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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