Great Circle vs Rhumb Line Routes

We use qtVlm to compare the distance saving with a great circle route over a rhumb line route as a function of latitude and distance. As a guideline the saving is only significant when both departure and destination are at higher latitudes and the total distance between points is more than 2,000 nmi or so. Not to mention that a sailing route is usually determined by the wind pattern more so than the geometry, and the fact that a great circle route at higher latitudes often reaches up into the ice… at least for as long as there is any ice left!

[@chrispelon6812]

I am curious what you meant by “we’re assuming spherical earth“.

[@StarpathNav]

Most or many books on cel nav or ocean sailing do a great circle computation using a spherical earth of a specific radius that leads to 1' of Lat = 1 nmi. ie it is assumed that the circumference of the earth is 360 x 60 mi and from c = 2 pi R you find that radius. But the earth is more an oblate spheroid, ie beach ball compressed down a bit at the poles. In this real earth the intersection of plane and earth through the center is not a circle in general. So that is the detail hinted at. I am working on a short video to illustrate this and explain a common compromise solution. Thanks for noting this.

[@aklearns544]

Thank you so much for this video! I have a question! If someone lives in Toronto and they want to Face Mecca… should they pray towards the rhumb line bearing or the great circle route initial bearing?

[@StarpathNav]

The great circle is the direction to the target, but beyond that i do not know the answer to your question.

[@aklearns544]

@@StarpathNav I guess I should rephrase my question. If one is taking the great circles initial heading will he reach the target without having to steer?
The reason I’m asking is because in the example I provided , the great circle has an initial heading of NE. If you were to continue walking from that initial heading (now throw your compass away at this point) without steering, you would end up in Ireland if coming from Toronto. Even in perfect conditions(air traffic , wind etc) , planes have to steer right to go to a target that is south of the initial location.

[@StarpathNav]

@@aklearns544 No. to follow a GC route requires constant heading changes to keep you "pointed toward the mark." On a RL course you get there without steering (ie constant heading), but only as you approach the destination at the end are you actually pointed toward the mark.