Basic Surveying
CE 263
Introduction to Surveying
► Definition:
Surveying is the science and art of
determining the relative positions of points
above, on, or beneath the earth’s surface
and locating the points in the field.
The work of the surveyor
consists of 5 phases:
1.
2.
3.
4.
5.
Decision Making – selecting method, equipment and
final point locations.
Fieldwork & Data Collection – making measurements
and recording data in the field.
Computing & Data Processing – preparing
calculations based upon the recorded data to
determine locations in a useable form.
Mapping or Data Representation – plotting data to
produce a map, plat, or chart in the proper form.
Stakeout – locating and establishing monuments or
stakes in the proper locations in the field.
2 Categories of Surveying:
Plane Surveying – surveying with the reference base
for fieldwork and computations are assumed to be a
flat horizontal surface.
1.

2.
Generally within a 12 mile radius the pull of gravity is very
nearly parallel to that at any other point within the radius
and thus horizontal lines can be considered straight.
Geodetic Surveying – surveying technique to
determine relative positions of widely spaced points,
lengths, and directions which require the
consideration of the size and shape of the earth.
(Takes the earth’s curvature into account.)
7 Types of Surveys:
1.
2.
3.
4.
Photogrammetry – mapping utilizing data obtained
by camera or other sensors carried in airplanes or
satellites.
Boundary Surveying – establishing property corners,
boundaries, and areas of land parcels.
Control Surveying – establish a network of horizontal
and vertical monuments that serve as a reference
framework for other survey projects.
Engineering Surveying – providing points and
elevations for the building Civil Engineering projects.
7 Types of Surveys:
Topographic Surveying – collecting data and
preparing maps showing the locations of natural
man-made features and elevations of points o the
ground for multiple uses.
Route Surveys – topographic and other surveys for
long – narrow projects associated with Civil
Engineering projects.
5.
6.

Highways, railroads, pipelines, and transmission lines.
Hydrographic Surveying – mapping of shorelines and
the bottom of bodies of water.
7.

Also known as bathymetric surveying.
Brief History of Surveying:
Surveying had it’s beginning in Egypt about 1400 BC
1.



Land along the Nile River was divided for taxation.
Divisions were washed away by annual floods.
“ROPE-STRETCHERS” Egyptian surveyors were created to
relocate the land divisions (measurements were made with
ropes having knots at unit distances).
Extensive use of surveying in building of Egyptian
monuments
Greeks: expanded Egyptian work and developed
Geometry.
2.

Developed one of the earliest surveying instruments
– Diopter (a form of level).
Brief History of Surveying:
Romans: developed surveying into a science to
create the Roman roads, aqueducts, and land
division systems.
3.


Surveyors held great power, had schools and a
professional organization
Developed several instruments:
•
•
•
Groma – cross instrument used to determine lines and right angles
Libella – “A” frame with a plumb bob used for leveling
Chorobates – 20’ straight edge with oil in notch for leveling
Middle Ages: land division of Romans continued in
Europe.
4.

Quadrans – square brass frame capable of turning angles
up to 90° and has a graduated scale developed by an
Italian named Von Piso.
Brief History of Surveying:
18th & 19th Century in the New World: the need
for mapping and marking land claims caused
extensive surveying, especially by the English.
5.
1785: United Stated began extensive surveys of public
lands into one mile square sections

•


30 states surveyed under the U.S. Public Land System
(also called the Rectangular System)
1807: United States Geological Survey founded to
establish an accurate control network and mapping
Famous American Surveyors: George Washington, Thomas
Jefferson, George Rogers Clark, Abe Lincoln and many
more.
Brief History of Surveying:
20th Century and Beyond: As technology advanced,
population increased, and land value caused
development of licensure for surveyors in all states.
6.




Educational requirements for licensure began in the early
1990’s
Capable of electronic distance measurement, positioning
using global positioning systems, construction machine
control, and lidar (scanning) mapping
Involvement in rebuilding of the infrastructure and
geographic information systems (GIS)
Shortage of licensed professionals is projected well into
the 21st century
Measurement of Distance
►
Linear measurement is the basis of all surveying and even
though angles may be read precisely, the length of at least one
line in a tract must be measured to supplement the angles in
locating points.
Methods of measuring a horizontal distance:
►
Rough Measuring: Pacing, Odometer readings, Tacheometry
(stadia), Taping, EDM, and GPS
 Only the last three meet survey accuracy requirements
 Distance from stadia: (High wire-Low wire) * 100 = Distance (ft)
►
►
►
More accurate measuring: taping, EDM (1966), GPS
EDM and GPS are most common in today’s surveys
In pacing, one establishes the # of paces/100’ by counting the
# of paces over a pre-measured 300’ line
Measurement of Distance
►
Taping: applying the known length of a graduated
tape directly to a line a number of times.
2 Problems exist in Taping:
1.
2.
Measuring the distance between two existing points
Laying out a known distance with only the starting
point in place
Measurement of Distance
1.
2.
3.
4.
5.
6.
6 Steps of Taping
Lining in – shortest distance between two points is a
straight line.
Applying tension – rear chain is anchor and head
chain applies required tension.
Plumbing – horizontal distance requires tape to be
horizontal.
Marking tape lengths – each application of the tape
requires marking using chaining pins to obtain total
length.
Reading the tape – the graduated tape must be read
correctly.
Recording the distance – the total length must be
reported and recorded correctly.
Types of Chains and Tapes
► Before
the ability to make steel rods and bands, sticks
were cut into lengths of 16.5’ (Rod) and they were
laid end to end to measure.
► Gunter’s Chain
 66’ long with 100 link w/each link being 7.92 inches or 66
feet long
 Developed by Edmund Gunter in 1600’s in England and
made with individual wires with a loop at each end
connected
 Chain had between 600-800 wearing surfaces which with
hard use would wear and cause chain to elongate
 Measurements were recorded in chains and links
 7ch 94.5lk = 7.945 ch = 7.945 X 66’/ch = 524.37’
 1 chain = 4 rods; 80 chains = 1 mile
Types of Chains and Tapes
►
Engineer’s Chain
 Same construction as Gunter’s Chain, but each link is 1.0’
long and was used for engineering projects
►
Surveyor’s and Engineer’s Tapes
 Made of ¼” to 3/8” wide steel tapes in 100’; 200’; 300’
lengths
 Multiple types of marking and graduation:
► Available
in chains, feet, and metric
► Graduated:
 Throughout – feet and tenths marked the entire length
 Extra foot – feet marked the length of the tape with additional foot at
the 0 end graduated in tenths and hundreds of the foot
Types of Chains and Tapes
► Invar
Tapes
 Made of special nickel steel to reduce length variations due
to temperature changes
 The tapes are extremely brittle and expensive
 Used most of the time for standard comparison of tapes
► Cloth,
Fiberglass, and PVC Tapes:
 Lower accuracy and stored on reels. Used for measurement
of 0.1’ accuracy requirements
Accessories
1.
2.
3.
4.
Chaining Pins – set of 11, used to mark the tape lengths
Hand Level – used to determine required plumbing height
Plumb Bob – used to transfer the mark from the tape to ground
Tension Handle – used to maintain correct tension on tape
Taping (Field Process)
The line to be taped should be marked at both ends
1.



Keeps measurement on line
Rear chain person should keep the head chain person on
line
1’ of line error/100’ = 0.01’ error in length
Applying Tension
2.

Rear chainman is anchor and should hold 100’ mark over
point
►
►
Tension is applied by head chain person – normally 12 to 30 pounds
of pull
Tapes are standardized at 12 lbs., but greater is utilized to
compensate for sag
Taping (Field Process)
Plumbing
3.

One end of tape is raised to maintain a horizontal
measuring plane. ONLY one end is elevated
►
►
This allows measurements to be made on uneven ground
If a high spot exists in center, “break” tape by measuring to the
top and then move forward to complete the distance
Slope Measurements:
► Generally,
measurements are made horizontally, but
on even, often man-made slopes the distance can be
measured directly on the slope, but the vertical or
zenith angle must be obtained.
 Horizontal Distance = sin Zenith Angle X Slope Distance
 Horizontal Distance = cos Vertical Angle X Slope Distance
Stationing:
► Starting
point is 0+00 and each 100’ is one
station 700’ from starting point is Station
7+00
► If distance is 857.23’ from starting point, it is
expressed as Station 8+57.23
Taping Error:
1.
2.
3.
Instrumental Error – a tape may have different length due to
defect in manufacture or repair or as the result of kinks
Natural Error – length of tape varies from normal due to
temperature, wind and weight of tape (sag)
Personal Error – tape person may be careless in setting pins,
reading the tape, or manipulating the equipment
► Instrumental and natural error can be corrected mathematically, but
personal error can only be corrected by remeasure.
► When a tape is obtained, it should either be standardized or checked
against a standard.
► Tapes
standardized at National Bureau of Standards in Maryland
► Standardized at 68 degrees F and 12 lbs. tension fully supported.
Tape Error Correction:
1)
Measuring between two existing points:
1) If a tape is long, the distance will be short, thus any
correction must be added
2) If tape is short, the distance will be long, thus any
correction must be subtracted
3) If you are setting or establishing a point, the above rule is
reversed.
Generally can correct for tape length,
temperature, tension, and sag, but tension and
sag are negated by increasing tension to
approximately 25 – 30 lbs.
Error in Taping:
► Tape
Length: Correction per foot = Error in 100’/100’
 If tape was assumed to be 100.00’ but when standardized
was found to be 100.02’ after distance measured at 565.75’
 then: Correction =(100.02-100.00)/100.00 = 0.0002’ error/ft
 565.75’ X .0002’/’ = 0.11’ correction and based upon rule,
must be added, thus true distance = 565.86’
 If tape had been 99.98’ then correction would be subtracted
and true distance would be 565.64’
Error in Taping:
► Temperature
– Tapes in U.S. are standardized at
68F; the temperature difference above or below that
will change the length of the tape
 Tapes have a relatively constant coefficient of expansion of
0.0000065 per unit length per F
 CT = 0.0000065(Temp (F)-68) Length
 Example: Assume a distance was measured when
temperature was 30°F using a 100’ tape was 872.54’
(68 – 30) X 0.00000645 X 872.54’ = 0.21’ error
tape is short, thus distance is long, error must be subtracted
and thus 872.54’ – 0.21’ = 872.33’
(note: temperature difference is absolute difference)
Surveying Metric Conversion
►1
Survey Foot = 1200 / 3937 meters
► 1 Meter = 3937 / 1200 Survey Feet
Transit
►
Transit is the most universal of
surveying instruments – primary use is
for measurement or layout of horizontal
and vertical angles – also used to
determine vertical and horizontal
distance by stadia, prolonging straight
lines, and low-order leveling.
3 Components of the Transit
1.
2.
3.
Alidade – Upper part
Horizontal limb – Middle part
Leveling-head assembly – Lower part
Transit
► Alidade
(upper part)
 Circular cover plate w/2 level vials and is connected
to a solid conical shaft called the inner spindle.
 Contains the vernier for the horizontal circle
 Also contains frames that support the telescope
called STANDARDS
 Contains the vertical circle and its verniers, the
compass box, the telescope and its level vial
Transit
► Horizontal
Limb (middle part)
 This is rigidly connected to a hollow conical shaft
called the outer spindle (which holds the inner
spindle)
 Also has the upper clamp, which allows the alidade
to be clamped tight
 Also contains the horizontal circle
Transit
►
Leveling-Head Assembly (lower part)
1.
2.
3.
4.
5.
6.
4 – leveling screws
Bottom plate that screws into tripod
Shifting device that allows transit to move ¼ to 3/8”
½ ball that allows transit to tilt when being leveled
The SPIDER – 4-arm piece which holds the outer spindle
Lower clamp – allows rotation of outer spindle
► Telescope:
shorter
Similar to that of dumpy level, but
 Parts – objective, internal focusing lens, focusing
wheel, X-hairs, & eyepiece
► Scales:
horizontal plate or circle is usually graduated
into 30’ or 20’ spaces with graduations from 0 to 360
in both directions
 Circles are graduated automatically by machine and then
scanned to ensure accuracy
 They are correct to with in 2” of arc
Verniers
► Least
count = Lowest # of reading possible –
determines accuracy
► Least Count = (Value of smallest division on scale)/(#
of divisions on vernier)
Scale Graduation
Vernier Divisions
Least Count
30’
30
1’
20’
40
30”
15’
45
20”
10’
60
10”
Verniers
►
3 Types of Verniers
1. Direct or single vernier – reads only in one direction &
must be set with graduations ahead of zero
2. Double vernier – can be read clockwise or
counterclockwise–only ½ is used at a time
3. Folded vernier – avoids a ling vernier plate


½ of the graduations are placed on each side of the index mark
Use is not justified because it is likely to cause errors
Verniers
► The
vernier is always read in the same direction from
zero as the numbering of the circle, i.e. the direction
of the increasing angles
► Typical mistakes in reading verniers result from
1.Not using magnifying glass
2.Reading in the wrong direction from zero, or on the wrong
side of a double vernier
3.Failing to determine the least count correctly
4.Omitting 10’, 15’, 20’, 30’ when the index is beyond those
marks
Properties of the Transit
1.
Designed to have proper balance between:
 Magnification and resolution of the telescope
 Least count of the vernier and sensitivity of the plate and telescope
bubbles
2.
3.
Average length of sight of 300’ assumed in design
Specifications of typical 1’ gun:





Magnification – 18 to 28X
Field of view - 1 to 130’
Minimum focus – 5’ to 7’
X-hairs usually are + with stadia lines above and below
The transit is a repeating instrument because angles are measured by
repetition and the total is added on the plate
► Advantages
of this:
1. Better accuracy obtained through averaging
2. Disclosure of errors by comparing values of the single and multiple readings
Handling the Transit
► Hints
on handling and setting-up the transit
 Pick up transit by leveling head and standards
 When carrying the transit, have telescope locked in position
perpendicular to the leveling head with objective lens down
 When setting-up, keep tripod head level and bring plumb
bob to within ¼” of point to be set over, then loosen
leveling screws enough to enable you to move transit on
plate, then move transit until it is over the point
Operation of Transit
A
B
►
9 Steps
C
1. Set up over point B and level it. Loosen both motions
2. Set up the plates to read 0 and tighten the upper clamp.
(Upper and lower plates are locked together)
3. Bring Vernier to exactly 0 using upper tangent screw and
magnifying glass.
4. Sight on point A and set vertical X-hair in center of point,
by rotating transit
5. Tighten the lower clamp and entire transit is locked in
6. Set X-hair exactly on BS point A using the lower tangent
screws. At this point the vernier is on 000’ and the Xhairs are on BS
Operation of Transit
A
B
C
7. Loosen the upper clamp, turn instrument to right until you
are near pt. C. Tighten the upper clamp
8. Set vertical X-hair exactly on pt. C using the upper tangent
screw.
9. Read  on vernier
►
►
If repeating , loosen lower motion and again BS on A (using only
lower motion), and then loosen upper motion to allow  to
accumulate.
If an instrument is in adjustment, leveled, exactly centered,
and operated by an experienced observer under suitable
conditions, there are only 2 sources for error.
1.
2.
Pointing the telescope
Reading the plates
Transit Field Notes
1d
Mean 
0-90
(4d)4
90-180
(4d + 360)  4
180-270
(4d + 720)  4
270-360
(4d + 1080)  4
Use longest side for backsite
TOTAL STATIONS
TOTAL STATION SET UP
►
WHEN TOTAL STATION IS MOVED OR
TRANSPORTED, IT MUST BE IN THE CASE!!!!!!!!
1.
ESTABLISH TRIPOD OVER THE POINT.
OPEN THE CASE AND REMOVE TOTAL STATION, PLACING IT ON THE HEAD
OF THE TRIPOD AND ATTACH SECURELY WITH CENTER SCREW.
CLOSE THE CASE.
GRASP TWO TRIPOD LEGS AND LOOK THROUGH THE OPTICAL PLUMB,
ADJUST THE LEGS SO THAT BULLSEYE IS OVER THE POINT (KEEP THE
TRIPOD HEAD AS LEVEL AS POSSIBLE).
UTILIZING THE TRIPOD LEG ADJUSTMENTS, LEVEL THE TOTAL STATION
USING THE FISH-EYE BUBBLE.
LOOSEN THE CENTER SCREW TO ADJUST THE TOTAL STATION EXACTLY
OVER THE POINT IF NEEDED.
COMPLETE LEVELING THE TOTAL STATION USING THE LEVEL VIAL.
CHECK TO MAKE SURE YOU ARE STILL ON THE POINT.
2.
3.
4.
5.
6.
7.
8.
TURNING ANGLES WITH TOTAL STATION
1.
2.
3.
4.
5.
SIGHT ON THE BACKSIGHT UTILIZING THE HORIZONTAL ADJUSTMENT
SCREW.
ZERO SET THE INSTRUMENT (THIS PROVIDES AN INNITIAL READING OF
0 SECONDS.
LOOSEN TANGENT SCREW AND ROTATE INSTRUMENT TO FORESIGHT.
TIGHTEN TANGENT SCREW AND BRING CROSS HAIR EXACT ON TARGET
WITH ADJUSTMENT SCREW.
READ AND RECORD ANGLE AS DISPLAYED.
TO CLOSE THE HORIZON:
1.
SIGHT ON FORESIGHT POINT FROM ABOVE AND ZERO SET INSTRUMENT.
2.
ROTATE TO FORMER BACKSIGHT AND ADJUST INSTRUMENT TO EXACT.
3.
READ AND RECORD ANGLE AS DISPLAYED.
ANGLE FROM DIRECT AND INDIRECT SHOULD EQUAL 360 DEGREES.
TOTAL STATION DISTANCE MEASUREMENT
1.
2.
POINT THE INSTRUMENT AT A PRISM (WHICH IS VERTICAL OVER
THE POINT.
PUSH THE MEASURE BUTTON AND RECORD THE DISTANCE.
YOU CAN MEASURE THE HORIZONTAL DISTANCE OR THE SLOPE
DISTANCE, IT IS IMPORTANT THAT YOU NOTE WHICH IS BEING
COLLECTED.
1.
IF YOU ARE MEASURING THE SLOPE DISTANCE, THE ZENITH
ANGLE MUST BE RECORDED TO ALLOW THE HORIZONTAL
DISTANCE TO BE COMPUTED.
2.
IF YOU ARE COLLECTING TOPOGRAPHIC DATA WITH ELEVATIONS,
IT IS IMPORTANT THAT THE HEIGHT OF THE INSTRUMENT AND
THE HEIGHT OF THE PRISM BE COLLECTED AND RECORDED.
THIS CAN ALSO BE SOLVED BY SETTING THE PRISM HEIGHT THE SAME AS
THE INSTRUMENT HEIGHT.
TOTAL STATION RULES
1.
2.
3.
4.
5.
6.
NEVER POINT THE INSTRUMENT AT THE SUN, THIS CAN DAMAGE
THE COMPONENTS OF THE INSTRUMENT AS WELL AS CAUSE
IMMEDIATE BLINDNESS.
NEVER MOVE OR TRANSPORT THE TOTAL STATION UNLESS IT IS
IN THE CASE PROVIDED.
DO NOT ATTEMPT TO ROTATE THE INSTRUMENT UNLESS THE
TANGENT SCREW IS LOOSE.
AVOID GETTING THE INSTRUMENT WET, IF IT DOES GET WET,
WIPE IT DOWN AND ALLOW TO DRY IN A SAFE AREA BEFORE
STORAGE.
BATTERIES OF THE TOTAL STATION ARE NICAD AND THUS MUST
BE CHARGED REGULARLY. AT LEAST ONCE PER MONTH, THE
BATTERY SHOULD BE CYCLED.
CARE SHOULD BE TAKEN AT ALL TIMES, THESE UNITS ARE
EXPENSIVE ($8,000 - $45,000)
Angles and Determination of
Direction
►
Angle – difference in direction of 2 lines
 Another way of explaining is the amount of rotation about a central point
 3 kinds of Horizontal angles: Exterior ( to right); Interior; Deflection
 To turn an angle you need
►A
reference line
► Direction of turning
► Angular distance
 Angular Units
► Degrees,
minutes, seconds (sexagesimal system)
 Circle divided into 360 degrees
 Each degree divided by 60 minutes
 Each minute divided into 60 seconds
► Radians
 1 radian = 1/2 of a circle = 0.1592*360 = 5717’44. 8”
► Grads
(Centesimal System) – now called Gon
 1/400 of a circle or 054’00” (100 gon = 90)
Angles and Determination of
Direction
Angles turned in field must be accurate: 3X least count is
max. error
► Check #1 – Close horizon when turning
► If traverse closes: sum of the interior angles should equal the
sum of
►
 (N-2)X180, N = Number of sides
►3
angles = (3-2) 180 = 180
► 4 angles = (4-2) 180 = 360
► 8 angles = (8-2) 180 = 1080
► 25 angles = (25-2) 180 = 4140
 If an exterior angle exists, subtract it from 360 to obtain the interior 
 Angular closure should be checked before leaving the field
Angles and Determination of
Direction
If angular adjustment does not divide out equally:
►
1.
2.
3.
Do not go to decimal unless instrument reads to decimal
Observe field notes for angles with poor closure or where problems
turning angles existed. Apply excess to these angles evenly.
If unable to view field notes or no apparent source, generally apply
excess to angles with shortest sides
Bearings/Azimuths
►


Bearing of a line is the acute horizontal angle between a reference
meridian (North and South) and a line
Azimuth of a line is the horizontal angle measured from the North
meridian clockwise to the line
Example
M
L
N
P
Q
Angles and Determination of
Direction
4 Point Comparison
Bearing
Azimuth
1. Numeric Value
0-90
0-360
2. Method of Expressing
2 letters & number
Number only
3. Direction
Clockwise & counterclockwise
Clockwise
4. Position of 0 point
North and South
North
It is always very important to have your field
sketch properly oriented
Angles and Determination of
Direction
Rectangular Coordinates
►
►
►
Totally based on computation of right triangle
North – South Movement = Latitude = D X cos A
East – West Movement = Departure = D X sin A
Latitude running North are +, South are –
Departure running East are +, West are –
Angles and Determination of
Direction
►
Basic Procedure
1.
2.
3.
4.
5.
Determine Latitude and Departure
Sum Lat. and Departure to calc. closure
Obtain balanced Lat. and Dept. (Compass Rule)
Determine coordinates
Once rectangular coordinates are known on point, their
exact location is known with respect to all other points in
the network
Example
B
F
A
E
C
D
Angles and Determination of
Direction
►
Balancing Methods
1.
Compass Rule: (Bowditch) Used when accuracy of  and length
measurement is equal
►
►
2.
Transit Rule: Used if angles are more accurate than distances (more
accurate direction)
►
►
3.
4.
(Error Lat./Perimeter length) X Distance = Latitude Correction
(Error Dept./Perimeter length) X Distance = Departure Correction
Correction Latitude (Side) = (Lat. Side/Sum all Lat.) X Lat. error
Correction Departure (Side) = (Dept. Side/Sum all Dept.) X Dept. error
Crandall Method: Used when larger random error exists in linear
measurements that angular. Directional adjustments from balancing
are held fixed and distances are balanced by a weighted least squares
procedure
Least Squares: Based on the theory of probability. Angular and linear
adjustments are made simultaneously. Hand methods are long and
complex not often done. Computer adjustment through existing
software make it feasible, which is why it is often used today
Area, Inverse, Intersection
►
Once rectangular coordinates are established on all
points, the relationship to all other points is known.
You can:
1. Determine area of all or any portion
2. Determine length and direction between any 2 points
3. Locate new points by intersection
Area, Inverse, Intersection
► Area:
Method is area by cross multiplication
Using example from traverse lecture:
NA X EB + NB X EC + NC X ED + ND X EE + NE X EF + NF X EA = Sum N
EA X NB + EB X NC + EC X ND + ED X NE + EE X NF + EF X NA = Sum E
A
10000.0000
5000.0000
B
10326.7981
5356.3614
C
9938.7277
5298.7122
D
9448.9156
4560.3990
E
9854.7405
4760.8417
F
10070.8565
4583.9559
A
10000.0000
5000.0000
Difference in Sums/2 = Square feet
Square feet/43560 = Acres
Sum N = 294,119,678.8
Sum E = 293,663,353.6
456,325.2 / 2 = 228,162.6 ft2 = 5.24 Ac
Area, Inverse, Intersection
Example: Determine Area of A, D, E, F, A
A
10000.0000 5000.0000
D
9448.9156
4560.3990
E
9854.7405
4760.8417
F
10070.8565
4583.9559
A
10000.0000
5000.0000
N = 186,116,759.8
E = 185,971,439.3
145,320.5 / 2 = 72,660.25 ft2 = 1.67 Ac 
Area, Inverse, Intersection
►
Inverse: With known coordinates of any two points on a
system, you find the distance and direction between the two
C
D
►
9938.7277
9448.9156
489.8121
5298.7122
4560.3990
738.3132
To find the Inverse between 2 Points
1. Find difference in N & E of coordinates
2. Plot
►
►
3.
4.
5.
6.
Use point you are going from 1st
Plot longest side 1st
Determine
Determine
Determine
Determine
length using Pythagorean (a2 + b2 = c2)
reference direction
local  using tan A = a/b
line direction
Area, Inverse, Intersection
► Example:
Determine direction and distance D-A
D
A
9448.9156
10000.0000
551.0844
4560.3990
5000.0000
439.6010
Area, Inverse, Intersection
►
Intersection: Determination of unknown point
location with directions from two points known
1.
Determine difference in coordinates
Plot points and line projections
Set up dual formulas (as Latitude and Departure)
Solve for length
Compute coordinate as sideshot
2.
3.
4.
5.
C
D
9938.7277
9448.9156
489.8121
5298.7122
4560.3990
738.3132
Area, Inverse, Intersection
► Example:
What are the coordinates of the point of
intersection of line C-F and D-A.
Azimuth D-A = 3834’46”.
Coordinates of D: N = 9448.9156, E = 4560.3990
C
F
9938.7277
10070.8565
132.1288
5298.7122
4583.9559
714.7563
Horizontal and Vertical Curves
►
Horizontal curves are the basis for most Right of Ways:
 Go through formulas
 Angle at PC and PT are always 90
 Given any 2 elements T, L, C, R, D; the remainder can be completed
Example: Horizontal curve, PC STA 201+00








D = 3615’00”
R = 1200.00’
T=
L=
C=
Seg =
PI STA =
PT STA =
Horizontal and Vertical Curves
Vertical Curves – Two major methods used to calculate
vertical curves: Tangent offset and Equation of Parabola
Information needed:
►
1.
2.
3.
Grade or slope on each side of curve
Elevation and station of PVI
Curve length (Horizontal distance PVC – PVT)
Horizontal and Vertical Curves
Tangent Offset Method
►
Procedure:
1.
2.
3.
4.
5.
6.
7.
Compute the elevation of the PVC and PVT
Compute the elevation of Chord midpoint
Compute offset to curve at midpoint
Determine total number of stations covered
Determine tangent elevations at stations
Compute curve offset at stations
Combine data and determine vertical curve elevations
Horizontal and Vertical Curves
Equation of Parabola Method
►
Equation: r = g2 - g1 / L




►
g1 = initial grade
r = change in grade/sta.
g2 = final grade
L = length of curve in stations
Procedure:
1. Compute PVC and PVT elevations
2. Calculate total change in grade/station
3. Insert data to chart and compute final curve elevations
To find the elevation at the high point or low point,
find the station at which it fall and include that
-g1
station in the elevation computations
xpt =
The equation gives the distance from the PVC in stations
r
Leveling
►
Leveling is the determination of the elevation of a point or
difference between points referenced to some datum
Terms:
1. Datum – any level surface to which elevations are referenced
2. Mean Sea Level (MSL) – the average height of the surface of the sea for
all stages of the tide over a 19 year period at 26 tide stations along
Pacific, Atlantic and Gulf
3. National Geodetic Vertical Datum – nationwide reference surface for
elevations throughout the U.S. – made available by National Geodetic
Survey (NGS), based on 1929 adjustment.
4. Benchmark – relatively permanent object bearing a marked point whose
elevation above or below an adopted datum.
Leveling
► Most
often Mean Sea Level is used
 MSL varies along the coasts
 Pacific is almost 2’ higher than Atlantic and Gulf
► U.S.
System: National Geodetic Vertical Datum of
1929
 Has been used as reference for extensive network of BM’s
 BM’s are periodically adjusted as to elevation
► Best
to check with USGS or NGS for current elevation of a BM and
also best to check between two known BM’s to verify elevation
difference.
Leveling
►
The level surface parallels the curvature of the earth a level
line is a curved line, normal () at all points to plumbline
 Line of sight is only normal at point of instrument
 A line with a sight distance of 1 mile using the earth’s radius as 3959
mile, curvature change is 0.667 feet.
 Refraction of line of sight of level is downward by a small amount
 The combined curvature & refraction amounts for short distances
(normal sight dist. for levels) are:




100’
200’
300’
500’
=
=
=
=
0.0002’
0.0008’
0.0019’
0.0052
Value is small  for most instances
can be neglected
Leveling
Most common leveling instrument today is the Automatic or
Self-leveling level – has an internal compensator that
automatically provides a horizontal line of sight and
maintains this through gravity (prism hanging on pendulum)
Differential Leveling: (Spirit Leveling) Most common type
today
►
►
Determine the difference in elevation using a horizontal line of sight
and readings on graduated rod
Circuit must be closed on BM of origin or on BM of equal accuracy
Process:



1.
2.
3.
4.
Reading on point of known elevation (BS)
BS reading + BM elevation = HI
Reading on point of unknown elevation (FS)
HI – FS = elevation of new point
Leveling
►
Systematic Error in Leveling
1.
Inclination of line of sight due to curvature of earth and
refraction – generally very minimal due to short sights
Inclination due to maladjustment of instrument
2.

3.
Changes in scale of rod due to temperature


4.
Both can be alleviated by equalizing length of BS and FS legs
Usually ignored except in very precise work
Would use same process as tape correction
Rod not held plumb

Minimized by carefully plumbing the rod or more commonly known as
“Rocking the Rod” and taking the lowest reading
Leveling
►
1.
Peg Test
Set 2 marks at 300’ apart, also mark center point in a relatively
flat area
2. Set level at midpoint and take readings at each end
3. Determine difference in readings (difference in elevation)
4. Move level to one end and setup so that level is just in front of
rod on point
5. Read rod by looking backward through scope (X-hair not
visible), hold pencil on rod to determine reading
6. Read rod at other end in normal manner
7. Difference in readings should equal #3
8. If values are not equal, there is error
 Most instruments have adjustment screws
 Adjust and repeat test as a check
Seven Basic Rules of
Differential Leveling
1.
2.
3.
4.
5.
6.
7.
Balance length of BS and FS (300’ max)
Make sure gun is level and pendulum free
Turn through all BM’s
Give complete description of BM’s and TBM’s
Have rod rocked
Make sure turning points are solid
Close all circuits on BM of same degree of accuracy
Other Random Errors
Incorrect rod reading – most common viewing foot
number above and recording it
2. Parallax – having the X-hair not properly focused
3. Heat Waves – limit shot lengths
1.
Field Notes
STA
► Sum
BS
HI
FS
ELEV
BS – Sum FS = Difference of Elevation
Closure Error
► Difference
in measured elevation and know elevation
► Correction factor = closure / # turns
Error = 0.09’
Turns = 12
► If
Correction = 0.0075’ / turn
TBM’s set, break circuit into sections
► Figure correction factor the same
► Figure correction by taking CF X # turns in section
Precise Leveling
Precise Leveling – Accuracy obtained by quality of instruments
and care taken in the field
► High quality automatic levels are utilized
► Level rods are equipped with rod level, rod shoe (to allow
better setting on BM’s); scale (on rod) is made of invar steel
(not affected by temp – generally called Invar Rod)
► Reading either taken by optical micrometer or a process called
3-wire leveling is used (all 3 wire are read and averaged)
►
 Optical micrometer: line of sight deflected by turning micrometer screw
to read subdivision on rod.
► Rod
division is read as normal & then fractional reading taken from
micrometer screw, thus on normal rod readings to 0.0001’ are possible
Topographic Surveying
► Topographic
surveying is the process of determining
the positions, on the earth’s surface, of the natural,
and artificial features of a given locality and of
determining the configuration of the terrain.
 Planimetry – location of features
 Topography – configuration of the ground
► Both
produce a topographic map which shows the true distance
between objects & their elevations above a given datum
► Topos can be done by field methods, or by photogrammetric
methods. (Photo also requires some field work)
► Topo map is 1st step in a construction project
Topographic Surveying
► Scale
and accuracy: Both depend on what used for
► Method of Representing:
 Most common is Contour Line – Imaginary line on surface of
the earth passing through points that have equal elevation
 Contour Interval – Vertical distance between lines
Topo map with contour lines shows elevation of points on ground &
shapes of topographic features (hills, etc.)
► USGS Topo – 10’ or 20’ contour intercal
► Subdivision – 2’ or 4’
»
 Index Contour – every 5th contour drawn heavier on maps
 Slopes & X-sections can be obtained from contours
Topographic Surveying
 Interpolating – can find elevation of any point or find
contour line with known elevation of point
 Contour lines that close represent either a hill or depression
and can be represented as:
► Marks
are called hatchures (used most in depressions)
Characteristics of Contours
1.
2.
3.
4.
5.
Each contour must close upon itself with within a
map or outside its borders – a contour line cannot
end on a map except at the edge
Contours do not cross or meet except in caves, cliffs
& vertical walls where they can meet
Contour lines crossing streams form V’s pointing
upstream
Contour lines crossing a ridge form U’s pointing down
the ridge
Contour lines tend to parallel streams
Characteristics of Contours
Contour lines are uniformly spaced on uniform slopes
7. Horizontal spacing between contour lines indicated
steepness of slope on ground
8. Contours are generally perpendicular to direction of
maximum slope
9. Contours can never branch into 2 contours of the
same elevation
6.
Field Methods of Topos
Factors That Influence Method
1. Scale of map
2. Contour interval
3. Type of terrain
4. Nature of project
5. Equipment available
6. Required accuracy
7. Existing control
8. Extent of area to be mapped
Field Methods of Topos
Methods:
1. Cross section – railroad of highway
2. Trace contour – drainage or impoundments
3. Grid – small areas
4. Controlling point – large area, plane table
5. Theodolite & EDM - radial
Field Methods of Topos
Cross Section Method (Plus Offset):
Equipment used: Transit, tape, and level
1. Establish horizontal control – traverse between
control points – stakes set at cross section intervals
2. Run profile of traverse line
3. Take cross section
4. Locate planimetric features from traverse line
Field Methods of Topos
Trace Contour:
1. Contour is by traverse
2. Establish elevation of each station
3. Contour elevation established and is then followed by
rodperson
4. Contour elevation is marked, then tied to traverse line
by plus-offset



Most accurate and expensive work
Elevation of reservoir water line
2 transit use
Field Methods of Topos
Grid Method:
1. Establish baselines
2. Estimate grid of uniform size – smaller grid = more
accurate
3. Number grid
4. Shoot elevation at each point
5. Tie existing objects to grid points
Field Methods of Topos
Controlling Point Method: (old and sketched in field)
1. Determine position & elevation of pre-selected
control points
2. Depends greatly on experience & judgment of people
doing work
3. Required traverse of area (CP’s)
4. Locations are made & elevations obtained along
control points – then intermittent topo sketched in
Field Methods of Topos
Theodolite & EDM (Radial)
 Replaces tacheometry (stadia)
Establish control points (horizontal and elevation)
2. Shoot locations and turn vertical angles
3. Used for large areas
1.
Field Methods of Topos
Common mistakes in topo surveys:
1. Improper selection of contour interval
2. Unsatisfactory equipment or field method for the
particular survey and terrain conditions
3. Insufficient horizontal and vertical control of suitable
precision
4. Omission of some topographic details
Mine Surveying
►
1.
2.
3.
4.
Points are on roof of mine
Reasons needed
Location in respect to boundaries
Location in respect to other shafts
Accurate maps (above and below ground)
Quantities
Equipment and Terms
►
►
►
►
►
►
Spad – Beams that you hold plumb bob from
Bracket – Mounting instrument from timber supports
Trivet – Tripod that’s about 1’ tall
Gyroscope – Locate north
Laser vertical collimator – located point at top of vertical shaft platform
Plumb shaft – Using piano wire then wiggle in at bottom
Global Positioning Systems (GPS)
Developed in early 1980’ s (Dept. of Defense)
► Made up of 26 satellites (24 functioning & 2 spares)
► Each satellite is 20,000 km high (off Earth’s surface)
► Each satellite is in a fixed position
► Minimum of 3 satellites needed, but 4-5 preferred
► Need satellites at least 15° above horizon
► Locate positions on Earth by distance-distance intersection
► Need 2-3 receivers ($80-$100K per system)
► Most accurate with double occupancy (no other checks)
► Differential GPS – one receiver on known point, other receiver
on unknowns
►
Global Positioning Systems (GPS)
Biggest advantage
► Distance and direction in-between 2 points without
being seen
Downfalls/Limitations of GPS
► Multipath – bouncing off of walls of buildings
► Blocked signals – clouds, trees, etc.
► Sunspot – defraction from atmosphere
► DOP (Delusion of Position) – bad satellite position
► Set up error – not set up exactly over point (human
error – most common)
Global Positioning Systems (GPS)
Methods
► Static – observation time is at least an hour
 Ideally set points in triangular fashion
 Accuracy – 1/10 million
► RTK
(Real Time Kinematic) – stand for 30-60 seconds
minimum
 Base receivers transmission, does corrections, sends
corrections to receivers
 Limitations – limitation of transmitter signal
Geographic Information Systems
(GIS)
► GIS
are computer programs that allow users to store,
retrieve, manipulate, analyze and display spatial data
► Spatial Data (Geographic data) – any data that
represents information about the Earth
GIS components
 Recent definitions of GIS suggest that is consists of:
1. Hardware (computer and operating system)
Geographic/Spatial
2. Software
3. Data
Non-Geographic/Aspatial/Attribute
4. Human Operators and Institutional Infrastructure
GIS Data Structures
►
Vector – Made up of points, lines, and polygons
GIS Data Structures
► Raster
(Grids) – Made up of pixels of computer screen
GIS Data Structures
► DEM
(Digital Elevation Model) – Digital terrain
representation technique, where elevation values are
stored in raster cells
Future of Surveying
► Major
advances in future
 Remote Sensing (Government and Military)
 Arial Photographs
► Design
Professions
 Every 10 years, must justify to Legislature that need for our
license exists
 Surveyor have ULTIMATE liability
 Standards → Laws
 Continuing Education – Enough points every 2 years