L6: Control Surveys Flashcards
What is the purpose of control surveys?
To provide horizontal and vertical positions of points
What are the three methods of control surveying (briefly describe each)?
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
Define traverse
A series of stations tied together by angle and distance
List three uses of traverses
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
Define vertical angle
Angle between from horizontal line to a line
AKA the altitude angle
Define zenith angle
Angle from vertical line down to a line
Complimentary to the vertical angle
Define nadir angle
Angle from lower vertical line up to a line (for objects below observer)
Define meridian
A line on the mean surface of the Earth joining north and south poles
Which is used in general, the geographic or magnetic meridian? Why?
Geographic meridians are fixed
Magnetic meridians vary with time and location
Therefore, geographic meridians are generally used
Define azimuth
The direction of a line given by an angle measured clockwise from north
Define bearing
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
How do you find the azimuth of the reverse direction from the direct direction (course)?
Add 180 degrees
Subtract 360 degrees if necessary (overflow)
How do you calculate the bearing (b) from the azimuth (a) in each quadrant?
I: a = b
II: b = 180 - a
III: b = a - 180
IV: b = 360 - a
What are the three methods to measure angles or directions of traverse line?
1) Interior angles
2) Angles to the right
3) Azimuths
How are distances measured in a traverse?
Often EDM or tape
Total station popular since combines angle and distance measurements
What are three main standards of accuracy and the corresponding equipment for a traverse?
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
What is the formula for acceptable misclosure of angles for a traverse?
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”
What is the difference between an open and closed traverse (define both)? Which one should be avoided and why?
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
Describe radial traversing
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
Define loop traverse
A traverse that begins and ends at the same point
The angles can be closed geometrically and calculated mathematically
What are the general steps for traverse computations?
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
What is the formula for a theoretical sum of interior angles?
(n-2)180 degrees for an n-sided polygon
Describe the process of balancing angles
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
What is required for the calculation of the preliminary azimuths of the sides of a traverse?
All of the interior angles and the azimuth (or bearing) of at least one side
Define departure and give its formula
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
Define latitude and give its formula
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
What is the formula for linear misclosure?
linear misclosure = sqrt[ (departure misclosure)² +(latitude misclosure)² ]
What is the formula for relative precision?
relative precision = linear misclosure / traverse length
What is the basis of the compass rule?
Adjust departures and latitudes of traverse courses in proportion to their lengths
What are the formulas in the compass rule?
Correction for departure in AB = - Total departure misclosure * (Length AB / Traverse perimeter)
Correction for latitude in AB = - Total latitude misclosure * (Length AB / Traverse perimeter)
