GEOM 2015 – GEOMATICS FOR CIVIL AND ENVIRONMENTAL ENGINEERS 2 – Distance Measurement Sunil Lalloo
Dec 03, 2015
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
DIRECT LINEAR MEASUREMENT
Odometer/Measuring Wheel Fixed circumference Distance = # of revolutions x circumference Generates terrain distances Problems with alignment Accuracy of ~ 1:200
DIRECT LINEAR MEASUREMENT
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
DIRECT LINEAR MEASUREMENT
Taping accessories Range rods and chaining pins Tension handles or spring balances Tape clamps Plumb bobs Hand level Abney level Pocket thermometers
DIRECT LINEAR MEASUREMENT
Taping procedures depend on Type of tape available Terrain to be measured Project requirements/specifications Personal preferences Established practices
DIRECT LINEAR MEASUREMENT
To obtain horizontal distances Horizontal tapingSlope tapingDynamic taping
DIRECT LINEAR MEASUREMENT
tapePlumb bob
Horizontal taping
DIRECT LINEAR MEASUREMENT
Slope Taping
DIRECT LINEAR MEASUREMENT
Dynamic taping
DIRECT LINEAR MEASUREMENT
Taping techniques for type of terrain Flat ground without obstructions – horizontal
taping Obstructions – catenary taping Sloping ground – slope taping
DIRECT LINEAR MEASUREMENT
Mistakes/blunders in taping Adding or dropping a full tape length Adding a unit Confusing zeroes Reading numbers incorrectly Calling numbers incorrectly/unclearly
DIRECT LINEAR MEASUREMENT
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
DIRECT LINEAR MEASUREMENT
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 OF STEEL TAPING
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 OF STEEL TAPING
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
OPTICAL DISTANCE MEASUREMENT
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.
OPTICAL DISTANCE MEASUREMENT
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
OPTICAL DISTANCE MEASUREMENT
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.
OPTICAL DISTANCE MEASUREMENT
Since the parallactic angle is constant, the equation reduces to
s = bk
OPTICAL DISTANCE MEASUREMENT
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
OPTICAL DISTANCE MEASUREMENT
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’
OPTICAL DISTANCE MEASUREMENT
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
OPTICAL DISTANCE MEASUREMENT
Similarly the vertical distance is given by
V = ssin = 100b’sin = 100b(cossin) = 100b(1/2 sin2)
s
OPTICAL DISTANCE MEASUREMENT
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
OPTICAL DISTANCE MEASUREMENT
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).
OPTICAL DISTANCE MEASUREMENT
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.
OPTICAL DISTANCE MEASUREMENT
Incorrect interval This is a random error due to the human
operators inability to read the stadia interval exactly
OPTICAL DISTANCE MEASUREMENT
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
OPTICAL DISTANCE MEASUREMENT
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
OPTICAL DISTANCE MEASUREMENT
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.
OPTICAL DISTANCE MEASUREMENT
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
67
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