I am trying to figure out how to calculate a rhumb line course between
two airports. Lets say, for example, Austin 30.194 -97.670 and San
Antonio 29.534 -98.470. What equation should I use. And please not a
generic equation but actually what I would type in excel. |
Request for Question Clarification by
mathtalk-ga
on
31 Aug 2004 04:36 PDT
Hi, utrico-ga:
Would it suffice to calculate some variable number of points along the
"rhumb line course" between the two airports? I guess I have in mind
that one might write a function in Excel VBA which returns an array
formula containing latitude and longitude for a prescribed N
intermediate points.
Alternatively perhaps you'd like a formula which, given a longitude
between the two airports, computes a latitude.
Note that the rhumb line, if extended beyond the endpoints
corresponding to the airports in your case, becomes a sort of spiral
path around the globe.
regards, mathtalk-ga
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Clarification of Question by
utrico-ga
on
31 Aug 2004 09:16 PDT
Well, I actually got what I wanted to work last night but my formula
is pretty ugly and I am not sure I trust it yet. I think what was
confusing is that I did not want a whole course, just an initial
course or heading. So between those two airports, the initial heading
should be 046 degrees. I will post my equation below and if you have
any suggestions on that, I would appreciate it. One thing that I know
would help is if I did not have to type radians() all the time. I
imagine I can wait or do something towards the end of the equation to
convert radians to degrees or vice versa but I was not sure.
As far as returning a number of points along the route. I would love
that. That would allow me to calculate a lot more things that I was
trying to figure out, like airports nearby along the way and stuff
like that. So if you could tell me how to do that too, that would be
great.
Here is my ugly equation:
=(IF((RADIANS(D4)-RADIANS(D3))>(RADIANS(D3)-RADIANS(D4)),ATAN2(LN(TAN(RADIANS(C4)/2+PI()/4)/TAN(RADIANS(C3)/2+PI()/4)),MOD(RADIANS(-D3)-RADIANS(-D4),2*PI())),6.283185-(ATAN2(LN(TAN(RADIANS(C4)/2+PI()/4)/TAN(RADIANS(C3)/2+PI()/4)),MOD(RADIANS(-D4)-RADIANS(-D3),2*PI())))))*180/PI()
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Request for Question Clarification by
mathtalk-ga
on
31 Aug 2004 12:12 PDT
One suggestion: The "IF" test could simply be D4 > D3. You shouldn't
have to worry about conversion to radians or about "wrap around" if
you only plot courses in North America (but beware the Bering
Straits!).
-- mathtalk-ga
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Request for Question Clarification by
mathtalk-ga
on
01 Sep 2004 02:21 PDT
Just to clarify, I only meant that the IF test could be simplified,
not that this would affect (directly) the rest of your formula. The
trigonometric functions in Excel do expect values in radians. You
might simplify the appearance of your formula by setting up extra
cells that contain the conversions of C3,C4,D3,D4 to radians.
The formula you've given looks like one that assumes a spherical shape
for the Earth. A somewhat more complicated formula can be based on
"eccentricity" of the shape, i.e. an ellipsoid rather than a sphere.
regards, mathtalk-ga
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