| Author | Message | ||
     Ted Lavino Moderator Username: tlavino Post Number: 117 Registered: 01-2006 |
I've found a fairly approachable introduction to the concept of a loxodrome (the technical term for a rhumb line) at http://www.cwru.edu/artsci/math/alexander/mathmag349-356.pdf complete with formulae for computing both great circle and rhumb line courses. However, for our purposes I did an experiment. I created a waypoint on the Makapuu Point Light on Oahu from my house. My Garmin GPSMap 76 has that waypoint at 2,238nm at 261T. CE on the other hand has it at 2,244nm and 251T. Looking at the route in CE, it appears to be a rhumb line. I also plotted a great circle route in Visual Passage Planner (http://www.digwave.com). The initial course given was 261T, duplicating the GPS bearinhg. The distance is 2,234nm, 4nm less than the Garmin GPS. I would summarize at this point that the GPS actually gives great circle routes, whereas CE gives rhumb line routes. I know that Nobeltec's VNS has a separate menu item to generate a great circle route. I don't seem to find that feature in CE. For those of you interested, I've uploaded some reports from Visual Passage Planner. Note that the great circle course changes along the route, and VPP gives you courses based on any increment you would like (I left it at the default of 100nm segments). The little dots all over the map are locations of wind and current rose information gleaned from Pilot Charts. In VPP you can scroll around the map over these wind/current roses to see the expected average current and wind speeds for that particular area-very cool if for example to get you started in trying to pick a route around the Pacific high going to HI from the mainland. | ||
| David Sheriff Board Administrator Username: admin Post Number: 305 Registered: 01-2004 |
Well, I just answered my part of the question by looking in Bowditch chapter 22 which gives all the basic navigational calculations. You also need reference to chapter 24, The Sailings, which is the collective term for mathematically solving navigational problem at global distances. At "short" distances, there is no practical difference between a rhumb line and a great circle route. | ||
| David Sheriff Board Administrator Username: admin Post Number: 304 Registered: 01-2004 |
Rather than tell you what I believe is true, which is not very authoritative, let me expand the question. What are the mathematics for plotting a course between any two points? What function generates the course given the endpoints as inputs? I'm sure there are a slew of programmable calculator based navigation programs based around this math, I just haven't spent any time digging up the references. A neighbor who is just retiring as a civilian engineer working in US Naval research asked me if I knew the answer. He ran across the problem years ago and said that he found a function in Cobol or some other early language that kicked out either answer. Now he needed it again and couldn't find it. | ||
| Ted Lavino Moderator Username: tlavino Post Number: 116 Registered: 01-2006 |
I've been wondering for some time whether the bearing to a waypoint given by either a chartplotter application or GPS is based on a Mercator or Gnomic projection, i.e. is it a rhumb line or great circle? For instance if you're in Dana Point and create a waypoint in Hawaii, would the course you follow to that waypoint be a great circle route? |
