Survey Exam 2 (weeks 6-8)

Traverse Surveying

a series of connected lines whose lengths and angles at the junctions have been observed, used say for strip of highway

Angular Permissible Misclosure

for a closed-polygon traverse: c= K(sqrt)n where: c is the angular misclosure n is the # of sides K is a constant that depends of the accuracy specified by the FGCS table

Angular Misclosure

for an interior angle traverse: the difference between the sum of observed angles and the geometrically correct total of the polygon [sum=(n-2)180] *misclosures result from the accumulation of random errors*

Forward vs Backward Azimuths

forward azimuths are converted to back azimuths and vice versa by +180 (if smaller than 180) or -180 (if larger than 180)

Open Traverse

geometrically and mathematically open, consists of a series of lines that are connected but do not return to the start point or close upon a point equal or greater than the starting *this type of traversing should be avoided bc it offers no means of checking for observation error or mistakes

Computing Azimuths

given your first azimuth calculate the back azimuth of it by adding or subtracting 180 then add the angle observed as connection point 𝐴𝑧 𝐵𝐴 = 41°35′ + 180 = 221°35′ 𝐴𝑧 𝐵𝐶 = 221°35′ + 129°11′ = 350°46′

Link Traverse (closed)

when you finish upon another station that should have a positional accuracy equal to or greater than the starting point, geometrically open but mathematically closed *start and end BM are known*

Traverse Computation: Final Step- Determine Final angles based on all adjustments above

{the Angle at st.A = AZ(AE) +Angle A} there for Angle A= AZ(AB) - AZ(AE) *if negative you must add 360*

Steps for Traverse Computation

1. Adjust angles or directions to fixed geometric conditions 2. Determine prelim. azimuths (or bearings) of traverse lines 3. Calculate departure and latitude and adjust them for the misclosure 4. Computing rectangular coordinates of the traverse stations 5. Calculating the lengths of azimuth (or bearing of the traverse lines after adjustment)

Kinds of Traverses

1. Closed Traverse a. Polygon b. Link 2. Open Traverse

Typical Field Angle Measurements

1. Direct 2. Direct and Reverse 3. Closing the Horizon 4. Traverse Angles 5. Layout

Common Mistakes in Traverse Computations

1. Failing to adjust the angles before computing azimuths (or bearings) 2. Applying angle adjustments in the wrong direction and failing to check the angle sum for proper geometric total 3. Interchanging departures and latitudes or their signs 4. Confusing the signs of coordinates

Types of Traverse Angles

1. Interior angle 2. Angles to the right 3. Deflection angles 4. Azimuths

Three basic requirements to determine an angle

1. reference or start line 2. direction of turning 3. angular distance (value of angle)

Zenith + Nadir =

180 degrees

Traversing by Interior Angles

Angles should be turned to the right (clockwise) from the backsight (rear) station to the foresight (forward) station *as a check exterior angles may be observed to close the horizon* (interior+exterior angle = 360)

Comparing Azimuths to Bearings

Azimuths: vary from 0-360, require only numerical value, may be geodetic, magnetic, grid, assumed, forward or back, measured clockwise only, usually measured from the north Bearings: vary from 0-90, require two letters and a numerical value, may be geodetic, magnetic, grid, assumed, forward or back, measured from north and south

Traverse Computation: STEP 3 pt.1- Calculate Departure and Latitudes

Departure (eastings or westings)= L Sin(angle or azi) Latitude (northing or southing)= L Cos(angle or azi) where L= length of course *east dept. and north lat.=plus* *west dept. and south lat.=minus*

Traversing by Angles to the Right

Depending on the direction of the traversing (moving from one station to another), angles to the right may be interior or exterior angles in a polygon traverse: • If the direction of traversing is counter-clockwise around the traverse, then clockwise interior angles will be observed. • If the direction of traversing is clockwise, then exterior angles will be observed.

East Declination vs West Declination

East = positive West = negative

Traverse Computation: STEP 1- Balancing Angles (bowditch method)

Find the geometrically correct angle sum with (n-2)180 and find the difference between this and the actual sum of the interior angles, the difference is then divided by the # of sides of angles and distrusted evenly to all (always round correction to nearest whole inch)

Traverse Computation: STEP 4- Computing Rectangular Coordinates

Given the X(easting) and Y(northing) coordinates of any starting point (A) the X coordinate of (B)= Ax coordinate + adjusted departure of AB and the Y coordinate of (B)= Ay coordinate + adjusted latitude of AB

Converting Azimuths to Bearings and vice versa

NE quad: Bearing = Azimuth SE quad: Bearing = 180-Azimuth SW quad: Bearing = Azimuth-180 NW quad: Bearing = 360-Azimuth

Traverse Computation: INTERMIDIATE STEP- Calculate Relative Precision

RP= Linear misclosure / traverse perimeter or total length *always represented in fraction form to the nearest thousandth*

Traverse Computation: INTERMIDIATE STEP- Calculate Linear Misclosure

The distance between A and A' is termed the linear misclosure of the traverse. It is calculated from the following formula: Linear Misclosure= SQRT(dept mis.)^2 + (lat mis.)^2

Traversing by Azimuths

This process permits reading azimuths of all lines directly and thus eliminates the need to calculate them

The sexagesimal system

US (and many other countries)system based on degrees, minutes and seconds for units of measurement of an angle

Traverse

a series of consecutive lines whose ends have been marked in the field and whose lengths and directions have been determined from observations

Polygon Traverse (closed)

all lines return to starting point thus forming a closed figure that is both geometrically and mathematically closed

Bearings

defined as the acute horizontal angle between reference meridian and the line, angle either observed from north or south towards the east or west

Traverse Computation: STEP 5 pt.2- Calculating final Lengths

due to all the previous adjustments you must change the length of the courses, the new adjust length is found by: SQRT(dept)^2+(lat)^2

Geodetic (Geographic) Meridian

fixed line that joins the north and south pole (all lines of longitude are geodetic meridians)

Traverse Computation: STEP 3 pt.2- Adjust Departure and Latitudes

for a closed polygon traverse: sum of dept should= 0 sum of lat should= 0 for closed link traverse: sum of dept should= total difference in departure between starting an ending control points sum of lat should= total difference in latitude between starting and ending control points Adjustment= -(dept or lat misclosure/ total perimeter) x L of course

Computing Bearings

given your first bearing add in the angle being observed and subtract that sum from 180 to find bearing Bearing angle of line BC: 180 − 41°35′ + 129°11′ = 9°14′ Bearing of BC = N9°14′𝑊

Azimuth

horizontal angles observed clockwise from any reference meridian (usually observed from north) can range in value from 0-360 degrees *used advantageously in boundary, topographic, control, and other kinds of surveys, as well as in computations*

Traverse Computation: STEP 5 pt.1- Calculating final Azimuth or Bearing Direction

if departure and latitude of line AB are known: 𝐴𝑧𝑖𝑚𝑢𝑡ℎ 𝑜𝑟 𝐵𝑒𝑎𝑟𝑖𝑛𝑔 𝐴𝐵 = 𝐴𝑟𝑐 tan (𝐷𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒 𝐴𝐵 / 𝐿𝑎𝑡𝑖𝑡𝑢𝑑𝑒 𝐴𝐵) + 𝐶 where C= if dept>0 and Lat>0: C=0 if dept>0 and Lat<0: C=180 if dept<0 and Lat>0: C=360 if dept<0 and Lat<0: C=180 *if answer comes out negative you need to add 360*

Direction of a line

is defined by the horizontal angle between the line and an arbitrarily chosen reference line called a meridian (Different meridians are used for specifying directions)

Angles to the right (horizontal angle)

measured clockwise form the rear to the forward station (most data collectors require an angle in the field to be turned to the right)

Magnetic Meridian

meridians that are parallel to the directions taken by freely moving magnetized needles (as in compass) *varies with time and location*

Traversing by Deflection

needs to be designated as an angle to the left or right and cannot exceed 180, these angles can be obtained by subtracting 180 from angles to the right *positive values denote right deflc. and negative values are to the left*

Traverse Computation: STEP 2- Computing Preliminary Azimuths or Bearings

requires that at least one course with in the traverse is either known or assumed...find the back azimuth to the first given/known one by +180 or -180 then add the observed angle to get the next forward azimuth *page check is that you should be able to close the polygon and end back on your given/original azimuth/bearing*

Referencing Traverse Stations

stations are often found and then reoccupied months or even years after they're established, they can also be destroyed during construction or other activity so it's important to create observational ties to them so they can be relocated if obscured or reestablished if destroyed

Horizontal Angles

the basic observations needed for determining bearings and azimuths

Magnetic Declination

the horizontal angle observed from the geodetic meridian to the magnetic meridian *An east declination exists if the magnetic north is east of geodetic north; a west declination occurs if it is west of geodetic north* Geodetic (Geographic) Azimuth = Magnetic Azimuth + Magnetic Declination

Zenith (vertical angle)

the point directly above the observer

Nadir (vertical angle)

the point directly below the observer

Angles to the left (horizontal angle)

turned counterclockwise from rear station to forward station

Closed shape surveying

used for say boundary of land

Vertical Angles

used in trigonometric leveling, stadia, and for reducing slope distance to horizontal

Deflection angles (horizontal angle)

angle observed from an extension of the back line to the forward station and is always smaller than 180 (angles can be to the right+ or to the left- )

Exterior angle (horizontal angle)

angles located on the outside of a closed polygon [each exterior angle + interior angle of each point should add up to 360 degrees]

Interior angle (horizontal angle)

angles observed on the inside of a closed polygon [angles should add up to (n-2)180 where n= # of sides]

Closed Traverses

provide checks on the observed angles and distances (extremely important)