Peter wrote:
I am sure it is quite impossible to construct a polynomial with a finite number of terms which would work at the poles
Yes, you are right, on a perfect sphere actually there is none apart from a constant one !
Mathematically, ZeroRoots , relies on the fact that the “sphere is not flat”, but it has nothing to do with the two poles tough, nothing special over there apart from being points that are stretched in the 2D projection 
Practically, you will find it hard to sell this argument to both flat earthners or less than perfect sphere guys…
What I meant was that at the poles you get a discontinuity which cannot be represented with a polynomial, but this is right at the edge of my understanding of maths
Yes, but you can take any arbitrary two points on earth call them poles and do the 2D projection and then interpolate, your polynomial should work everywhere except on those two points…
Qalupalik wrote:
Flying a constant track value will result in a loxodrome (rhumb line) which is typically inefficient over large distances. A track angle is nothing more than the direction of a tangent to the path measured at the position of the aircraft.
I do not get your point at all. Flying long distances (or close to the poles) with a constant heading is equally inefficient. That problem is unrelated to the track/heading distinction.
huv, I read your “track is what gets us where we want” as advocating for constant track values which is clearly an over-interpretation.
Airborne_Again wrote:
An interesting question is if we really need the compasses. Airplanes are always moving so there is always a GPS track.
Quite some GA airplanes are quite capable of not moving (with reference to the earth) in a 50kts wind. More relevant, other flying machines (e.g. helicopters) are able to not move.
Peter wrote:
AIUI every certified IFR GPS includes a means of calculating the mag variation from the GPS position, and this is how it can fly a “magnetic” track etc.If, or how often, this gets updated, I have no idea…
The Garmin G500’s AHRS’ magnetic variation database updates is bundled with aviation database updates. So if you install the latter from time to time, you get the former. Else the ICA contain a reference to “Section 1.9 of the G500/G600 AML STC Installation Manual” which would contain an alternative way to install magnetic variation database updates, but I don’t have that document.
I don’t find a reference of how GPS NAV units do it, but the same solution would make sense.
Yes; the low speed / strong crosswind / ground movement case is why one needs a heading and a GPS track alone is not good enough.
Products like TAS (traffic warning / TCAS) need the heading so you know where relative to the aircraft nose the target is. Helicopters for example are able to hover and thus TAS boxes installed in them must have a heading input (actually all the proper TAS installations have a heading input but for example the entry-level TAS600, IIRC, doesn’t).
Also, using a heading as the primary parameter (the “setpoint”), rather than a GPS track, in a control loop for flying a bearing gives you better performance because it can be determined more or less instantly, whereas GPS track involves a time lag. This is why aircraft autopilots, whether flying enroute tracking a GPS track, tracking a localiser, etc, use the heading as primary, and adjust it as required.
lionel wrote:
Quite some GA airplanes are quite capable of not moving (with reference to the earth) in a 50kts wind.
Indeed, but if the GS is zero, then the heading is irrelevant!
It is relevant if you want to produce an airport map, for products such as Safetaxi.
It is hard to use such a presentation if you cannot see which way you are pointing on the map. This is why Safetaxi works somewhat badly on a handheld GPS because there is no heading input; you have to start taxiing before you can see your direction.
It is like using a smartphone with a compass which is either buggered or has lost its magnetic calibration (like most of mine ) to walk somewhere… you cannot see which way you are walking until you start walking
I’ve just merged in an old thread of same topic.
