A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Antoine Couëtte
Date: 2018 Jan 8, 06:11 -0800
As complement to my post dated Dec 27th, 2017, and just by curiosity I dug out my [last millennium] student notes about the various airborne bubble sextant corrections.
In order to validly ignore the effects of ground speed magnitude variations let us consider here-after only constant magnitude horizontal ground speeds (e.g. GS = 457 Kts) in which only the Aircraft headings can change.
- When an Aircraft follows a Great Circle, only comes to play the Coriolis correction which is proportional to both the Ground Speed and to the Sine of Latitude. Hence the Coriolis effect is maximum at the Poles and zero at the Equator. The Coriolis Acceleration Tables are available and published in the Air Almanac and it is easy to verify that such Coriolis corrections are proportional to the ground speed itself.
- When an Aircraft follows a Rhumb Line:
- The Coriolis instantaneous correction is the same as above (i.e. no difference at all for an Aircraft having the same instantaneous ground speed vector and following either a Great Circle or a Rhumb Line, or any other curve actually). And:
- To the "general and always applicable case" of the Coriolis correction, an additional and specific Rhumb Line Correction is to be added. What is interesting to see is that such specific Rhumb Line correction is:
- Proportional to the square of the Ground Speed. And:
- Proportional to the sine of the Ground Speed Track, hence equal to zero for North and South tracks in which cases Rhumb Lines become Meridians therefore Great Circles. And also:
- Proportional to the Tangent of the Latitude, hence also equal to zero if Latitude stays at zero in which cases Rhumb Lines simply become the [Great Circle] Equator itself. Hence the Rhumb Line correction increases towards infinity when closing up from the Poles since it is proportional to the Tangent of the Latitude.
- My handwritten notes also indicate for that for such Rhumb Line case Air Navigators preferably use the published Combined Coriolis and Rhumb Line Correction Tables. Indeed, this point is fully covered in the "FAA NAV Course faa-h-8083-18.pdf" document mentioned by Gary in a subsequent post on a different nonetheless related topic (Re: HeadingSpeed-Acceleration-Error-Card-LaPook-dec-2017-g41054) on that same day.
- These Combined Coriolis and Rhumb Line Correction Tables are also interesting to study since - after carefully removing the Coriolis acceleration effects and after correcting the remaining figures for round-off errors - you can hands-on verify that such specific Rhumb Line Correction is proportional to the square of the ground speed itself as earlier mentioned here-above.