| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
Hi,
Can anyone here provide me with the formula of a RHUMB line between any
two (lat,long) points on the surface of the earth?
I have the great circle formula, but need the rhumb line distance. I
used to have this formulae about 5 years ago but I cannot find what I
did with it (came from the Ti-59 Navigation program).
My math is no longer up to trying to derive either of these formula so
would appreciate your responses.
Thanks
Peter
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1835.1 | AUSSIE::GARSON | Hotel Garson: No Vacancies | Tue Jan 25 1994 01:41 | 6 | |
re .0
I hadn't even heard of Rhumb line so I looked it up in the dictionary
which said that "rhumb" means "loxodromic" (enlightening, huh?).
Recursive use of the dictionary gave "making oblique angles with all
meridians". I guess you need to pay a visit to the library.
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| 1835.2 | try this off the cuff derivation | 3D::ROTH | Geometry is the real life! | Tue Jan 25 1994 13:16 | 40 |
If you stereographically project the globe onto a plane, then
a loxodromic spiral is just an exponential spiral in the plane.
To stereographically project, put the south pole of the globe
at the origin of the plane and project points on the globe onto
the plane from the point at the north pole. (A nice feature is that
all plane points at infinity wind up at the north pole - this is
the one point compactification of the complex plane.)
In polar coordinates in the plane, let (r1,theta1) be the first
point, and (r2,theta2) be the second point.
We know r2 = r1^k for some exponent k, so k = log(r2/r1).
We also reqire that
(theta1 - phi)*k = theta2 - phi
for some phi, so
phi = (k*theta1 - theta1)/(1-k)
And that gives you the parameters for a loxodoromic spiral in the
plane between two points.
I'm pretty sure the way the navigation formula is derived is
to map this back onto the sphere. The longitudes are just the
theta's above, so the only problem is to get the r's from the
latitudes.
By trigonometry the r's are proportional to (you only need the ratio
above...)
r = 1/tan(90-latitude)/2)
You'd get intermediate points no the rhumb line by applying these
formulas with intermediate values of k and mapping back to
latitudes from the r's.
- Jim
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