Great circle navigation

[Sempati]

Example: inserting an origin Amsterdam (EHAM) and a destination Singapore (WSSS) in my GPS supported FMS, without waypoints in between, the FMS will calculate and draw on my MFD a great circle.

Initial heading 081.7 means I am pointing the nose of the aircraft towards Singapore.
As long as I do not refer to any compass or meridian, while keeping wings level I will - along the great circle - eventually reach Singapore.

Question: how does FMS keep me on track?

[Dont Hang Up]

I cannot speak for the specifics of your FMS but I can describe the general principle of maintaining a flight path profile.

This holds true not just for area navigation but beacon navigation such as VOR or even ILS glideslope/localiser.

The current position of the aircraft is continuously measured against the required flight profile. Any difference between the required profile and aircraft position is measured as a control error. The flight controls will be continually adjusted to reduce that error to zero. So a deviation to the right of the track will cause a left-turn input, to the left a right-turn input.

Control laws specific to the performance of the aircraft will ensure that these adjustments are smooth and properly balanced between the error becoming too large or, at the other extreme, the aircraft being over-controlled such that it is constantly see-sawing uncomfortably through the zero-error state.

In your specific case the aircraft is not so-much keeping itself pointing at Singapore so much as continually measuring its deviation from the great circle track line that the FMS has drawn on the map.

Others may argue the finer points to whether the FMS directly controls the aircraft or if flight-profile adjustment is processed through a further level of automation (the Flight Control Computer). However, as a basic principle, the above is valid.

[Sempati]

It's hard to imagine, but by keeping the wings level we will always fly a great circle (in a no wind environment).

By the same token, if Singapore had a NDB powerful enough to reach Amsterdam, by keeping the ADF needle on the nose, I would follow the same great circle (again, in a no wind environment, and ignoring other atmospheric disturbances).

But it's the calculated track that FMS uses as a reference along the flight, and adjusts deviations by giving instructions to FCCs.

Thank you for pointing my nose in the right direction.

[Dont Hang Up]

It's hard to imagine, but by keeping the wings level we will always fly a great circle (in a no wind environment).

You are correct of course. In that idealised World of you would only need your FMS to compute the initial heading (provided this heading was accurate to at least 3 decimal places for the route length!). After that you could switch off the FMS, set the autopilot to 'wings level' mode, sit back and relax.

It is perhaps even more startling to recognise that if you set off from Amsterdam going due East, you would end up in Western Australia!

[rogerg]

It is perhaps even more startling to recognise that if you set off from Amsterdam going due East, you would end up in Western Australia!

Am I thick, I dont get it. Please explain!!

[cossack]

Play with this:
Great Circle Mapper (http://www.gcmap.com/)

[Dont Hang Up]

It is perhaps even more startling to recognise that if you set off from Amsterdam going due East, you would end up in Western Australia!
Am I thick, I dont get it. Please explain!!

A totally stable aircraft, ignoring all external influences, will not maintain a heading. Instead it will maintain a Great Circle. That simply means that it will fly a circle around the centre of the Earth.

What that effectively means is that if you set off going due East at 50 degrees North then by the time you get to the opposite side of the globe you will be travelling due East but at 50 degrees South.

[megan]

you would end up in Western AustraliaNot even, you'd miss Australia completely by about 360 miles south.

[cossack]

No, really, you would. CVQ is Carnarvon, WA which is about 900km north of Perth.
Great Circle Mapper: AMS-CVQ (http://www.gcmap.com/mapui?P=ams-cvq)

[megan]

My apologies, you are of course correct.

[merch]

I think there are some misconceptions in the posts above .

A great circle is a circle the plane of which passes through the centre of a sphere, if it doesn't it is a small circle.

If an aircraft flies due east (true) at 50deg north it will continue at that latitude until it reaches its original position after flying around the world. (ignoring fuel).

To fly a great circle route the course flown must be adjusted either continuously or at preset intervals. At sea the course would be adjusted every 5deg of longitude, but with the fancy electronic gizmos the course is continually adjusted.

For example if flying London to Perth the initial course is 93deg T final course is 133deg T.

Hope that that helps.

[Dont Hang Up]

merch

I think you are describing the way an aircraft will really maintain a great circle. This is because in any real situation aircraft lateral navigation is based on maintaining a heading or track, not on maintaining absolute, straight-line stability.

The scenario of total stability, with no external influences is totally theoretical and never to be achieved in real flight. However such a flight would follow a great circle.

The simple Newtonian principle of continuing in a straight line unless made to do otherwise by an external force applies here. The only external force is gravity (we have ideally removed all of the others) and that acts towards the centre of the Earth. Our theoretical aircraft could no-more maintain a latitude under these circumstances than could a satellite in orbit.

If it helps, think about an extreme example: An aircraft at 89.9N flying due East. Now 89.9N is a circular track just 12NM in diameter. It is then relatively easy to visualise that the aircraft will be in a continuous banked turn to maintain that heading. Allowed to fly straight and level the aircraft will depart 89.9N pretty much immediately. The same will apply at any other latitude (other than 0 degrees) but clearly the departure from heading will be more gradual.

[Sempati]

Which brings me back to my original post:

Flying from Amsterdam to Singapore (or to whichever longer distance destination), a compass (magnetic or IRS generated) is only a disturbing instrument.

FMS calculates an orthodrome (a part of the great circle) and commands my FCCs to stay on that line.

Charles Lindbergh, flying from New York to Paris, had indeed to change his heading every 100 miles or so. Starting with 054 and ending with 112 (I don't know the variation at that time, AD 1927).

With today's fancy electronic gizmos we don't have to do this anymore. Just stay on the line, as if it was painted on the ground!

[Tinstaafl]

Merch, to *maintain* an Easterly heading at your given latitude will require the aircraft to adjust its heading. Think of the convergency of the meridians at latitudes >0deg. However, the original condition was for the aircraft to *start* with an E. heading - and then continue without adjustment, so it no longer adjusts its heading to keep an angle of 090deg w.r.t. each meridian.

[merch]

Thanks gents for the explanations. I was indeed looking at it from a practical point not theoretical.

The part I still don't understand is why the aircraft follows a GC track rather than a spiral.The satellite example is clear as the only forces are gravity and the initial forward motion. Perhaps with the example of plane I should be thinking more satellite.

It must be old age, I first did GC theory too long ago.

[compressor stall]

ISSTracker ~ Real-Time Location Tracking of the International Space Station (http://www.isstracker.com)

See the sine wave pattern? That's the satellite travelling in a straight line. It appears curved for the same reason you can't lay an entire orange peel flat.

[Dont Hang Up]

The part I still don't understand is why the aircraft follows a GC track rather than a spiral.

This is just another "ideal" assumption that the Earth's rotation can be ignored.

If we assume a completely stable atmosphere that is fixed to the rotation of the Earth then this is probably very nearly true. The atmosphere will tend to "carry" the aircraft along with the Earth's rotation. This is the major difference between our theoretical, perfectly stable aircraft and a satellite. The satellite is also flying a circle around the Earth but it is outside the atmosphere and the Earth is rotating beneath it giving the classic spiral (sinusoidal) track.

In reality there will still be some tendency for the aircraft to drift away from a perfect great circle due to Earth rotation. And so yes, a spiral. However I suspect the pitch of that spiral would be difficult to calculate, having to consider the viscosity of the atmosphere or some such. Well beyond my simple arithmetic!

So perhaps the old wisdom that an ounce of simplification saves a ton of explanation is well served here.