Mercator Sailing: Course and Distance

[VadimV]

(08-31-2018 05:46 AM)Dieter Wrote:  

(08-31-2018 02:15 AM)Gene222 Wrote:  I see what I am doing wrong. The course is 270 (due west) on a Mercator map. I was looking a polar map. I guess starpath.com online Mercator calculator was right.

For the record: my 35s program returns 1875,78 miles and a course exactly West, true course 270°.

By the way, the result 1875,4003 nm of the starpath.com Mercator Calculator simply is 180°·60·cos(80°). This is a simplified formula that ignores (!) the ellipsoid's eccentricity. That's why there is another factor in my same-latitude-formula – which returns the correct result.

(08-31-2018 02:15 AM)Gene222 Wrote:  I still have errors in my program. The Latitude difference for the above problem is 600' and the Meridional parts for point 1 and 2 are not the same.

This really sounds like there are errors. ;-)
For 80° the meridional parts (WGS84) should be 8352,48.

Your results of –3456,8203 and –4507,4040 are the meridional part values for latitudes of –50° and –60°, respectively. Maybe this helps finding the error.

(08-31-2018 02:15 AM)Gene222 Wrote:  My procedure for East-West courses needs to be cleaned up, which should be easy to do.

I can't read your program (no Prime here), but from what I see when I open it in a text editor the program distinguishes various cases for different hemispheres. For instance in one case the absolute values of the meridional parts are added. I don't think this is required – the sign convention handles this automatically. Try it.

Here is the way I do the calculation, in pseudocode. I hope I got it right. ;-)

Code:

e=0,08181919...

M1=Meridionalparts(lat1)    
M2=Meridionalparts(lat2)
DMP=M2-M1

dlong=long2-long1
if dlong < -180 then dlong=dlong+360
if dlong > +180 then dlong=dlong-360    // edit: corrected this line

dlongminutes=60*dlong
dlatminutes=60*(lat2-lat1)

if DMP=0 then
   course=0
   distance=abs(dlongminutes)*cos(lat1)*(1-e^2*sin^2(lat1))/(1-e^2)
else
   course=arctan(abs(dlongminutes/DMP))
   distance=abs(dlatminutes)/cos(course)
end

Finally the true course is calculated. I do it wih the 35s "ARG" command which returns something like ATAN2 in some programming languages, a quadrant-adjusted angle (0...180 for Q1 and Q2, 0...-180 for Q3 and Q4, in this case add 360°), and it also works for DMP=0. You'll know how to do it on the Prime. ;-)

Dieter

Dieter,

Thank you for this. Using your equations (in Excel) for MP and dLon when MP=0, namely:

MP = 60*180/PI()*(ATANH(SIN(RADIANS(Lat)))-0.081819190842622*ATANH(0.081819190842622*SIN(RADIANS((Lat)))))

dLon = Distance/(COS(RADIANS(Lat))*(1-0.081819190842622^2*SIN(RADIANS(Lat)^2))/(1-0.081819190842622^2))

and an e value per WGS84, I get a strange dLon value when traveling E/W along the equator. For a course of either 090 or 270 and a distance of 600nm I calculate a dLon value of 595.98337. Shouldn't this value be 600 (i.e., 10 degrees of Lon)?

Thanks in advance for your assistance.

Vadim