You know what? It does matter whether the course is true or magnetic because of magnetic variation. While the compass may stay on a constant 45 degrees, the true course will vary quite a bit, especially so in the higher latitudes.
From a pure mathematics viewpoint, it doesn't matter, but in the real world, it does. One of the drawbacks of relying solely on models.
I would fly a great arc thru the United States so that I would be over land as much as possible and more specifically, friendly territory.
No Russia, No China, No Africa, No Middle East, No Central America.
Paul in PA, post: 395155, member: 236 wrote: RFC,
Sorry,
If you fly at 45å¡ true you will eventually have a wingtip over the pole and after a few more laps you would be over the pole.
If you started at 45å¡ on a great circle route one would be continually changing the true direction.
It is simple Geodesy, but then again, you do not have a formal education.Paul in PA
True enough (in the case of geodesy), but the question was asked in the context of aviation. Try setting (and leaving) a gyrocompass to 045 and get to the pole from anywhere on the equator. Won't happen.:)
MathTeacher, post: 395164, member: 7674 wrote: Constant bearing courses are rhumb lines, or loxodromes. On a spherical earth, they lead to a pole if followed far enough. It doesn't matter if the course is, say, 45 degrees true or 45 degrees magnetic; both will ultimately to to a pole, but they will follow different tracks.
Look here for more information: https://en.wikipedia.org/wiki/Rhumb_line
The result on an ellipsoidal earth is left as an exercise.
But not the same pole, North Geodetic Pole or North Magnetic Pole.
Paul in PA
Paul in PA, post: 395178, member: 236 wrote: But not the same pole, North Geodetic Pole or North Magnetic Pole.
Paul in PA
I think that maintaining a 45-degree magnetic heading would create an erratic track as one proceeded north and passed through many different changes in declination. At some point, the compass would become unreliable and the true heading would be largely unknown.
My assumption was that declination would remain constant so that, if a magnetic heading of 45 degrees was a true heading of 50 degrees at the point of departure, that relationship would be maintained. Were that true, the track would still lead to the geodetic pole.
Hardly useless information. I gave a numerical example on another site years back and some geodetic programs would not solve for the shortest
distance. This is basic geodesy that Loyal gave the answer to first and its also interesting to note that George Thien (Captain, U.S. Army Corps of Engineers; at the time) in 1967 at Ohio State Univ. his Thesis for his Masters degree was " A solution to the Inverse problem for nearly-Antipodal Points on the Equator of The Ellipsoid of Revolution. Some Authors even after 1967 do not have the antipodal solution in their inverse program ( see Pittman, Surveying and Mapping
Vol. 46, No. 1, March 1986, pp. 47-54).
JOHN NOLTON
I don't think it matters I seem to remember a similar question asked years ago. If considering mileage you can fly N,S,E,W, the mileage is almost the same.
I am rethinking because of the oblate ellipsoid shape it may be shorter to go N or S.
Too much wine last night
Just a quick-n-dirty calc (John will probably be back with the answers to the nanometer)
North-South = ~12,429.8 miles
East-West = ~12,450.7 miles
edit:
and of course the "down" = 7,926.4 miles
Loyal
Certainly, the "down" would be the quickest way. It's refreshing to see the things that people in other fields disagree on.
http://discovermagazine.com/2016/nov/journey-through-the-center-of-the-earth
Scott Zelenak, post: 395098, member: 327 wrote: Suppose I want to fly a plane from a mythical airport at the equator and 0 degrees longitude to another mythical airport at the equator and 180 degrees longitude.
Which direction should I fly?
Forward.
Scott Zelenak, post: 395098, member: 327 wrote: And why?
It takes too much effort to fly backward.
Flying that distance the earth's rotation would absolutely be a factor; if you were looking for the shortest time you'd want to go west. Assuming of course that the wind was the same - the last flight I was on from California to Louisiana had an 80mph (knot?) tail wind at altitude; obviously that makes a huge difference, I think the flight was an hour shorter than the one going out.
Global and cross country flights will follow or avoid the upper windstream to avoid as much drag as possible..
I've been on a flight where the pilot ordered everyone to strap themselves down because he was going to "punch it" to avoid being intercepted by a storm with strong cross winds. When he accelerated it was like launching a dragster, everyone was pressed against the seat and headrest.
Going to Asia from LAX it was clear and calm and we practically went due west just south of Hawaii at 35,000 ft.
On the flight back from China the path took us up to near 50,000+ feet and north to near Alaska and just offshore of Canada all the way to LAX to stay in the upper GulfStream.
I've learned to put my headphones on and try to sleep on flights.
A Harris, post: 395253, member: 81 wrote:
On the flight back from China the path took us up to near 50,000+ feet and north to near Alaska and just offshore of Canada all the way to LAX to stay in the upper GulfStream.
Wow. I didn't know the Gulf Stream went that far north in the pacific.:p
North of 42,000 feet... not sure if I've been up there. Of course, back in the '80s and 90's you had no way of knowing.
Scott Zelenak, post: 395098, member: 327 wrote: Suppose I want to fly a plane from a mythical airport at the equator and 0 degrees longitude to another mythical airport at the equator and 180 degrees longitude.
Which direction should I fly?
And why?
Any direction.
If you fly a 'straight' ground path then any direction you start off on should get you there. All the great circles heading off from your location will intersect again at a location diametrically opposite.
Rod Deakin has addressed the problem rigorously. You only have to read the first few paragraphs to get the gist. The rest of the paper provides the justification.
http://www.mygeodesy.id.au/documents/Loxodrome on Ellipsoid.pdf
MathTeacher, post: 395325, member: 7674 wrote: Rod Deakin has addressed the problem rigorously. You only have to read the first few paragraphs to get the gist. The rest of the paper provides the justification.
http://www.mygeodesy.id.au/documents/Loxodrome on Ellipsoid.pdf
If the question were 'which compass bearing must the pilot maintain?' then this paper addresses it. But I didn't get that from the original question. Flying a straight ground path shouldn't result in tracing a loxodrome I don't think. tracing a loxodrome would need constant steering. If the question intended an answer like this then, IMO, it wasn't stated clearly enough.
Right, Conrad. I didn't make that very clear. The first few paragraphs address RfC's correct statement that sailing due east or west would not take one to a pole.
The paper does not address the original question.
Scott Zelenak, post: 395098, member: 327 wrote: Suppose I want to fly a plane from a mythical airport at the equator and 0 degrees longitude to another mythical airport at the equator and 180 degrees longitude.
Which direction should I fly?
And why?
Summary:
1. Conrad's got it: Any direction at all, Maintain that direction (gyrocompass) until reaching the equator at the International Date Line.
2. Shortest time: West.
3. Shortest Distance: North or South
4. Most Scenic: ???
