Traverse Surveying MCQ Quiz - Objective Question with Answer for Traverse Surveying - Download Free PDF

Explanation:

Traverse Surveying:

• In traverse surveys, angles are measured as part of the angular calculation for determining the positions of stations.

Counterclockwise Direction:

• If the direction of progress in the survey is counterclockwise, the angles measured between two consecutive lines are considered included angles.

• These are the angles that are measured on the inside of the traverse, in the counterclockwise direction.

Included Angles:

• When traversing in the counterclockwise direction, the angle between the two lines at the station is the included angle, meaning the angle formed on the inside of the boundary.

Additional Information Traverse Surveying:

• Traverse surveying is a method used in land surveying to establish control points by measuring horizontal and vertical angles between successive survey lines, and/or their lengths.

• The method consists of a sequence of straight lines (called traverse legs) connecting each station or point to the next.

• The main goal of traverse surveying is to accurately define the boundaries or layout of a survey area.

Explanation:

The process of adjusting the latitudes and departures to make the algebraic sum of latitudes or departures to zero is called balancing of errors.

The two types of balancing rules to eliminate errors in traverse surveying are as follows:

1) Bowditch rule (Compass rule): 

• It is most commonly adopted when angular measurement and linear measurement both are nearly of same precision.
• The correction is considered directly proportional to the length of the side.
• This method is based on assumption that the errors in the linear measurements are proportional to √l and that the errors in angular measurements are inversely proportional to 1/√l where l is the length of a line.

Correction for Latitude/Departure = - Total error in Latitude/Departure × \(\frac{{{\bf{length}}\;{\bf{of}}\;{\bf{the}}\;{\bf{side}}}}{{{\bf{perimeter}}\;{\bf{of}}\;{\bf{the}}\;{\bf{traverse}}}}\)

2) Transit rule: 

When angular measurements are more precise than linear measurement, the transit method is adopted.

Correction to latitude of any side = - Total error in latitude × \(\frac{{{\bf{Latitude}}\;{\bf{of}}\;{\bf{the}}\;{\bf{side}}}}{{{\bf{Arthmetical}}\;{\bf{sum}}\;{\bf{of}}\;{\bf{all}}\;{\bf{latitudes}}}}\)

Correction to departure of any side = - Total error in departure × \(\frac{{{\bf{Departure}}\;{\bf{of}}\;{\bf{the}}\;{\bf{side}}}}{{{\bf{Arthmetical}}\;{\bf{sum}}\;{\bf{of}}\;{\bf{all}}\;{\bf{departures}}}}\)

Concept:

Traverse Survey

• A traverse is a series of connected lines whose lengths and directions are to be measured and the process of surveying to find such measurements is known as traversing.

Method Traverse Survey Plotting

The following are the five main methods of plotting a traverse survey:

• By Parallel Meridians through Each Station
• By Included Angles
• By Central Meridian or Paper Protractor
• By Rectangular Co-Ordinates
• By Chords.

Hence, the coordinate method is not an angle and distance method traverse survey plotting.

Explanation:

Deflection Angle Concept:

The deflection angle is the angle between the prolongation of the previous line (AB) and the next line (BC), measured clockwise (Right) or anticlockwise (Left).

Since both bearings are with respect to North and both in the 1st quadrant, the angle between them is simply:

δ=52^∘45′−34^∘30′=18^∘15′

Now determine the direction:

• Since BC turns to the right from AB (as 34°30′ is less than 52°45′), the deflection is to the Right.

Explanation:

Algebraic Sum of Deflection Angles in a Closed Traverse

The algebraic sum of the deflection angles in a closed traverse is based on the principle that the sum of all angles in a closed geometric figure must equal a specific value. In this case:

• Deflection angles represent changes in direction between consecutive traverse lines.

• A closed traverse forms a loop, where the starting and ending points coincide.

• In such a closed system, the total turning or change in direction must be 360°.

Concept:

For an error-free plotted traverse:

ΣL = 0, ΣD = 0

ΣL = Algebraic sum of Latitudes of all the sides

ΣD = Algebraic sum of departure of all the sides

For a segment AB

Latitude = L cos θ & Departure = L sin θ

Departure: The departure of a line is its projection on the east-west meridian.

Latitude: The Latitude of a line is its projection on the North-south meridian.

In whole circle bearing, Bearings are taken w.r.t North Direction

Calculation:

As  Latitude is -ve & Departure is +ve

So, the line lies in the second Quadrant.

So, The whole circle bearing of the error of closure will be between 90° and 180° 

Confusion PointsThe angle is measured clockwise in this, hence the when ΣL = -ve and ΣD =+ve, the angle will be 90^o to 180^o. 

Concept:

In general, the closing error(e) in the traverse survey is given as:

\(e = \sqrt {{{\left( {{\rm{\Sigma }}L} \right)}^2} + {{\left( {{\rm{\Sigma }}D} \right)}^2}}\)

ΣL = Summation of Latitudes of all lines involved in traverse or also called error in Latitude

ΣD = Summation of Departure of all lines involved in traverse or also called error in Departure

However, in a closed traverse in which bearings are observed, the closing error in bearing may be determined by observing the bearing of the last line, and correction in the bearing of the last line is the closing error.

Calculation:

Given data

Number of sides of closed traverse(n) = 5

Error(e) = 1^o

Now the correction on sides(or lines) of closed traverse as follows:

Correction to the first line

= e / n = 0°12′

Correction to the second line

= 2e /n = 0°24′

Correction to the third line

= 3e / n = 0°36′

Correction to the fourth line

= 4e / n =0°48′

Correction to the fifth line

= 5e / n = 1°0′

Concept:

Balancing of errors: The process of adjusting the latitudes and departures to make the algebraic sum of latitudes or departures to zero is called the balancing of errors.

The two types of balancing rules to eliminate errors in traverse surveying are as follows:

1) Bowditch rule (Compass rule)/Compass rule: 

It is most commonly adopted when angular measurement and linear measurement both are nearly of same precision.

The correction is considered directly proportional to the length of the side.

By Bowditch rule Correction to a particular line is given by

\( {C_L} = \;l \times \frac{{{\bf{\Sigma }}L}}{{{\bf{\Sigma }}l}}\)

\({C_D} = \;l \times \frac{{{\rm{\Sigma }}D}}{{{\rm{\Sigma }}l}}\)

Where CL, CD is corrections in latitude and longitude for a line.

Correction for Latitude/Departure = Total error in Latitude/Departure ×  \(\frac{{{\bf{length}}\;{\bf{of}}\;{\bf{the}}\;{\bf{side}}}}{{{\bf{perimeter}}\;{\bf{of}}\;{\bf{the}}\;{\bf{traverse}}}}\)

2) Transit rule: 

When angular measurements are more precise than linear measurements, the transit method is adopted.

Correction to latitude/departure of any side = Total error in latitude/departure ×  \(\frac{{{\bf{Latitude/Departure}}\;{\bf{of}}\;{\bf{the}}\;{\bf{side}}}}{{{\bf{Arthmetical}}\;{\bf{sum}}\;{\bf{of}}\;{\bf{all}}\;{\bf{latitudes/departure}}}}\)

1. When the adjustment is made by the Bowditch rule, the length of the sides becomes less and the angle becomes more than that when the adjustment is made by the transit rule.

2. In Bowditch rule, it is assumed that the errors in linear measurements are proportional to \(\sqrt l \) and angular measurements are proportional to \(\frac{1}{{\sqrt l }}\)

Explanation

Loose needle/Free needle method-

• In this method we try to measure magnetic meridian of each traverse line. In this method the linear measurements are taken with chain or tape and angular mneausrements are taken with the help of a compass.

Fast needle method-

• In this method we measure magnetic bearing of any one line. Generally it is first traverse line and included angle at all other stations will be measured. In this method the linear measurements are taken with chain or tape and angular measurements are taken with the help of a theodolite.

Included angle method-

• In this method we measure magnetic bearing of any one line and included angle at all stations will be measured.
• The disadvantage of this method is that the traverse can be checked only if it is closed. 

• This is the most accurate method. The order of accuracy in above three method will be-
• Method of included angles > Fast needle method > Loose needle method

Direct angle method-

• In this method, direct angles i.e angle towards right directions are measured.

Deflection angle method-

• Deflection angle method is used for open traverse, in which traverse line make small deflection like railway, canal, sewer etc.

Concept:

For an error-free plotted traverse:

ΣL = 0, ΣD = 0

ΣL = Algebraic sum of Latitudes of all the sides

ΣD = Algebraic sum of departure of all the sides

For a segment AB

Latitude = L cos θ & Departure = L sin θ

In whole circle bearing, Bearings are taken w.r.t North Direction

Calculation:

As  Latitude is +ve & Departure is - ve

The line AB lies in 4 ^th quadrant ( > 270 ° )

From the figure 

\(\tan \theta = \frac{{\sum D}}{{\sum L}} = \frac{{-45.1}}{{78}}\)

∴ θ =  - 30°

The whole circle bearing of the line AB is

Concept:

The equation for closing error and angle fo misclosure is given by,

\({\rm{e}} = \sqrt {{{\left( {{\rm{Σ L}}} \right)}^2} + {{\left( {{\rm{Σ D}}} \right)}^2}} \)

\({\rm{\theta }} = {\tan ^{ - 1}}\left[ {\frac{{{\rm{Σ D}}}}{{{\rm{Σ L}}}}} \right]\)

Where,

e = closing error, θ = angle of misclosure

ΣL = Algebraic sum of latitudes of all lines  

ΣD = Algebraic sum of departures of all lines

The relative error of closure (r)

\({\rm{r}} = \frac{{{\rm{Closing\;error\;of\;a\;traverse}}}}{{{\rm{perimeter\;of\;a\;traverse}}}} = \frac{{\rm{e}}}{{\rm{P}}}\)

Where, P =perimeter of a traverse = Total length of a traverse

The degree of accuracy or the relative precision

\({\rm{Relative\;precision}} = \frac{1}{{\frac{{\rm{P}}}{{\rm{e}}}}} \)

Calculation:

Given,

ΣL = 0.4m, ΣD = 0.3 m

P = 1 km = 1000 m

we know that

\({\rm{e}} = \sqrt {{{\left( {{\rm{Σ L}}} \right)}^2} + {{\left( {{\rm{Σ D}}} \right)}^2}} \)

\({\rm{e}} = \sqrt {{{\left( {{\rm{0.4}}} \right)}^2} + {{\left( {{\rm{0.3}}} \right)}^2}} \)

e = 0.5 m

\({\rm{Relative\;precision}} = \frac{1}{{\frac{{\rm{P}}}{{\rm{e}}}}}=\frac{1}{{\frac{{\rm{1000}}}{{\rm{0.5}}}}} =\frac{5}{{10000}} = \frac{1}{{2000}}\)

Total closing error(c) = \(\sqrt {{{\left( {\sum L} \right)}^2} + {{\left( {\sum D} \right)}^2}}\)

Sum of latitude = 0.4 m

Sum of Departure = 0.3 m

\(C = \sqrt {{{\left( {0.4} \right)}^2} + {{\left( {0.3} \right)}^2}} \)

C = 0.5m

Relative error of closure or Relative precision of this traverse = \(\frac{c}{p}\)

p ⇒ Perimeter of traverse = 1 km = 1000 m

Relative precision = \(\frac{{0.5}}{{1000}} = 5 \times {10^{ - 4}} = \frac{1}{{2000}}\)

Concept:

L = Latitude is the projection on North-South meridian

D = Departure is the projection on East-west meridian

θ = Bearing angle

l = Length of the line

L = l × Cos θ 

D = l × Sin θ 

\({\rm{Line}}\;{\rm{closure = L}}{\rm{.C = }}\sqrt {{{\left( {{\rm{\Sigma L}}} \right)}^{\rm{2}}}{\rm{ + }}{{\left( {{\rm{\Sigma D}}} \right)}^{\rm{2}}}} \)

Calculation:

Given,

l = 100 m, θ = 30° 

L = + 100 × cos 30° = + 86.60 m

D = + 100 × sin 30° = + 50 m

The latitude and departure respectively of the line AB are + 86.60 m and 50 m

Calculation:

Given data

Two points P and Q located on a map have the following coordinates:

The length of the line PQ is

\(= \sqrt{[40-(-10)]^2+[(30-10)]^2}\) = \(\sqrt{2900}\) = 53.85 m

Explanation

Loose needle/Free needle method-

• In this method we try to measure magnetic bearing of each traverse line. In this method the linear measurements are taken with chain or tape and angular mneausreme4nts are taken with the help of a compass.

Fast needle method-

• In this method we measure magnetic bearing of any one line. Generally it is first traverse line and included angle at all other stations will be measured. In this method the linear measurements are taken with chain or tape and angular measurements are taken with the help of a theodolite.

Included angle method-

• In this method we measure magnetic bearing of any one line and included angle at all stations will be measured.
• The disadvantage of this method is that the traverse can be checked only if it is closed. 

• This is the most accurate method. The order of accuracy in above three method will be-
• Method of included angles > Fast needle method > Loose needle method

Direct angle method-

• In this method, direct angles i.e angle towards right directions are measured.

Deflection angle method-

• Deflection angle method is used for open traverse, in which traverse line make small deflection like railway, canal, sewer etc.