Introduction to Surveying

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. Decision Making – selecting method, equipment and
final point locations.
2. Fieldwork & Data Collection – making measurements
and recording data in the field.
3. Computing & Data Processing – preparing
calculations based upon the recorded data to
determine locations in a useable form.
4. Mapping or Data Representation – plotting data to
produce a map, plot, or chart in the proper form.
5. Stakeout – locating and establishing monuments or
stakes in the proper locations in the field.

Object of Surveying
►The primary object of survey is the
preparation of plan of estate or buildings
roads, railways, pipelines, canals, etc. Or to
measure area of field, state, nation.
►Object of geodetic surveying is to determine
precise positions on the surface of the earth
of widely distant points.

Uses of Surveying
►To prepare a topographical map this shows
the hills, valley, rivers, villages, town, etc, of
a country.
►To prepare a cadastral map showing the
boundaries of fields houses, and other
properties.
►To prepare an engineering map to show
details like roads, railways, canals, etc.

Uses of Surveying
►To prepare military map showing roads and
railways, communication with different parts
of country.
►To prepare contour map and to determine
capacity of a reservoirs and ton find the
best possible route for roads, railways etc.
►To prepare archeological map including
places where ancient relics exist.

Types of Surveying
Classification

A. Primary Classification or
Primary Division :
1. Plane surveying
2. Geodetic surveying

1. Plane Surveying
 The shape of the earth is spherical. Thus
the surface is obviously curved. But in plane
surveying the curvature of earth is not
taken into account. This is because plane
surveying is carried out over a small area,
so the surface of the earth is considered as
a plane. The degree of accuracy required in
this type of surveying is completely low.
Plane surveying is done on an area of less
than 250 sq.km.

2. Geodetic surveying
 In geodetic surveying the curvature of the
earth is taken into consideration. It is
extended over a large area greater than 250
sq.km. The line joining any two points
considered as a curved line. Very refined
methods and instruments are used in this
type of surveying. In this method very high
precision or accuracy is required.

B. Secondary Classification
►Survey can be classified on different bases:
1. Based on instrument:
►Chain Survey
►Compass survey
►Plane Table survey
►Theodolite survey
►Tacheometric Survey
►Photographic survey

2. Based on methods:
►Triangulation Survey
►Traverse Survey

3. Based on Objects:
►Geological survey
►Mine survey
►Archeological Survey
►Military survey

4. Based on nature of field
►Land Survey
►Marine survey
►Astronomical survey

Other Types of Surveys:
1. Photogrammetry – mapping utilizing data obtained
by camera or other sensors carried in airplanes or
satellites.
2. Boundary Surveying – establishing property corners,
boundaries, and areas of land parcels.
3. Control Surveying – establish a network of horizontal
and vertical monuments that serve as a reference
framework for other survey projects.
4. Engineering Surveying – providing points and
elevations for the building Civil Engineering projects.

Other Types of Surveys:
5. Topographic Surveying – collecting data and
preparing maps showing the locations of natural
man-made features and elevations of points of the
ground for multiple uses.
6. Route Surveys – topographic and other surveys for
long – narrow projects associated with Civil
Engineering projects.
 Highways, railroads, pipelines, and transmission lines.
7. Hydrographic Surveying – mapping of shorelines and
the bottom of bodies of water.
 Also known as bathymetric surveying.

Brief History of Surveying:
1. Surveying had it’s beginning in Egypt about 1400 BC
 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
2. Greeks: expanded Egyptian work and developed
Geometry.
 Developed one of the earliest surveying instruments
– Diopter (a form of level).

3. Romans: developed surveying into a science to
create the Roman roads, aqueducts, and land
division systems.
 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
4. Middle Ages: Land division of Romans continued in
Europe.
 Quadrans – square brass frame capable of turning angles
up to 90° and has a graduated scale developed by an
Italian named Von Piso.

5. 18th & 19th Century in the New World: the need for
mapping and marking land claims caused extensive
surveying, especially by the English.
 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.

6. 20th Century and Beyond: As technology advanced,
population increased, and land value caused
development of licensure for surveyors in all states.
 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.
► Old surveys were often measured using a Surveyors
Chain. These were literally chains made up of 100
links. Each Chain was 66 feet long. Each link was
0.666 of a foot.

Units of Measurement
►Acre - The (English) acre is a unit of area
equal to 43560 square feet, or 10 square
chains. A square mile is 640 acres. The
Scottish acre is 1.27 English acres.
►Chain - Unit of length usually understood to
be Gunter's chain, from the heavy metal chain
of 100 links that was used by surveyors to
measure property bounds.

►Hectare - Metric unit of area equal to
10,000 square meters, or 2.471 acres.
►Link - Unit of length equal to 1/100 chain
(7.92 inches).
►Rood - Unit of area usually equal to 1/4
acre.
►Engineer's Chain - A 100 foot chain
containing 100 links of one foot a piece.

►Furlong - Unit of length equal to 40 poles
(220 yards).

Methods of Measuring Distance
►Direct Method of Measuring Distance:
1. Pacing: Where approximate result is required,
distance may be determined by pacing. This method
is used for reconnaissance survey, for preparation of
military plans. Also used for approximate checking
distance. The method consists of walking over a line
and counting the number of paces (80cm) the
required distance may be obtained by multiplying
the number of paces by the average length of pace.

 The length of pace varies with the:
►Individual, age, height and physical
condition
►The nature of the ground (uphill and down
hill)
►The slope of the country and
►The speed of pacing

2. Passometer:
It is a pocket instrument. It automatically
records the number of paces. It should be
carried vertically, in waistcoat pocket or
suspended from a button. The mechanism
being operated by motion and strain of the
body.

►3. Pedometer:
► It is similar to passometer. But it registers the
distance walked by the persons carrying it. The
distance is read by means of an indicator. It is
fitted with a stud or knob, which when pressed
release indicator to zero, it may be carried in the
same way as the passometer.

4. Odometer:
It measures the distance approximately. It
can be attached to the wheel of any vehicle,
such as carriage, cart bicycle, etc. It registers
the number of revolution of the wheel.
Knowing the circumference of the wheel, the
distance traversed may be obtained by
multiplying the number of revolutions. By the
circumference of the wheel

5. Speedometer: The Speedometer of an
automobile may be used to measure distances
approximately. It gives better results than
pacing, provided the route is smooth.

6. Perambulator: It can measure distance
rapidly. It consist a single wheel provided with
forks and a handle. It is wheeled along the line,
the length of which is desired. The distance
traversed is automatically registered on the dial.
The reading approximates on rough ground.

7. Judging distance:
This is very rough method of determining
distance. It is used reconnaissance survey.
8. Time Measurement:
Distance is roughly determined by time intervals
of travel. Knowing the average time per km for a
person at walk or a horse, the distance traversed
may be easily obtained.

9. Chaining: Measuring distance with chain or
rope is the most accurate and common method,
called as chaining. For work of ordinary precision
a chain is used. Where great accuracy is
required, a steel tape is used.

► Taping: applying the known length of a graduated
tape directly to a line a number of times.
2 Problems exist in Taping:
1. Measuring the distance between two existing points
2. Laying out a known distance with only the starting
point in place

6 Steps of Taping
1. Lining in – shortest distance between two points is a
straight line.
2. Applying tension – rear chain is anchor and head
chain applies required tension.
3. Plumbing – horizontal distance requires tape to be
horizontal.
4. Marking tape lengths – each application of the tape
requires marking using chaining pins to obtain total
length.
5. Reading the tape – the graduated tape must be read
correctly.
6. 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 0.66
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

► 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

► 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. Chaining Pins – set of 11, used to mark the tape lengths
2. Hand Level – used to determine required plumbing height
3. Plumb Bob – used to transfer the mark from the tape to ground
4. Tension Handle – used to maintain correct tension on tape

Taping (Field Process)
1. The line to be taped should be marked at both ends
 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
2. Applying Tension
 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)
3. Plumbing
 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

Taping Error:
1. Instrumental Error – a tape may have different length due to
defect in manufacture or repair or as the result of kinks
2. Natural Error – length of tape varies from normal due to
temperature, wind and weight of tape (sag)
3. 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. Alidade – Upper part
2. Horizontal limb – Middle part
3. 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. 4 – leveling screws
2. Bottom plate that screws into tripod
3. Shifting device that allows transit to move ¼ to 3/8”
4. ½ ball that allows transit to tilt when being leveled
5. The SPIDER – 4-arm piece which holds the outer spindle
6. Lower clamp – allows rotation of outer spindle

►Telescope: Similar to that of dumpy level, but
shorter
 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. Average length of sight of 300’ assumed in design
3. 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

C
A
B
Operation of Transit
► 9 Steps
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 X-
hairs are on BS

Operation of Transit
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. Pointing the telescope
2. Reading the plates
C
A
B

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 STATION SET UP
► WHEN TOTAL STATION IS MOVED OR
TRANSPORTED, IT MUST BE IN THE CASE!!!!!!!!
1. ESTABLISH TRIPOD OVER THE POINT.
2. OPEN THE CASE AND REMOVE TOTAL STATION, PLACING IT ON THE HEAD
OF THE TRIPOD AND ATTACH SECURELY WITH CENTER SCREW.
3. CLOSE THE CASE.
4. 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).
5. UTILIZING THE TRIPOD LEG ADJUSTMENTS, LEVEL THE TOTAL STATION
USING THE FISH-EYE BUBBLE.
6. LOOSEN THE CENTER SCREW TO ADJUST THE TOTAL STATION EXACTLY
OVER THE POINT IF NEEDED.
7. COMPLETE LEVELING THE TOTAL STATION USING THE LEVEL VIAL.
8. CHECK TO MAKE SURE YOU ARE STILL ON THE POINT.

TURNING ANGLES WITH TOTAL STATION
1. SIGHT ON THE BACKSIGHT UTILIZING THE HORIZONTAL ADJUSTMENT
SCREW.
2. ZERO SET THE INSTRUMENT (THIS PROVIDES AN INNITIAL READING OF
0 SECONDS.
3. LOOSEN TANGENT SCREW AND ROTATE INSTRUMENT TO FORESIGHT.
4. TIGHTEN TANGENT SCREW AND BRING CROSS HAIR EXACT ON TARGET
WITH ADJUSTMENT SCREW.
5. 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. POINT THE INSTRUMENT AT A PRISM (WHICH IS VERTICAL OVER
THE POINT.
2. 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. NEVER POINT THE INSTRUMENT AT THE SUN, THIS CAN DAMAGE
THE COMPONENTS OF THE INSTRUMENT AS WELL AS CAUSE
IMMEDIATE BLINDNESS.
2. NEVER MOVE OR TRANSPORT THE TOTAL STATION UNLESS IT IS
IN THE CASE PROVIDED.
3. DO NOT ATTEMPT TO ROTATE THE INSTRUMENT UNLESS THE
TANGENT SCREW IS LOOSE.
4. AVOID GETTING THE INSTRUMENT WET, IF IT DOES GET WET,
WIPE IT DOWN AND ALLOW TO DRY IN A SAFE AREA BEFORE
STORAGE.
5. BATTERIES OF THE TOTAL STATION ARE NICAD AND THUS MUST
BE CHARGED REGULARLY. AT LEAST ONCE PER MONTH, THE
BATTERY SHOULD BE CYCLED.
6. 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)

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

Direction
► If angular adjustment does not divide out equally:
1. Do not go to decimal unless instrument reads to decimal
2. Observe field notes for angles with poor closure or where problems
turning angles existed. Apply excess to these angles evenly.
3. 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

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

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 –

Direction
► Basic Procedure
1. Determine Latitude and Departure
2. Sum Lat. and Departure to calc. closure
3. Obtain balanced Lat. and Dept. (Compass Rule)
4. Determine coordinates
5. Once rectangular coordinates are known on point, their
exact location is known with respect to all other points in
the network

Direction
► Balancing Methods
1. Compass Rule: (Bowditch) Used when accuracy of  and length
measurement is equal
► (Error Lat./Perimeter length) X Distance = Latitude Correction
► (Error Dept./Perimeter length) X Distance = Departure Correction
2. Transit Rule: Used if angles are more accurate than distances (more
accurate direction)
► Correction Latitude (Side) = (Lat. Side/Sum all Lat.) X Lat. error
► Correction Departure (Side) = (Dept. Side/Sum all Dept.) X Dept. error
3. 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
4. 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: 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
Difference in Sums/2 = Square feet
Square feet/43560 = Acres
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
Sum N = 294,119,678.8
Sum E = 293,663,353.6
456,325.2 / 2 = 228,162.6 ft2 = 5.24 Ac

Example: Determine Area of A, D, E, F, A
N = 186,116,759.8
E = 185,971,439.3
145,320.5 / 2 = 72,660.25 ft2 = 1.67 Ac 
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

► Inverse: With known coordinates of any two points on a
system, you find the distance and direction between the two
C 9938.7277 5298.7122
D 9448.9156 4560.3990
489.8121 738.3132
► To find the Inverse between 2 Points
1. Find difference in N & E of coordinates
2. Plot
► Use point you are going from 1st
► Plot longest side 1st
3. Determine length using Pythagorean (a2 + b2 = c2)
4. Determine reference direction
5. Determine local  using tan A = a/b
6. Determine line direction

► Example: Determine direction and distance D-A
D 9448.9156 4560.3990
A 10000.0000 5000.0000
551.0844 439.6010

► Intersection: Determination of unknown point
location with directions from two points known
1. Determine difference in coordinates
2. Plot points and line projections
3. Set up dual formulas (as Latitude and Departure)
4. Solve for length
5. Compute coordinate as sideshot
C 9938.7277 5298.7122
D 9448.9156 4560.3990
489.8121 738.3132

► 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 9938.7277 5298.7122
F 10070.8565 4583.9559
132.1288 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 =

► Vertical Curves – Two major methods used to calculate
vertical curves: Tangent offset and Equation of Parabola
Information needed:
1. Grade or slope on each side of curve
2. Elevation and station of PVI
3. Curve length (Horizontal distance PVC – PVT)

Tangent Offset Method
► Procedure:
1. Compute the elevation of the PVC and PVT
2. Compute the elevation of Chord midpoint
3. Compute offset to curve at midpoint
4. Determine total number of stations covered
5. Determine tangent elevations at stations
6. Compute curve offset at stations
7. Combine data and determine vertical curve elevations

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
station in the elevation computations
The equation gives the distance from the PVC in stations
1
pt
-g
x =
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’ = 0.0002’
 200’ = 0.0008’
 300’ = 0.0019’
 500’ = 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. Reading on point of known elevation (BS)
2. BS reading + BM elevation = HI
3. Reading on point of unknown elevation (FS)
4. 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
2. Inclination due to maladjustment of instrument
 Both can be alleviated by equalizing length of BS and FS legs
3. Changes in scale of rod due to temperature
 Usually ignored except in very precise work
 Would use same process as tape correction
4. Rod not held plumb
 Minimized by carefully plumbing the rod or more commonly known as
“Rocking the Rod” and taking the lowest reading

Leveling
► Peg Test
1. 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. Balance length of BS and FS (300’ max)
2. Make sure gun is level and pendulum free
3. Turn through all BM’s
4. Give complete description of BM’s and TBM’s
5. Have rod rocked
6. Make sure turning points are solid
7. Close all circuits on BM of same degree of accuracy

Other Random Errors
1. 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

Field Notes
STA BS HI FS ELEV
►Sum BS – Sum FS = Difference of Elevation

Closure Error
► Difference in measured elevation and know elevation
► Correction factor = closure / # turns
Error = 0.09’
Turns = 12 Correction = 0.0075’ / turn
► If 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

► 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

 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. 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
2. Contours do not cross or meet except in caves, cliffs
& vertical walls where they can meet
3. Contour lines crossing streams form V’s pointing
upstream
4. Contour lines crossing a ridge form U’s pointing down
the ridge
5. Contour lines tend to parallel streams

Characteristics of Contours
6. 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

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

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

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

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

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

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

Theodolite & EDM (Radial)
 Replaces tacheometry (stadia)
1. Establish control points (horizontal and elevation)
2. Shoot locations and turn vertical angles
3. Used for large areas

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
► Points are on roof of mine
Reasons needed
1. Location in respect to boundaries
2. Location in respect to other shafts
3. Accurate maps (above and below ground)
4. 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

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)

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)
2. Software
3. Data
4. Human Operators and Institutional Infrastructure
Geographic/Spatial
Non-Geographic/Aspatial/Attribute

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

Introduction to Surveying

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Introduction to Surveying