The Earth has a flatenning of about 1 in 300. So this is the rough size of maximum distance errors you can expect by assuming the Earth to be a sphere rather than an ellipsoid. For example, the distance between Washington D.C. and Los Angeles is 3,711 km (2,004 nautical miles) assuming the earth to be a sphere with a radius of 6371 km but 3,719 km (2,008 nautical miles) using the best fitting (WGS 84) ellipsoid. -- Richard Langley
On Thu, 16 Nov 2000, Fernando Cabral wrote: >Hello Richard > >Minutes after sending my previous message (should this always happen?) I found >a >page on the Internet which seems to give me what I need. > >I have checked it with some coarse calculations. Since I don't have my GPS >here with me, I can't compare the results I got with the GPS'. > >Nevertheless, they seemed right to me. > >Previously I had been using two formulae given by J. Meeus in his book >"Astronomical Algorithm" (if my memory is of any avail), one of which >he says is not very precise. They both have agreed very well with >the results given by the GPS. With the less precise I have obtained >results within 0,3% and with the more precise numbers are the same. > >Now, in this page by Fiona Vincent, it seems I found a still simpler >way to calculate both distances and azimuth. > >Can you give me an idea on what magnitude of error should I expect from them >(perhaps due to the Earth flattening)? > >Thank you. > >- fernando > >[Image] > > > > > >Richard Langley wrote: > >> On Thu, 16 Nov 2000, Fernando Cabral wrote: >> >> >Hello Friends >> > >> >It's been a long, long time since I last disturbed you with my novice >> >questions. >> >I was just acculating credits do be entitled to ask the following >> >question >> >that has more to do with navigation than any other thing: >> > >> >a) If I am using UTM coordenates, what is the easiest way to calculate >> > the bearing from point A to point B in the chart; >> >b) Same questions if am using latitude and longitude >> > >> >When using UTM I have come accross a solution that works but I must >> >confess I hate it because I don't think it is elegant and it takes a lot >> >of >> >time so I am sure there must be a better solution. >> > >> >For the UTM it is much simpler because I can always create a Pythagorean >> > >> >triangule whose sides are the difference of Northing and Easting of the >> >points, >> >so I have three sides and an angle. Now, if I make the origin point the >> >origen >> >of a Cartesian system I can find the Azimuth adding together the angle I >> >found >> >plus 0, 90, 180 or 270 if the destination point is on the first, second, >> >third or >> >fourth quadrant. >> > >> >I does work, but there must be a simpler way to do it. >> >> Nothing realy wrong with your approach but if you use the ATAN2 Fortran >> function (or the equivalent in other programming languages or the Cartesian >> to >> polar coordinate function on many calculators), you can specify the sign of >> delta x and delta y and the azimuth will then be automatically reported in >> the >> correct quadrant. >> >> >If what I have are the geographic coordinates it takes me much more time >> > >> >with the spherical triangles and I am never sure I've done the right >> >thing. >> > >> >I've read some books on celestial navigation and position astronomy. I >> >can see >> >the solution is there, but it does not seem I have the expertise to >> >convert all those >> >useful information in a simple formula for this specific calculation. >> > >> >And I feel very unhappy when I have to fill out a couple of pages with >> >ugly >> >calculations just to find out an azimuth I can easily find with a GPS or >> >with >> >a protactor and a map! >> >> The use of plane trigonometry to find distances and angles is an important >> feature of UTM. But for highest accuracies one has to be careful about the >> differences between geodetic and grid azimuth. See my article in the >> February >> 1998 issue of GPS World magazine for more details. >> >> -- Richard Langley >> Professor of Geodesy and Precision Navigation >> >> >Best regards >> > >> >- fernando >> > >> > >> > >> > >> > >> >-- >> >Fernando Cabral Padrao iX Sistemas Abertos >> >mailto:[EMAIL PROTECTED] http://www.pix.com.br >> >Fone Direto: +55 61 329-0206 mailto:[EMAIL PROTECTED] >> >PABX: +55 61 329-0202 Fax: +55 61 326-3082 >> >15? 45' 04.9" S 47? 49' 58.6" W >> >19? 37' 57.0" S 45? 17' 13.6" W >> > >> > >> > >> >> >> =============================================================================== >> Richard B. Langley E-mail: [EMAIL PROTECTED] >> Geodetic Research Laboratory Web: http://www.unb.ca/GGE/ >> Dept. of Geodesy and Geomatics Engineering Phone: +1 506 453-5142 >> University of New Brunswick Fax: +1 506 453-4943 >> Fredericton, N.B., Canada E3B 5A3 >> Fredericton? Where's that? See: http://www.city.fredericton.nb.ca/ >> =============================================================================== > >-- >Fernando Cabral Padrao iX Sistemas Abertos >mailto:[EMAIL PROTECTED] http://www.pix.com.br >Fone Direto: +55 61 329-0206 mailto:[EMAIL PROTECTED] >PABX: +55 61 329-0202 Fax: +55 61 326-3082 >15? 45' 04.9" S 47? 49' 58.6" W >19? 37' 57.0" S 45? 17' 13.6" W > > =============================================================================== Richard B. Langley E-mail: [EMAIL PROTECTED] Geodetic Research Laboratory Web: http://www.unb.ca/GGE/ Dept. of Geodesy and Geomatics Engineering Phone: +1 506 453-5142 University of New Brunswick Fax: +1 506 453-4943 Fredericton, N.B., Canada E3B 5A3 Fredericton? Where's that? See: http://www.city.fredericton.nb.ca/ ===============================================================================
