L6: Control Surveys

Question 1

What is the purpose of control surveys?

Answer 1

To provide horizontal and vertical positions of points

Question 2

What are the three methods of control surveying (briefly describe each)?

Answer 2

TRAVERSING: set up a traverse; measure distances (EDM or taping) and angles (theodolite)

TRIANGULATION: triangulation network is a series of single or overlapping triangles; position is determined by measuring all the angles in the network and measuring the length of one or more baseline

TRILATERATION: trilateration network is also a series of single or overlapping network; measure all of the distances of the network rather than the angle (sometimes just one angle); difficult to do accurately before EDM; how GPS works

Question 3

Define traverse

Answer 3

A series of stations tied together by angle and distance

Question 4

List three uses of traverses

Answer 4

1) To locate topographic detail for preparation of topographic plans and engineering design plan and profiles

2) To lay out engineering works

3) For the processing and ordering of earthwork and other engineering quantities

Question 5

Define vertical angle

Answer 5

Angle between from horizontal line to a line

AKA the altitude angle

Question 6

Define zenith angle

Answer 6

Angle from vertical line down to a line

Complimentary to the vertical angle

Question 7

Define nadir angle

Answer 7

Angle from lower vertical line up to a line (for objects below observer)

Question 8

Define meridian

Answer 8

A line on the mean surface of the Earth joining north and south poles

Question 9

Which is used in general, the geographic or magnetic meridian? Why?

Answer 9

Geographic meridians are fixed

Magnetic meridians vary with time and location

Therefore, geographic meridians are generally used

Question 10

Define azimuth

Answer 10

The direction of a line given by an angle measured clockwise from north

Question 11

Define bearing

Answer 11

The direction of a line given by the acute angle between the line and a meridian

The bearing angle is always accompanies by letters which locate the quadrant

Question 12

How do you find the azimuth of the reverse direction from the direct direction (course)?

Answer 12

Add 180 degrees

Subtract 360 degrees if necessary (overflow)

Question 13

How do you calculate the bearing (b) from the azimuth (a) in each quadrant?

Answer 13

I: a = b
II: b = 180 - a
III: b = a - 180
IV: b = 360 - a

Question 14

What are the three methods to measure angles or directions of traverse line?

Answer 14

1) Interior angles

2) Angles to the right

3) Azimuths

Question 15

How are distances measured in a traverse?

Answer 15

Often EDM or tape

Total station popular since combines angle and distance measurements

Question 16

What are three main standards of accuracy and the corresponding equipment for a traverse?

Answer 16

GEODETIC / PRECISE: 1 in 50 000 or better; 0.1” theodolite; EDM

GENERAL: 1 in 5 000 to 1 in 50 000; 1” or 20” theodolite; EDM or steel tape

LOW ACCURACY: 1 in 500 to 1 in 5 000; 20” or 1’ theodolite; synthetic tapes, stadia tacheometry

Question 17

What is the formula for acceptable misclosure of angles for a traverse?

Answer 17

C = K*sqrt(n)

Where:
C - acceptable misclosure
n - number of angles
K - determined based on code

code for K:
First Order: 1.7”
Second Order, Class I: 3.0”
Second Order, Class II: 4.5”
Third Order, Class I: 10”
Third Order, Class II: 12”

Question 18

What is the difference between an open and closed traverse (define both)? Which one should be avoided and why?

Answer 18

Open traverse: a series of lines that are connected to but do not return to the starting point or close upon a point of equal/greater accuracy

Closed traverse: one that begins and ends at the same points or begins and ends at points whose positions have been accurately, precisely determined

Open traverses should be avoided since they offer no means of checking for observational errors and mistakes

Question 19

Describe radial traversing

Answer 19

Set up the instrument in the middle and for all points do a measurement of the angles and distances

Useful for quickly establishing large number of points in an area, especially with a total station

Question 20

Define loop traverse

Answer 20

A traverse that begins and ends at the same point

The angles can be closed geometrically and calculated mathematically

Question 21

What are the general steps for traverse computations?

Answer 21

1) Adjust angles or directions to fixed geometric conditions

2) Calculate preliminary azimuths (or bearings) of traverse lines

3) Calculate departures and latitudes and adjust for misclosure

4) Compute rectangular coordinates of traverse stations

5) Calculate lengths and azimuths of traverse lines after adjustment

Question 22

What is the formula for a theoretical sum of interior angles?

Answer 22

(n-2)180 degrees for an n-sided polygon

Question 23

Describe the process of balancing angles

Answer 23

Find the total error from the theoretical sum of interior of angles compared to the actual sum

Divide the total angular misclosure by the number of angles to get the correction for each angle (swapping signs)

Apply the correction to each angle

Note: there is also a method where the angles are adjusted arbitrarily to force the closure

Question 24

What is required for the calculation of the preliminary azimuths of the sides of a traverse?

Answer 24

All of the interior angles and the azimuth (or bearing) of at least one side

Question 25

Define departure and give its formula

Answer 25

The orthographic projection of a course on the east-west axis of a survey (eastings or westings)

departure = L*sinα

Where:
L - horizontal length
α - azimuth of the line

Question 26

Define latitude and give its formula

Answer 26

The orthographic projection of a course on the north-south axis of a survey (northings or southings)

latitude = L*cosα

Where:
L - horizontal length
α - azimuth of the line

Question 27

What is the formula for linear misclosure?

Answer 27

linear misclosure = sqrt[ (departure misclosure)² +(latitude misclosure)² ]

Question 28

What is the formula for relative precision?

Answer 28

relative precision = linear misclosure / traverse length

Question 29

What is the basis of the compass rule?

Answer 29

Adjust departures and latitudes of traverse courses in proportion to their lengths

Question 30

What are the formulas in the compass rule?

Answer 30

Correction for departure in AB = - Total departure misclosure * (Length AB / Traverse perimeter)

Correction for latitude in AB = - Total latitude misclosure * (Length AB / Traverse perimeter)