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    Re: Mercator vs. Great Circle Charts
    From: Richard B. Emerson
    Date: 2001 Aug 29, 10:04 AM

    Young, Derrick writes:
    [...]
     > 1. Can true direction be determined in the same manner for all locations on
     > a
     > Mercator chart?  Yes - that is what the compass rose helps you with.  How
     > about on a great circle chart?  Again, yes.
    
    The question is unclear to me.  What is meant by "true direction"?  Is
    this the course to be steered or just a bearing?  A quick walk through
    Bowditch and the discussion of gnomic projections or "great circle
    charts" will be helpful here (Chapter three - Bowditch is available
    online from NIMA - http://pollux.nss.nima.mil/pubs/ - Bowditch is
    Pub. 9, The American Practical Navigator - and also at
    http://www.sailingissues.com/bowditch.html).
    
     > 2. How is the compass rose used on each of these charts?  The compass rose
     > shows a lot of information.  It provides you with the true rose (the outer
     > ring), the next ring in the compass rose provides you with the magnetic
     > heading.  This is what your magnetic compass should read if there are no
     > other external influences (but there are - that is why you also have a
     > deviation table for the boat).  You can remember all of this by the TVMDC
     > formula - True + Variation (from the nearest Compass Rose to the area you
     > are working) gives Magnetic plus Deviation (unique to your boat/ship) gives
     > Compass.
    
    This holds for charts over relatively small areas but a compass rose
    for a nearly global chart has little value beyond transferring lines
    of bearing and azimuth.  Large charts (e.g., ocean charts) have
    several compass roses to indication changes in magnetic variation but,
    for gnomic charts, this is a problem.  The question, as asked, is vague.
    
     > 3. If I were to draw a straight line between two points (say Tokyo and Cabo
     > San Lucas) on both a Mercator chart and a great circle chart, would either
     > straight line represent a great circle?  Yes - both are.
    
    No, the one on the Mercator chart is a rhumb line and not a great
    circle (see 4 below).
    
     > 4. Given the straight line drawn between Tokyo and Cabo San Lucas (see
     > above), which chart, the Mercator or the great circle, would give me the
     > shortest route between these two points?  By definition, a great circle
     > route is the shortest sailing route.  The thing to remember here is that the
     > Mercator chart is most accurate at the middle latitudes, so I would expect
     > the Mercator chart to provide a longer distance than a great circle chart.
     > But the sailing direction would be the same.
    
    The part about "middle latitudes" is not, strictly speaking, correct.
    A Mercator projection can be centered on any degree of latitude and,
    in fact, this is how most charts (although using a modifcation of
    Mercator projection) are drawn.  So, any Mercator chart is at its most
    accurate at the *chart's* middle latitude.  See Bowditch (chapter three)
    for more on this.
    
    As to a straight line on a Mercator chart and one on a gnomic chart,
    they are *not* equivalent.  Refer to Figures 309c and 309d in Bowditch
    for a demonstration of the difference.
    
     > 5. Would sailing a great circle course always be the best way to travel
     > across the ocean, or would ships have to take into consideration unfavorable
     > winds, currents, or storms that might cause a delay?  Any navigator must
     > apply the general prudence rule and take into account those items that will
     > influence their voyage.  The thing to remember here is that there are three
     > phases to navigation, planning (good old DR) the whole voyage - this is
     > where you lay out the overall course and intended stops.  The next is the
     > detailed planning, where you will consult the sailing directions, current
     > information, weather forecasts and other external influences (like ice
     > flows, etc.) and then make detail corrections that you may need to make your
     > intended destination.  The last is recording what course was actually
     > steered, speed actually made turns for and use this to determine where you
     > actually went.  This will then require you to redo the detailed planning for
     > the next step of the voyage.
    
    This question speaks to the issue of shortest route (a great circle is
    the shortest path on the surface of a sphere) versus fastest route.
    The difference comes practical issues such as weather, ocean currents,
    etc. to say nothing of a great circle route passing over land.  Even
    on a trip as short as Newport, RI to Bermuda, there may be time
    savings in how one approaches the Gulf Stream and uses warm and cold
    eddys to speed up the trip or avoid being slowed.  The short answer, a
    great circle route is the shortest but, practically speaking, not
    always the fastest route.  The answer to question 6 addresses this
    issue.
    
     > 6. Do most large ships today use computer assistance to help them choose the
     > best course across the ocean?  Yes they do.  They use GPS, LORAN, and some
     > still have the old SATNAV system.  They also use RDF (radio direction
     > finding) - but you normally see this on the older smaller ships.  They also
     > use celestial navigation and the good old DR plot.
    
    I responded to this question earlier but, recapping, there are a
    number of computer-based routing systems including some available at
    the consumer level.
    
    Rick
    S/V One With The Wind, Baba 35
    

       
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