CE200 Study Guide

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CE 200 - Surveying

Student Study Guide

Prepared by

Dr. Laramie Potts

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Introduction to Surveying

• History of Surveys ( 1.3 ك)

o Egyptians - procurement for taxation inventory

o Greeks - develop science of Surveying (through geometry)

o Romans - enhance art of Surveying by developing instrumentation & field

procedures

o Middle Ages - little progress - Arabs kept the art of mapping alive

o 18 & 19cy - England and France enhance art due to demands on:

Boundaries of ownership

Location of resources (to exploit & preserve)

o ‘60-’70’s - major development in analogue survey equipment (e.g., Theodolite,

Dumpy level, Steel tape)

o 80’s – present: Space exploration impact Surveying

Instrumentation (e.g., Total Station, etc.,)

Calculation

Solutions to Environmental Issues

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• Classification of Surveys

o Plane Surveying

Assume Earth is flat over a limited range

Requires projection to representing surveyed points

Survey is of high resolution

o Geodetic Survey

Approximate Earth by Ellipsoid (mathematically defined shape)

Cartesian Coordinates in Earth Centered Fixed (ECF) frame

Survey is of medium to low resolution

o Spatial Data

Traditional Survey Measurement

• Distances (horizontal, vertical, slope)

• Angles (vertical & horizontal), Azimuth w.r.t.. True North

• Analogue data collection – field books etc.,

Geodetic Surveys (Satellite based Observations)

• Ranging - from transmitter to receiver (3-d Geometry)

• Digital data collection – data collector, on-board memory

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• Math Review and Field Notes

o Basic formulas in Plane Surveying

Law of Sines:

Cc

Bb

Aa

sinsinsin==

Law of Cosines:

Cabbac cos2222 ∗−+=

Distance S:

αcos∗= SLOPEHOR SS , where α is the slope angle

Angle: anti-clockwise differencing two directions

ii rrA rv −=∠ +1 , where subscript i refers to the ith direction

o Field Notes

Analogue Surveys (traditional)

• Hand written in field book

• No Erasures, Carbon Copy, Legible, Meteorology

Digital Surveys

• Original data in digital form

• Requires I/O formatting to optimize Survey output

More information about Surveying, check out http://www.geomatics.net/

a

bc

C

A

B

ri+1 ri

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2.0 Theory of Measurements and Errors

All aspects of surveying computation require thorough understanding of measurement quality,

characteristics, and measurement reductions and corrections.

2.1 Surveying Measurements

Measurements are made (using electronic device or a scale) in specified units

(length = km, m, mm, ft, in, etc)

(angles = deg., gon., min., etc)

to estimate x, the observed quantity of X, where X is the unknown true value.

Measurements are characterized as follows:

• all observation have errors

• No observation is exact

• Errors present are unknown

Therefore we compute the estimate x of the true value X

2.2 Theory of Errors

Definition: Error (e) =: x - X

e.g., observation with scale divided to 101 th facilitates interpolation to

1001 th

2.2.1 Source of Errors in a measuring system

1. Natural (environment)

2. Instrumental (limitation in manufacturing and/or electronics)

3. personal (limitation in human senses)

2.2.2 Types of Errors

1. Systematic error (biase)

a. Errors introduce from factors comprising the measuring system (i.e.,

environmental, instrumental, personal). For example;

1). a 100-ft tape measures 0.02ft too long - reflects a constant biase

2). Variable temperature differences during tape usage – introduce a variable

biase

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2. Random Error

a. Obeys laws of probability. Random errors cannot be eliminated absolutely,

but can be estimated by estimation procedures

2.2.3 Probability and Most Probable Value

Events that happen randomly are governed by mathematical principles referred to as probability

(e.g., flipping a coin, rolling dice, Russian roulette etc.,)

Most Probable Value requires redundancy for estimating its true value X. The most probable

value is defined mathematically as

∑=n

iix

n1µ

where n is the total number of observations, x is the measurement and i is the measurement

index.

Residual of the observation is defined as

ii x−= µν , with i=1,…,n

Histogram shows the distribution pattern of the measurement

Elements of distribution include the following

• Frequency - number of occurrences

• Range - [minimum value; maximum value]

• Dispersion - D = νmin+ νmax

• Class interval - D/M where M denotes the number of classes (see example in

Table 3.1 and Figure 3.2 given below)

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2.2.4 Precision and Accuracy

a) Discrepancy: The difference (∆) between two observations of the same quantity X

example: 1212 xxx −=∆ where x1 and x2 are two measurements of X

b) Precision: A small discrepancy between observations of the same quantity X indicates

high precision

c) Accuracy: denotes nearness of observations to their true value X

Example: A 100-ft tape measures 0.05 ft too long. Two measurements of a distance

give results of x1=453.270, x2=453.272 ft, respectively. We obtain the following

statistics and information:

i. Mean value: 2

21 xx +=µ = 453.271

ii. Systematic error: 4.53* 0.05 = 0.23 ft

iii. Precision: µ

12x∆ =

000,2201

iv. Accuracy: µ

biase = 271.453

23.0 =000,21

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2.3 Review of Statistical Concepts

The Figure below shows a histogram and the distribution curve of the residuals for

measurements given in table 3.1 (Wolf & Ghilani, 06)

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2.3.1 Occurrence of random errors

Standard deviation

11

2

−±=∑=

n

n

iiν

σ where n is the

number of observations.

E50 = 0.6745σ

E90 = 1.6449σ

E95 = 1.9599σ

The Figure below shows the relation between error and percentage of area under the normal

distribution curve

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In-class exercise:

observation x1 x2 Residual v1 Residual v2

1 205 160

2 255 165

3 195 160

4 220 155

5 235 148

6 222 157

7 198 155

8 215 150

9 230 165

10 240 156

∑ =1x ∑ =

2x =

1xµ =2xµ

Range = [ ; ] Range = [ ; ] Dispersion =

1xD =2xD

Dispersion =1xσ =

2xσ C. Int. (for M=11) = C. Int. (for M=11) E90 = E90 = Plot a histogram, and distribution curve for the observations given in the table above

Size of residuals

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2.3.2 Gaussian (Normal) Distribution of observations (errors)

1-Dimensional normal distribution is the most frequently used distribution in statistical theory

and application. Its density function is give by:

2

21

21)(

−−

= x

xx

x

exf σµ

πσ

The two parameters that specify the distribution are;

xµ = expectation or mean value of X, and σx = standard deviation of X, ie., the variance

or dispersion of X = 2xσ

The cumulative normal distribution function of the standardized random variable

x

xxz

σµ−

= where xµ =0, σx =1 so that the distribution function is given by

),0(:21)( 2

2

DNedxexfx

=⇒=−

π

2-Dimensional normal distribution of a random variable vector (X,Y) is defined by the density

function:

+−•−

=]2[

222

21

2112

21

22

21

21),(

zzz

z

eyxf σσσ

γσσ

λπ,

where 1222

21 σσσγ −= , ( yx µµ , ) are the means, and ( 22 , yx σσ ) are the variances (dispersions) of

(X,Y), respectively.

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3.0 Leveling: Theory and Methods

Basic terms in leveling

• Vertical line: A line that follows the local direction of gravity vector

• Horizontal line: A line perpendicular to the local direction of the gravity vector

• Level Surface: A curved surface that local plumb line. A still body of water is best

example of a level surface. Level surfaces are known as equipotential surfaces.

Globally, a level surface approximates a spheroid. Locally, two level surfaces at

different elevation are considered concentric.

• Elevation: The distance measured along a vertical line from a refrerence (datum) to a

point

• Vertical Datum: Any level surface to which elevation is referred. North American

Vertical Datum 1929 (NAVD29), North American Vertical Datum 1988 (NAVD88).

Established by network of benchmarks tied to tide gauges. NAVD29 – tied to 26 tide

gauges -> described MSL. NAVD88 tied to 1 TG (not describe MSL)

• Mean Sea Level (MSL): The average height of the sea’s surface for all stages of the

tide over a 19-year period. It was derived from hourly readings at 26 TG along the

Atlantic, Pacific, and Gulf of Mexico coaist of USA.

Z

α B

ABH∆

Local horizon through B

Level Surface

MSL

A

Reference Ellipsoid Surface

AH Geoid

Figure 3.1: Leveling

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• Geoid: An equipotential surfacec that gobally approximates mean sea level

• Leveling: The process of finding elevation of points or the process of finding elevation

differences between points.

• Vertical Control: A series of points of known elevation established throughout an area.

Control networks are ranked according to pre-determined accuracy standards. [Zero

Order, First Order, Second Order, Third Order., etc]

3.1 Differential leveling

Notation: BS: Back sight, FS = Foresight (station ahead in the direction of the forward leveling

loop)

In general, the elevation difference between points A and B is given as

FSBSAB hhH −=∆ , where h is the stadia reading on the level rod.

=3.24-0.54 = 2.80 m

Then the elevation of point B is given as follows;

ABAB HHH ∆+=∴ = 820.00 +2.80 = 822.80 m above the reference (mean sea level)

B

0.54

Datum Elevation = 0 Reference Level Surface

FS BS

A Level surface thru’ A

3.24

Level surface thru’ A

820.00m

Figure 3.2: Differential leveling and procedures

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3.1.1. Leveling Loop

A general procedure is to start at a point of known elevation, called a bench mark (BM).

The first reading is a back-sight (BS), taken on the established BM. The next reading taken is

the foresight (FS), in the forward moving direction of the leveling route. Fore-sight readings

taken at intermediate points are called turning points, also labeled TP. At every setup along the

leveling route, alternating BS and FS readings are taken until the final reading is taken on

another BM. The final reading is a FS.

Height differences between points are:

FSBSAB −=∆

Height of Instrument (HI):

HI = ELEVBM + BS,

or at intermediate points

HITP= ELEVTP+ BSTP

In any leveling loop (circuit), accumulated errors (systematic errors) will result in a small

difference in the computed elevation of the closing bench mark. This difference is called

3.1.2 Leveling Loop Misclosure

The misclosure Ce is defined as COMPBM

GIVENBMe HHC −=

Any level loop will have a misclosure. The magnitude of the misclosure provides a basis to

compute a correction to each observation. By applying corrections to the observation, the

computed elevations of all intermediate points are adjusted. These adjusted elevations are

considered final elevations. Below is an example of a level circuit from the benchmark Mill to

Oak and back to Mill. The back leveling loop follows a different route than the forward loop.

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The following example is given in Figure 5.5 of Worlf and Ghilani (2006)

Station BS (+) H.I. FS(-) Elevation Adj. Elev.

BM Mill 1.33 2053.18 2053.18

2054.51

TP1 0.22 8.37 2046.14 (-.004) 2046.14

2046.36

TP2 0.96 7.91 2038.45 (-.008) 2038.44

2039.41

TP3 0.46 11.72 2027.69 (-.012) 2027.68

2028.15

BM OAK 11.95 8.71 2019.44 (-.016) 2019.42

2031.39

TP4 12.55 2.61 2028.78 (-.020) 2028.76

2041.33

TP5 12.77 0.68 2040.65 (-.024) 2040.62

2053.42

BM Mill 0.21 2053.21 (-.028) 2053.18

Σ = +40.24 Σ=-40.21

Page Check: 2053.18 + 40.24 = 2093.42

2093.42 - 40.21 = 2053.21 check

Misclosure Ce: 2053.18 - 2053.21 = -0.03

Adjustment: ∆ = setupsno

misclosure.

= 7

03.0− = -0.0043’

Correction per setup = c = ∆* setupi ; For example at setup # 2 c= -0.0043*2 = -0.0086

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3.1.3 Leveling Computation

In-class example (Exercise 5.15 Wolf & Ghilani)

A differential leveling loop started and closed on BM Juno, elevation 2485.19 ft. The

backsight(-) and foresight (+) distances were kept approximately equal. Readings (in feet)

listed in order taken are 5.49 (BS), 3.46 (FS), 8.48 (BS), 5.34 (FS), 6.51 (BS), 8.27 (FS) 4.03

(BS), 9.46 (FS), 7.89 (BS) and 5.92 (FS). Prepare, check and adjust the notes.

Station BS (+) H.I. FS(-) Elevation Adj. Elev.

BM Juno 5.49 2485.19

TP1 8.48 3.46

TP2 6.51 5.34

TP3 4.03 8.27

TP4 7.89 9.46

BM Juno 5.92

Σ = Σ=

Page Check:

Misclosure Ce:

Adjustment: ∆ = setupsno

misclosure.

=

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3.2 Source of errors (Also see section 5.12)

1. Instrumental Errors (Systematic): Collimation error, Alignment, Rod Graduations,

Tripod maladjustments.

2. Natural Errors (Systematic & Random): Earth curvature, Refraction, Thermal effects

and wind, Instrument settling

3. Personal Errors (Systematic & Blunders): Bubble not centered, Parallax, Faulty rod

readings

3.2.1 Reductions and Corrections to Survey Measurements

Q. What observation procedure reduce/eliminate the collimation error?

• Curvature of Earth, Cm ,in meters, is given by

Cm = 0.0785 K2, where K is distance in km

• Refraction, Rm, is given by

Rm = HT

∂∂

⋅− −31022.1 ( tests at msl shows 1.0−=∂∂HT )

• Combined curvature and refraction effect:

(Cm+ Rm) = 0.0675 K2

3.2.2 Precision

Precision is the allowable discrepancy between the computed elevation and the fixed elevation.

Formula by FGCS is

C = KmCmm = where K is the total length of the leveling route in kilometers and m is

a constant.

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Table: Federal Geodetic Control Subcommittee (FGCS) recommendation)

m Order Class

4 O1 I

5 O1 II

6 O2 I

8 O2 II

12 O3

3.3 Three-Wire Leveling and Adjustments (See Figure 5.9 W/G)

3-wire leveling has several advantages over

1. check against rod blunders

2. greater accuracy by averaging three observations

3. furnish sight lengths

3.4 Profile (See W/G section 5.9)

Purpose of profile plots:

1. Determine depth of cut-fill for Engineering projects

2. Studying grade-crossing problems

3. Investigate & select most economical route for pipelines, tunnels etc.,

4. Estimating gradients

Definition: Gradient is the rise (fall) in feet per 100-ft.

2.5% gradient means 2.5 ft elevation difference per 100 ft

horizontal separation

3.5 Barometric Leveling: Using an instrument that measured pressure (air, water, etc.,) to find

relative elevations.

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3.6 Trigonometric leveling:

This approach is best suited for long lines over undulating topography.

Using basic trigonometric relationships, the slope distance SS and height of the reflector, hr,

observations obtain various elevation differences;

rHAB

SSIR

hHISHZSSVH

−+=∆===∆

αα

tancossin

Z α

B

ABH∆

V hr

Horizontal

SS

SH

HI

A

Figure 3.3: Trigonometric leveling

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4.0 Survey Measurements Basic surveying measurements include measuring distances and angles between points 4.1. Distance Measurements Measured lines are horizontal distances between two points. Several distance measuring include the following methods

1. pacing : counting steps (calibrated) – to detect blunders

2. Odometer: converts number of revolutions of a wheel of known radius 200S

S ≈σ where

S is the measured length along the ground and is given by RnS π2= where n is the number of revolutions Q: What is the horizontal distance measured by 20 odometer revolutions up a slope of 12o for an odometer with radius of 6 inches?

3. Taping: Six steps mentioned in W/G p130

4. Optical rangefinder:

governing equations: 21

111fff

+=

The instrument solves for the object distance f2 given the focal length f and the image distance f1

150S

S ≈σ for S up to 150 ft

Disadvantage:

1. Requires adequate lighting 2. Time required to measure is long 3. Subjectivity associated with focusing optics

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5. Tacheometer (stadia)

Stadia measures the horizontal distance and the elevation of a point

CIKS +⋅= where I is the stadia interval constant K = 100 (manufacturer specified) biase C≈0

500S

S ≈σ

6. Subtense Bar:

An indirect distance measuring procedure obtain S by measuring the angle α D is the fixed distance between targets on the bar (typically 4-m long) S is the deduced horizontal distance from the center of the bar to the transit

Measurements involves conversion of horizontal angles between target precisely spaced and at a fixed distance apart on a subtense bar

Q. a) What is the horizontal distance measured by a 4-ft subtense bar with an angle subtended of 1o

b) Same as before but with the subtense bar 15ft higher in elevation then the theodolite (transit)?

α

S

Dtransit

target

Figure 4.1: Subtense bar measurement systems

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7. Electronic Distance Measuring (EDM) Device Distance measurements are based on the rate and manner by which electromagnetic energy propogates through the atmosphere. The basic equation for the rate of propagation is

ncV =

where c is the velocity of electromagnetic energy in a vacuum (=299,792,458 m.s-1), n is the atmospheric refraction index The temperature, atmospheric pressure, and relative humidity all have an effect on n

The group index of refraction (for standard air): 42

06800.088660.46155.287λλ

++=gN

Where λ is the wavelength in µm

Actual group refractive index for atmosphere : 61027.1125.1013

1 −

+

−+

⋅+=bte

btPNbn g

a ,

where

b = 273.15 ( a constant)

e = partial water vapor pressure (hPa) 100

hE ⋅=

7858.05.7

10

++

=

=

btt

E

α

α

h = relative humidity (%) P = pressure in hPa t = try-bulb temperature in oC 7.1. Principle of EDM

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Distance is given by the following relation: ( )

2ϕλ +

=nS , where φ is the phase shift and given as;

mRAD

m λπαϕ +

=

2

λ φ

λ

S

Reflector EDM

Figure 4.2: Electronic Distance measurement

λ

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From “Statistics & Data Analysis in Geology” by John C. Davis (1985)

Reduction of Short lines

• Elevation difference:

( ) ( )rBiA hHhHH +−+=∆

22 HSS SH ∆−=

• Zenith (or vertical) angle

ZSS SH sin=

Z α

B

H∆

hr

Horizontal

SS

SH

hi

A

Figure 4.3 EDM leveling

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riH hhSH −+=∆ αtan

Errors in EDM measurements:

ε = const + proportionality factor ( 10 ppm = 000,000,1

10 )

the 1st part is (± mm) and the 2nd part is in (ppm)

21

2222 ])([ LcriS SppmEEEE ⋅+++=

Where Ei is mis-centering of instrument

Er is mis-centering of rod

Ec is slope offset error

SL is slope distance

ppm is specified scalar error for EDM

Further reading: See section 6.24 in W/G

4.2 Angles, Azimuth and Bearings

Directions are given by azimuth or bearing. Angles measured in Surveying are either horizontal

or vertical angles. Angles are direct measurements using a transit or total station.

4.2.1 Angles: are directly measured in the field using as transit or theodolite

Units degrees ( º) minutes (') and seconds (")

Example 5.5º = 5º 30' 00"

• Angles to the right measure clockwise from the back (rear) station to the forward

station.

• Sum of all interior angles of closed polygon = (n-2)*180º where n is the number of

angles

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Ex. Boundary surveys are examples of closed polygons.

4.2.2 Direction of a line is defined as the horizontal angle between the meridian and the line to

a point object

• Geodetic meridian: N-S line passing through the average position of Earth’s

geographic poles.

• Astronomic meridian: N-S line passing through the instantaneous position of the

Earth’s geographic poles.

• Magnetic Meridian: is defined by a freely suspended magnetic needle that is

only influenced by the Earth’s magnetic field

4.2.3 Azimuth (AZ) of a line is the horizontal angle measured clockwise from any reference

meridian (RM). Az can be read directly from a graduated circle in a total station that is oriented

w.r.t. true north

AZB = 125º

4.2.4 Bearing (BZ) of a line is the acute

horizontal angle between a reference meridian

and the line

BZA = N50ºE

T N

120º

215º

A

B

Figure 4.4: Azimuth of line

T N

50º

45º

A

B

Figure 4.5 : Showing bearing of lines

C35º

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BZB = S35ºE

BZC = S45ºW

Q. What is the bearing of AZ = 128º13'46" (NB: It’s always a good idea to draw a sketch) Computing Azimuth and angles:

AZ(A-B) = 81º

AZ

(B-A) = 81º+180º = 261º

Angle ABC=350º – 261º = 89º

Computing Bearing and angles:

AZ(B-A) = 81º+180º = 261º

AZ

(B-C) = 261º+89º = 350º

BZ(B-C) = N10ºW

(also from the sketch)

T N

81º

A

Figure 4.6: Showing Azimuth and direction

C

261º

B

350º

T N

T N

81º

A

Figure 4.7: Showing bearing and direction

C

10º

B

81º

89º

T N

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5.0 Traverse and Traverse Computation 5.1. Instrumentation and Observations (8.4 ك) 5.1.1 Parts of the total station instrumentation (TSI) (8.4 ك)

• Tribrach with optical plummet (laser) enable centering accurately over station

• Micrometer facilitates the following operations: Instantaneous horizontal circle zeroing Repetitive measurements done easily Increase overall speed of survey operations

• Servo-driven & remote operation Useful in construction stake out (i.e., computer retrieves coordinates from database) Remote Positioning Unit (RPU) uses built-in telemetry link for communication

Observations with a TSI include electronic distance measuring (EDM) and angle measurement 5.1.2 EDM observations As discussed previously, the Distance measured by the EDM is given by

( )2ϕλ +

=nS , where φ is the phase shift

Important meteorological observations must be made for later processing and reduction of distances. 5.1.3 Angle observations

A mathematical relationship for angles and distances are:

θRS =

R

S θ

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Where S is the arc length subtended at a distance R by an arc of θ (in radians)

Radian = 8.4206262958.571802

360 ′′=== ooo

ππ

5.1.3.1 Horizontal measurement and adjustment Assume the TSI is oriented where the Refering Object (RO) is located due north of the station setup. With the circle in the direct position, the observations proceed in the clockwise direction from RO, T1, T2 and “close” on RO again. Flip the telescope and sight on RO. This operation sets the circle readings in the reverse position. Read the circle readings for sighting on the RO, T2, T1, and close on the RO. A sample field book is shown below Table 1: Sample field book entries for horizontal observations and adjustment Station Direct Reverse Average Adjusted

RO 0º 00' 25" 180º 00' 15" 20" 0º 00' 20" T1 30º 15' 36" 210º 15' 30" 33" (+1") 30º 15' 34" T2 227º 45' 37" 47º 45' 43" 40" (+3") 227º 45' 43" RO 0º 00' 20" 180º 00' 10" 15" (+5") The adjustments, as shown above, are made to remove the collimation error in the horizontal observations 5.1.3.2 Vertical (Zenith) angle observations and adjustments Table 2: Sample field book entries for vertical (zenith angle) observations adjustment Station Direct Reverse Sum Adjusted

RO T1 92º 37' 14" 267º 12' 50" 64" (-4/2)" 92º 37' 12" T2 89º 59' 45" 270º 00' 13" 58" (+2/2)" 89º 59' 46" RO A vertical angle is the angle above or below the horizontal plane through the observation point. Direct face (face Left): Z−= o90α Reverse face (face right): o270−= Zα

R.O.

TSIº

T1

T2

Figure 5.1: Horizontal direction (angle) measurements

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An index error exists when the TSI 0º circle setting in the “direct face” position does not coincide with the true zenith. In general we write a relation for the index error ( indexε ):

nZZn REVDIR

index 2)(360 +Σ−

=o

ε , where n is the number of ZDIR and ZREV pairs

5.2 Trigonometric Leveling with TSI ( 8.18 ك)

• Limitations in accuracy, compared to differential leveling, are due to instrumental error and effect of refraction

• Advantage of trigonometric leveling with TSI over differential leveling is the speed of operation over rough terrain

5.3 Sources of error in TSI fieldwork (8.20 ك)

• Instrumental: -Vertical axis not to plate level vial -Horizontal axis not to vertical axis -Axis of line of sight not to horizontal axis

• Environmental: -Wind causes instrument vibrations -Unequal refraction – keep sights well above ground -Tripod uneven settling

• Personal: -Mis-centering over a survey point -Poor and improper focusing -Careless plumbing and rod placement on survey points 5.4 Traversing Field procedures consist of a series of consecutive direction and distances measurements.

• Closed: i) polygon configuration where lines return to the starting point ii) link configuration where the endpoint is a known station

• Open: traverse terminates on an unchecked point or a point of lesser order accuracy than the starting point (Q: Why avoid “open” traverses?)

5.4.1 Methods to obtain traverse line directions:

1. interior angles (used in boundary surveys)

2 3 4 5 61Angular accuracy (")

Max

imum

Sig

ht (m

)

100

200

300

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2. angles to the right (used by data collections) 3. deflection angles (used in route surveys) 4. azimuths (used in TSI when properly oriented w.r.t true north)

To perform traverse computations it is generally a good idea to convert the above type of field observations to directions.

5.4.2 Methods to obtain traverse line distance:

1. steel tape (apply appropriate reductions and field precautions) 2. subtense bar (limited accuracy over long distances) 3. EDM (apply appropriate meteorological corrections) 4. Other methods as discussed before

5.4.3 Selection of traverse stations (9.4ك) Important criteria used to select traverse stations include the following

1. ensure accuracy of measurements 2. ensure optimal sighting lengths 3. ensure optimal utility (GPSABLE???)

5.4.4 Source of error in Traversing (9.10ك)

1. poor station selection 2. errors in measurements 3. errors in field operations and procedures

5.4.5 Mistakes in Traversing (9.11ك)

1. occupy the wrong stations 2. incorrect orientation 3.

5.5 Traverse Computation Departures and Latitude (a.k.a. Forward problem) is used to compute the consecutive position of surveyed point along the traverse route. Departure of a line (point) of its orthographic projection onto the E-W axis.

TN

A

B

C

Figure 5.2: Traverse measurement for departures and latitudes

αAB

∆X Departure

∆Y

Latit

ude

E (X)

N(Y)

SAB

SBC

αBC

O

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Latitude of a line (point) is its orthographic projection onto the N-S axis. α is the measured azimuth (A) of the line AB (AAZ)

αα

cossin

SYSX

=∆=∆

5.5.1 Closure condition for traverses

• Linear misclosure 22 dydxL +=ε where dx is the misclosure in departure and dy is the latitude misclosure

• Relative precision = linear misclosure /traverse length S

=∑=

+n

iiS

dydx

1

22

where n is the number if traverse legs

5.5.2 Traverse Adjustments The Compass (Bowditch) rule adjusts the ∆X’s and ∆Y’s of the traverse legs appropriately.

Adjustment for the departure (or X) components: ABn

ii

n

ii

AB SS

dxdx ×=

∑

∑

=

=

1

1

Adjustment for the latitude (or Y) components: ABn

ii

n

ii

AB SS

dydy ×=

∑

∑

=

=

1

1

Example:

15º51'54" 720.35

284º35'20" 610.24

126º55'17" 647.25

178º18'58" 203.03

206º09'42" 285.13

5,000.00 N(Y) 10,000.00 E(X)

234º17'18"

E

C

D

B A

W

N(Y)

Figure 5.4: Polygon traverse points with directions and distances measured

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Unadjusted Balanced Coordinates

Station Az Si ∆X ∆Y ∆X’ ∆Y’ E(X) N(Y) A (-.007) (-.020) 10,000.00 5,000.00 126º 55' 17" 647.25 517.451 -388.815 517.440 -388.835 B (-.002) (-.006) 10,517.44 4611.16 178º 18' 58" 203.03 5.966 -202.942 5.964 -202.948 C (-.008) (-.023) 10,523.41 4408.22 15º 31' 54" 720.35 192.889 694.045 192.881 694.022 D (-.006) (-.019) 10,716.29 5102.24 284º 35' 20" 610.24 -590.565 153.708 -590.571 153.689 E (-.003) (-.009) 10,125.72 5255.93 206º 09' 42" 285.13 -125.715 -255.919 -125.718 -255.928 A 10,000.00 5,000.00 Σ=2466.00 Σ=0.026 Σ=0.077 Σ= 0 Σ= 0 Corrections in departures and latitudes are as follows;

003.013.2852466

026.0=×=EAdx , and 009.013.285

2466077.0

=×=EAdy

Linear misclosure: ftdydxL 081.0077.0026.0 2222 =+=+=ε

Relative precision: 000,301

2466081.0

1

22

==+

∑=

n

iiS

dydx

5.5.3 Rectangular Coordinates (10.8ك) In surveying, the to the X-Y axis is oriented such that the Y-axis point N-S with North in the +ve Y-direction. The X-axis runs E-W with East in the +ve direction Coordinates are useful for the following reasons:

1. Determine lengths and directions (inverse problem) 2. Calculate areas of the land parcel 3. Curve computations 4. Locating inaccessible points 5. plotting map features

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Hence, given XA,YA, SAB and AAB we can compute departures and latitude to obtain XB,YB. Specifically,

ABABAB

ABABAB

ASYYASXX

cossin

+=+=

5.6 The inverse Problem Given XA,YA and XB,YB find SAB and AAB: For Figure 5.3, we write the following

−−

=

−−

=

−

AB

ABAB

AB

ABAB

YYXXA

YYXXA

1tan

tan

and the distance AB is given by

( ) ( )22ABABAB YYXXS −+−=

5.7 Mistakes in Traverse adjustments (see 10.17ك)

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6.0 Coordinate Geometry Review the basic trigonometric formulae 6.1 Equation of Line (11.2 ك)

( ) ( )[ ][ ]2122

21

22

ABAB

ABAB

P

yxAB

yyxxAB

Cmxy

∆+∆=

−+−=

+=

Azimuth from point to point B is given by

α+

∆∆

= −

AB

ABAB y

xA 1tan where

∆∆∆∆∆

=0;0360

01800;0

fpa

pa

fa

o

o

ABAB

AB

ABAB

yxy

yxα

Slope m of the line is given by

AB

AB

xym

∆∆

=

NB: m ≠ AAB in general. [prove α+

= −

mAAB

1tan 1 ]

Q. Given (xA, yA) = (1130.52, 930.71) and (xB, yB) =(1432.92, 501.55), compute AAB and the slope m

A

Figure 6.1: Point on a line

B

P

X

Y

AAB (xA,yA)

(xB,yB)

∆yA

B

∆xAB C

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6.2 Perpendicular distance from a point to a line ( 11.3 ك)

Application:

A. Check alignment - e.g., of survey markers on a block

B. Subdivision design C. Position in-accessible point D. other

Given (xA, yA), (xB, yB) and (xC, yC), find the length of PC Steps:

1. Compute AAP 2. Compute AAB 3. Compute “offset” angle α 4. Compute length AP 5. Compute PC = AP sin α

Example: Using Figure 6.2, the following coordinates pairs of P (1123.82, 509.41), A (865.49, 416.73), and B (1557.41, 669.09). What is the perpendicular distance from P to the line AB? Answer:

4.49517068.9233.258tan

73.41641.50949.86582.1123tantan 111 ′′′=

=

−−

=

∆∆

= −−− o

AB

ABAP y

xA

24756973.41609.66949.86541.1557tan 1 ′′′=

−−

= − oABA

4.078102475694.495170 ′′′=′′′−′′′= oooα

[ ]( ) ( )[ ] ftAP

yxAP APAP

45.27473.41641.50940.86582.1123 21

22

21

22

=−+−=

∆+∆=

ftPC 866.0)4.07810sin(45.274 =′′′= o

A

Figure 6.2: Offset distance

C

X

Y

A

B (xB,yB)

P (xB,yB)

α

T.N

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6.3 Intersection ( 11.4 ك) Intersection is for determining the location of an unknown point P by using direction (Azimuth) from two or more fixed (known) stations Ex., Given directions AP (AAP) and BP observed from fixed station A and B respectively. Determine the position (xP, yP) of point P. Steps:

1. Compute AB and AAB 2. Compute angle P A B and P B A 3. Use law of sines to compute AP and BP 4. use length AP and AAP to compute P(x, y)

from A 5. use length BP and ABP to compute P(x, y) from B

Example: Given the following coordinates for points A and B, compute the intersection point P (xA, yA) = (1425.07, 1971.28) and azimuth from A to P AAP = 76º 04' 24" (xB, yB) = (7484.80, 5209.64) and azimuth from A to P ABP = 141º 30' 16"

[ ] ( ) ( )[ ] 757.687028.197164.520907.142580.7484 21

2221

22 =−+−=∆+∆= ABAB yxAB

8.46256136.323873.6059tantan 11 ′′′=

=

∆∆

= −− o

AB

ABAB y

xA

2.3711148.462561424076ˆ ′′′=′′′−′′′= oooBAP 8.46252418.462561180 ′′′=′′′+= ooo

BAA 8.302210061031418.4625241ˆ ′′′=′′′−′′′= oooABP

( ) 2552658.30221002.371114180ˆ ′′′=′′′+′′′−= ooooBPA

ftAP 224.7431255265sin

8.3022100sin757.6870 =

′′′′′′

=o

o

83.3759424076cos743128.1971cos

85.8637424076sin743107.1425sin

=′′′+=+=

=′′′+=+=o

o

APAP

APAP

AAPyy

AAPxx

T.N

A

Figure 6.3: Intersection (Forward Problem)

B

P

X

Y

AAP

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Check

=

′′′′′′

=255265sin2.371114sin757.6870

o

o

BP =+=

=+=

BPBP

BPBP

ABPyy

ABPxx

cos

sin

6.4 Resection ( 11.7 ك) Resection establishes the position (x, y) of the unknown occupied point P by measuring horizontal angles to three or more fixed and visible stations Example: Given (xA, yA), (xB, yB) and (xC, yC), and the measured angles α1 and α2 at station P, find the intersection point P (xP, yP) The main problem is to solve first for the orientation (azimuth) correction. Then apply the orientation correction to the angles to obtain the directions w.r.t. true north Steps:

1.

( ) )ˆ(360ˆˆ360ˆˆˆ

180)2('

21

21

αα

αα

++−=+

=++++

−=∠∑

BCA

CBA

ns

o

o

o

2.

+++

= −

)ˆˆcos(sinsin)ˆˆsin(sintanˆ

12

11

CABCABCABCA

ααα (eq. 11.27 W/G)

++

+= −

)ˆˆcos(sinsin)ˆˆsin(sin

tanˆ21

21

CAABBCCAAB

Cαα

α (eq. 11.28 W/G)

3. In triangle 1:

AAA

ABPAAAABP

ABAP

BABP

ˆ

)ˆ(180 1

+=

∠−=+−=∠ αo

Use law of sine to compute AP and BP Compute latitude and departures of P from A Compute latitude and departures of P from B (√ check)

4. repeat step 3 for triangle 2

T.N

A

Figure 6.4: Resection (Inverse Problem)

C

P X

Y

θ

B

α1α2

1 2

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6.5 Two-Dimensional Coordinate Transformation ( 11.8 ك) Coordinate transformations are used to convert point positions from one survey coordinate system to another. A conformal transformation preserves angles. Minimal requirements for transformation is two points (a.k.a. control points) in both coordinate systems Steps

1. Rotate the coordinate axis by amount θ 2. determine the scale factor between the

two systems 3. determine the amount of shift

(translation) between the two systems’ origins

βαθ −= where the azimuth ABA′=α is in the

x'y' system and ABA=β is the azimuth in the XY system.

Scale factor [ ][ ] AB

AB

ABAB

ABAB

sS

yx

YXs′

=′∆+′∆

∆+∆=

21

22

21

22

Translation (shift) is given as AAy

AAx

yYTxXT′−=

′−=

Rotation θ is given by θθθθ

cossinsincos

AAA

AAA

ysxsYysxsX′′−′′=

′′−′′= =

′′

−′

A

A

R

yx

s44 344 21θθθθ

cossinsincos

Hence we write the following;

yA

xA

TYNTXE

+=+=

;

+

′′

′=

y

x

A

A

TT

yx

RsNE

6.7 Computing Area by Coordinates ( 12.5 ك) For cosed polygons, such as obtained by traversing around a property or digitizing parcels from a map. Procedures involves projecting nodes perpendicular to the Y-axis to form a series of trapezoids and triangles (See Figure 12.4 in W/G)

A

Figure 6.5: Coordinate Transformation

B

X

Y

θ

x'A

x'B

y'A

y'B

XA XB

YB

YA

x'

y'

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Useful formula to compute the area of a closed polygon given the coordinate pairs (x, y) of all the corner points of the polygon: 2 Area = XAYB + XBYC + XCYD + XDYA

-(XBYA + XCYB + XDYC + XAYD) Visual arrangement

Area of the shaded trapezoid:

( )

( )DDEDDEEE

DEDE

yxyxyxyx

yyxx

cba

−+−=

−×+

=

×

+

=

21

2

2

Total area = 0.5[ xAyB + xByC + xCyD + xDyA

-(xByA + xCyB + xDyC + xAyD)]

XA YA XB YB

XC YC

XD YD XA YA

A

Figure 6.6: Area Computation using coordinates

D

E

X

Y

C

B

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Example (12.3 W/G) Given (x, y) coordinate pairs of a closed polygon as shown in Figure 7.6, compute the area of the polygon.

Shift all coordinates by Tx=10,000.00 and Ty=4408.22 so that coordinate axes are defined by x'y'

(-ve) x*y Station x y (+ve) x*y A 0.0 591.78 306,211 B 517.44 202.94 → 0.0 106,221 ← C 523.41 0.0 0.0 0 D 716.29 694.02 363,257 87,252 E 125.75 847.71 607,206 0 A 0 591.78 74,398 Σ=499,684 Σ=1,044,861 Area = 0.5(1,044,861-499,684) = 272,588 ft2

and AreaCAREA ∗= 2σσ , where Cσ is the uncertainty in the coordinates

Station X Y

A 10,000.00 5,000.00

B 10,517.44 4611.16

C 10,523.41 4408.22

D 10,716.29 5102.24

E 10,125.75 5255.93 Figure 6.7: Area Computation using coordinates

X

Y

TX

TY

y'

x'

D

B

A

C

E

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7.0 Topographic Surveys To determine natural and cultural features on the Earth’s surface and to define the relief on that surface

• Natural features: Vegetation, rivers, lakes etc., (shown by map symbols, lines) • Artificial features: Roads, railroads, buildings etc., (shown by symbols) • Relief: Hills, valleys etc., (shown by contours, digital elevation model, etc.)

7.01 Map scale (16.3 ك) Is the ratio of length of mapped object (features) to its true length on the ground. 3 ways that map scale can be shown;

1. Ratio (1:2000) Note: same units apply 2. Equivalence i.e., 1in – 200 ft 3. Bar Scale (graphic on the map) Choice of scale depends on the following

• Purpose of the finished map • Size of the finished map • Precision of the map

7.02 Classification of Map scale

• Large scale (required high accuracy) e.g., subdivision • Medium scale (moderate accuracy) for preliminary planning • Small scale (lower accuracy suffice) for large areas

Map scale dictates the accuracy with which features must be surveyed. Ex: For 1in = 20ft (1/20) and scaling distance x within 1/50 th inch gives a scaling error of ± 0.4 ft

ft4.050120 =×

7.03 Survey Control for Topographical Surveys ( 16.4 ك)

Horizontal control (by traversing, triangulation, GPS) is provided by two or more (semi) permanent monuments and precisely fixed/referenced to the state plane coordinates (SPC) Vertical control (fixed by differential or trigonometric leveling) is provided by benchmarks that are required to reference a survey to a vertical datum. Note: Any errors in the control points will propagate to the details on the map. Therefore, first adjust the control points/network position before locating map details on the map.

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7.04 Depicting Relief ( 16.8-16.5 ك) Contours are defined as a line connecting points of equal elevation. Some characteristics of contours:

• Must close • Perpendicular to slope • Distance between contours indicate steepness of slope • Irregular contours signify rough/rugged terrain

Spot elevation (represented by a cross mark) indicates elevation of critical points such as peaks, highway crossing etc. 7.05 Digital Elevation Model (DEM) 3-D arrays of x, y, z-triplet provides digital representation of continuous variation of relief in the form of a grid.

Advantage: facilitates computer generated contouring Disadvantage: critical high/low points may not coincide with grid points.

7.0.6 Triangular Irregular Network (TIN) TIN is constructed by connecting points in an array to create a network of adjoining triangles. Required critical information such as breaklines or faultlines

Advantage: improved representation of relief compared to DEM Disadvantage: algorithm-driven contouring based on incorrect assumptions result in erroneous relief representation

7.2 Maps and Map Design ( 17 ك) Maps are visual expressions/representation of a portion of the Earth’s surface. It can also be considered a communication tool for conveying spatial relationships of mapped features Three basic elements of a map include;

• Points • Lines • Blank spaces

Digital maps can be stored, analyzed, modified, enlarges (reduced), in scale and contour intervals changed in digital form. Digital maps are essential in development and operation of Land Information Systems (LIS), Geographic Information Systems (GIS) for storage, retrieval, manipulation, merging, analysis, and display of geospatial data.

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7.2.1. Accuracy Standards of Mapping (17.4 ك) A) National Mapping Accuracy Standards (NAMS) specification for hard-copy maps

Horizontal (positional) accuracy: • For map of 1:20,000 and larger; no greater than 10% of well-defined points will have

errors greater than 1/30 inch (0.8mm) • On maps with smaller scales than 1:20,000 error not greater 1/50 in (0.5mm) e.g., for

scale 1in=200ft then the error limit is: 200*1/30=6.67ft

Vertical accuracy: defined in terms of contour interval (CI) • Class I: RMS error of well-defined points not greater than 1/3 CI • ClassII: RMS error of well-defined points greater than 2/3 CI

B) National Mapping Accuracy Standards (NAMS) specification for digital maps specifies 95% confidence for;

• Coordinates of points • Distances • Elevations Implementation of these standards on digital map products carry confirmation statements regarding accuracy validation.

7.2.2 Map Design Effective map design follows to explicitly important criteria/questions:

• Purpose • Audience

Effectiveness of map design (and, hence communication) requires: 1) Clarity: - communicate completely and unambiguously 2) Order: - hierarchy to direct the reader’s eye 3) Balance: - map elements weighted around the visual center of the map 4) Contrast: - line type & lettering should enhance clarity 5) Unity: - avoid conflicts such as background color (eg., bad power-point slides) 6) Harmony: - avoid too many different font & few overbearing symbols 7.2.3 Map Layout

1) centering 2) alignment (w.r.t. cardinal directions)

7.3 Photogrammetry

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Photogrammetry is the art and science if obtaining reliable geospatial information from photographs. Two components:

• Metrical – determine spatial relationship (i.e., distance, triangle, height differences) from measurements made on the photographs

• Interpretive – recognize and judge the significance of photographic images

7.3.1 Principles of Photogrammetry (27.8-27.6 ك) Photogrammetry involves the application of perspective geometry which, in turn, involves the characteristics of the optics such as focal length. The camera focal length (f) is pre-defined for the specific application of the photographic system. Two coordinate systems: Ground system: The X-Y axes define the coordinate system either local of regional fixed. Point O, in the datum plane, is the origin of the coordinate system, Point A is located at (XA, YA) Photographic Systems: The x-y axes defined by the fiducial marks, define the photographic system. The origin o' corresponds to the point O in the datum plane. Point a in the photograph is located at xa, ya. 7.3.2 Ground Coordinates from a single photograph Using similar triangle Lo'a' and LOAA' we get;

aA

AAA

aa

AA

AA

a yf

hHYhH

fYy

AAaax

fhHX

hHf

Xx

OAao

⋅

−=⇒

−==

′′

=⋅

−=⇒

−==

′′

7.3.3 Scale of a vertical photograph Definition: Scale is interpreted as the ratio of a distance on a map to the distance on the ground of the same object (i.e., in photograph and ground system). As before, envision similar triangles where Lab and LAB are co-planar (also see Figure 27.6 in W/G), then we write;

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AA

A hHfs

hHf

LALa

ABabs

−==

−===

Subscripts in the above equation express the scale at the point A. Hence, photo-scale increases at the higher elevation and decreases at the lower elevation. In general, the scale s at any point whose elevation h is above the datum is expressed as

avgavg hH

fs−

=

Ex 1: Using a camera with focal length of 6 in at flying height H=10,000 ft above mean sea level (i.e., the datum) compute; a) photo-scale at A where hA = 2500 ft b) photo-scale for average terrain elevation of 4,000ft.

a) 000,15:11250

1500,2000,10

6==

−=

−=

ftin

hHfs

AA

b) ?:1000,4000,10

6==

−=

−=

AA hH

fs

Ex 2: A length of runway of 5280 ft is measured on a photograph as 4.15 inches. What is the approximate flying height, assuming the camera focal length is 6 inches

=⇒

===

avg

avg

H

Hf

ABabs

528015.4

Stereoscopic parallax is defined as the displacement of the position of an object w.r.t. the reference frame due to a shift in the point of observation. Parallax (apparent motion) is a function of its relief. Hence, by measuring parallax we obtain information on relative elevations. For stereo mapping, each imaged footprint will have been covered by two photographs with a 60% overlap (endlap). In this way a long strip of the earth surface can be mapped stereoscopically (where each photographic image contains 60% information in the adjacent photograph). The distance between camera exposure stations is called the air base. Another strip of photography, parallel to the previous strip, can be obtained in the same manner. For stereoscopic imagery of the landscape, however, a minimum of 25% overlap (sidelap) is required. Stereoscopic Viewing Stereoscopic viewing refers to seeing an object in three dimensions where the observer’s eyes are separated by a distance called the eye base

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The left eye and right eye focuses on the same object taken from two (different) exposure stations and the brain fusses these two images (left and right) into a 3-D model. Objects and features are located (x, y, z) in this 3-D virtual model. The (x, y, z) locations of these features are referenced to the photographic system. Invoking a coordinate (conformal) transformation obtains point locations of the virtual 3-D image in the ground systems.

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8.0 Horizontal Curves An arc, in a horizontal plane, that connects two straight tangent sections is called a horizontal curve. Two types of curves are used in general engineering projects; circular arcs and spirals. A simple curve is a circular arc connected by two tangents. A compound curve is composed of two or more circular arcs of different radii tangent to each other with their centers on the same side as the alignment. A reverse curve consists of two circular arcs tangent to each other with their centers on opposite sides of the alignment. A spiral is circular arc of uniformly decreasing radius from infinity at the tangent to that of the curve it meets. Several applications of curves for engineering projects

• railroad tracks • roller coasters • roads • bridges • large-scale physics experiments

8.1 Definitions and Formulae (24.4 – 24.3 ك) The degree of a curve (D) is defined by the angle subtended by a circular arc of 100 ft.

)(58.5729

2100

360 ftRD

RD

=⇒=πo

Example: With a radius of 700m, what is the degree of the curvature?

1292248910.228083.370058.5729 ′′′==

×= ooD

[Question: What is the unit of the numerator?]

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PI = point of intersection PC = point of curvature PT = Point of tangency R = Radius of curvature

T = Tangent distance (

=

2tan IRT )

L = Length of curve ( IRL ×= , I in radians)

LC = Chord Length (

=

2sin2 IRLC )

Radian = 180º/π = 57º.29577951

Figure 8.1: Horizontal Curve

LC

I

L

T

O

PT

I

R

PC

Back Tangent

Forward Tangent

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Example: Given I = 8º.24' and degree of curvature D=2º. What is stationing of PT when PC stationing is zero? Solution:

ftIRLC

ftradsIRL

ftR

62.4192

sin2

42029578.57

42879.2864)(

79.28642

58.5729

=

=

=′

×=×=

==

o

o

PT station = PC station + L = 0 +420 = 4 + 20.00 ft

Curve Layout (24.5 ك) Steps

1. Establish PC and PT by measuring T from PI along tangent 2. Measure total deflection angle at PC from PI to PC

Methods for setting out horizontal curves

a) Deflection Angle: a. Minimal computation b. Obstruction from vegetation – requires re-computing c. No check at end of curve (disadvantage)

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kSaa =δ where LIk

2=

kSii =δ where ni ,...,1=

In general

ii RC δsin2=

2) Coordinates d. Requires reference coordinate systems e. Azimuth of back-sight must be known f. Compute latitude and departures

Figure 8.2: Setting out Horizontal Curve

C1

L

O

PI

R

PC 0+00

Tangent

δ1

δ2

C2

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Example: Given R=400m, I= 24.32 and back azimuth-326,40.20, Compute the data to stake out the 1st and 2nd point on the curve (POC’s) at 20m increments. Assume the PC stationing is 458.53m

L = 400 x24º32'

o180π =171.275m

T = 97.862

2324tan400 =

′o

m

Dep Lat Coordinates Pt Station Dist

(Si) Def Ang

(δi) Chord

Ci Azi =

Azi-1+ δi ∆X ∆Y X Y

0 458.53 5770.97 3656.28 1 460.00 1.470 0º06'19" 1.47 326º34'01" -0.810 1.227 5770.16 3657.51 2 480.00 21.47 1º32'16" 21.468 325º 08' 04" -12.272 17.616 5758.695 3673.894

kSii =δ , where ( 071617.0275.17122324

2=

×′

==o

LIk )

=×=×= 071617.047.1071617.011 Sδ 0º06'19″ Az1 = 326º40'20″ - 0º06'19″ = 326º34'01″ C1 = 1.470 ∆X1 = 1.47 sin (326º34'01″ ) = -0.810 ∆Y1 = 1.47 cos (326º34'01″ ) = 1.227 δ2 = 21.470 x 0.071617 = 1º32'16" Az2 = 326º40'20″ - 1º32'16" = 325º08'04" ∆X2 = 21.468 sin (325º08'04" ) = -12.272 ∆Y2 = 21.468 cos (325º08'04" ) = 17.616 Coordinates of POC X1 = X0 + ∆X1; X2 = X0 + ∆X2 Y1 = Y0 + ∆Y1; Y2 = Y0 + ∆Y2 (More details are describe in W/G section 24.13 and table 24.4)

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9.0 Vertical Curves The main basic function of a vertical curve is to provide a gradual change in grade from an initial incline (back tangent) to the grade of the second decline (forward tangent). Parabolas are ideal in applications of vertical curves used by vehicular traffic because parabolas provide a constant rate of change of grade. Vertical curves are generally represented by a parabolic curve of the form

2cxbxaz ++=

9.1 Two types of vertical curves

a) Crest curve → the curve turns downwards (i.e., -ve change of grade) b) Sag curve → the curve turn upwards (i.e., +ve change of grade)

Constraints on vertical curve design include the following:

a) Good fit with the existing ground profile b) Balance and minimizing depths of cut/fill c) Not exceed maximum specified grade d) Maintain adequate drainage e) Fit the grade lines they connect f) Provide sufficient sight distance for safe vehicle operation

Ground profile

B

H∆

Back tangent

Crest Curve

Back tangent

Forward tangent

Sag Curve

Figure 9.1: ground profile and grade lines for proposed road.

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9.2. Equation of equal tangent (25.3 ك)

VPI = Vertical point of intersection (i.e., vertex is the intersection of the two tangents) VPC = Vertical point of curvature (i.e., beginning of vertical curve BVC) VPT = Vertical point of tangency (i.e., end of vertical curve EVC) L = Length of the curve

g1 is the grade line that precedes to meet the curve (i.e., back tangent) g2 is the grade of the line that the curve will meet (forward tangent)

Figure 9.2: Vertical parabolic (Crest) curve relationships

g1XP

g2

O

VPT

VPI

X

VPC

Back Tangent

Forward Tangent

g1

L

XP

P

ZVPC

0.5(rX2P)

Z

c×L2

Datum = MSL

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From the Figure 9.2 we get

2

1 PpVPCp cXXgZZ ++= , where g1 is the slope of the back tangent (i.e., g1 is in percent grade which means that X is in 100-ft station intervals or

units of 100m 100X

2212 r

Lggc =

−= , where g2 is the slope of the forward target

Substituting, we write the general equation for vertical curves

2

1 2XrXgZZ VPCp

++=

Example: Given the tangents of a vertical curve have grades of g1 = -3.629% and g2 = 0.151%. The Stationing and elevation at its vertex is 5+265 and 350.52m, respectively. The equal-tangent parabolic curve (L) of 240-m length will join the tangents. a) What type of curve is this? b) What is the elevation of the lowest point on the curve? c) what is elevation of points 95, 200 and 450 m from the PVC? Answer: a) draw the curve and decide! b) compute the elevation at the beginning of the curve

( )

875.354

120100

1629.352.350

2

0.240

1

=

×

×+=

+=

=

VPC

VPC

VPIVPC

Z

Z

LgZZ

L

Now, compute the elevation of the point of tangents (end of curve)

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( ) 701.350174.4875.3544.22575.1

100240)629.3(875.354

22

21

=−=

+

−+=

++=

VPT

VPCVPT

Z

LrLgZZ

The lowest point of the equal-tangent vertical curve is at half the distance L (X=120m)

( ) 654.351221.3875.3542.12575.1

100120)629.3(875.354

22

21

=−=

+

−+=

++=

LOW

VPTLOW

Z

XrXgZZ

c) Table: Notes for curve lay-out

Station Distance from PVC

X/100 Xg1 2

2rX Curve

Elevation PVC+00 0.0 0.0 0.0 0.0 354.875 PVC+95 95.0 0.95 -3.448 0.711 352.138 PVC+200 200.00 2.0 -7.258 3.15 350.767 PVC+450 450.00 4.50

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10 Earthworks Earthworks involve determining volumes of various types of materials such as concrete, dirt etc., for planning and construction projects.

Units: Volumes: m3 (35.315ft2) o Liquids Acre-foot o Water flow ft3/sec

10.1 Methods to estimate Volumes

a) Cross-section involves profiles at pre-determined station intervals centerline of linear construction

b) Unit Area involves construct of DEM. The volumes of each cell is given

by AreahVi

ic ×

= ∑

=

4

141 , and the Total Volume = ∑

=

=n

iiVV

1

, where n = # of grid cells

c) Contour-Area involves the use of a planimeter that measures area enclosed by each contour

a. The volume is obtained by multiplying the area by the contour interval (CI) b. This method is suitable for large areas such as cut/fill estimates at proposed

airport runways, capacity of reservoirs created by a proposed dam 10.2 Examples of estimating Volumes

In general, we write the formula for volume for a road works

Figure 10.1: Terrain

C

15.0

B

L

H

A2

A1

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LAAmV ×+

=2

)( 213 , where

A1 and A2 are the end-areas (from profile) and L is the horizontal distance between the end profiles.

Using generalized cross-section of Area1 we will apply two methods to estimate volumes: 10.2.1 Volume Computation by Simple Figures First we generalize the cross-sections into trapezoids (or regular geometric shapes) as shown below.

Figure 10.2: Cross-Section of typical end profile (A1)

A

O

24.0

C

10.0

19.0

C

15.0 15.0

15.0

B

B’

LR

D

GH12

.0

X

Y L

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Figure Computation Area

BCGB’ [(18+19)·35]/2 647.5 (+)

CRG [(19×10)/2] 95 (+)

LBB’ [4×18]/2 36 (+)

LB’H [5×12]/2 30 (-)

Σ=748.5 ft2

10.2.2 Volumes Computation by Coordinates: Set up a local coordinate system with origin at L

(-ve) x·y Station x y (+ve) x·y

L 0.0 (+ve) 0 0 B 4 6 → 0 (-ve)

234 ← C 39 7 28

343 R 49 -2 -78

-78 G 39 -12 -588

-108 H 9 -12 -468 0 L 0 0

Σ=391 Σ=-1,106

Area = 22 5.748

23911106)( ftmA =

−−=

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11.0 Construction Surveys Construction surveys involve establishing; from the survey control point the azimuth, horizontal distance, and elevation differences of points of a stake-out project. These survey data are called setting-out data from control network points 11.1 Equipment for Construction Surveys

• Total Station Instrument – for construction, roads and engineering projects • Visible laser beam – grade staking at airports etc., • GPs to establish geodetic survey control for maps and planning purposes • Better boards – for building layouts

11.2 Survey Control for Construction Projects (¶) Horizontal and vertical control provides a basis for positioning structure, utilities and engineering projects. As-built projects: Inventory of infrastructure, utilities, buildings, and engineering projects performed from control network of survey points. For example, a laser scanner can produce a 3-D CADD rendering of as-built construction projects such as historical building, bridges, and railroads etc., Control points provide the survey framework for the 3-D CADD and subsequent data analysis. Optimal and convenient placement of control points is essential to ensure permanence and/or accuracy of survey results. Stake-out projects include

• Pipeline o establish reference off-set line ℓ to centerline o Precise alignment and grades of pipeline placement done by batterborads or

laser beam

• Building o Nails on batterboards guide the line that defines the outside wall of a building.

Check diagonals for symmetry and square o Radial method using TSI to set Azimuth, and distance to place building corner,

Azimuth and distances computed from control points to building corners using coordinate geometry.

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• Highways o Establish sufficient control points to provide checks on accumulated survey

errors o Start staking, at full stations, from 1st tangent run to 1st Point of intersection o Turn deflection angles and continue staking along new azimuth o Insert horizontal curve point (PC, POT, PT) o Set Benchmark no greater than 1000ft apart o Set appropriate grade stakes per projects specification

• Other construction i) Causeways, bridges, offshore platforms require hydrographic surveys using some mapping devised to establish/plot dredging cross-section for underwater engineering projects

ii) Earthworks (dams, levees) projects require fixed and permanent stations for Horizontal and vertical control in addition to subsequent deformation monitoring

iii) Underground (tunnels, mines) surveys require transfer of Azimuth and elevation from above ground, down a shaft

11.3 Stake-out Surveys using Total Station Instrument

To establish Azimuth using coordinates or by resection Establish elevation by trigonometric leveling

HRHISHH AP −++= αsin Where is the vertical angle, HI is the height of the instrument above the control station, and HR is the height of the reflector above the control point S is the slope distance. HA id the elevation of the control A above the datum (msl)

11.4 Stake-out Surveys using GPS

To establish project control and locate construction stakes Produce maps for planning and design

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12.0 Introduction to Global Positioning Systems (GPS) The Global Positioning System (GPS) can show you your exact position on Earth any time, anywhere, in any weather. The system consists of a constellation of 24 satellites (with about 6 "spares") that orbit 200,000 km above Earth’s surface and continuously send signals to ground stations that monitor and control GPS operations. GPS satellite signals can also be detected by GPS receivers, which calculate their locations anywhere on Earth within less than a meter by determining distances from at least three GPS satellites. No other navigation system has ever been so global or so accurate. First launched in 1978, the development of a global navigation system dates back to the 1960s when The Aerospace Corporation was a principal participant in the conception and development of GPS, a technology that has significantly enhanced the capabilities of our nation’s military and continues to find new uses and applications in daily life. We’ve helped build GPS into one of history’s most exciting and revolutionary technologies and continue to participate in its ongoing operation and enhancement Positioning with GPS involves computation of point locations in a coordinate system. Locations can be given in X, Y, Z Cartesian coordinates or in geographical coordinates such as latitude, longitude, and height. Position defined by GPS observations is determined by precise range (distances) from the GPS satellites flying at 20,000 km above the earth, to a receiver located on the earth. Specifically, the positioning using timing and signal information 12.1 The GPS Signal The GPS signal has a reference (fundamental) frequency of =10.23 MHz. The signal is broadcast on tow frequency bands;

• L1=1575.42MHz L1=154× of • L2 = 1227.60 MHz L2=120× of

The broadcast message consists of;

1. Almanac 2. Ephemeris 3. Clock error 4. Ionospheric corrections 5. Satellite condition (health) 6. Review the basic trigonometric formulae

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12.2 GPS System Configuration (13.2 ك) 12.2.1 Space Segment

1. 24 satellites in 6 orbital planes. 2. Orbital planes are spaced 60º degrees apart. 3. Orbital inclination of 55º degrees with respect to the equator. 4. GPS provides 24hr satellite coverage ±80º latitude. 5. Orbits at 20,000 km above the Earth every 12 hrs. 6. Precise atomic clocks

onboard satellite and quartz clocks in receivers

12.2.2 Control Segment

• 5 Stations track the satellites and upload broadcast ephemeris

• Broadcast ephemeris include X,Y Z, t) of satellite and clock biase

12.2.3 User Segment

• Standard Precision Service (SPS) on L1 broadcast frequency.

• L1 has horizontal positional accuracy of approx.100m

• Precise Positioning Service (PPS) broadcast on tow frequencies; L1 and L2 with horizontal accuracy of approx 18m and vertical accuracy of approx 28m.

12.3 Satellite Reference Coordinate System The orbit of the GPS satellite follows Kepler’s law of motion. The “elliptical” orbit has a closest approach (perigee) and apogee (point of furthest distance) The origin of the coordinate system is at the center of Mass of the Earth. A Geocentric Coordinate System relates points in space physically to the Earth. Figure shows the orbital configuration with respect to the Earth.

The satellite position is described by six Keplerian elements (semi-major axis (a), orbital inclination (i), right ascension of ascending node (Ω), argument of perigee (ω), true anomaly (f), orbital period (P). The relationship (and conversion) between the satellite coordinate system and the geocentric coordinate system is described by four angular parameters (orbital inclination (i), right ascension of ascending node (Ω), argument of perigee (ω), and the Greenwich hour angle of the vernal equinox (γ)

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The Geodetic Coordinate System In general, the association between a 3-D Cartesian system and the Geographic coordinate is specified through a uniquely defined mathematical model of the earth called the ellipsoid of revolution with

• semi-major axis a (or radius) of the Earth

• The mass (GM) as the Earth

• The same rate of rotations on its spin axis

• The gravity dynamic form factor (J2)

The origin of the Cartesian system is at the center of mass (COM) of the Earth

i

Sat(X,Y,Z,t)

Z (CIO)

X (THRO’ GREENWICH)

Y

Equator plane

Meridian

Orbit

Figure 13.1 Geocentric Coordinates system and GPS satellite orbit

COM E ω

f

perigee

Ω

Ascending Node

γ

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A point located by GPS on the surface of the Earth is defined by geographical coordinates in a Cartesian systems as follows;

λϕ coscos)( PR hNX += λϕ sincos)( PR hNY += ϕsin])1([ 2

PR heNZ +−= with the geometric quantities N as the radius of the Earth

ϕ22 sin1 eaN R

−= ;

22 1

−=

abe ;

( )fab −= 1 and the GPS height of the point A is given by h≈H+N . The orthometric height (H) is generally obtained from leveling. Leveling process transfers elevation difference relative to mean sea level. The geoid undulation (N) is the departure of the mean sea level from the ellipsoid. The geoid is determined from very precise gravity measurements. Mean sea level approximates the geoid on a global average. The values H and N are distances relative the ellipsoid. The ellipsoid is an international standard – every GPS user (in the world) is tied to the GRS80 ellipsoid. The ellipsoid is a well defined mathematical surface so that every point on its envelop is uniquely defined. H is the orthometric height derived from leveling – i.e., height above the mean sea level. N is the deviation of the geoid (or global mean sea or level equipotential surface) from the ellipsoid. The geoid can be thought of as undulating topography. So in some places the geoid will be above the ellipsoid (N is positive) and other areas the geoid will be below the ellipsoid (N is negative). However, the above equation still holds. 12.4 Positioning with GPS The fundamental equation is the geometric range ρ from the satellite to the receiver is given by;

tcSR ×=ρ where c (=299,792,458 m.s-1) is the speed of light and t is the time traveled

from the satellite to the reciever. By observing three satellites simultaneously from one receiver at located at A we write;

λ

h P(φ, λ, h)

Z

X

Y

φ

Equatorial plane

Meridian

Ellipsoid

Figure 13.2 Point location by GPS

Topography

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( ) ( ) ( )2121211AAAA ZYX ∆+∆+∆=ρ

where AA XXX −=∆ 11 ; AA YYY −=∆ 11 and AA ZZZ −=∆ 11

( ) ( ) ( )2222222AAAA ZYX ∆+∆+∆=ρ

( ) ( ) ( )2323233AAAA ZYX ∆+∆+∆=ρ

Errors in GOS observations include the following;

• Satellite and receiver clock biase • Ionospheric and tropospheric refraction (delays) effects • Multipath • Poor Satellite Geometry • Receiver antenna not properly centered over the control point

12.4.1Geometry of the Observed Satellites (13.6.4) Weak geometry of the simultaneously observed satellites results in larger errors in their computed GPS receiver positions. The effects of satellite geometry on the accuracy of the GPS solution are called dilution of precision (DOP) Several DOP factors are named for convention:

• PDOP – DOP in position • HDOP – DOP in horizontal position • HDOP- DOP is heights • GDOP – DOP is satellite geometry.

The lower the DOP value the better the expected positional precision. Sky Plots Sky plots as also called satellite visibility diagrams. Satellites are not normally tracked below an elevation of 15° to 20° due to large atmospheric refraction errors at low elevation angles. Generate a skyplot before deciding to accept GPS data for processing – The skyplot provides the following information

1. satellite geometry – suggest estimates on DOP values 2. illustration of GPS satellite trajectories over a given ground site 3. reveal impact of possible obstructions on satellite visibility.

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Example of a sky plot generated for September 2, 1995 for station GRAZ, Germany.

Reference:

Marshall, J., (2002) GPS Solutions, 6:118-120, doi 10.1007/s10291-002-0017-3 Numerical Example: Compute the geocentric coordinate of station A which has latitude of 39º 27'07".58, longitude 86º 16 '23 ".49 and elevation above the ellipsoid of 203.245 m (Reference ellipsoid parameters: e2=0.0066 943799; a=6,378,137 m)

15o masking angle

Local Horizon

Trajectory of satellite # 18

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Answer

ϕ22 sin1 eaN R

−= =

λϕ coscos)( PR hNX += = 49.326186cos58.707239cos)( ′′′′′′+ ooPR hN =

λϕ sincos)( PR hNY += = 49.326186sin58.707239cos)( ′′′′′′+ ooPR hN =

ϕsin])1([ 2PR heNZ +−= = 58.707239sin])1([ 2 ′′′+− o

PR heN = 12.5 Surveying and Mapping with GPS Relative positioning using dual frequency (L1, L2) receivers are preferred over single frequency (L1) receivers for the following reasons;

• Faster data collection • Observing longer baselines • Eliminating ionospheric delays effects on GPS signals

A minimum of four (4) satellites should be tracked simultaneously to determine a receiver position optimally. 12.5.1 Types of GPS Surveys for relative positioning (14.2)

• Static: Rover-rover receiver configuration; occupy station> 1 hr Survey complete when baseline form a geometrically closed figure Applicable for Geodetic Control Survey

• Rapid Static

Master-rover receiver configuration for baselines length (BL) up to 25 km. Mater receiver never moves from its location until survey completed

Applicable for small control surveys • Kinematic

Receiver initialize to determine integer ambiguity Initialization methods include

• Observe a short known baseline • Antenna swap

One rover receiver collects survey points for later processing Applicable for construction and topographic surveys

• Real-time Kinematic (RTK)

Similar to Kinematic positioning but points positions are determined simultaneously

Baselines are limited to 10 km with most radio links Application for construction stakeout and real-time mapping

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12.5.2 Observing Scheme (14.3.4) The planned sequence of observing sessions must ensure that every station in the network except for Kinematic Surveys) is connected to at least one other station by a baseline plus redundancy for checking purposes plus improving precision and reliability of work. [CORS site data used to strengthen baseline links to CORS station] 12.6. Conversion of Geocentric coordinates to Geodetic Coordinates

• Longitude of point P

= −

P

PP X

Y1tanλ

• Latitude of point P

−

=′ −

)1(tan 2

1

eDZ

P

PPφ where,

[ ]21

22PPP YXD +=

• Geodetic height RP

PP N

Dh −

′

=φcos

for φ'P ≤ 45º

)1(sin

2eNZ

h RP

PP −−

′

=φ

for φ'P > 45º

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Example: Given (X=1,241,581.343, Y=-4,638,917.074, Z=4,183,965.568) coordinates of a GPS receiver location at point P. Find the geodetic height of the point P. [Use 2444.815141 ′′′=′ o

Pφ , 3148.440,387,6=RN m]

[ ]21

22PPP YXD += = 4,802,194.8993

RP

PP N

Dh −

′

=φcos

= 313.28 m

EP

X

Z

GS

H

N

YNR

G = Geoid E = Ellipsoid S = Surface H = Orthometric Height N = Geoid height NR = Radius

λφ

YP

XP

ZP

hGPS ≈ H + N

Figure13.3 Coordinate Geometry of GPS station position

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13.0 Introduction to Geographic Information Systems GIS is a “toolkit” for the input, storage, retrieval, manipulation, and output of geospatial data GIS output is based on simultaneous analysis of heterogeneous data, co-located (georeferenced) in a common geographic reference (coordinate) system. The output forms the basis for decision making for planning, design, management etc. Accuracy of spatial data is a significant component of the integerty of GIS solution. Specifically, after data input, the subsequent analyses and data display (map) form the basis for decisions regarding planning, management and development. Hence, the accuracy of the geospatial data in a GIS impacts the quality of GIS output results and decision making. Analysis of GIS data is generally performed on data sets that are referenced in a common geographic coordinate system such as state plane coordinates, UTM grid or a local system. Coordinate transformation is a significant component in GIS data management.

• Input x,y,z-triplets (or other geographic coordinates) are entered (terminal input, download, uplink, scanning, digitizing, etc).

• Storage Massive data volumes require huge archiving and storage. Digital

storage on hard drives, magnetic tape, scuzzy disks, and optical drives. New approaches to digital data storage include holograms.

• Retrieval Huge inventories and data catalogue have to be accessed for data

analysis. Sophisticated computer algorithms require to efficiently and quickly access specific data records.

• Manipulation Map-algebra includes Boolean operations. Sophisticated data

manipulations such as spectral analysis, correlations, regression, and statistical analysis require sophisticated software.

• Output Data display could be in forms of Tables, Charts, or Maps. Results of

geospatial data analysis in map form are a combination of art and science. All elements of map making are important considerations for effective computer generated map display.

GIS has important applications for planning, design, impact assessment, and predictive modeling. The successful implementation of a GIS relies on the effective collaboration of of inter-disciplinary team of professional. For example, data themes could include soil science, agriculture, conservations, forestry, hydrology. Specialists involved in developing a GIS other than surveying include computer scientists, geographers, and landscape architecture. Land Information Systems (LIS) is a subset of GIS is a focused primarily of land records data such as parcel information, lot improvements, parcel value, and ownership.

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13.2 Spatial data Geospatial data consist of natural and cultural features which must be represented and spatially located in digital form.

Natural features include • Visible feature such as topography, rivers, marshes, wetlands, shorelines,

and vegetation. • Invisible features such as minerals (deposit), gravity, • Dynamic features such as precipitation rates, atmospheric conditions.

These naturally occurring features can be depicted by various mapping conventions (symbols, linear, area, contours)

Cultural features include

• Utility terminals/connecters (light poles, fire-hydrants,) and utility routes (overhead electric wires (sags), sewer lines, buries cables)

• Transportation infrastructure such as roads, bridges (traffic movement and traffic patterns)

• Engineering projects such as buildings, reservoirs, and harbours. 13.2.1 Database Elements The fundamental elements of spatial data in digital databases are

1. Points [nodes] 2. Lines [string] 3. Polygon [Area] 4. Pixel [equal-size cell] 5. Grid cell

Pixel size defined data resolution and symbiotic trade-off with storage 13.2.2 Fundamental Formats

• Vector (nodes, strings, area) Each node has a point ID and (x,y,z) triplets plus an attribute link in tabular forms

• Raster (pixel, grid cell). Each pixel has row and column ID that is unique plus attributes

value The attribute describes the characteristic (color, texture, value) of the spatial feature.

• Topological Relationship are listed in tables and stored in GIS database

o Connectivity: Specifies node connection of chains o Direction: Defined “FROM” and “TO” directions of a line o Adjacency: Assigns polygon to “LEFT” and “RIGHT” side of a chain o Nestedness: Identify which spatial object (i.e., node, line, polygon) are inside another polygon

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Non-spatial data, or attribute data, is stored as alpha-numeric characters describing the value of the features. The common identifier links the spatial data and attribute data. 13.3 Data Format Conversion

• Vector –to-raster: i. Predominance (what is most?)

ii. Precedence (hierarchy) iii. Center-point

• Raster-to-Vector This type of conversion generally appears as a “staircase” outline. Subsequent rectification algorithms are costly and cannot retrieve the original detail. Raster-to-vector conversion is dangerous due to irretrievable loss of accuracy and information. Precision of data conversion depends on the size of the grid cell; coarse resolution raster result in low accuracy representation of the origin al data. Conversely, a high resolution raster provide high accuracy representation but demands huge storage requirements

13.4 Creating a GIS Database To create GIS database the following considerations are important

• Data types and formats • Reference coordinate System • Accuracy of each data type • Provision for database updating

13.4.1 Digital Data Inputs

1. Surveys: Download point data from Total Station and data collector (COGO routines transform survey data to coordinate list)

Download x,y,z-triplets from Photogrammetric solutions.

2. Digitizing: Initializing the digitizing tablet. Initialization requires coordinate transformation to obtain scale, rotation and translation parameters [See chapter 11 in W/G for details]. Proceed by digitizing each point. The

coordinate of each digitized point is converted (transformed) to the reference coordinate systems and stored in the digital database.

3. Scanning: Converts a graphical document (i.e., maps, plans) to digital form and output a raster file. Post processing in the form of editing is important to ensure the integrity of the digital database. Coordinate transformation is required to represent features in a geodetic (or other) coordinate system

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Meta data described the content, quality, condition, modification and other characteristics about geospatial data 13.5. GIS Analytical Functions Most GIS are equipped with basic data analysis capabilities. User-specified analyses functions are either add-ons or developed in-house. In-house developed software must be rigorously validated and tested using field data and varied scenarios.

• Proximity: To create new polygons (around points or lines) to perform radius search Polygons are generated by a process called buffering.

Buffering allows analysis of relative position by boundary operations; • Adjacency – identify adjoining polygons and attributes for

zonation inquiry. • Connectivity – identify intersection of linear features for

infrastructure maintenance and management.

• Overlay: Co-registered disparate data layers (e.g., point or line in polygon) • Logical Operations: Union, Difference, etc.

• Other Functions: Statistics

Geometry Volume 13.6 GIS application Land-use planning [Korea] - Analysis of landscape patterns (agricultural, urban, natural) he GIS used to asses demographic and land use characteristics on local transit services in relation to regional transportation system Resource mapping and Management – Coastal and watershed application for analysis on oil spills sensitivity. Determine flow characteristics of watershed and classify streams (i.e.., morphological and zonation criteria). Environmental impact assessment [Brazil] - To investigate water control. GIS used to improve organizational capabilities and formulate environmental policies. Route Selection [India] – To satisfy transportation and infrastructure requirement of a county in concert with its development pace. GIS requirements included network analysis, statistical analysis and spatial analysis. Infrastructure and Utility mapping/ Management - GIS used in planning (locate and identify) potential emergency (security) management of infrastructure; to mitigate hazards and assess risks; to develop preparedness protocol.

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13.7 Projected Future Role of Surveyors

• Design and develop GIS • Implement and manage the GIS • Establish quality control and assessment strategies f geospatial data • Establish protocol on quality assurance for GIS I/O operations • Other