Aircraft position calculation

[budipro]

Hi all,

I have a question here:

How do you calculate an aircraft current position (latitude, longitude, and altitude) based on:
- the aircraft last position (latitude, longitude, and altitude),
- the elapsed time (now - last position time),
- the aircraft speed (knot), and
- the aircraft direction (stated using angle from north)?

Thanks a lot.

[FlyingForFun]

The easiest way of doing it is to draw a line on a map. Assuming that the aircraft speed/direction that you have are a ground speed and a track (rather than an airspeed and a heading) this is trivial.

Or are you looking for a mathematical formula that you can use? In this case, you can probably use some basic trigonometry, as long as you're not talking about huge distances and you're not too close to the poles. One minute of lattitude is one nautical mile. One minute of longitude is (cos lattitude) nautical miles. There's no need to worry about your altitude. Then just use the sin and cosine of the heading, multiplied by the total distance (calulated from speed and time), to work out the distance travelled east/west and the distance travelled north/south, convert from miles to degrees and minutes, and add to your starting position.

If you are travelling long distances (especially north/south) or you are near the poles it gets very much more complicated - I wouldn't know where to start.

FFF
----------------

[Fly Stimulator]

multiplied by the total distance (calulated from speed and time

Not forgetting to account for the likely difference between air speed and ground speed of course. :)

[FlyingForFun]

Yes. Hence my first paragraph:Assuming that the aircraft speed/direction that you have are a ground speed and a track (rather than an airspeed and a heading):D

FFF
-------------

[CSX001]

Assuming that what you really need is the maths rather than the waffle, you'll find it here:

http://williams.best.vwh.net/avform.htm

Charlie
x

[Circuit Basher]

FFF / Fly Stimulator - I agree that the 'classical' calculations are probably fair estimations, but when I first read budipro's question, for some reason, I started thinking that this will not give an exact answer. The map projection is, of course, an approximation (based on a specific projection technique, such as Mercator, etc). Technically, I would have thought that the precise answer requires calculation using Spherical Geometry (http://www.ga.gov.au/nmd/geodesy/datums/distance.jsp) and taking into account the altitude (as this will affect the circumference of the circle that the pilot is flying along).

For short distances / lower altitudes, this will not be significant, but for trans continental flights at the altitudes used by heavies, this must surely be factored in.

Maybe I'm barking up the wrong tree and will be shot at dawn for fundamentally misunderstanding all my PPL Nav training, but I'll risk it for a biscuit!! :D

[CSX001]

Unless he plans to fly a Satellite, the altitude won't make any real difference. All the spherical geometry you'll ever need and more is on the link I posted.

Charlie
x

[Fly Stimulator]

FFF, sorry, missed that on first reading. I must concentrate properly on PPRuNe and stop letting work get in the way! ;)


Charlie - Thanks for that link - I had it once but had lost it.

[FlyingForFun]

Charlie - I'm off to read your link now. Hope it's not going to do my head in too much!

Completely agree with Circuit Basher, by the way, about the "classical" solution only being an approximation, which is why I said it wouldn't work over long distances or near the poles. But a further thought occurs to me. Budipro specified that the aircraft's direction was given as an angle from north, implying that he's flying a rhumb line. But in the situations where "classical" maths breaks down (long distances or polar transits) you wouldn't do that anyway - you'd either fly a great circle, or for polar transits you may use grid navigation. In either case, your track will be far from constant, so the question isn't valid anyway! (Wonder if Charlie's link will address these issues.....)

FFF
-------------

[CSX001]

(Wonder if Charlie's link will address these issues.....)

You'd better believe it ;)

Charlie
x

[J.A.F.O.]

Erudite as your answers are I much prefer the answers that Budipro got on the Military Aircrew Forum.