Re: Loxodromic Distance Formula?

Dr Distance wrote:
> What is the formula for loxodromic ("Rhumb") distance.

If we approximate the earth as a sphere of radius R, then it's pretty
easy. The loxodromic distance between latitudes A1 and A2 (in
degrees) with constant bearing B will be
(pi R / 180) |A1 - A2| sec B.

This formula makes no sense for B = 90 or 270 degrees, because
latitude never changes in that case. In that case between longitudes
O1 and O2 at latitude A the distance is
(pi R / 180) |O1 - O2| cos A.


It is also possible to find loxodromic distances between two points
given by their longitude and latitude. I say use the plural because
there will in general be infinitely many such distances, each
corresponding to a different loxodrome that passes through the two
points. These solutions can be generated by adding or subtracting
multiples of 360 degrees to or from O2.

When A1 != A2, you can use
tan B = (O2 - O1) / (ln tan (pi/4 + (A2 - A1) / 2)),
and substitute into the first formula using
sec B = sqrt(1 + (tan B)^2).


- Tim
.

Relevant Pages

  • Re: GPS for range testing radio devices?
    ... sorts of distances *in feet*? ... compute line-of-site distances between two points on the ... The calculations are quite easy. ... One minute of latitude is one nautical ...
    (comp.arch.embedded)
  • Re: GPS formulas
    ... > degree to correspond 111.11 km and multiply the east-west ... > difference with the cosine of the avreage latitude ... the average latitude of the two points, and then use Pythagoras. ... distances, but doesn't work too well near the poles or over very large ...
    (comp.arch.embedded)
  • Re: Finding nearby zip codes (or maybe area codes) programatically
    ... Bill H wrote: ... Mileage differences between the same two longitudes ... are different depending upon the latitude. ... distance of these records to see if they are within 100 miles of the ...
    (comp.lang.php)
  • Re: How to get around missing DTEDs..
    ... for the latitude and longitudes you need. ... that looks like the file boundaries. ... FROM NIMA DTED1" looks like latitude and longitude coordinate ...
    (comp.soft-sys.matlab)
  • Re: Distance formula from Long/Lat Coord
    ... Convert the latitudes and longitudes to radians, ... Let LHA be the difference between the two longitudes, ... Then the sine of the distance angle between the two points, ...
    (microsoft.public.dotnet.languages.vb)