Ce 311 - Tutorial Circle

Elementary & Higher Surveying

CE 311

Surveying Concept

What do surveyors do?

What do surveyors measure?

What distances do surveyors measure?

What angles do surveyors measure?

What positions do surveyors measure?

SURVEYING

is the art and science of

measuring distances, angles, and

positions of points, lines, areas on

or near the surface of the earth or

on other extra-terrestrial bodies

through applied mathematics and

the use of specialized equipment

and techniques.

1. PLANE SURVEYING – type of surveying in which the earth is considered to be a flat surface, and distances and areas involved are of limited extent that the exact shape of the earth is disregarded.

2. GEODETIC SURVEYING – are surveys of wide extent which take into account the spheroidal shape of the earth.

Two General Classifications of Surveying:

Types of Surveys:

1. Cadastral Surveys In urban and rural locations (municipalities, towns)

Purpose: determining and defining property lines and boundaries, corners, and areas

2. City Surveys Areas in and near a city

Purpose: planning expansions or improvements, locating property lines, fixing reference monuments

3. Construction Surveys In construction sites

Purpose: grades, reference lines, dimensions, ground configuration, location and elevation of structure

4. Forestry Surveys Forest management (production and conservation of forest land)

5. Hydrographic Surveys Bodies of water

Purpose: to map shorelines, chart the shape of areas underlying water surfaces, and measure the flow of streams

Water Supply, irrigations, flood control

Types of Surveys:

6. Industrial Surveys Ship building, aircrafts, machineries

7. Mine Surveys Determine the position of all underground excavations and surface mine

structures, surface boundaries, excavated volumes, and establish lines and grades

8. Photogrammetric Surveys (Aerial Survey) Photographs taken from airplanes

9. Topographic Surveys Determine the shape of the ground, location and elevations

10. Route Surveys Construction of highways, railroads, pipelines, canals, transmission lines,

and other linear projects

Determines the alignment, grades, earthwork quantities

SURVEYING INSTRUMENTS

TRANSIT

DUMPY LEVEL

TOTAL STATION TRIPOD

STAFF

STEEL TAPE METER

THEODOLITE

Measurement is the process of determining the extent , size or dimensions of a particular quantity in comparison to a given standard.

Two Kinds of Measurements

1. DIRECT MEASUREMENT • Comparison of measured quantity with a standard measuring unit employed for measuring a quantity of that kind

2. INDIRECT MEASUREMENT • Combination of many measurements

Surveying Measurements

UNITS OF MEASUREMENT Mega- = 1 000 000 Centi- = 0.01 Kilo- = 1 000 Milli- = 0.001 Hecto- = 100 Micro- = 0.000 001 Deca- = 10 Nano- = 0.000 000 001 Deci- = 0.1

1. Linear, Area, and Volume Measurements

1 km = 1 000 m

1 m = 1 000 mm 1 mm= 1 000 um 1 m = 10 dm 1 dm = 10 cm 1 cm = 10 mm 1 ha = 10 000 sq m 1 L = 1 000 cc 1 m3 = 1 000 000 cc

2. Angular Measurements 2π rad = 360 deg Sexagesimal Units 1 deg = 60 mins 1 min = 60 sec Centesimal Units 1 rev = 400 grads 1 grad = 100 centesimal mins 1 c.mins = 100 centesimal sec

Conversion

1 mile = 5280 ft

= 1.61 km

1 foot = 12 inches

1 yard = 3 ft

1 meter = 3.28 ft

1 km2 = 247.1 acres

1 inch = 25.4 mm

Significant Figures General Rules: Rule 1 : Zeroes between other significant figures are significant. ex. 4 SF: 12.03 35.06 4009 Rule 2 :For any value less than one, zeroes immediately to the right of the decimal are not significant. ex. 3 SF: 0.00325 0.000826 0.0589 Rule 3 : Zeroes placed at the end of the decimal numbers are significant. ex. 5 SF: 739.80 190.00 38.000

Rounding Off Numbers Procedures:

1.Digits less than 5.

When the digit to be dropped is less than 5, the number is written without the digit. 2. Digit is equal to 5.

When the digit to be dropped is exactly 5, the nearest even number is used for the preceding digit. 3. Digit is greater than 5.

When the digit to be dropped is greater than 5, the number is written with the preceding digit increased by one.

Errors vs. Mistakes Error is the difference between the true value and the measured value of the quantity. Mistakes are inaccuracies in measurements which occur because some aspect of a surveying operation is performed by the surveyor with carelessness, inattention, poor judgment, and improper execution.

Types of Errors 1.Systematic Errors

• can be computed and corrected

2.Accidental Errors • neglected

Sources of Errors 1.Instrumental Errors 2. Natural Errors 3. Personal Errors

Accuracy and Precision

Accuracy indicates how close a given measurement is to the absolute or true value of the quantity measured.

Precision Refers to the degree of refinement and consistency with which any physical measurement is made.

Theory of Probability

Probability The number of times something will probably occur over the range of possible occurrences. Most Probable Value (mpv) The most probable value of a group of repeated measurements made under similar conditions is the arithmetic mean or average.

Residual The difference between any measured value of a quantity and its mpv

xxv

n

xxx

n

xxmpv n

...21

Illustrative Problem: The angles about a point Q have the following observed values: 130°15’20”, 142°37’30”, and 87°07’40”. Determine the most probable value of each angle.

Probable Error Is a quantity which, when added to and subtracted from the mpv, defines a range within which there is a 50% chance that the true value of the measured quantity lies inside (or outside) the limits

16745.0

2

n

vPEs

)1(6745.0

2

nn

vPEm

PEs = Probable error of a single measurement PEm = Probable error of the mean n = number of observations

Relative Precision * Usually expressed in fraction having 1 as numerator

quantityfrmeasuredmagnitudeo

ferrormagnitudeoRP

Weighted Observation

2

1

EW

W = weight being assigned E = probable error

Interrelationship of Errors

1. Summation of Errors (Perimeter)

2. Product of Errors (Area)

22

2

2

1 .... nS PEPEPEPE

PES = Probable error of the sum PE1, PE2 , PEn = Probable error of each measurement

2

12

2

21 )()( PEQPEQPEP

PEP = Probable error of the product Q1, Q2 = Measured quantity PE1, PE2 = Probable error corresponding to each Q

Illustrative Problem

1. The ff values were determined in a series of tape

measurements of a line: 1000.58, 1000.40, 1000.38,

1000.48, and 1000.46. Determine the ff:

A. MPV of the measured length

B. PE of single measurement and mean

C. Final expression of the most probable length (MPL)

D. Relative precision of the measurement

Illustrative Problem

2. The three sides of a triangular shaped tract of land is given

by the following measurements and corresponding

probable error:

a = 180.21 ± 0.05m

b = 275.26 ± 0.02m

c = 156.31 ± 0.04m

Illustrative Problem

3. The two sides of a rectangular lot were measured with

certain estimated probable error as follows:

W = 271.35 ± 0.1m

L = 458.65 ± 0.08m

Determine the area of the lot and the probable error in the

resulting calculation.