmission lines and similar structures. A deflection angle is a horizontal angle measured clockwise or counterclockwise from the prolongation of the preceding line to the succeeding line.

Latitudes

directed to the north are positive (+) and to the south, negative (-)

Departure

to the east are positive (+) and to the west, negative (-)

The linear error of closure (LEC)

usually a short line of unknown length and direction connecting the initial and final stations of the traverse. It is computed as the hypothenuse of a right triangle whose other sides are error in closure of the latitudes and departures