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APG3017D
SURVEYING III
HYDROGRAPHIC
SURVEYING
Hydrographic surveying
TEXTS
Hydrography for the Surveyor and
Engineer - A E Ingham 3rd Edition -
revised by V J Abbot (1992)
Manual on Hydrography. Publication
M-13, International Hydrographic
Organisation, May 2005
INTRODUCTIO
N
Intro: Hydrographic surveying
Mapping at sea
Position fixing at sea
How is this different from surveying on the land?
Instantaneous position – afloat
Work outside the control framework
Not precise
Platform a constant height above the geoid
Accuracies required:
Position of the vessel - absolute
position of the vessel wrt the sea bed and other structures
or features – relative
Repeatability?
X, Y and depth, Z
Intro: Hydrographic surveying
Intro: Hydrographic surveying
Units of measure:
Sea mile: the length of 1 minute of arc along the
meridian at the latitude of the position.
International Nautical Mile: this is a constant 1852
metres (this is derived from the width of the English
Channel). 1 land mile = 1.609 km; 1 nautical mile =
1.852 km.
Fathom: is used to measure depth. 1 Fathom = 6
feet
TIDES
Tides affect
the following
concerns:
fishing
launching/berthing of vessels
managers of harbours and ports
swimmers
surfers
micro-climate
tidal currents
hydrographic surveyor: correction
for height of tide
Use of tidal data
Real Time: instant determination of water level and
direct transmission to the user. Examples:
on-line echo sounding
shipping movement control in large ports
surge and storm warnings - combinations of wind, weather
and tide can be very destructive, in the South China Sea
for example
control of engineering activity - pipelines and harbour
construction
Historical/Statistical: Analysis of data after the
event. Examples:
control for hydrographic survey of the sea bed
to determine MSL for the Land Levelling Datum (LLD)
to determine the high water mark for cadastral purposes
prediction of frequency of abnormalities
compilation of co-tidal charts and tables
physical or mathematical models of estuaries and lake
systems etc.
land/sea movements for geodesy
Use of tidal data
Definitions
tide: periodic vertical movement of the sea
tide raising forces: those exerted by the moon and the sun to generate tides and tidal streams
tidal streams: periodic horizontal movements of the sea
currents: horizontal movements of the sea not caused by tide raising forces e.g. prevailing wind, differential salinity and water temperatures
high and low water:the extremes reached in any tidal cycle
semi-diurnal tide: two highs and two lows in the lunar day (25 hours)
lunar day: the moon returns to the same position w.r.t. the earth; 25hrs has an astronomical reason - relation to the angular velocity of the moon)
Definitions
diurnal tide: one high and one low in a lunar day (diurnal
means occupying one day)
mixed tide: diurnal and semi-diurnal on different occasions
range of tide: difference between high and the preceding low
spring tides:when the average range of two successive tides
is greatest, on two occasions in a cycle of 29.5 days (i.e.
once a fortnight for 24 hours) when average declination of the
moon is 23.
neap tides: when the range is the smallest in the same cycle
Definitions
mean high water springs: average over a year of heights of
two (MHWS) successive high waters at
springs. Varies from year to year in a cycle of 18.6 years.
mean low water springs: average of lows........ as above......
(MLWS)
mean low water neaps: average of neaps .......as above.....
(MLWN)
low water of ordinary spring tides (LWOST): found in
acts of parliament; no exact definition; not as low as MLWS
Definitions
mean sea level (MSL): average of hourly readings taken
over one tidal cycle at least, or better a lunation (29.5 days)
or 6 months or 18.6 years (one cycle of moons nodes).
Length of period and date should be quoted.
mean tide level (MTL): average of all highs and lows over
a period
lowest astronomical tide: lowest level of sea under average
meteorological
(LAT) conditions. Can only be calculated by predicting
tide levels over 18.6 years. Usually selected for chart datum
for soundings. Will not be reached every year; excludes
surges.
Definitions
LPLW: Lowest possible low water - used by France
for its chart datum definition
similarly for high: HAT; HATOM (of the month); HATOY
(of the year); HATOFF (of the foreseeable future). Also
LATOM; LATOY; and LATOFF.
chart datum: level to which soundings on a
published chart are reduced; datum for tide tables, in SA
= LAT
sounding datum: level to which soundings are reduced
during a survey - may be the chart datum
off-shore datum: usually derived from the co-tidal chart
Definitions
standard port: for which all data is published enabling
high and low water to be calculated
Land Levelling Datum: generally mean sea level. In SA
the (LLD) LLD is offset from MSL by
varying amounts at different ports. For offsets of the LLD
from the Chart Datum, see next slide.
British Admiralty Chart Datum (B.A.C.D.): in SA until
1979 the B.A.C.D.=MSL - 1,1 (M2+S2)
where M2 = semi -amplitude of lunar semi-diurnal cycle
S2 = semi-amplitude of solar semi-diurnal tide
Datums in SA
Tidal Theory
Theory of Equilibrium (Darwin)
Newton’s Law of Universal Gravitation: A body attracts another with a force acting in a straight line between the bodies the magnitude of which is proportional to the product of their masses and inversely proportional the square of the distance between them.
The close celestial bodies exert a force on the earth which causes ocean and crustal tides.
Assumptions:
Earth has a complete envelope of water of uniform depth
The inertia and viscosity of water is negligible
Lunar Tides
G = centre of rotation of Moon
Tidal Theory – Lunar Tide
Tidal Theory – Lunar Tide
At A: superior lunar tide (tide of moon’s upper
transit - over the meridian)
At B: inferior lunar tide (tide of moon’s lower transit)
Tidal Theory – Lunar Tide
LUNATION: when the moon returns to its former phase i.e. new moon to new
moon
The revolution of the moon is the same direction as the diurnal rotation of the earth (west to east).
relative to the sun, one revolution = 29.53 earth days.
LUNAR DAY Interval between transits of the moon across the observer’s
meridian, or one earth rotation relative to the moon
In 29.53 solar (earth) days the moon transits 28.53 times.
29.53 days x 24 hours = 708.72 hours
708.72 hours/28.53 days = 24 hrs 50.5 minutes =LUNAR DAY
High tide is experienced at A every 12 hrs 25.25 min (SEMI-DIURNAL=one tide cycle per half day)
Tidal Theory – Solar Tide
Period = 12 hours
Approximation: differential attraction, or tide-producing-force, is proportional to the mass of the attracting body and inversely proportional to the cube of the distance.
i.e.: where S = 331000 x Earth
M = 1/81 x Earth
s = 92 800 000 miles
m = 239 000 miles
therefore solar tide = 0.0458 x lunar tide
Combined Tide Raising Forces
Remember:
tide: periodic vertical movement of the sea
tide raising forces: those exerted by the moon and
the sun to generate tides and tidal streams
The relative positions of the sun and moon can
strengthen or counteract each other. This is done in
two ways:
by variation in tidal range (springs and neaps)
by variation in tidal day (priming and lagging)
Phases of the Moon
Springs and Neaps
The combined forces of the moon and the sun depend on their relative positions i.e. the phase of the moon
In alignment - Spring
Conjunction: on the same side of the earth – max spring tide –called spring tide of new moon
Opposition: on opposite sides – large spring tide – called spring tide of full moon
Out of alignment – Neap
Elongation: angle to moon and sun are 90 deg apart
Neap tide of first quarter – elongation = 90 deg
Neap tide of last quarter – elongation = 270 deg
Priming and Lagging
Variation of the time of tide due to changing relative
positions of moon and sun.
High tide occurs either before or after the moon
transits the observer’s meridian.
Subject: Tide
Object: moon’s transit
Priming: Tide occurs before moon’s transit
Lagging: Tide occurs after moon’s transit
Priming and Lagging
Moon in: Elongation Phase Moon’s
age
Tide Range Tiday
Day
Conjunction 0 degrees New 0 days Spring
(max)
Great Normal
Priming
Quadrature 90 deg 1st ¼ 7.5 days Neap Small Normal
Lagging
Opposition 180 deg Full 15 days Spring Great Normal
Priming
Quadrature 270 deg 3rd ¼ 22 days Neap Small Normal
Lagging
Conjunction 360 deg New 29.5 days Spring
(max)
Great Normal
Long term effects – ellipticity of
orbits
Moon:
ellipse with eccentricity of 0.055 (f)
f=(1-0.055)/(1+0.055)
Anomalistic month: the period of this disturbance between
successive perigees = 27.55 days
neaps and springs are increased at perigee and
decreased at apogee
Range of the moon causes change of tide raising force of
15-20%
the longitude of the perigee moves with a period of 8.85
Long term effects – ellipticity of
orbits
Earth:
ellipse with eccentricity of 0.0166 (f)
neaps and springs are increased at perihelion and
decreased at aphelion
Anomalistic year: the period of this disturbance between
successive perihelions = 365.26 days
Range of the sun causes change of tide raising force of
3%
Long term effects – declination of
orbits
Sun: Plane of the sun varies 2327’ N and S of Equatorial plane –
solstices
Line from the Earth to the sun = ecliptic
When declination 0, Sun crossing Equator – equinoxes
Tropical Year: time between autumnal equinoxes = 365.24 days
Moon: Orbital plane varies 58’ either side of the ecliptic
2327’ + 58’ = 2835’ ; 2327’ - 58’ = 1819’
Period =18.61 years: called nodal regression, or period of the moon’s nodes
Hence tidal data needs to be observed for 18.61 years to take into account full period of planetary effects.
Amplitude and Phase Angle
Inertia of the water mass: causes phase lag
Friction against the seabed.
Restriction of land masses.
Shallow water effects
Resonance of ocean basins
Corriolis Force
Meteorological
Seismic activity
Oceanographic
Prediction of Tides
Cosine curves – one per effect (called a constituent)
Harmonic analysis of tide data to determine these
curves and coefficients
Constituents M (and O, N, etc.): lunar constituents
Constituents S(and R, T, etc.): solar constituents
One cycle per day (diurnal) = suffix 1
Two cycles per day (semi-diurnal) = suffix 2
61 constituents!
Prediction of Tides
There are four principal constituents which will be
encountered (here we consider the earth stationary
and the moon and sun revolving around it):
M2 = Principal Lunar Constituent, moving at twice the
speed of the mean moon (because it must happen twice in
one lunation)
S2 = Principal solar constituent, moving at twice the speed
of the mean sun
K1 = part of the effects of the Sun’s and the Moon’s
declinations
O1 = remaining part of the Moon’s declination.
SOUNDING DATUMS
Sounding is determination of depth
A sounding datum is the reference surface for sounding
Ideally: should agree with the Chart Datum
Arbitrary datum: established from using a tide gauge to take tidal observations
tide should not fall under chart datum usually
do not be too pessimistic
the datum should be in harmony with the datums of neighbouring surveys
Sounding Datums
LAT .... Tidal observations over 19 years
Chart Datum = LAT
LLD differs from CD
-0.716m in East London to -1.055m in Luderitz.
In Cape Town: -0.825m at Granger Bay and -0.843 at
Simonstown
Preservation
TGBM or FBM
Sounding Datums
Obtaining a sounding datum:
Is tidal regime diurnal or semi-diurnal?
If x amplitude of the solar semi-diurnal constituent
at Standard Port (i.e. (H of S ) x ) is greater than
twice the sum of the amplitudes of the principal
diurnal constituents (2 x (H of K + H of O )) the tide
can be said to be semi-diurnal.
Otherwise the tide may be regarded as diurnal.
Diurnal and Semi-diurnal tides
Interpolate between
known sounding
datums
Use GPS
Tide corrections: cotidal charts
M2 tidal constituent: Amplitude is indicated by color, and the white lines are cotidal differing
by 1 hour. The curved arcs around the amphidromic points show the direction of the tides,
each indicating a synchronized 6-hour period.
Cotidal charts
Time and height differences:
Any time shift translates into a height of tide shift
Maximum at the half-tide
Tide corrections - Chart Datum
“the vertical datum used for tidal observations
should be connected to the general land survey
datum via prominent fixed marks in the vicinity of
the tide gauge/station/observatory. Ellipsoidal height
determinations of the vertical reference marks used
for tidal observations should be made relative to a
geocentric reference frame based on ITRS,
preferably WGS84, or to an appropriate geodetic
reference level” (IHO)
Tide corrections - Chart Datum
antenna correction, which is a purely geometric
quantity
Geometric offset/correction
the height of the chart datum referred to the
ellipsoid; this height is comparable to geoid heights
in that it constitutes a connection between a
geometrical surface - the ellipsoid - and the chart
datum, which is a tidal dependent surface
Knowledge of the LAT (Chart Datum) relative to the
ellipsoid – model similar to a geoid model
Chart datum modelling
GNSS levelling at tide gauges
At each tide gauge determine the height of the chart
datum (LAT) above the ellipsoid.
LAT computed at these stations from water level
observations,
use the heights of a quasi-geoid as preliminary reference
surface for mean sea level determination
Result: chart datum heights above ellipsoid
Tide corrections using GNSS
Ellmer and Goffinet, Tide Correction Using GPS - The Determination of the Chart Datum. Shaping the Change, XXIII FIG Congress, Munich, Germany, October 8-13, 2006
(AA Mather, GG Garland, DD Stretch, African Journal of Marine
Science 2009, 31(2): 145–156)
(AA Mather, GG Garland, DD Stretch, African Journal of Marine
Science 2009, 31(2): 145–156)
Tide Gauge Data sourced from Permanent Service for Mean Sea Level (PSMSL) atwww.pol.ac.uk/psmsl
Sea level trends
Sea level rising
West coast +1.87mm/yr
South coast +1.48 mm/yr
East coast +2.74 mm/yr
Barometric pressure contributes
Vertical crustal motion:
Max East coast +1.1 mm/yr
(AA Mather, GG Garland, DD Stretch, African Journal of Marine Science 2009, 31(2): 145–156)
Error in tide reductions in SA …
“The main problem with the South African tide gauge records is confined mainly to the period between 1998 and 2002 when the data for recorded tide levels were confused with the mean level (ML) at each site. In the derivation of the chart datum (CD) to land levelling datum (LLD) conversion, an error was inadvertently introduced. This error was first identified during the analysis of the Durban sea level records (Garland and Mather 2007) and has subsequently been found in other South African tide gauge records. The magnitude of the error varies between sites (Table 1). This over-correction resulted in artificially raising sea levels for the period 1998–2002 (Garland and Mather 2007). To obtain the correct LLD sea levels for the tide gauge locations, it was necessary to correct all records. This was achieved using Table 2, which is based on the South African Navy’s conversion table (SAN 2008).
Due to these problems, we used the PSMSL revised local reference (RLR) data, excluding Durban, where additional data-correction processes have been applied. It should be noted that data for the period 1998–2002 have been largely removed from the RLR data by the PSMSL, possibly for the abovementioned reasons.”
(AA Mather, GG Garland, DD Stretch, African Journal of Marine
Science 2009, 31(2): 145–156)
Offsets of the Chart Datum below
LLD in SA
Walvis Bay -0.966Luderitz -1.055
Remember:
Chart Datum
is LAT, which
is below msl
Application in SA …
Ellmer and Goffinet, Tide Correction Using GPS - The Determination of the Chart Datum. Shaping the Change, XXIII FIG Congress, Munich, Germany, October 8-13, 2006
• 1D corrections calculated around the coast from tide gauge offsets from LLD
• No offshore model
• LLD – WGS84 ellipsoid relies on geoid model
Tide Gauges
remove the effect of short term motion of the water
to isolate the effects due to tide raising forces
Types:
Flotation
hydrostatic pressure
Acoustic (in air and water)
electronic
UNDERWATER ACOUSTICS
Surveyor is blind – cannot see what
he/she is surveying
Relies on sensors
Hazards may depend on the tide
Incorrect charting renders navigators
vulnerable
Depth spot shots underwater (sounding)
Many reductions.... Contour plan
Infill using other sensors
Underwater acoustics - charting
What is charted:
the positioning of navigational hazards
the determination of the sea bed material
the recommendations, with guaranteed safety, of clearing and
leading lines
the position of topographical detail and conspicuous objects on
shore of use to the navigator
the delineation of the high and low water lines
the depiction to scale of shoreline view as seen from the sea
the writing of recommendations for incorporation into the Sailing
Directions regarding safe navigation in the area surveyed.
Underwater acoustics - sounding
Sounding is the operation whereby an area is
methodically covered by depth measurements
(soundings) in order to portray the relief of the
seabed
Depth poles
LIDAR
Sonar
Echo-sounding: like spot shots directly under the
vessel for charting (off-shore charts: SAHO) and
mapping for specific projects (e.g. FUGRO)
Underwater acoustics – echo sounding
Underwater acoustics – echo sounding
Underwater acoustics – echo sounding
Underwater acoustics – echo sounding
Underwater acoustics – echo sounding
OPERATIONAL CONSIDERATIONS
- A bit like photogrammetry flight planning!
Line Spacing
Footprint of echosounder
Beamwidth
depth of the seabed
Increase if side-scan sonar available
the sonar sweeps out at 90 degrees to the left and right of the
direction of the vessel
Reveals features between echo sounding lines
Underwater acoustics – echo
sounding
2. Line Direction
90 degrees to the slope
Sandy bottoms form waves perpendicular to the direction
of flow - side-scan sonar is useful.
3. Sounding Speed
navigational safety
fixing interval
Echosounder pulse repetition frequency
Sea state
Underwater acoustics – echo
sounding
4. Scale of the Survey
accuracy and density of the coverage required
Determines the sounding speed, fixing method and the
line spacing.
SONAR
SONAR is an acronym for SOunding NAvigation
and Ranging
SONAR instrumentation:
Echo Sounder - fixed beam with a vertical axis
Underwater Acoustic Beacons and Positioning
Side Scan Sonar
Sector Scan Sonar
Passive (military) systems
Multibeam echosounder
SONAR instrumentation
Range using SONAR
Speed of propagation of acoustic energy in water
determine ranges
speed of sound in sea water needs to be determined
Job of the hydrographic surveyor
varies with temperature, pressure and composition (salinity
etc.)
Sound velocity profile
Range using SONAR
Propagation loss:
Geometric spreading
Attenuation
absorption
scattering
Range using SONAR: shadow
zone
Range using SONAR: speed adj
Measured depth needs to be corrected for speed of
travel of sound in water:
but we don’t know c(t):
Measure cm : sound velocity profile
Use a preset cp : correct for difference:
r
t
t
t
dttcd )(2
1tcd m .
2
1
tcd pm 2
1
p
mmt
c
cdd
p
pm
mmtc
ccdddd
Range using SONAR: mean
velocity
Cm :
Bar check:
lower bar to known depths and measure to determine
correction in terms of c
Measure sound velocity directly using a velocimeter:
Lower to depths and read velocity of sound through water
Measure water characteristics:
temperature, pressure, salinity at chosen depths in water
column
Determine Cm from tables
Reduction of soundings
Chart depth = Observed depth + Instrument correction +
Sound Velocity Correction + Dynamic Draft Correction +
Water level (Tidal) correction.
Start with OBSERVED DEPTH: from raw measurement
Reduction of soundings
Instrument corrections: not necessary with
electronic instruments
Now we have ELAPSED TIME DEPTH
Reduction of soundings
Velocity correction – for speed of sound in water
Dynamic draft correction – Static draft
Squat
Settlement
Now we have ACTUAL DEPTH
Reduction of soundings
Water level (tidal) correction Motion of vessel Heave: up and down: Averaging or IMU
Roll: sideways, Pitch (HRP): fore/aft
Heading: vessel axis not aligned to motion
Timing: latency of return echo signal
Now we have SOUNDING DEPTH
Reduction of soundings
Correct offset between sounding datum and chart datum
Now we have CHART DEPTH
Operational Accuracy - influences
Resolution
Pulse duration: resolution = ½ pulse length
2 objects within ½ pulse length reflect once
2 objects greater than ½ pulse length apart reflect twice
Angle of incidence
Skew – effective pulse length increased
Degrades resolution
Sensitivity and resolution of recording medium
only for analogue
Nature of target
Function of density – denser reflects stronger signal
Operational Accuracy - influences
Beam width of transducer
Cone at which intensity ½ that along the beam’s central axis
Non-vertical beam or skew sea bed:
Earliest return ≠ depth measurement
Error sources
Instrumental: beam width
Environmental: c, waves, unwanted echoes (fish,
bubbles), meterological
Operational accuracy - specs
Standard deviation of depth ≤ horizontal accuracy
horizontal accuracy with GPS ≤ 5m
where for d<100 m, a=0.5m and b=0.013
and for d>100m, a=1.0m and b=0.023
Much better accuracies are achievable with
advanced DGPS : 2cm!
22 )( dba
20m 50m 100m 500m 2000m
0.56 m 0.82 m 1.39 m 11.5 m 46.0 m
Operational accuracy - checks
Observe cross lines:
transverse (or between 45 and 90 degrees) to the
direction of the echo soundings
accuracy and reliability of
surveyed depths and
plotted locations
Side Scan Sonar
Swath 90 to direction of travel
Reflection of acoustic pulse
Measurement = strength of return pulse (not TOF)
Picture of sea bed
High resolution – high frequency, short wavelength
Therefore : short distance
High quality
Towed behind vessel
One fish
Two fishes – oblique to vessel
Side Scan Sonar
Detect 1m cube
Side scan sonar
Multibeam Echosounding
Swath 90 to direction of travel
Reflection of acoustic pulses
Measurement = time of flight ... depth
Picture of sea bed
High resolution – high frequency, short wavelength, short
distance
High quality
Integrated systems – mix of different frequency
instruments – depth variations. 240 beams possible.
Echo sounder transducer is beneath vessel
Overlap or use with side scan sonar
Multibeam Echosounding
near-nadir beam is required to detect objects with a high degree of accuracy side scan sonar in combo
Many data points
depths ≥40 meters min detectable target size 10 % depth for horizontal dimensions
5% depth for vertical dimensions
vertical resolution ≤1 centimetre
Multibeam Echosounding
Positioning the survey vessel
Some terminology:
Acoustics: production, control, transmission, reception and
effects of sound
Sound Waves:
Alternating pressure – compression/rarefaction
Particles oscillate
Frequency, wavelength, period, speed, direction (both =
velocity), amplitude (pressure in decibels, dB; 0dB = 20 Pa)
Transponder: transmitter and responder (active reflector)
Transducer: loudspeaker for signals (sounds) underwater
Hydrophone: microphone for signals (sounds) underwater
Positioning the survey vessel
Positioning the survey vessel
GPS for absolute positioning at sea
Stand alone
DGPS
Relative positioning w.r.t. sea bed/other objects:
Acoustic positioning
Local, accurate, real-time
Long baseline (range-range):
acoustic beacons (transducers) and transponder
on sea bed
hydrophone on vessel
Positioning the survey vessel
Short baseline (range-range, range-bearing, time difference)
1 or more submerged acoustic beacons
3 or more transducers (hydrophones) on vessel
range-range:
3 hydrophones in triangle below ship
Poor geometry
Affected by ship’s movement
noise fields surrounding each transducer: systematic error
Range-bearing (ultra-short baseline)
Small hydrophone array on vessel
Bearing interpreted from relative phase of signals received at each hydrophone
Poor resolution
Time difference
Position vessel over a location precisely
Hydrophone on vessel
Transponder on location – eg well point
SPECIALIZED
INSTRUMENTATIONLASER INTERFEROMETER
GYROSCOPIC ORIENTATION
Gyrotheodolite
Gyrocompass
Laser interferometer
Principles of measurement
Laser interferometer
Gyroscopic orientation
Principle of gyroscopic orientation
Gyrotheodolites
Gyrocompasses
Principles
How do we get orientation
underground/at sea?
where we cannot see “control”?
Gyroscopic orientation
Different from gyroscopes):
A gyroscope (APG3016C) maintains the direction of its axis in relation to some distant fixed point in outer space due to conservation of angular momentum
A gyrotheodolite or gyrocompass automatically positions this same axis to true north by applying a torque due to the earth’s gravity. A weight is usually incorporated
Two elements:
The rotating earth
The spinning mass element in
the gyro
Gyroscopic orientation
Gyro: The Rotating Earth
Like a flywheel
Angular momentum = cos
in horizontal
Angular momentum = sin
in vertical
RH rule: L=I.
Lbody=Ibody. E cos
Lbody ≈ E cos if Ibody ≈ small
Gyro: The spinning mass element
gyro flywheel
Angular momentum: L G =I G. G
Gyro torque vector/precession
moment
Cross Product of L G and Lbody :
M= L G x Lbody
M = IG. G x E cos
= L G x E cos
Gyro – precession to North
M area of L G and Lbody
If L G and Lbody unidirectional, M= 0
smallest when vector L G (along the spin axis of the gyro) is
directed parallel to the meridian
If L G and Lbody 90, M= maximum
vector L G (along the spin axis of the gyro) is directed East -
West
Torque f(cos )
maximum at the equator
zero at the poles
Gyro – precession to North
In summary; the angular momentum caused by the
rotation of the earth around its axis is directed
northwards, a component of this can be resolved in
the horizontal plane. The angular momentum of the
spinning gyro is also in the horizontal plane and
directed along the gyro spin axis. These two angular
momentums combine and induce a torque around
the vertical axis at the gyro, causing it to precess
until its spin axix is parallel to the gyro’s meridian
and directed northwards.
Images
Precession and measurement
Gyrotheodolite
Gyrotheodolites
Gyromat 3000
Gyromat 2000, from: Brunner & Grillmayer, 2002from: http://www.leica-geosystems.com/en/Gyromat-3000_1743.htm
Gyrotheodolites
Mass inertia – precession is an oscillation with
decreasing range over time
Model this to determine North direction
Instrument precision 1”
North determined = the instantaneous rotation axis, and
should be corrected for polar motion (0",3)
Vertical axis = gravitational axis ≠ ellipsoid normal
Astronomical meridian ≠ geodetic meridian
Astronomical azimuth, not geodetic azimuth (correction
required)
Gyrotheodolites – approx method
Set up, level, approx orientation to within 30-40 of N
gyro is set spinning and the brake is released, allowing
the gyro to precess towards North
Track index mark on the gyro by turning the slow motion
screw of the theodolite so that the index remains within
the centre of the V-notch
When index mark reverses its direction of motion
(turning point), read the horizontal circle
Repeat
Average two horizontal circle readings to get N to 2-3’
Gyrotheodolites - Turning Point
Method
Approx method first
spinning gyro is set free to precess
track continuously using the slow motion screw
A multiple number of turning points is observed (usually 6 to 10)
The processing of the observations takes into account the damping of the oscillations
Gyrotheodolites - Turning Point
Method
Schüler mean is used:
= [ ( r1 + r3 )/2 + r2 ] /2
= [ ( r2 + r4 )/2 + r3 ] /2
= [ ( r3 + r5 )/2 + r4 ] /2 , etc.
10" - 20"
Gyrotheodolites - Transit Method
Aprox method
Clamp horizontal circle
spinning gyro is set free to prece
Time the passage of the index mark through the V-notches
If oriented in the meridian, then the time spent by the index to the West of the notch = the time spent to the East of the notch
difference, t, is linearly related to the misorientation of the theodolite
Gyrotheodolites - Turning Point
Method
The time intervals between passages through the V-notch are given by the first differences:
differences will alternate between large and small
The second differences, which should be constant in magnitude, provide a measure of the misalignment from N:
,
,
3443
2332
,1221
ttt
ttt
ttt
etcttt
ttt
ttt
,
,
,
435453
324342
213231
N = c.a. t
Gyrotheodolites - Turning Point
Method N = c.a. t
a = mean amplitude of gyro swing in scale units
Read on the scale
Oscillation must be small enough to fit in the scale
t : timing a number of passages of the gyro index through the V-notch and differencing
c = proportionality factor
Determined from readings in two positions:
N = N1 + c.a1. Dt1
N = N2 + c.a2.Dt2
2211
12
.. tata
NNc
10" - 20"
10" - 20"
Gyrotheodolites
Index error
Electronic theodolites:
R300 000 in 2001!
1-2”
Mine surveying
Tunnel surveying
Images
Calibration
Gyrocompasses
Gyrocompasses
Calibration of a gyrocompass in
harbour:
GPS heading of vessel
Gyrocompass reading
Baseline on the jetty at the harbour – fixed ground
stations
Baseline on the vessel – in fore/aft direction (would
be heading) – set up targets
Survey vessel baseline from the two jetty points –
obs all 3 other stations from each jetty station.
At sea ….
Set GNSS software Geodetic ellipsoid parameters
Set up DGNSS antennae at two Vessel baseline
stations
Observe DGNSS position as (x,y)1 and (x,y)2
Calculate join direction (geodetic azimuth)
Compare to gyrocompass (astronomic azimuth)
DGPS Integrity check
Set up GNSS antenna on Jetty station 1
Compare DGNSS coordinate against known
coordinate
THE END!!!Please complete the course evaluations on VULA