Surveying Examination Study Guide: Key Concepts and Definitions
SURVEYING EXAMINATION QUESTIONS
Land Survey
Land survey is the process of making all necessary measurements of an area of interest to obtain a topographical map.
Stakeout
Stakeout is the process of identifying in the field, using surveying techniques, all the details necessary for the development of works related to a project.
Maps and Types
A map is a flat representation of the land surface or a part thereof, whose large extension requires the use of cartographic methods. Their scales are generally small.
Types:
- Letters: Marine maps
- Geographical: Cover large areas (continents, countries, etc.)
- Physical: Represent a certain type of feature (rivers, etc.)
- Political, historical
Contours and Their Properties
A contour is a line connecting points on the same level. Its representation on a plane is given by the intersection of a level ground surface with a reference plane.
When the reference surface is the mean sea level, the altitudes are called slopes.
If the reference surface is chosen arbitrarily, the altitudes are called elevations.
Equidistance is the constant altitude difference between two adjacent contour lines.
Properties:
- The direction of the horizontal line coincides with the contour line, and the maximum slope of the land is perpendicular to the horizontal.
- The calculation of the slope with respect to any direction is given by the ratio of equidistance and the distance between two contours.
P = tan(α) * a
Tg = e / mn
Contours are classified as intermediate and director. Every 5 intermediate contours, a director contour is drawn with a thicker outline, inserting its altitude in meters.
Natural Distance, Gap, and Gradient
The natural or geometric distance is the distance AB measured on the ground. It is reflected on the plane by the projection on the reduced distance AB. The elevation difference between the ends is known as the gap.
[Drawing]
Planimetry
Planimetry is the part of surveying that determines the position of land points in the XY projection plane. Planimetric surveying instruments and methods are used for measurements that allow us to obtain a planimetric representation of the terrain.
Altimetry
Altimetry deals with the vertical axis. Altimeter surveying instruments and methods are used to determine the elevation of various points in the field. The planimetric representation of the terrain is usually completed with contours.
UTM Projection
The Universal Transverse Mercator (UTM) projection is a transverse cylindrical system tangent to the ellipsoid along a meridian of origin. These coordinates are located around the world in points by signs.
UTM Coordinates
UTM coordinates are world coordinates that relate the points.
Col
A col is the lowest part on the crest of a ridge, often used to transit from one side to another.
Scales
Scale is the ratio between a distance on the plane or map (ab) and the corresponding distance on the ground (AB).
E = ab / AB = 1 / m = plane / ground
Mistakes and Errors
In surveying, mistakes are discrepancies between the actual magnitude and the measured magnitude, caused by neglect of the observer. Mistakes are usually of larger magnitude than errors and could and should be avoided with necessary care.
Errors are due to limitations of human eyesight and the surveying equipment used. They can never be completely eliminated, but we should aim to reduce them.
Vertical Error
Vertical error is the error we make when leveling, which depends on the sensitivity of the level.
Pointing Errors
Pointing errors occur when we try to place the crosshair on a division in the sights or the center of the prism. These errors are due to the limit of visual perception.
Reading Error
Reading errors occur when determining the limbus reading. These errors are also due to the limit of visual perception, estimated at two-thirds of the assessment.
Addressing Error
Addressing error is the error made by placing the instrument on the point to be surveyed.
Systematic Errors
Systematic errors always occur in the same direction and are caused by a permanent factor, usually an imperfection in the device. They can be mitigated with adequate contrast and adjustment. They are classified into constant and variable.
Accidental Error
Accidental errors take random values and cannot be eliminated like systematic errors. They tend to be partially compensated.
True Error
True error is the difference between the actual value of a magnitude and the value obtained by measurement. The true magnitude will never be known, and therefore neither will the true error.
Apparent Errors
Apparent errors are also known as discrepancies, residuals, or deviations. Apparent accidental errors cannot be eliminated in measurement, but their compensation is feasible. It has been demonstrated that small errors are more frequent than large ones. The number of positive errors is virtually equal to the number of negative errors. Systematic errors and mistakes must be absent in the observations.
Absolute Error and Relative Error
Absolute error is the difference between the actual value of a magnitude and the value as measured.
Relative error is the ratio of the absolute error to the actual value of the magnitude. Er = e.absolute / actual value.
Azimuth Concept
Azimuth is the angle between the alignment and the direction of a meridian, measured from the north and in the forward direction clockwise. The XY axis of our Cartesian coordinate system will coincide with the direction of the meridian, so the azimuth refers to this axis or one parallel to it.
Azimuthal Angle or Horizontal Angle
An azimuthal angle is measured with limbs located in the horizontal plane. There are several cases:
- Referral to true north (azimuths): If the instrument’s blade is aligned with the direction of the meridian, we say that the instrument is oriented. Azimuthal readings will be referred to true north and are called azimuths.
- Referral to magnetic north (bearings): It is possible to orient to magnetic north. Azimuthal angles referred to the magnetic meridian are called magnetic bearings. To transform a bearing into an azimuth, we must know the magnetic declination at the time of measurement.
- Arbitrary referral: It is common to measure azimuthal angles without having previously oriented the instrument. The reference of these angles is arbitrary, and we have to perform certain calculations if we want to transform them into azimuths.
Vertical Angles or Zenith Angles
Zenith angles are measured with vertically positioned limbs, called eclimeters. The zenith angles are measured with reference to a well-determined direction, which can be:
- The line-nadir zenith: In this case, the zero graduation of the eclimeter is placed on top of it. The readings are made with reference to the vertical line, and the angles and distances measured are called zenith angles. This is the normal case.
- The horizontal plane: Readings with the eclimeter graduated with zero at the horizontal are called horizon height. For a given vertical angle α, the values of α and β are complementary.
Measurement of Distance
In topography, we are interested in determining the reduced distance. Therefore, all instruments must have procedures to reduce the natural distance. These consist of determining the natural distance and the vertical angle or slope between two points. Distance can be measured in two ways:
- Direct method: This method consists of comparing the distance measuring instrument with a standard whose length is known.
- Indirect method: This method takes advantage of certain properties to calculate distances without the need to establish direct contact between the measuring instrument and the ground to be measured. These methods are the most commonly used.
Measurement of Level Differences
The determination of level differences is necessary for altimeter surveying. The altimetric reference for the work is the level surfaces. These are defined as equipotential. For topographic surveys affecting small areas, it is permissible to neglect the curvature of the earth and assume flat level surfaces without introducing significant errors.
Elevation
Elevation is the height relative to an arbitrary level surface.
Types of Topographic Instruments
- Measurement of angles: Goniometers. Theodolites, a type of goniometer, measure azimuthal and vertical angles. Other instruments, such as the tachometer, can measure angles and distances.
- Measurement of distance: This can be done by the direct method using a measuring tape or by indirect methods using total stations, tachometers, and sometimes other instruments.
- Measurement of level differences: The most specialized instruments for measuring level differences are levels or equialtimeters with horizontal sights. Tachometers and some compasses can also determine level differences through slope measurements.
Tachometer
The tachometer is a surveying instrument that incorporates the ability to measure distances through a stadia telescope. This makes it possible to determine the coordinates of any target point relative to the station point. The tachometer is used in radiation due to its ability to measure distances.
Theodolite
The theodolite is similar to the tachometer, but it is more suitable for the intersection method because of its ability to measure angles with great precision.
Level
The level, also called an equialtimeter, is an instrument used to determine level differences by means of horizontal sights. Many levels incorporate a stadia telescope for determining the reduced distance. Others also incorporate an azimuth limb. Neck levels measure zenith angles.
Gyrotheodolite
The gyrotheodolite is a tool used to determine the direction of the meridian. It is based on the gyroscope, which consists of an inertia wheel or disc rotating at high speed around an axis AB. The gyroscope is able to orient itself in any direction.
Laser
A laser is a light wave similar to normal light but containing a single wavelength. Therefore, it does not suffer scattering or absorption as normal light does. Its use is more common in highlighting alignments in civil engineering (e.g., redesign of inaccessible points).
Total Stations and Semitotal Stations
These instruments perform the functions of a traditional tachometer. The difference is that they are equipped with automatic reading of angles and distances and can additionally store the obtained data on magnetic media. This allows for data transfer to a computer for further processing, including the layout of the topographic map.
Angle Graduation System
Angle units:
- Sexagesimal unit: The sexagesimal degree is each of the 360 parts that divide a circle. The sexagesimal degree is divided into 60 minutes, and the minute into 60 seconds.
- Centesimal unit: The centesimal degree, or gon, is each of the 400 parts that divide a circle. The gon is divided into 100 centesimal minutes, and the centesimal minute into 100 centesimal seconds.
- Radian unit: The radian is the plane angle between two radii of a circle that cut an arc on the circumference of that circle equal in length to the radius.
Theorems
- Law of Sines: a / sin A = b / sin B = c / sin C
- Law of Cosines: a² = b² + c² – 2bc * cos α
- cos α = b² + c² – a² / 2bc
- Law of Tangents: …
Dimensioned Drawing
A dimensioned drawing is the planimetric representation of the surveyed points, together with their altitude or elevation. By comparing the altitudes of points, you can see the level difference between them and determine whether the ground ascends or descends.
Conditions to Be Met by Contours
Contours must be closed (without affecting the boundaries of the drawing), not intersect (except in cliffs), and not fork.
Interpretation of Contours
- If the contours are spaced at equal intervals, this indicates a constant slope.
- If the contours are close together at higher elevations and farther apart at lower elevations, the slope will be concave.
- If the contours are closer together at lower elevations, the slope will be convex.
- Closely spaced contours indicate a steep slope. The equidistance of the contours can also be influenced by the scale of the drawing in addition to terrain features.
- Widely spaced contours (while maintaining the same equidistance as in the previous case) indicate a gentle slope.
- If there is a level of magnitude m equidistance, this should be maintained throughout the plan, except in any area where more information is needed. In such areas, intermediate contours may be added between existing ones, represented by a line of reduced thickness.
- If the contours are concentric and their dimensions increase towards the center, they represent a summit or elevation.
- If the contours are concentric and their dimensions decrease towards the center, they represent a depression.
- An exception may occur in the case of a cliff, where the contours do not close and intersect.
- The boundary line separating two slopes is called a ridge line. The contours in these cases have a convex curvature. The significance of this line is that a drop of water placed on it would split into two halves, each following the line of maximum slope.
- A valley line connects two vertices. Unlike the ridge line, this line indicates water collection.
- For the formation of a stream, contours bend upstream.
- The steepest line is located between two contours and is the shortest segment connecting two correlative contour points. The slope at a point between two contours is determined by the steepest line that passes through the point.
Cadastral Surveying
Cadastral surveying deals with the calculated surface area of properties and the resolution of problems related to them. It uses a series of methods suitable for the measurement of very large surfaces.
Concept of Agricultural Land
Agricultural land is the projection on a horizontal plane of a piece of land. It is based on the fact that all types of crops grow vertically, regardless of the inclination of the land on which they stand. Similarly, the surface area of a building is measured horizontally. Therefore, the actual surface area is the one that takes into account the different slopes, while the agricultural land area is equal to or less than the actual surface area. It is also called the legal area. The legal area is what appears in the title of ownership of the land and whose extension is similar to that shown by the agricultural area.
Boundary and Parceling
- Boundary: The action of defining and drawing the boundaries of a property with respect to adjacent properties. These limits must be defined on the ground through milestones, landmarks, roads, etc.
- Parceling: The division of land is one of the most common problems in surveying. The reasons for parceling include sale, exchange, inheritance, etc.
Demarcation and division are two closely related operations.
Earthwork and Cubic Volume
Earthwork is the modification of the original shape of the land affected by a project to obtain a regular surface on which to situate the relevant works.
- Platform: This is the level surface that we intend to achieve with the earthmoving operation. Platforms tend to be horizontal. To counteract the centrifugal force of vehicles, they are built with a specific curved inclination, called camber, in the transverse direction.
- Cut: This is the operation of removing earth until a certain altitude is reached.
- Fill: This is the opposite of the cut operation, consisting of filling an area of land to obtain a platform.
- Side slope: Side slopes are flat surfaces whose inclination depends on the characteristics of the material that is excavated or used for filling.
- Volume: The estimated volume of earth to be moved in a particular project, specifically whether it is cut or fill. Methods for calculating volume include profiles, grids, and prismatic contours.
Stakeout
Stakeout is the process of materializing on the ground a point or a series of points that form part of a straight or curved alignment, whose position in relation to one or more other points already located is known. It is the reverse procedure to surveying. Types of stakeout include: point stakeout, straight alignment stakeout, curve alignment stakeout, and crest stakeout.
Polar Coordinates
Surveying instruments are limited to the measurement of polar coordinates, angles, and distances. Cartesian coordinates are derived by calculation from the polar coordinates. Using these tools, we can determine small distances and azimuths.
Cartesian Coordinates
The Cartesian coordinate system consists of two perpendicular axes: the YY axis aligned with the direction of the meridian and the XX axis perpendicular to it. The two axes intersect at a point called the origin.
Planimetric Methods
- Intersection method: This method aims at obtaining the coordinates of isolated points with high accuracy by setting up the instrument at points of known coordinates. It can be performed as direct intersection or reverse intersection.
- Traverse method: This method is based on one or two points of known coordinates and allows for obtaining the coordinates of a series of points connected by a polygon.
- Radiation method: This method is used to determine the position of a number of points from which no other point will be surveyed. It is the simplest and least accurate planimetric method.
Altimeter Methods
Altimetry deals with the vertical axis Z, whose origin can be on the plane or surface of zero elevation, the comparison dimension, or another conventionally set point.
- Geometric leveling: This method uses a level with horizontal sights.
- Trigonometric leveling: This method uses inclined sights and a tachometer.
- Barometric leveling: This method determines altitude based on atmospheric pressure differences.
Geometric Leveling
Geometric leveling is an altimetry method performed with a level employing horizontal sights.
Trigonometric Leveling
Trigonometric leveling is an altimetry method conducted with inclined sights, using a tachometer.
Barometric Leveling
Barometric leveling is an altimetry method that determines altitude based on atmospheric pressure differences.
Horizontal Angles or Azimuthal Angles
- Reference to true north (azimuths)
- Reference to magnetic north (bearings)
- Arbitrary reference
Vertical Angles or Zenith Angles
- Readings with zero graduation at the horizontal are called horizon height.
- Readings whose reference is the vertical line are called zenith angles.
Topographic Tangent
The topographic tangent, or trigonometric tangent, is the ratio of the vertical distance between the center of the telescope and the projection of the central thread of the telescope on the sights.
Magnetic Declination
Magnetic meridians form a certain angle with the geographical meridian at each point on the earth’s surface. This angle, called magnetic declination, is variable because the magnetic north-south direction is variable. Magnetic declination can also be defined as the difference between the azimuth of an alignment and the bearing of that alignment.
Contour Interval
Contour interval is the distance between contour lines, which is constant for a given representation to ensure clarity and precision. The value of the contour interval depends on the scale of the plan, the slope of the terrain, and the purpose of the work.
Ridge
A ridge is a line separating two slopes. The contours in these cases have a convex curvature.
Valley
A valley is a low area that collects runoff.
Profile
A profile is an irregular line marking the section produced by a vertical secant plane (perpendicular to the picture plane).
Platform
In the corresponding alignment, the stages should be clearly recorded, both horizontal and inclined. For inclined stages, both the slope and the length of the projection should be indicated.
Reference Plane
The reference plane is the plane that has served as a benchmark for constructing the profile.
Cut and Fill
Cut and fill values correspond to the height difference between the ground and the grade of the road. Depending on the sign of the cut or fill value, earthwork will involve either excavation or filling.
Cliff
A cliff is a steep slope close to vertical or with a value exceeding 70%. It is synonymous with escarpment.
Ridge
A ridge is a sinuous line that separates two areas with steep inclines.
Valley
A valley is a depression formed by low-lying elevations.
Cirque
A cirque is a very large depression surrounded by very considerable heights.
Cornice
A cornice is an edge with a gentle side and a steep slope.
Basin
A basin is a closed depression.
Defile
A defile is a depression or part of a valley between two slopes with steep walls.
Watershed
A watershed is a line separating two river basins.
Bench
A bench is a part of a slope with a gentler inclination between two parts with steeper inclinations.
Sunny Slope
A sunny slope is the name given to the south-facing slopes of elevations.
Talweg
The talweg is the line joining the lowest points of a valley. In valleys covered by a permanent channel, the bed of the channel generally coincides with the talweg.
Shady Slope
A shady slope is the name given to the north-facing slopes of hills.
Valley
A valley is an elongated depression in the land, generally covered in its lower part by the waters of a river current.
Fold
A fold is a valley on the side of a mountain.
Angle Graduation System
- Sexagesimal unit: The sexagesimal degree is each of the 360 parts that divide a circle. 1° = 60′ and 1′ = 6″.
- Centesimal unit: The centesimal degree, or gon, is each of the 400 parts that divide a circle. 1g = 100c and 1c = 100cc.
- Radian unit: The radian is the plane angle between two radii of a circle that cut an arc on the circumference of that circle equal in length to the radius. 1° = (π/180) rad and 1g = (π/200) rad.
Geodesy
Geodesy deals with the shape and dimensions of the earth and provides methods and tools to determine the relative positions of a number of points.
Map
A map is a flat representation of the earth’s surface whose extension requires the use of cartographic methods.
Leveling Platform
A leveling platform is a platform with three leveling screws that are adjusted with the help of a level. The platform is an equilateral triangle supported by screws that slide on a bar, which is in turn supported by another screw at its base.
Compass
A compass is a guidance tool based on the properties of magnets and used essentially to determine directions from the north-south magnetic poles. It consists of a magnetic needle free to rotate on a vertical support.
Compass Levels
Compass levels are air levels consisting of a closed glass ampoule containing an air bubble that always occupies the highest area of the bulb.
- Tubular level: A ring-shaped tube closed at both ends and containing an air bubble. The upper side is graduated with 2 mm divisions. The radius of curvature is 50 to 60 meters, which is related to the sensitivity of the level. When the bubble is aligned with the center of the level, the level is said to be leveled.
- Circular level: A low-precision level in which the glass tube is replaced by a cylindrical metal box closed at its top by a glass cover. The inside circumference of the cover has a spherical bubble engraved on it. The bubble is centered with the help of adjusting screws.
- Double-face level: A reversible level that can rotate around an axis parallel to the level. It has a spindle-shaped surface that is graduated on both sides. It is used with instruments whose telescope is reversible.
- Coincidence levels: These levels do not have graduations and incorporate a total reflection system. When looking through the eyepiece, it appears as if the bubble were divided longitudinally into two parts moving in opposite directions. The two sides simply move one after the other to be leveled.
Magnetic Declination
Magnetic declination is the angle between magnetic north and geographical north.
Solar Declination
Solar declination is the angle between the sun’s rays at the time of maximum culmination (at true solar noon) and the plane of the equator. This angle varies from day to day.
Planimetric Distance
Planimetric distance is the horizontal projection of the actual distance measured in the field.
Valley
A valley is an elongated depression in the land, generally covered in its lower part by the waters of a river current.
Fold
A fold is a valley on the side of a mountain.
Angle Graduation System
- Sexagesimal unit: The sexagesimal degree is each of the 360 parts that divide a circle. 1° = 60′ and 1′ = 6″.
- Centesimal unit: The centesimal degree, or gon, is each of the 400 parts that divide a circle. 1g = 100c and 1c = 100cc.
- Radian unit: The radian is the plane angle between two radii of a circle that cut an arc on the circumference of that circle equal in length to the radius. 1° = (π/180) rad and 1g = (π/200) rad.
Geodesy
Geodesy deals with the shape and dimensions of the earth and provides methods and tools to determine the relative positions of a number of points.
Map
A map is a flat representation of the earth’s surface whose extension requires the use of cartographic methods.
Leveling Platform
A leveling platform is a platform with three leveling screws that are adjusted with the help of a level. The platform is an equilateral triangle supported by screws that slide on a bar, which is in turn supported by another screw at its base.
Azimuth
Azimuth is the angle between the direction of true north and the alignment to a generic point P.
Bearing
Bearing is the angle between the direction of magnetic north and the alignment to a generic point P.
Reading
Reading is the angle formed by a reference direction and the alignment to a generic point P.
Declination
Declination is the angle between the direction of true north and the direction of magnetic north. It depends on the place and time of measurement.
Orientation
Orientation is the angle between true north and a reference alignment.
Horizon Height
Horizon height is the reading taken with zero graduation at the horizontal position.
Plane
A plane is a surface used for representation, smaller in scale than maps. It does not take into account the curvature of the earth and often forms the basis for surveying work.
Altitude
When the reference surface is the mean sea level, the height is called altitude.
Elevation
When the heights of the points are chosen arbitrarily, the heights are called elevations.
Limit of Visual Perception
The human eye can perceive magnitudes of ¼ mm, with errors less than 1/5 mm. This limit of visual perception is related to the scale.
Compass
A compass is a guidance tool based on the properties of magnets and used essentially to determine directions from the north-south magnetic poles. It consists of a magnetic needle free to rotate on a vertical support.
Compass Levels
Compass levels are air levels consisting of a closed glass ampoule containing an air bubble that always occupies the highest area of the bulb.
- Tubular level: A ring-shaped tube closed at both ends and containing an air bubble. The upper side is graduated with 2 mm divisions. The radius of curvature is 50 to 60 meters, which is related to the sensitivity of the level. When the bubble is aligned with the center of the level, the level is said to be leveled.
- Circular level: A low-precision level in which the glass tube is replaced by a cylindrical metal box closed at its top by a glass cover. The inside circumference of the cover has a spherical bubble engraved on it. The bubble is centered with the help of adjusting screws.
- Double-face level: A reversible level that can rotate around an axis parallel to the level. It has a spindle-shaped surface that is graduated on both sides. It is used with instruments whose telescope is reversible.
- Coincidence levels: These levels do not have graduations and incorporate a total reflection system. When looking through the eyepiece, it appears as if the bubble were divided longitudinally into two parts moving in opposite directions. The two sides simply move one after the other to be leveled.
Magnetic Declination
Magnetic declination is the angle between magnetic north and geographical north.
Solar Declination
Solar declination is the angle between the sun’s rays at the time of maximum culmination (at true solar noon) and the plane of the equator. This angle varies from day to day.
Planimetric Distance
Planimetric distance is the horizontal projection of the actual distance measured in the field.
Valley
A valley is an elongated depression in the land, generally covered in its lower part by the waters of a river current.
Fold
: it is a valley of a mountain side surface.
ANGLE Grading System:
Sexagesimal-Unit: sexagesimal degree is each of the 360 parties that divides a circle. 1 º = 60 ‘and 1’ = 60 “
-Percentage unit: it is Grad each of the 400 parties that divides a circle. 1g = 100c and 1c = 100cc
Unit-level corner: The radiating plane is the angle between two radii of a circle on the circumference of that circle, cut an arc equal in length to the radius. 1 º = (pi/180) rad and 1g = (pi/200) rad.
GEODESY: deals with the shape and dimensions of land, provides methods and tools to determine the relative positions of a number of points.
MAP: flat representation of the earth’s surface whose extension requires the use of cartographic methods
LEVELING PLATFORM: a platform of three leveling screws, which are leveled with the help of a level, the platform is an equilateral triangle, supported by screws that slide onto a bar, which is subject to the other screw base.