TRAVERSE SURVEY
INTRODUCTION
Traverse simply refers to a survey method of providing a series of stations whose positions (or coordinates) are obtained from bearing and distance observations of adjacent stations
Coordinates of any station can be determined by observing its bearings and distances from an adjacent station whose coordinates are already known
Map coordinates are expressed as Northings (N) and Eastings (E)
Negative northings (-N) and eastings (-E) denote south and west respectively
Bearings are normally measured in the range 0° to 360° from the north direction, and is commonly termed as the whole circle bearings (wcb)
There are instances where bearings are written with respect to the north-south direction, known as quadrant bearings. Example : N45°E, S60°W, etc.
By observing the bearings and distances of adjacent stations, a series of coordinated points would be created
The lines connecting the series of controls are known as traverse lines
THE BASIC EQUIPMENTS
Angle Measuring Equipments
Theodolites
Vernier
Optical
Digital
TPYES OF TRAVERSE
Distance Measuring Equipments
Distance & Angle Measuring Equipments (Total Stations)
Steel Tape
Fibreglass tape
Theodolite & Electronic Distance Meter (EDM) and Prism Set
Closed
A traverse that begins and ends at known stations
Link traverse
Loop traverse
Open
A traverse that starts and ends at
unknown points
TRAVERSE APPLICATIONS
To provide controls points for the survey work needed to obtain the plan of the construction site
To provide reference points in carrying out
setting out work
CLASSES AND ACCURACY OF TRAVERSE
Class: 1
Linear Misclosure (accuracy): ≥ 1 : 8,000
Angle measurement (minimum): 1”
Distance measurement (minimum): 0.001m (EDM, steel tapes)
Class: 2
Linear Misclosure (accuracy): ≥ 1 : 4,000
Angle measurement (minimum): 10” / 20”
Distance measurement (minimum): 0.001m (steel tapes)
Class: Std
Linear Misclosure (accuracy): ≥ 1 : 25,000
Angle measurement (minimum): 1”
Distance measurement (minimum): 0.001m (EDM)
TRAVERSING FIELDWORK
Angle Observation
(Angular Measurement)
Distance Measurement
Reconnaissance
Station marking, identify location, intervisibility
Horizontal angles to determine bearings
Vertical angles to reduce slope distances
Distance between adjacent stations
Highly likely slope distances
ANGLE OBSERVATION
Operations
Targets are normally placed at the observed stations
Measuring angles between adjacent traverse lines
Setting up the theodolite/total station
over each station
Measure horizontal angles. (Angle
between adjacent traverse lines)
ANGLE OBSERVATION
Face Right (FR) Reading: Angles observed when theodolite is on the face right
Refer to the theodolite’s vertical circle to determine FL/FR
Face Left (FL) Reading: Any angle observed while theodolite is on face left
The horizontal circle is graduated clockwise
Angles are observed on face left and face right
The vertical circle is graduated with its index 0° pointing towards zenith
How do we change the face of a theodolite?
Vertical angle
Why observe both faces?
By taking the mean of FL and FR horizontal circle readings the effect of systematic errors of the instrument is eliminated (collimation error)
Taking vertical circle readings on both faces would detect any vertical circle index error
To check against gross errors
Two rounds are needed so that errors can be detected when angles are calculated, since each round is independent
Angles must be observed at least in two complete rounds with zero changed between rounds
Zero change
Means setting horizontal angle to read differently for each round
DISTANCE MESUREMENTS
Distances along slopes are measured in short horizontal segments. Skilled surveyors can achieve accuracies of up to one part in 10,000 (1 centimetre error for every 100 metres distance)
Sources of errors
To measure distances, land surveyors traditionally have used 100-foot (30m) long metal tapes that are graduated in hundredths of a foot (mm)
Steel Taping
In traversing work, distance simply means the horizontal distance between the traverse stations, i.e. length of the traverse legs
Flaws in the tape itself, such as kinks
Since the 1980s, electronic distance measurement (EDM) devices have allowed surveyors to measure distances more accurately and more efficiently than they can with tapes
Variations in tape length due to extremes in temperature
Human errors such as inconsistent pull
Allowing the tape to stray from the horizontal plane
Incorrect readings
To measure the horizontal distance between two points, one surveyor uses an EDM instrument to emit an energy wave toward a reflector held by the second surveyor.
Because the wavelength of the energy beam is known precisely, the instrument can quickly calculate the distance as a function of the shape of the wave as it returns from the reflector
Typical accuracies up to one part in 20,000, twice as accurate as taping
The required horizontal distance is computed from the slope distance and vertical angle measured. Total stations normally have this facility built-in.
EDM
Corrections needed
Atmospheric Effects
Scale Error
Zero error
Cyclic Error
CALCULATION OF WHOLE CIRCLE BEARING (WCB)
WCB can be derived from the angles observed at each traverse station
Coordinate computations make use of WCB instead of angles in order to ensure that the computed coordinates lie in the correct quadrant (i.e. north, east, south or west)
Where is North?
Bearing Calculations
Forward bearing = Back bearing + Left-hand angle
In a closed-loop traverse, the observed left-hand angle would be the internal angle if the direction of the traverse is anticlockwise
If the direction of the traverse is clockwise then the observed left-hand angles would be the external angles
COORDINATE SYSTEMS
Rectangular cartesian system
The north direction
How are these north directions determined?
True North: earth’s true north
Magnetic North: earth's rotaton axis
Grid North : based on map’s grid system
Arbitrary (assumed) North
True North
Magnetic North
Grid North
Gyro-theodolites
GPS
Compass
Maps of the area
Magnetic north changes with time and differ from one location to another
Polar coordinate system
ERRORS IN TRAVERSING
ANGULAR MISCLOSURE
Systematic errors due to instrument imperfections have been discussed and corrected for
Traverse misclosures
An Error Free Traverse
(No Misclosure)
What measurements are observed in
a traverse survey?
There are no gross errors, only errors that have to be dealt with are random errors
Traverse with Angular Angular Error Only
Traverse with Distance Error Only
Angles
Distances
Traverse with Both Angular and Distance Errors
In engineering applications, the standard set for second class traverse is adopted i.e. maximum angular misclosure is ±2’ 30”
Errors in the angular observations (angle misclosure) are analysed to
Loop Traverse
Ascertain whether the misclosure obtained is within the acceptable limits or otherwise
Distribute equally the acceptable angular
misclosure to each of the traverse leg
∑ Internal angles = (2n – 4) × 90°
∑ External angles = (2n + 4) × 90°
Link Traverse
Bearing misclosure = computed final forward bearing -
known final forward bearing
Corrections
Apply to each of the traverse legs
Cummulative
LATITUDE & DEPARTURE
The bearing and distance measured for each traverse leg are then used to compute latitudes and departures (or sometimes called as coordinate differences)
Latitudes & departures are needed to obtain the coordinates of the traverse station
In essence, latitude refers to the difference in northings of two traverse stations whereas departure denotes their difference in eastings
LatitudeAB (∆NAB) = DistanceAB × cos (bearingAB)
DepartureAB (∆EAB) = DistanceAB × sin (bearingAB)
TRAVERSE MISCLOSURE
If the traverse is a closed-loop (polygon)
∑latitudes = 0
TRAVERSE ADJUSTMENTS (DISTRIBUTION OF LINEAR MISCLOSURE
For link traverse
In practice, due to random errors
Such conditions give rise to what is termed as linear misclosure
∑latitudes = Northingp – Northingq
∑departures = Eastingp – Eastingq
Where p is the last station & q is the first station
∑departures = 0
∑latitudes = eN
∑departures = eE
Linear misclosures are evaluated and appropriate correction is applied to the traverse
Linear misclosures are indicators to the accuracy of the traverse
Supposing the total traverse distance is ∑S metres, then the linear misclosure is e : ∑S or 1 : ( ∑S / e )
For engineering applications, an accuracy of 1 : 4,000 (second class) is used as the minimum
COMPUTATION OF FINAL COORDINATES
CALCULATING AREAS FROM LOOP TRAVERSE
Bowditch
Latitude AB = eE*(length AB / ∑length of traverse)
Latitude AB = eN*(length AB / ∑length of traverse)
The coordinates of the starting station are normally needed in order to be able to proceed with the calculations
Checks against arithmetic mistakes can be made by comparing the computed coordinates against the actual coordinates of the final station
The final coordinates of traverse stations are computed using adjusted (corrected) latitudes and departures
2 * Area = (N1E2 + N2E3 + N3E4 + N4E1) − (N2E1 + N3E2 + N4E3 + N1E4)