12.215 Modern NavigationReview of Last ClassToday’s LectureDirection determinationMagnetic North PoleCompassesDip or InclinationDeclination or VariationMotion of North PoleDead ReckoningBasic ocean currentsMagnetic variationsSextantStudent SextantScale readingScalesVernier scalesCorrections needed for sextant measurementsSummary and Next class12.215 Modern NavigationThomas Herring09/30/2002 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 solutions09/30/2002 12.215 Modern Naviation L07 3Today’s 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)09/30/2002 12.215 Modern Naviation L07 4Direction determination• Before GPS it was difficult to determine direction of motion relative to true north. – From latitude and longitude determinations at two points, the direction between them could be determined. – Geodetic maps show the directions between monuments in the ground but these monuments need to be found. – Some geodetic monuments (triangulation stations have vanes on top that can be seen from a long distance).09/30/2002 12.215 Modern Naviation L07 5Magnetic North Pole• For navigation, most common method of finding direction is relative to the magnetic North Pole• The Earth magnetic field is largely a dipole field but it has higher order variations as well.Notice that the direction of the dipole axis does not align with the rotation axisA compass needle tries to align with the field lines09/30/2002 12.215 Modern Naviation L07 6Compasses• Since a compass wants to align with the field lines it will point either up or down (relative to gravity) when it is away from the magnetic equator.True NorthMagnetic NorthField LinesDirection compassneedle pointsTo compensate for the tendency to point up or down, good compasses have weights to make the needle lay flat09/30/2002 12.215 Modern Naviation L07 7Dip or Inclination• The angle that the needle wants to tilt to is called the dip or inclination of the needle.• Normally, a compass designed for use in the Northern Magnetic hemisphere can not be used in the Southern hemisphere unless the weighting mass can be moved to opposite side of the needle.• Magnetic dipole field equations: Hr=−2mcosθ/r3Hθ=−msinθ/r3 θ is colatitudeTotal Intensity F = (m/r3)1+ 3cos2θ r is radiusInclination I = tan−1(2cotθ) m is field strength(Guass)09/30/2002 12.215 Modern Naviation L07 8Declination or Variation• The angle between true north and magnetic north is call the declination or variation (with variation being the marine term).• This angle can be computed approximately from the location of the North magnetic pole.• In 1994 North Magnetic Pole was located on the Noice Peninsula, southwest Ellef Ringnes Island, at 78.3° N, 104.0° W. • The yearly motion of the pole is about 15 km per year.http://www.geolab.nrcan.gc.ca/geomag/e_nmpole.html09/30/2002 12.215 Modern Naviation L07 9Motion of North PoleFrom http://geo.phys.uit.no/articles.htmlImage courtesy of Prof. Truls Lynne Hansen, University of Tromsø, Auroral Observatory.09/30/2002 12.215 Modern Naviation L07 10Dead Reckoning• Full book on subject available at:http://www.irbs.com/bowditch/• Basic problem with dead reckoning is that measurements are made 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 dead reckoning:– Cross currents will have motion of vessel not in direction that it is 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 frequent celestial fixes are needed to compensate for variations.09/30/2002 12.215 Modern Naviation L07 11Basic ocean currentsFrom http://www.physicalgeography.net/fundamentals/8q_1.html09/30/2002 12.215 Modern Naviation L07 12Magnetic variations• For dead reckoning variations in the magnetic field and compass also need to be accounted for • Major changes:– For compass: Deviation is a local correction to compass because of nearby objects (important on a ship)– Magnetic field:• Diurnal variations (tendency to point towards Sun) — 2-5’• Annual variations — 1’• Secular variation (due to changes in dipole field) — 5-10’/yr• Local attractors (potential problem on land)09/30/2002 12.215 Modern Naviation L07 13Sextant• Basic instrument for measuring altitude or elevation angle to celestial bodies.• Schematic of sextant: http://www.tecepe.com.br/nav/inav_c12.htmSmall mirror is half a mirror so that direct ray and reflected rays are both visible.09/30/2002 12.215 Modern Naviation L07 14Student SextantThis is the sextant we will be using for making measurements.Scales are read through a combination of a micrometer wheel and a vernier.09/30/2002 12.215 Modern Naviation L07 15Scale readingReading on sextant is 45 deg 13.6 minutes45 degs (main scale)13’ (micrometer)0.6’ (venier)09/30/2002 12.215 Modern Naviation L07 16Scales• Micrometer scale is a method a turning rotation in to small displacements (basically a screw drive). One full turns moves scale a set amount. The amount of the turn (angle between 0-360deg) can then be used to interpolate between graduations• Vernier scales provide another method of interpolating between graduations.• Example JAVA program:http://www.phy.ntnu.edu.tw/java/ruler/vernier.html09/30/2002 12.215 Modern Naviation L07 17Vernier scales• The idea of a vernier scale is to make a scale that has N markings in the same distance as N-1 markings on the original scale. The fractional difference between the scales sets the scale that the vernier reads:So if N=10, then 10 graduations on the vernier take up 9 markings on the original (see note)From http://www.tpub.com/math1/7e.htm09/30/2002 12.215 Modern Naviation L07 18Corrections needed for sextant measurements• Basic sextant measurement is to measure the elevation angle of the sun at its highest elevation and to note the time this occurs.• Generally, this is done as series of measurements