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MIT 12 215 - Lecture Slides

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112.215 Modern NavigationThomas Herring ([email protected]),MW 11:00-12:30 Room 54-322http://geoweb.mit.edu/~tah/12.21510/7/2009 12.215 Modern Naviation L07 2Review of Last Class• Almanacs: Paper and electronics– Paper Almanacs: Nautical Almanac– Electronic: Available on many web sites• Homework #1 due today.210/7/2009 12.215 Modern Naviation L07 3Todayʼs Lecture• Dead reckoning and conventional navigation– Magnetic North pole– Distance measurements• Use of Sextant– Principles of instrument– Vernier Scale reading (ex. Pierre Vernier(1580?–1637), French mathematician.)– Corrections needed for sextant measurements– (Next class we make sextant measurements)10/7/2009 12.215 Modern Naviation L07 4Direction determination• Before GPS it was difficult to determine direction ofmotion relative to true north.– From latitude and longitude determinations at twopoints, the direction between them could bedetermined.– Geodetic maps show the directions betweenmonuments in the ground but these monumentsneed to be found.– Some geodetic monuments (triangulation stationshave vanes on top that can be seen from a longdistance).310/7/2009 12.215 Modern Naviation L07 5Magnetic North Pole• For navigation, most common method of findingdirection is relative to the magnetic North Pole• The Earth magnetic field is largely a dipole field but ithas higher order variations as well.Notice that the direction ofthe dipole axis does not alignwith the rotation axisA compass needle tries toalign with the field lines10/7/2009 12.215 Modern Naviation L07 6Compasses• Since a compass wants to align with the field lines itwill point either up or down (relative to gravity) when itis away from the magnetic equator.True NorthMagnetic NorthField LinesDirection compassneedle pointsTo compensate forthe tendency to pointup or down, goodcompasses haveweights to make theneedle lay flat410/7/2009 12.215 Modern Naviation L07 7Dip or Inclination• The angle that the needle wants to tilt to is called thedip or inclination of the needle.• Normally, a compass designed for use in the NorthernMagnetic hemisphere can not be used in the Southernhemisphere unless the weighting mass can be movedto opposite side of the needle.• Magnetic dipole field equations:€ Hr= −2m cosθ/r3Hθ= −m sinθ/r3 θ is colatitudeTotal Intensity F = (m /r3) 1+ 3cos2θ r is radiusInclination I = tan−1(2cotθ) m is field strength(Guass)10/7/2009 12.215 Modern Naviation L07 8Declination or Variation• The angle between true north and magnetic north iscall the declination or variation (with variation beingthe marine term).• This angle can be computed approximately from thelocation of the North magnetic pole.• In 1994 North Magnetic Pole was located on the NoicePeninsula, southwest Ellef Ringnes Island, at 78.3° N,104.0° W.• In 2005 82.7N 114.4W• The yearly motion of the pole is about 15 km per year.http://www.geolab.nrcan.gc.ca/geomag/northpole_e.shtml510/7/2009 12.215 Modern Naviation L07 9Motion of North PoleFrom http://geo.phys.uit.no/articl/roadto.html10/7/2009 12.215 Modern Naviation L07 10Recent Magnetic pole locationsLongitude ( 。W)Latitude ( 。N)Year110.881.32001112.482.02003111.681.62002113.482.32004114.482.72005610/7/2009 12.215 Modern Naviation L07 11Dead Reckoning• Full book on subject available at:http://www.irbs.com/bowditch/• Basic problem with dead reckoning is that measurements aremade relative to the water and the water can be (usually is)moving with respect to the land beneath• Knowledge of ocean currents is necessary for accurate deadreckoning:– Cross currents will have motion of vessel not in direction that itis pointed– Along-track currents will make speed relative to water (“knots”)different from speed relative to ocean bottom.• General character of ocean currents remains fixed, but frequentcelestial fixes are needed to compensate for variations.10/7/2009 12.215 Modern Naviation L07 12Basic ocean currents710/7/2009 12.215 Modern Naviation L07 13Magnetic variations• For dead reckoning variations in the magnetic fieldand compass also need to be accounted for• Major changes:– For compass: Deviation is a local correction tocompass because of nearby objects (important on aship)– Magnetic field:• Diurnal variations (tendency to point towards Sun) — 2-5ʼ• Annual variations — 1ʼ• Secular variation (due to changes in dipole field) — 5-10ʼ/yr• Local attractors (potential problem on land)10/7/2009 12.215 Modern Naviation L07 14Sextant• Basic instrument for measuring altitude or elevationangle to celestial bodies.• Schematic of sextant:http://www.tecepe.com.br/nav/inav_c12.htmSmall mirror ishalf a mirror sothat direct ray andreflected rays areboth visible.810/7/2009 12.215 Modern Naviation L07 15Student SextantThis is the sextantwe will be using formakingmeasurements.Scales are readthrough acombination of amicrometer wheeland a vernier.10/7/2009 12.215 Modern Naviation L07 16Scale readingReading on sextant is45 deg 13.6 minutes45 degs (main scale)13ʼ (micrometer)0.6ʼ (venier)910/7/2009 12.215 Modern Naviation L07 17Scales• Micrometer scale is a method a turning rotation in tosmall displacements (basically a screw drive). Onefull turns moves scale a set amount. The amount ofthe turn (angle between 0-360deg) can then be usedto interpolate between graduations• Vernier scales provide another method of interpolatingbetween graduations.• Example JAVA program:http://www.phy.ntnu.edu.tw/java/ruler/vernier.html10/7/2009 12.215 Modern Naviation L07 18Vernier scales• The idea of a vernier scale is to make a scale that hasN markings in the same distance as N-1 markings onthe original scale. The fractional difference betweenthe scales sets the scale that the vernier reads:From http://www.tpub.com/math1/7e.htmSo if N=10, then 10graduations on thevernier take up 9markings on theoriginal (see note)1010/7/2009 12.215 Modern Naviation L07 19Corrections needed for sextantmeasurements• Basic sextant measurement is to measure the elevation angle ofthe sun at its highest elevation and to note the time this occurs.• Generally, this is done as series of measurements across thetransit of the sun and the highest point is interpolated.• Corrections that need to be applied:– Atmospheric refraction (already covered)– Index error in sextant (does not read zero when direct andreflected signal are parallel– Sunʼs diameter if measurement made to lower limb


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