Engineering Surveying Chapter 5

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Questions and Answers

What is the Easting (E) of station A?

2000 (correct)

2010.169

2049.429

2018.376

What is the change in Easting (ΔE) from station A to station B?

39.26

29.901

-49.426

18.569 (correct)

What is the Northing (N) of station C?

1529.901 (correct)

1519.93

1554.15

1500.002

What is the change in Northing (ΔN) from station B to station C?

-34.220 Signup and view all the answers

What is the Easting (E) of station D?

2000.003 Signup and view all the answers

What is the change in Easting (ΔE) from station D to station A?

-49.426 Signup and view all the answers

What is the first step to set the leveling of theodolite?

Set the leveling of the theodolite by using the same procedure as the level instrument Signup and view all the answers

What is the purpose of measuring angles by repetition?

To increase the accuracy of the reading Signup and view all the answers

What is the term for the angle between the inclined line of sight and the horizontal?

Vertical angle Signup and view all the answers

What is the change of face method used for?

To determine the average reading for angles Signup and view all the answers

What is the purpose of setting zero on the instrument?

To start measuring the angle Signup and view all the answers

What happens when the object is below the horizontal plane?

The angle is an angle of depression Signup and view all the answers

What is the purpose of bisecting the target point?

To carefully bisect the target point Signup and view all the answers

How many readings are taken in the change of zero method?

Two readings Signup and view all the answers

Why do many surveyors prefer azimuths to bearings for directions of lines?

Because azimuths are easier to work with Signup and view all the answers

What is the bearing angle of a boundary line with an azimuth of 128°13′46″?

S51°13′E Signup and view all the answers

What is the equivalent azimuth of a bearing written as N37°13′W?

313°13′ Signup and view all the answers

What is the primary function of coordinates in surveying?

To describe the position of points on the surface of the earth Signup and view all the answers

In a plane rectangular coordinate system, what direction is the positive x-axis?

East Signup and view all the answers

What is the term for the change in the east-axis (ΔE) in a plane rectangular coordinate system?

Departure Signup and view all the answers

What is the term for the change in the north-axis (ΔN) in a plane rectangular coordinate system?

Latitude Signup and view all the answers

In which quadrant would a line with a bearing of S37°13′E be located?

Southeast Signup and view all the answers

What is the formula to calculate the departure for each side?

ΔE = L × sin θ Signup and view all the answers

What is the purpose of calculating the error of closure for Latitude and Departure?

To check the accuracy of the traverse calculations Signup and view all the answers

What is the formula to calculate the closing error?

e = √(ΔE² + ΔN²) Signup and view all the answers

What is the purpose of the Bowditch method?

To correct the latitude and departure values Signup and view all the answers

What is the formula to calculate the relative accuracy?

β = σ / L Signup and view all the answers

What is the first step in determining the coordinates of each station?

Assume one coordinate Signup and view all the answers

What is the purpose of calculating the latitude and departure for each side?

To calculate the coordinates of each station Signup and view all the answers

What is the direction of the observed angles in the example?

Counter-clockwise Signup and view all the answers

What is the value of the circumference of a circle in terms of its radius?

2π R Signup and view all the answers

What is the equivalent of 360 degrees in Gradian system?

400ᵍ Signup and view all the answers

What is the primary function of a Theodolite instrument?

Angular measurement Signup and view all the answers

What is one of the uses of a Theodolite instrument?

Measuring the horizontal distance between two points Signup and view all the answers

What is the first step in setting up a Theodolite instrument?

Stand the tripod approximately over the survey station Signup and view all the answers

What is the value of the right angle in the Radian system?

π/2 Signup and view all the answers

What is the purpose of a plumb-bob in setting up a Theodolite instrument?

To ensure the tripod is exactly over the station Signup and view all the answers

What is the last step in setting up a Theodolite instrument?

Move the pair of tripod feet or extend individual legs until the center of the optical piece is near the station Signup and view all the answers

Study Notes

Theodolite Instrument

Theodolite is a precision instrument used for angular measurement.
Parts of a theodolite include the tripod, optical piece, and plummet or laser.

Setting up the Theodolite

Stand the tripod over the survey station, keeping the head reasonably horizontal.
Attach the plumb-bob to the tripod head (may not be used).
Move the whole tripod or unclamp a tripod leg and slide it in or out until the plumb-bob is exactly over the station.
Put the theodolite on the tripod and clamp it.
Move the pair of tripod feet or extend individual legs until the center of the optical piece or laser is near to the nearest location of the station.
Determine the bearings of side AB and side BC, and check the bearing of CA.

Measuring Angles

Angles can be measured in two cases, and then determining the average reading for angles at face right and face left.
Horizontal angle: Set up the instrument on survey point A, direct the instrument on target point B, and bisect the target point carefully.
Change of zero: Set zero at point one and read point two, then set zero at point two and read point one, and determine average data for two readings.
Change of face: Measure the angle in two cases and determine the average reading for angles.

Vertical Angles

A vertical angle is an angle between the inclined line of sight and the horizontal.
It can be an angle of elevation or depression, depending on whether the object is above or below the horizontal plane.

Radian System (Circular System)

Radian is a central angle for the circle arc that is equal to the radius of the circle.
The circle circumference is (2π R).
Relation between the three systems: 360° 00’ 00 “ = 400ᵍ 00ᶜ 00ᶜ ͨ = 2π.

Uses of Theodolite

Measuring horizontal angles.
Measuring vertical angles.
Measuring deflection angles.
Measuring the horizontal distance between two points.
Finding the vertical height of an object.
Finding the difference in elevation between various points.
Ranging of a line.

Plane Rectangular Coordinates

In surveying, coordinates are used to provide an address for a point.
Coordinates in a plane system are split into four quadrants with the typical mathematical convention of the axis to the north and east being positive and to the south and west being negative.
In surveying, the x-axis is referred to as the east-axis (E) and the y-axis as the north-axis (N), with angles (θ) measured clockwise from the N-axis.

Determination of Coordinates

Assume one coordinate, based on corrected ΔE and ΔN, determine other coordinates.
E2 = E1 + ΔECor. E3 = E2 + ΔECor. N2 = N1 + ΔNCor. N3 = N2 + ΔNCor. ….etc

Error of Closure and Relative Accuracy

Find the error of closure for latitude and departure, and relative accuracy.
Find closing error: e = dE² + dN².
Find relative accuracy: β = σ / L.
If the tolerance of work permits the relative accuracy, it is OK. If the tolerance of work did not permit the relative accuracy, correction must be applied.

Correction for Latitude and Departure

Bowditch method (Compass method):
- δ1 = σ 1 dE = σ 1 dN.
- δ2 = σ 2 dE = σ 2 dN.
- δLast = σ Last dE = σ Last dN.
These values are added to calculated ΔE or ΔN with opposite signs.

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Description

This quiz covers the procedures for setting up a theodolite instrument, including leveling and centering, in the context of engineering surveying and civil engineering.