Zeevaartkunde (2)

2de Bach NW Samenvatting zeevaartkunde 1/14

Times and hour anglesTimes and hour angles

References

Celestial bodies are reference for measuring passage of time Sundial

o 1500 – 1300 BCo Measure time of day by shadowo Hours shorter in winter

Water clocks / clepsydraso Water dripping at constant rate from small holeo Water filling up a container with markings on insideo Determine hours at night

Tower of Windso Octagonal structureo Sundials & mechanical hour indicators

Su Sung clock Mechanical clocks

o 14th centuryo Weight driveno Regulated by verge-and-foliot escapemento Period oscillation depended on driving force & friction => rate difficult to

regulate Spring-powered clocks

o Between 1500 & 1510o Smaller clocks & watches

Pendulum clocko 1656o Christiaan Huygenso Used natural period of oscillationo Error less than 1 minute a dayo Later refinements: less than 10 seconds a dayo William Clement

1671 Anchor / recoil escapement Less interferences with motion of pendulum

o George Graham 1721 Improvement accuracy to 1 second a day Compensating changes in pendulum’s length due to temperature

o John Harrison 1761 Refined temperature compensation techniques New methods to reduce friction Very accurate marine chronometer

Regional time zoneo 1850s


o Established in New England 1905 => radio time signal transmitted to help ships find longitude Quartz clock

o Based on piezoelectric property of quartz crystalso Electric field => changes shapeo Squeezing / bending => electric fieldo In suitable electronic circuit => vibration & generation electric signal of

relatively constant frequencyo No gears / escapemento Frequency depends on crystal’s size, shape & temperature

Atomic clocko Atoms have stable resonanceso New international unit of time => 1 second = 9 192 631 770 oscillations of

cesiumo Accuracy 30 billionths of a second per year

World time scaleso Greenwich Mean Time evolved as time reference for the worldo Coordinated Universal Time

Runs at rate of atomic clocks Difference with Earth near 1 second => adjustment in UTC


UT/GAT/time equation

Greenwich meridian time (GMT)o Former name for mean solar time at Royal Observatory in Greenwicho Now Universal Time (UT)

Mean solar timeo Related to mean sun

Running in plane of equator Constant velocity

o Begins at midnight Apparent (true) solar time

o Time interval between two successive lower transits of true sun for meridiano Begins at midnight

Time equation ()o Difference between mean time & apparent time (or passing mean sun and true

sun through meridian)o Given in Nautical Almanaco Causes for differences

Plane equator not same as plane Earth’s orbit around the sun (angle of obliquity = 23,5°)

Orbit of Earth around sun is ellipseo Remains practically constant from year to yearo No correction for 4 days in 1 year (16/04, 14/06, 02/09 & 25/12)o Maximum deviation on 03 or 04 / 11 = 16 min. 23 sec.

oo = C + Ro UT = GAT +/-


LAT/LMT

Local meridian of observer = reference UT = LMT +/- gt GAT = LAT +/- gt gt

o Added when easto Subtracted when westo Calculation

15° of longitude = 1 hour 1° of longitude = 4 minutes Parts of 1° longitude = parts of 4 minutes

o Nautical Almanac (Conversion of arc into time)

ZT/ZD

World subdivided into zones of 15° longitude Time same throughout each zone Each zone has zone description or delay (ZD) indicating with UT ZT = UT +/- ZD ZD = (g + 7°30’)/15° (alles na de komma laten vallen)

ST/Legal time

Adopted in 19th century Zones subdivided or altered in shape for convenience of inhabitants Nautical Almanac/Admiralty List of Radio Signals Sometimes Daylight Saving Time Basis is UT, indicated times added or subtracted as listed Date line on 180° of longitude East of date line is one day ahead

WT

Watch time kept on board Shift takes place in 00-04h watch Main idea: next day watch time 12h00 as close as possible to LMT 12h00

Corrections to time

Chronometer indicate exact UT High precision watch but still an error Radio time signals for comparison


Syntax times

GHA

Celestial bodies expressed by declination & Greenwich Hour Angle Angle between meridian of Greenwich & hour circle of body measured westward

from Greenwich meridian Groups of celestial bodies

o Suno Moono Planetso Stars

Add SHA to GHA of Aries to obtain GHA each celestial body Sun

o Sidereal hour angle changes 1° daily => GHA sun table insertedo GHA + I => GHA

Moono SHA changes more rapidly with average of 12,85° => separate tableo Extra correction due to irregular motiono GHA + I + v-correction => GHA

Planetso Irregular patterno Own table & v-correctiono GHA + I + v-correction => GHA

Starso Does not significantly change => NO separate tableo GHA Aries + I => GHA Aries => + SHA star => GHA star

LHA/P

Principle same, reference = local meridian GHA +/- g => LHA (+ if g = E, - if g = W) Polar angle (P)

o 000° < LHA < 180° => P = LHA & P = Wo 180° < LHA < 360° => P = 360° - LHA & P = E


Relation between time and hour angle

Correlation between time & hour angleo Same referenceso Differ 180° or 12 hours

Basis time measurement = sun => sun at anti-meridian (180°) => 00h00

Syntax hour angles

GHA mean sun + 12h00 = UT LHA mean sun + 12h00 = LMT GHA mean sun = GHA apparent sun +/-

Traditional astro-positionTraditional astro-position

Basic principle of the position line

Vikings used sun & pole star to sail line of latitude No certain method of fixing ships position until mid 18th century 1837

o Captain Thomas Sumnero Establishing position lines from sightso Sextant altitude increases when sailing towards point where line between

celestial body and centre of earth intersects the earth’s surfaceo Theory used to elaborate a method to determine a line of position

Determine altitude & azimuth for estimated position for given time Difference between observed altitude & calculated altitude Convert minutes of difference in altitudes to miles Line perpendicular to azimuth towards or away from geographic

position of body Principle line of position

o Each celestial body for certain moment has geographical positiono All observers sighting celestial body with same declination => circle around

geographical positiono Geographical positions move on surface of the Eartho Earth & celestial equators in same plane =>

Latitude geographical position = declination of star Longitude geographical position = GHA

o Zenithal distance = distance between observer & geographical positiono = 90° - ho At least 3 circles for one positiono No circles drawn on chart but tangents


The intercept

Difference between true altitude & calculated altitudeo True latitude = altitude by observationo Calculated altitude = expected altitude based upon assumed position

sin hc = +/-(sin * sin la) + cos * cos la * cos P

+ if & l same name & P < 90° - if & l same name & P > 90° - if & l not same name & P < 90°

hv – hc = h + => towards body - => away from body

Determination astronomical position

o Plot assumed positiono Line passing position in direction of Azimutho Measure intercept in right directiono Draw line of position perpendicular to Azimuth


Azimuth

3 elements at the same timeo Altitude by sextanto Reading chronometero Compass bearing

Compass not precise enough => calculate Azimuth

tg la / tg P – tg / sin P = cotg Az / cos la A + B = C (Nories, see practical navigation) sin Az = sin P * cos * sec hv

Amplitudo

Special case of azimuth Celestial body on true horizon Amplitude = arc between prime vertical & body Quadrantal starting from E/W towards N/S sin A = sin * sec l Nories

Determination of compass errors

Calculated azimuth and amplitude => true bearing Comparing with compass bearing => total error


Astro-position special casesAstro-position special cases

True latitude

Bearing due North or South Object crosses observer’s meridian (culmination) lv = * cu

cu = 90° - hcu

Exact momento Nautical Almanaco Calculation

Altitude and time of observation before estimated time of passage Note exact time when celestial body has same altitude tcu = (t1 + t2) / 2

True latitude with Polaris

lv = hv – 1° + a0 + a1 + a2 (Almanac) Polaris not exactly above true North Pole => corrections lv = hv + a0 + a1

o a0 = * cos Po a1 = ½ * ² * sin² P * sin 1’ * tg hv

Ex-meridian

Correction for meridian passage if not on true meridian lv = + cu

cu = - X X = ½ sec hv * sin 1’ * P² * cos l * cos X = A * P² A = in Nories


True longitude

Longitude tempered by time Time aboard & time at another place with known longitude

Line of position

Celestial body’s bearing due East or West 2 elements needed

o Altitudeo LHA / Polar angle

cos P = tg * cotg lo Nautical Almanac to find LMTo LHA star = LHA Aries + SHA staro LMT star = LMT Aries + t (conversion of SHA to time)

sin hv = sin * csc l Bearing due east or west => take exact time Nautical Almanac => GHA & cos P = tg * cotg l LHA – GHA = lon (g)

At meridian passage

LHA = 360° LHA – GHA = lon (g)

Position fixPosition fix

Graphic solution

Intersection two or more lines of position => fix Lines of position separated in time => running fix

Noon position and its value in navigation

Navigational reasonso Indication position logbooko Calculation mean speed over ground since departureo Calculation mean speed over ground since previous noon positiono Calculation ETAo Plotting progress of voyage on large scale chart

Economical reasonso Charter party: current conditions + renewal or new chartero Economical speed orderedo Ship’s agent: ETAo Liner serviceso …


Pagel method

Replaces graphical solution in case of true latitude and almost true longitude Find g to obtain true longitude g = cotg Az / cos lv * l g = C * l (Nories) gv = ge +/- g

Rise, set and twilightRise, set and twilight

Rise, set

Sunrise & sunset = times when upper limb of Sun is on visible horizon Moonrise & moonset = times when upper limb is on visible horizon Theoretical rise & set = relative to true horizon Visible rise & set = relative to visible horizon True horizon is 33,8’ above visible horizon Amplitude: when sun / moon with centre on true horizon

o Sun: lower limb semi-diameter above visible horizono Moon: 1/3 of surface visible above visible horizon (due to parallax)

Twilight

Before sunrise & after sunset Natural light provided by upper atmosphere (reflection of sunlight) Amount of light during twilight affected by state of atmosphere & local weather

conditions Limits applicable considering only position of sun below local horizon Civil twilight

o Sun geometrically 6° below horizono Terrestrial objects clearly distinguishedo Horizon clearly defined & brightest stars visible under good atmospheric

conditions & in absence of other illumination Nautical twilight

o Centre of sun 12° below horizono General outlines of ground objects distinguishableo Horizon = indistinct

Astronomical twilighto Centre of sun 18° below horizono Sky illumination very faint


Special diagramsSpecial diagrams

Eclipses

General

Two kindso Solar eclipseo Lunar eclipse

General conditions: centres Earth, Moon & Sun one line in space Types

o Totalo Annular (shadowing disk covering complete, but off-centre)o Partial (centres almost one line in space, but shadowed disk not complete)

Eclipse of sun occurs during new moono Every month new moon => NOT every month eclipseo Moon passes to north or south of sun

Eclipse of moon occurs during full moono Moon passes north or south of earth’s shadowo Orbit around earth not same as earth’s orbit around sun (tilted 5°)

Point twice a year where moon appears neither north nor south => eclipseo Ascending node (moon moving from south to north)o Descending node (moon moving from north to south)

Regular pattern (= Saros)o Periodicity = 18 years 11 days 8 hourso Subsequent eclipses are visible from different parts of the globeo Same geographic region every 3 saroseso Nodes shift eastward => saros series doesn’t last indefinitelyo Exact duration & number of eclipses is not constanto Different saros series in progress at the same time

Solar eclipse

Moon between sun & earth Total or annular => declination & GHA of sun & moon must be the same 3 zones

o Eclipse zone => all observers can see total or annular eclipseo Penumbra zone => observers in this zone see partial eclipse & intensity of light

decreaseso Free zone => observers don’t remark anything

Lunar eclipse

Earth between sun & moon Total or annular => declination sun & moon opposite sign & same value & GHA

differs 180° Moon becomes dark red due to refraction


Meridian passages of planets

In LMT In diagram

o Meridian passage sun in LMTo Meridian passage each planet in LMTo SHA sun & planets throughout yearo Possible conjunctions (verification if declination is same is necessary)

Zeevaartkunde (2)

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