2 - distance measurement (1)

GEOM 2015 – GEOMATICS FOR CIVIL AND ENVIRONMENTAL ENGINEERS

2 – Distance Measurement

Sunil Lalloo

OVERVIEW

Introduction & Learning Objectives Direct Linear Measurement

Pacing Odometers Taping

Indirect Linear Measurement Optical Distance Measurement Electronic Distance Measurement

Summary

SECTION OBJECTIVES To define linear measurement To introduce methods and equipment for

performing linear measurement To define sources of uncertainties in linear

measurement To introduce methods for dealing with

systematic errors in linear measurement To define direct and indirect linear

measurement, methods, equipment and theories of operation

LINEAR MEASUREMENT

Distance Measurement Direct measurement – comparison of point

against scale Indirect measurement – calculation of the

distance from ancillary measurements

LINEAR MEASUREMENT

Distance between two points may be Terrain Vertical Horizontal Slope

LINEAR MEASUREMENT

Terrain distance

Slope distance

Vertical distance

Horizontal distance

A

B

LINEAR MEASUREMENT

Direct linear measurement may be performed by

Pacing Odometer/measuring wheel Rigid rulers Chaining /taping

LINEAR MEASUREMENT

Indirect linear measurement may be performed by Stadia Subtense bar Electronic distance measurement (EDM)

DIRECT LINEAR MEASUREMENT

Pacing Determine average pace length Walking between points of interest Generates terrain distances Length changes going up or downhill Pedometer can also be used Accuracy of ~ 1:50 – 1:100


Odometer/Measuring Wheel Fixed circumference Distance = # of revolutions x circumference Generates terrain distances Problems with alignment Accuracy of ~ 1:200


Taping Using a tape between two ends of the line to

be measured Need to:

Properly align tape Apply tension Plumb tape when above ground Read & record


Taping accessories Range rods and chaining pins Tension handles or spring balances Tape clamps Plumb bobs Hand level Abney level Pocket thermometers


Taping procedures depend on Type of tape available Terrain to be measured Project requirements/specifications Personal preferences Established practices


To obtain horizontal distances Horizontal tapingSlope tapingDynamic taping


tapePlumb bob

Horizontal taping


Slope Taping


Dynamic taping


Taping techniques for type of terrain Flat ground without obstructions – horizontal

taping Obstructions – catenary taping Sloping ground – slope taping


Mistakes/blunders in taping Adding or dropping a full tape length Adding a unit Confusing zeroes Reading numbers incorrectly Calling numbers incorrectly/unclearly


Systematic errors in taping Tape not of standard length Tape not horizontal Variations in temperature Variations in tension Sag Incorrect alignment

TAPING CORRECTIONS Standard CorrectionCorrected length L' = L(l'/l)

54.395m = 54.375 (30.011/30) or the standardisation correction Cs can be

computed from Cs = L((l' – l)/l) Where:l = standard lengthl' = calibrated lengthL = observed lengthL' = corrected length

TAPING CORRECTIONS Slope Correction

Corrected length L'' = L' cos

For Slope Correction Ch = L' – L''

L' H

L''

TAPING CORRECTIONS Temperature Correction

Ct = L' ' (T0 – T) Where: L'' is the measured length and a is the coefficient of thermal expansion

(0.00000645/1F or 0.0000116/1C for steel)T = standard temperatureTo = observed temperature

TAPING CORRECTIONS

Tension Correction

where P is the applied tension in lbs or kgsP0 is the standardisation tension in lbs or kgs (units

consistent)L is the measured lengtha is the cross-sectional area of the tape in in2 or cm2

E is the modulus of elasticity of steel in lb/in2 or kg/cm2

aE

LPPCP 0

TAPING CORRECTIONSSag (Catenary) Correction

where w is the weight per unit length of the tape in lb/ft or

kg/mW is the total weight of the tape between the

supports in lb or kg (= wL)L is the distance between the supportsP is the tension applied in lb or kg

2

2

24P

LWCC


Random errors in taping plumbing to mark tape ends marking tape ends applying tension determining elevation differences and slope

angles standardisation

ACCURACY OF STEEL TAPING

A maximum accuracy of 1 in 5000 can be achieved over most ground surfaces applying only standardisation and slope corrections (using an Abney level for slope measurement)


Accuracy can increase to 1 in 10000 applying tension and temperature corrections

On specially prepared (cleared, roughly levelled ground) surfaces and over distances less than a tape length, in addition to careful standardisation and slope angle measurement (theodolite vertical angle measurement), accuracy can potentially reach 1 in 20,000.


Accuracy can be further increased using supported catenary taping applying sag corrections

INDIRECT LINEAR MEASUREMENT There are two main techniques employed for

indirect distance measurement; optical distance measurement (ODM), and electronic distance measurement (EDM)

There are several different methods involved in ODM, but the only ones still used today are stadia and subtense tacheometry

OPTICAL DISTANCE MEASUREMENT

ODM Optical distance measurement is based on

the principles of the parallactic triangle, where the distance s is derived from the relationships between the parallactic angle of the triangle and it’s base b


s = (b/2) cot(/2)

s b

To obtain a value for s, one parameter (either b or ) is held constant and the other is measured.

For stadia tacheometry, the base is measured and the parallactic angle held constant, and for subtense tacheometry the parallactic angle is

measured and the base held constant.


Stadia Tacheometry

The term ‘tacheometry’ means rapid or fast measurement

the angle is kept fixed while the base is measured This is achieved using two supplementary

horizontal lines (stadia) placed at equal distances above and below the central horizontal line in the telescope of an instrument


Stadia TacheometryThese lines serve both purposes Since they are fixed in the telescope, they form

a fixed angle with the optical centre of the instrument, and

Secondly they provide the lines for the measurement of the base.


Since the parallactic angle is constant, the equation reduces to

s = bk


Stadia Tacheometry For most modern instruments, the

relationship between the stadia and the parallactic angle is designed such that the multiplication constant k = 100, therefore

s = 100b


b can be simply measured by sighting a ruler or some other graduated instrument. Usually a levelling staff is used.

For an inclined sight, the horizontal distance H and the vertical distance V are required. For the equation to hold true, b must be perpendicular to the line of sight. For a vertical angle of , b will be inclined by . To obtain perpendicular base

b’ = bcos

b

b’


sos = 100b’ = 100bcos

This s is now the slope distance. To obtain the horizontal distance from s

H = scos = 100b’cos = 100bcos2

bb’

s

bb’

s

90-θθ


Similarly the vertical distance is given by

V = ssin = 100b’sin = 100b(cossin) = 100b(1/2 sin2)

s


Errors in stadia measurement Stadia interval factor (multiplication constant) not

that assumed Rod not standard length Incorrect stadia interval Rod not vertical Unequal refraction Errors in vertical angles


Stadia interval Interval factor depends on the relationship

between the optical centre of the instrument and the stadia crosshairs on the telescope. If this is not in exact adjustment this would produce a systematic error in the distances proportional to the error in the interval factor (e.g interval factor 98.99 instead of 100).


Rod length If the rod is not of a standard length, this will

produce systematic errors proportional to the measured base. These errors can be minimised if the rod is standardised and the appropriate corrections applied to the observed stadia intervals.


Incorrect interval This is a random error due to the human

operators inability to read the stadia interval exactly


Rod not vertical Relationships are only true if perpendicularity

is maintained. This produces a small error in the vertical angle and consequently a larger error in the observed stadia interval and computed distance


Unequal refraction Refraction has a greater effect on light rays

closer to the earth’s surface. Since measurements are taken in the vertical plane, the effects of refraction may vary over b


Accuracy of stadia measurements Ordinary levelling staves can be used for a

maximum distance of ~100m. Accuracy decreases with increasing distance, so

sights of 50 to 75m usually used as a reasonable limit.

Accuracies between 1/300 to 1/500 typical for horizontal measurements, but this can be improved to 1/1000 to 1/2000 using fixed targets instead of rods, repeated measurements and high order theodolites

OPTICAL DISTANCE MEASUREMENTSubtense Tacheometry In subtense tacheometry, the angle subtended by

two ends of a horizontal rod of fixed length known as a subtense bar is observed, and the horizontal distance computed.

The subtense bar has targets at both ends which are connected by an invar wire under slight tension.

A theodolite is used to measure the parallactic angle between the targets.


Subtense Tacheometry To obtain accuracies of 1/5000, distances should be

restricted to <175m and repeated angles should be measured to the nearest 1".

Subtense measurement is useful for measurements over rough terrain, and since only horizontal angles are measured, no slope distance corrections are required

E.D.M

Electronic distance measuring instruments provide a rapid, accurate and flexible method of distance determination.

The measurement principle is based on the invariant speed of light (electro-optical) or electromagnetic (microwaves) waves in a vacuum.

E.D.M Four basic ways in which distances are measured

using EDMI. These are

pulse, phase difference, Doppler and Interferometric methods.

Only pulse and phase difference techniques are on interest at this stage.

E.D.M

The principles of EDM measurement is based upon wave theory. A wave is defined as a disturbance that propagates in time or space or both. A periodic wave is one where the disturbance repeats itself in a periodic manner. Waves therefore have some distinctive features

· period P· wavelength · amplitude A· frequency f phase (the fractional part of the wave)

E.D.M The waves used in EDM measurement are part of

the electromagnetic spectrum.

The operation principles are based upon the basic theory that

distance = speed x time

E.D.M

Since we are dealing with electromagnetic radiation, the fundamental equation we are concerned with is

V = f

f

1

E.D.M

where V is the velocity of the em wave, f is the frequency of the wave and is the wavelength. The mode and velocity of the propagated wave is dependant upon

(i) the frequency, and (ii) the medium through which

the wave is travelling.

E.D.M.

Now for a wave that is emitted at a point A, reflected at a point B and returns to A

2d = Vt

where t is the flight time.

E.D.M Pulse Measurement In the pulse method, a short, intensive signal is

transmitted by an instrument. The signal travels to a target point and is reflected back. The total time taken between transmission and reception of the same pulse is measured.

2d = ct = c(tR – tE)d = c(tR – tE)/2

where c is the speed of the pulse (light) tR and tE are the received and transmitted times respectively .

E.D.M Since the speed of light is very large (299792.5

km/s), this method requires very accurate time measurement (0.1ns error in time gives ~15mm distance error)

E.D.M

Phase Difference Measurement The transmitter emits a continuous

sinusoidial measuring wave (YE) that is reflected and received by the instrument (YR). The instrument compares the outgoing and incoming waves and measures the difference in phase or phase lag .

E.D.M

YE = Asin

YR = Asin ( + )

Since a continuous wave is used, YE and YR

will change with time, but will remain constant.

E.D.M.

so in terms of the wavelength, the basic formula for phase difference measurement is given by

2d = m + therefored = m(/2) + (/2)where is measured directly by the instrument, /2

is the Unit length and m is the Ambiguity

E.D.M.

Reflectors For most type of EDM measurement, there is a

reflector to return the signal to the instrument. A reflector is basically a device at the other end of the line which reflects the light or infrared beam back to the EDM instrument. Some examples of common reflectors are plane front surface mirror spherical reflector glass prism reflector (most used) reflecting tape

E.D.M.Some of the properties of a good reflector

are1. Good reflectivity – a high percentage of

the incident ray is reflected (i.e. no absorption)

2. Complete illumination of the receiver optics of the instrument Small movements in the reflecting device should

not result in a change in direction of the emerging ray

E.D.M.

Basic properties of electro-optical EDM 1. They use visible light or NIR radiation as carrier

waves2. Normal telescopes can be used for transmitting

and receiving signals3. Different classifications based on range

Short range – 1m to 2 kmMedium range – 5 to 10 km

Long range – 15 to 70 km (based on factors of visibility and # of prisms)

E.D.M.

4. Classifications based on precision1st order < (1mm + 1ppm) 2nd order > (5mm + 1ppm)3rd order > (5mm + 5ppm)

ERRORS IN EDM MEASUREMENT

Some of the errors that affect EDM accuracy arei. effect of atmospheric conditionsii. uncertainty in the position of the electrical centre

of the transmitteriii. uncertainty in the effective centre of the reflectoriv. frequency driftv. instrument non-linearityvi. cyclic errorvii. zero error

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ERRORS IN EDM MEASUREMENT

Some of these errors are distance dependant, ((i), (iv), (vi)), while others are fixed. The error function for these EDMIs therefore have a fixed component as well as a distance dependant component

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Method

Tool Accuracy Range

Advantages/Disadvantages

Direct Tape 1:5000 (Std., Slope)1:10000 (Temp, Ten)1:20000(Sag, Theo. Ranging)

Multiple

+ simple theory and computations- time consuming- terrain dependent

Indirect(Optical)

Stadia Tacheometry

1:500 to 1:1000 100m + quick and easy+ simple computations- instrumental errors large effect- assumed value of k- large errors due to staff readings- large errors due to non-vertical staff- errors due to vertical circle measurement

Indirect (Optical)

Subtense Tacheometry

1:5000 to 1:10000

175m + always measures horizontal distances- laborious- instrumental errors- time consuming

Indirect(Electronic)

EDM 15mm +5ppm to 0.2mm + 1ppm

to 150km

+ quick and easy+ digital readout+ longer range+ high accuracy

SECTION OBJECTIVES To define linear measurement To introduce methods and equipment for

performing linear measurement To define sources of uncertainties in linear

measurement To introduce methods for dealing with

systematic errors in linear measurement To define direct and indirect linear

measurement, methods, equipment and theories of operation

2 - distance measurement (1)

Documents

taping tape

standard lengthl

tape lengthadding

type of tape availableterrain

type of terrain flat

tapeapply tensionplumb

observed lengthl

calibrated lengthl