Great Circle

[Jeroen D]

This might have been discussed before, but I could not find anything.

Does the FMC follow an exact great circle, or is this some approximation? e.g. multiple straight segments or something similar?
I am reading up on it in Bill Bulfer FMC User's guide, but it doesn't say specifically, although the suggestion is it would be a collection of straight lines, changing heading every so often?

I checked, the Bulfer FMC guide is from 1991! So things might have changed, of course.

Thanks

Jeroen

[Hardy Heinlin]

The FMC calculates exact great circles. It's based on a formula with many sine and cosine functions; so there's no sequence of small straight segments. Relevant is the course angle at the starting point of a course (at the aircraft nose or at a waypoint). The rest of the line is irrelevant for the current course calculation.

On the ND, however, there are and there must be straight lines, because the ND uses a stereographic projection where the center represents the aircraft position (map mode) or a waypoint (plan mode). All bearings and radials refer to the projection center, and from that perspective, all outgoing lines are straight courses. Abeam legs may be curved by DME arcs or RF arcs, or may be divided by waypoints to set multiple small straight legs. But those are so short you wouldn't see any difference to a great circle curve anyway.


Regards,

|-|ardy

[Jeroen Hoppenbrouwers]

I don't know the details under the hood, but it may be that there also is a steering heading rounding function. Heading references from IRS are precise to a few digits behind the point, but steering headings may not be. This would mean that the FMC may calculate exact headings that vary every second, while the steering instructions are rounded and only flip every so often, leading to flying straight lines. But likely not noticeable unless you pay attention during long boring crossings.


Hoppie

[Hardy Heinlin]

I guess this is only the case in HDG SEL mode, not in HDG HOLD, LOC, ROLLOUT, TO/GA or LNAV -- particularly not in NG FMC LNAV with its higher precision requirements.


|-|ardy

[Jeroen D]

Thanks for the quick and detailed responses.

If I would fly say an oceanic track or a leg in a airway, would the FMC fly a great circle between the waypoints of which that track/leg consists?

Jeroen

[Jeroen Hoppenbrouwers]

That is the design, yes. Otherwise there would be issues with very long legs. Or direct-tos that cut of 1000 nm.

[Hardy Heinlin]

The FMC provides 3 types of steering angles. The type is indicated on the LEGS page in small font above the name of the related target waypoint.

HDG = FMC maintains a specific heading; if that isn't 090 or 270 on the equator, and not 000 or 180, and there's no crosswind, then it's not a great circle.

TRK = Same as HDG plus wind correction angle.

(no indication) = That's the CRS mode; that's a great circle. These are usually airway legs.