MODULE9: Traversing

Traverse

• is a succession of straight lines along or through the area to be surveyed

• the directions and lengths of these lines are determined by measurements taken in the field

Purpose of Traversing

• for establishing a series or network of monuments with known positions

• such monuments are the horizontal control points or the horizontal controls for the project

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. It is usually marked by a peg or a hub driven on the ground and identified by consecutive letters or numbers as the survey progresses.

Traverse lines

are lines connecting traverse station and whose lengths and direction are to be determined

2 BASIC operations in traversing

• measurement of angles at the traverse station

• measurement of lengths of the traverse lines

Types of traverse

1. Open traverse

2. Closed traverse

Geometrically Open Traverse

• does not create a closed shape because it ends at some point other than the initially occupied point or the initial backsight.

• this type of traverse is sometimes expedient for the survey of a strip project such as pipeline or highway

Mathematically Open Traverse or simply an Open Traverse

• begins at a point of known position and ends at a point of previously unknown position

• there is no method to verify that the measurements of the angles and distances are free from error, hence, this is not a desirable survey method

• usually run for preliminary or exploratory route surveys like pipeline or highway

• use extra care when measuring the angles and lengths

• where possible the terminal points of an open traverse should be tied to nearby monuments or benchmarks

Geometrically Closed Traverse

• creates a closed geometrical shape

• traverse ends on one of two points, either on same point from which it began or on the initial backsight

Mathematically Closed Traverse or simply a Closed Traverse

• begins at a point of known position and ends at a point of known position

• calculations can be made to check for errors, hence, this method is preferred because the numbers can be confirmed

Types of Traverse (based on angle measured)

• interior angle traverse

• deflection angle traverse

• angle to the right traverse

• azimuth traverse

interior angle traverse

principally used in land surveying

deflection angle traverse

location survey of roads, railways, pipelines, canals, etc.

angle to the right traverse

commonly used in city, tunnel and mine surveys

azimuth traverse

used in topographic and other surveys where many details are to be located by angular measurements

known point

monument on the ground representing that point

foresight

measure an angle and a distance to the first unknown point

Angular error

Angular error = (n-2) 180° - Σ interior angles

Allowable error per angle

ea = ½ LC√t (t= number of angles)

Latitude

Lat = d cos θ

Departure

Dep = d sin θ

Linear error of closure or linear closure

• gives us an idea of how much error there was in the field measurements and suggests how well the measuring was done

• the amount by which a closed traverse fails to satisfy the requirements of a true mathematical figure, as the length of line joining the true and computed position of the same point.

small error

most likely due to the limitations on how precisely the angles and distances can be measured with the specific equipment.

large error

would indicate that there is a blunder in the measurements.

Bearing of the side of error

tan θ = (-CD) / (-CL)

Balancing the traverse

a procedure that distributes and apportions field measurement errors. Adjustments are made to give the traverse an exact closure.

closed-loop traverse

Northings and the Southings must be equal to each other and the Eastings must be equal to the Westings.

Compass rule (Bowditch rule)

• used when the accuracy of angular measurement is about equal to the accuracy of distance measurement

• it distributes the traverse error in proportion to the length of the individual legs. Although this method was designed for some early, low precision equipment, this method works well for an EDM-theodolite traverse.

• “The correction to be applied to the latitude (or departure) of any course is equal to the total closure in latitude (or departure) multiplied by the ratio of the length of the course to the total length or perimeter of the traverse.”

Transit Rule

• used when angular measurement is much better than distance measurement

• this procedure was developed for chain and transit surveys where angles could be measured rather precisely. The distances, on the other hand, were subject to all of the possible errors of break and slope chaining over rough terrain.

• it distributes the traverse error in latitude proportionally to the latitude of the individual legs. Traverse legs with the largest change in latitude absorb the most error in latitude.

• the traverse error in departure is distributed in proportion to the departure of the individual legs.

Graphical

• is essentially an application of the compass rule. It provides simple graphical means of making traverse adjustments.

• In this method each traverse point is moved in a direction parallel to the

  error of closure by the amount proportional to the distance along the traverse from the initial point to the given point.

Arbitrary

• The latitudes and departures are adjusted in a discretionary manner according to the surveyor’s assessment of the conditions surrounding the survey

• This method does not conform to established rules or mathematical equations since the surveyor simply relies on his own estimation and personal judgement.

• For example, if one traverse line is measured over rugged terrain requiring frequent plumbing and breaking tape, it might be that applying all or most of the correction into this one line would balance the survey satisfactorily. Such an arbitrary method of adjustment would likely be as good as, if not better than, any of the other conventional methods of adjustments.

Crandall Method

is also used when angular measurement is much better than distance measurement. It also distributes the error in a comparable way.

Least Squares Method

• works well whatever the relative accuracy of angular or distance measurements.

• Weighted values can be given for each measurement. This causes more reliable measurements to be given more influence in the adjustment.

• Can be applied to complex networks and traverses with measurements between multiple points. This allows more flexibility in establishing control and greater opportunities for locating blunders.

• Error distribution is similar to the compass rule. The calculations are much more complex and demand a computer.

Coordinate method

• When a survey is run and made to close on a distance terminal station or point of known coordinates, it will be expected that the computed coordinates of the terminal station will differ from its known coordinates.

• There will be error of closure along the x-axis and the y-axis.

• This is due to inherent errors in both angular and linear measurements during traversing.

• The coordinate method may be employed when the preliminary coordinates of stations along the traverse have been determined.

• This method is simply the application of compass rule since corrections are applied are proportionate to the lengths being adjusted.