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Engineering Graphics & Models

Part 1: Surveying Part 2: Engineering Graphics & Models

Lecture overview
Part 1: Surveying
Introduction to surveying Introduction to Height Measurement Angle & Distance measurement Detail survey

Lecture overview
Part 2: Engineering Graphics & Models
Introduction to Graphics Communication Sketching Engineering Geometry Modeling Fundamentals Multiviews and visualization Auxiliary Views Pictorial projections Section Views Dimensioning and Tolerancing Working Drawings and Assemblies

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Introduction to Surveying

What is surveying? What do surveyors do? Why is surveying important?

What is Surveying?
Acquisition, analysis and presentation of spatial data Positioning features on and below the surface of the Earth and representing these features on a map Position determined by measurement of angles, distances and heights

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What do surveyors do?

Acquire spatial data using a wide range of equipment and techniques Process and analyse measurements Visualise 2D and 3D data using AutoCAD, GIS, 3D Studio Max, Maya etc

Total Stations Taping Levelling GPS Laser Scanning

Coordinate Geometry Trigonometry Statistics GIS Excel StarNet Leica GeoOffice

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Surveyors in Civil Engineering...

Produce accurate, up-to-date plans for the project design process Map topography to assess the best locations for the construction of tunnels, bridges, roads etc. (i.e. Detailing ) Set out a site so that structures are built in the correct location and with the correct building dimensions Provide stations and benchmarks s to control and monitor the construction process Record final as-built positions Establish control networks for monitoring future movement of structures such as dams and bridges (deformation monitoring )

Other types of Surveying

Hydrographic Surveying Photogrammetry Remote Sensing

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Deformation Monitoring

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What skills does a good surveyor have?

good spatial awareness trigonometry and coordinate geometry statistical analysis computer-aided drawing project management using digital Geomatics resources using a wide range of specialist equipment data acquisition by a range of methods cartography Geographic Information Systems (GIS)

www.rics.org

1nd Year Surveying Curriculum

Lecture: Introduction to Surveying & Mapping Science Lecture: Introduction to Height Measurement Levelling Lecture: Introduction to Angle and Distance Measurement Lecture: Detail Survey

Practical: Levelling Practical: Total Stations Computer Class: AutoCAD Computer Class: ArcMap GIS

Map Scales
Ratio of map distance to ground distance
e.g. 1:10,000 scale implies that 1 unit on the map represents 10,000 units on the ground

The smaller the scale, the less detail will be shown

small scale > 1:50000 medium scale 1:500 to 1:50000 large scale < 1:500

The smallest distance discernable on a map is 0.2mm (i.e. the thinnest line width that can be seen by the human eye) For a 1:500m survey, what level of detail should be recorded?

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Accuracy and Precision

Inaccurate Precise

Accurate Imprecise

Accurate Precise

Types of Error

1. Gross 2. Systematic 3. Random

Plane Surveying
VS

Geodetic Surveying

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Rectangular Coordinate Systems

Y P
y
Location of P defined as (x, y)

Describe the location of London here -

SOURCE: Bostock and Chandler (1990, p. 75)

Fundamental Surveying Problem

E? N?
A B

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Trigonometry
sin = opposite/hypotenuse cos = adjacent/hypotenuse tan = opposite/adjacent
B

Opposite (b)
A

Adjacent (c)

Polar to Rectangular Conversions

If the coordinates of A (EA, NA) are known, the coordinates of B (EB, NB) are obtained from A as follows:

EB = EA + EAB = EA + DABsinAB NB = NA+ NAB = NA + DABcosAB

DAB= the horizontal distance from A to B AB= the whole circle bearing from A to B

Polar Coordinate Systems

N P
q r
Location of P defined as (r, q )

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Describe the location of London here -

SOURCE: Bostock and Chandler (1990, p. 75)

Polar to Rectangular Conversions

Horizontal Distance

EB = EA + EAB = EA + DABsinAB NB = NA+ NAB = NA + DABcosAB

Known coordinates Bearing

Bearings
The bearing () is the direction of a line between two points, measured as a clockwise angle from Grid North.
N

N q 2S 180 q 1S

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Polar to Rectangular Conversions: Example

The coordinates of A are 311.617m E, 447.245m N. Calculate the coordinates of B, where: DAB = 57.916m and AB = 371120.

SOURCE: UREN & PRICE (2006, p. 189)

Rectangular to Polar Conversions: Example

The coordinates of two points A and B are known as EA = 469.721m, NA = 338.466m and EB= 501.035m, NB = 310.617m. Calculate the horizontal distance DAB and whole-circle bearing AB of line AB.

Pythagoras Theorem: Distance

The distance formula for Cartesian coordinates is derived from the Pythagorean theorem. If (x0, y0) and (x1, y1) are points in the plane, then the distance between them is given by

D=

2 D=

(E2 + N2)

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Quadrants

SOURCE: UREN & PRICE (2006, p. 191)

If the change in E and change in N are both positive, your line lies in Quadrant I

If the change in E is positive and your change in N is negative your line lies in Quadrant II If the change in E and change in N are both negative, your line lies in Quadrant III

If the change in E is negative and your change in N is positive your line lies in Quadrant IV

Principle of Radiation
Calculate bearing from bearing AB and Hz angle

Calculate coords of P using bearing and distance

Calculate bearing from coords of A and B

A
(known coords) r = horizontal distance = horizontal angle subtended from line AB to the detail point

B
(known coords)

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Control Points
All survey work is based on a series of control points Located throughout a site at fixed positions within a coordinate system
q Starting points for detail survey (topographic mapping ) projects q Dimensional control for setting out q Measured repeatedly in deformation monitoring

Final Map

Control Points

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Detail Points

Control Surveys
Baselines, traverses, networks: all require measurement of angles and distances.

Extended by Intersection and Resection techniques

SOURCE: UREN & PRICE (2006, p. 242)

Definitions of North
Arbitrary North Common method used on site to define bearings and coordinates Magnetic North Defined using a prismatic compass Grid North This is the direction defined by the axes of a coordinate system and its grid. True North Based on the spin-axis of the Earth. Used only in special construction projects.

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Defining a 2D coordinate system Parameters Position (2), Orientation & Scale

i) define coordinates of one point for position ii) define the bearing of one line for orientation iii) incorporate distances in the survey for scale

315 (237,155) (237,155)

Establishing control on site

1S
BUILDING 1 BUILDING 2
Boundary

2S

BUILDING 3

4S

3S

Arbitrary Bearing

[Arbitrary]
2S
BUILDING 2

1S
1000 E 2000 N

BUILDING 1
Boundary

Arbitrary Coordinates

BUILDING 3

4S

3S
Key ____ Measured Horizontal Distances ____ Measured Horizontal Angles

By traversing

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Tying into an existing system Parameters Position (2), Orientation & Scale
a) start at one known point for position b) observe an angle from a 2nd known point (RO) for orientation c) incorporate distances in the survey for scale

Tying into existing grid

RO
Known Coordinates

BUILDING 1

BUILDING 2 2S
Boundary

1S
Known Coordinates

BUILDING 3

4S

3S
Key ____ Measured Horizontal Distances ____ Measured Horizontal Angles

By traversing

Determine forward bearings of all the traverse lines

If the internal angles have been measured:
forward bearing = back bearing - clockwise angle (Hz Angle)

If the external angles have been measured:

forward bearing = back bearing + clockwise angle (Hz Angle)

The forward bearings are then used in polar to rectangular conversions along with the measured horizontal distances to calculate E and N from one control point to the next

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Polar to Rectangular Conversions

Horizontal Distance measured by total station

EB = EA + EAB = EA + DABsinAB NB = NA+ NAB = NA + DABcosAB

Known coordinates (either arbitrary, existing or computed) Bearing is computed using the opening bearing (either arbitrary or calculated from two known points) and the horizontal angle measured by the Total Station

Intersection

Method of coordinating a point without setting up on it

Establish coordinates for landmarks around a site, e.g. church spires and tall buildings Fixing the framework of building structure surveys from ground level baselines

Used often in setting out, particularly during construction projects with tall structures

Geometry for horizontal observations and computation by intersection-from-a-baseline N

Elevated point of unknown coords
D DE

EBC BC

d
D N NBC D BC

b
A

g
qBC B
Baseline established from STN A to STN B

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Geometry for vertical observations and computation by intersection-from-a-baseline

C
hC= hB +hiB +DhBC
Dh BC
VABC

hi

HzDist d BC BC

hC

B
hB datum

Calculation
Step 1: Calculate the bearing BC Step 2: Distance BC cannot be measured directly so use the Sine Rule to compute it Step 3: Calculate the E and N from B to C Step 4: Apply E and N to coordinates of B to calculate Eastings and Northing of C Step 5: Calculate the height of Point C use the trigonometric height method, hC= hB +hiB +DhBC

The Sine Rule

AB sin C
^

AC sin B
^

BC sin A
^

BC =

AB sin C
^

. sin A

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Intersection: Measurements
To calculate Eastings and Northings of the elevated point, Hz Angles [b and g] at each station, along the baseline to the elevated point need to be observed

To calculate the height of the elevated point, the V Angle [V] from one station to the point needs to be observed

The height of the instrument above the ground mark [hi] must also be recorded for the trigonometric method for computing height.

Weak observation geometries for intersection-froma-baseline

C C A B

qBC A B

Example
The image part with relationship ID rId2 was not found in the file.

A baseline has been established between Point A and Point B. A third point, C, is located at the top of a nearby church spire.

Calculate the horizontal coordinates and height of point C.

Instrument height at B = 1.560 m

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Recap
After this introductory lecture you should begin to understand: Modern definitions of surveying, the importance of surveying and the role and activities of surveyors within civil engineering The structure of the surveying curriculum how it relates to the learning outcomes The importance of control to all survey projects How to define a 2D coordinate system The mathematics behind plane surveying

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