The maths is complex but plenty of references can be found on the www. And yes you do need degree level maths (which is why I cannot explain it even if I wanted to - I did maths at univ. but wasn't any good at it).

GPS works out heading and velocity using a different part of the position fixing algorithm, and it gets track and velocity calculated very accurately even if the position is not that accurately known.

As mentioned, there are GPSs which contain a conventional compass, either a traditional floating type one, or a solid state one. You can get wrist watches with such compasses in them - Tissot do one for example.

The confusion between HDG and TRK is probably just poor PPL training but the wider issue is the anal attitude towards GPS for so many years.

As an example or poor training, I have met so many pilots who think that the plane handles differently when flying with a tailwind v. headwind, etc.

ExSp33db1rd it can only show a heading relative to its own fore and aft axis, can it not ? If it isn't bolted along the fore and aft axis of the aircraft it won't show the aircraft heading

Nonsense. It doesn't have to be bolted to the aircraft at all. It has a compass needle, so if one aligns the lubber line with the fore aft axis of the aircraft (fairly easy to do with the mechanical bits already attached to the aircraft in that axis, then the needle does indeed point at magnetic north and the aircraft heading is shown under the lubber line.

Of course, it could have compass needle, which would point to magnetic North, but that's not the same.

As heading is relative to magnetic north in this example, then it is the same, all you need is a calibrated rose to show the relative bearing from magnetic north and the lubber line and there's your (magnetic) heading!

.. the track made good

Rubbish, TMG is the resultant track over the ground when a heading is combined with wind aloft and is effectively your track over the ground. The GPS map will show that whilst the lubber line (if the device is properly aligned) will show your heading.

Educate me.

I hope I have, else Google is your friend.

GPS works purely on position updating, which is determined by satellite triangulation. If you have travelled from point A to point B in a known period of time, then you can calculate the average velocity between the two points. This velocity has a magnitude and direction (ground speed and ground track). It is that simple.

It does..

Probably, if I understood it well enough, which I don't! But here's a go.

The Velocity problem is a step up in complexity from the Position problem.

Say with DME, we are familiar with how the distance readout from 1 DME gives us a position line (a circle in fact), 2 DME give us 2 possible positions and a 3 DME gives us an unambiguous position solution.

In GPS, we need 4 range spheres from 4 satellites to get 3D position fix and a solution for the clock error in the receiver.

Now let's go back to DMEs and the velocity problem

Instead of the DME range and unknown position, we look at the DME groundspeed readout S (to/from the station), and the unknown Track T of the aircraft and unknown speed G along that track (ie. T and G are the aircraft velocity)

The relationship between these is S = G cos a, where a is the angle between the track T and the bearing to the DME station.

You can see how the DME speed S gives us something analogous in Velocity terms to the DME position circle - for a given S, we could be flying right at the DME, in which case S=G and T=a, or we could be flying a bit away from it, in which case G is a bit higher than S and a is a bit more or less than T etc.

If the position of the aircraft is known, then it's fairly simple to solve for Velocity (G and T) with more DME stations and speed readouts - I think it takes 3 for an unambiguous velocity. If the position of the aircraft isn't known, then I'm not sure but I think with more stations it must be possible to solve.

Translate this to GPS and satellites moving about in 3D just as we did for the position solution: but what is the GPS equivalent of the DME's pulse method for speed? It's doppler. Your GPS knowns from the almanac the position and velocity of the satellites. It has an oscillator which generates the standard GPS L1 carrier frequency. It compares that with the L1 frequencies it's getting from various satellites to work out it's speed to/from each of those. It then solves for velocity using a method analogous to the above.

Of course, in the DME example, the same pulse data is being used for range and speed - so the velocity explanation above is just a way of doing the rate of change of position. However, the doppler method in GPS is inherently different from the GPS position data based on time-shift of the L1 signal - it's based on frequency shift. I don't really know in practice which boxes use which method, I suspect adavanced ones may use a combination of both.

brgds
421C

TRK (CoG) = TRUE HDG in zero wind of course ;). As charts reference TRUE north this is far more useful in reality than magnetic heading.

My Garmin 196 (and I suspect all Garmins) shows

Bearing
Course
Course to steer
Track


I've never understood the difference between Bearing and Course to steer.
ZA

No you're getting TRK and BRG mixed up.

Bearing is the heading to your next waypoint. Course to steer will attempt to get you back onto the track between your previous and next waypoints and then to your next waypoint.

Download this guide for a full explanation. Its got a lot of useful information about flying with a GPS.

My previous aircraft had a blue mountain EFIS system in it. This had it's own GPS map built in as well. This unit used an external magnometer (electronic compass) which had to be precisley aligned with the fore and aft axis of the aircraft but this was so that the primary flight display could show aircraft heading just as you would see on a compass. The GPS page still displayed track over the ground. I now have a Garmin 296 installed in my RV6 which does not have an external magnometer so it will only know track over the ground.

Interestling in my RV6 I have a vertical compass card which to be honest are not that accurate and a real pain to try and set up. On occasion when I have mentioned this to some people they have mentioned why don't I just align the DI with the GPS, so although I think it's quite obvious what the difference is between the GPS and the compass there are plenty of people who don't. Even when I explain it, it sometimes takes a while for the penny to drop. Not that these people are stupid in any way, they just hadn't quite thought about it enough.

I know some will say that this is why GPS is bad and can contribute to airspace busts but come on all modern GPS are moving maps and if air space is shown on your right then turn left a little untill you avoid it. I quite often let friends have a little go and show them on the GPS map any airspace near us and they are quite capable of steering the plane away without any knowledge of track, headings etc.

Just a shame I can't fit the new garmin 695 in my panel :(

See page 112 of your user manual.

As far as I can deduce:

Bearing is the track from your present position to the desired waypoint
Course is Spam-speak for 'Desired Track' - i.e. the track you'd planned to be on between the waypoint behind you and the next waypoint.
Course to steer is a recommended correction to recover to DTK by reducing track error, although I cannot find a good definition of precisely how Garmin compute this value. It is supposed to give you an 'efficient' turn demand, whereas 'TRN' is TRK-BRG, the angle to turn through to track direct to the desired waypoint. My guess is that Garmin continually generates a pseudo-waypoint somewhere ahead on your planned track and gives a turn demand to intercept it - perhaps so that the the triangle formed by this pseudo-waypoint, the next waypoint and your present position is an isosceles triangle, with the equal sides being from present position to pseudo-waypoint and from pseudo waypoint to next waypoint; thus CTS steadily reduces as you regain desired track?

I've now found out how CTS is computed:


The pseudo-waypoint is at point B, where dist AB=BC. CTS provides the track (or 'course' in Spam-speak) to steer to aim at B. As you fly towards it, point A (the perpendicular erected from present position to desired track) will change, so that the 'mid-point' B will also move, allowing a gradual track intercept.

Beagle,
Many thanks.
So course to steer will change as you get closer to C and just as you arrive at C you will be on the original course. Your explanation of using the 'halfway point' (which you never reach) clarifies how it does it.
The result will be a curved course arriving at C on the original heading.

By following the bearing to C you will follow a straight line directly to C but arrive pointing at the 'wrong' heading.

ZA

BackPacker,

You got me on a technicality. But here's the thing - velocities are calculated from position differences with respect to the satellites, rather than the solution of where on earth you are.


Beyond doppler shift, one of the neat technologies they came up with was to figure out the GPS solution in terms of the number of cycles of the carrier waves between the satellite and the receiver. And, they do this for both the L1 and the L2 frequencies, even though they can't use the military frequency to get the 'real' position information. Those clever devils. Novatel was one of the innovators of this technology back in the mid 90's.

GPS is all about using timing to figure out range from a satellite, then figuring out where the solutions considering all the satellites converge, or at least the closest guess. Like 421C says. Now, if you ignore the solution of where on earth you are, and use the GPS timing to figure out your rate of closure WRT the satellites, you can come up with a velocity figure even without great knowledge of where you are. That's my simplified explanation.

The position solution of where we are on earth tends to jump around because of errors either from the atmosphere, or selective availablity (like the bad old days). If you calculate your velocities directly from your time & distance to the satellites you take some of this error out of the calculation. GPS velocity tends to be a better measurement than absolute position.

-- IFMU

No problemo ZA - my pleasure.

My original assumption would actually have been easier to compute as the track to turn through would be simply (BRG-DTK). No need for pseudo-waypoint calculation and the values are continuously computed in any case. And it would allow resumption of desired track slightly earlier than Garmin's CTS does.

You can get a heading from two GPS but they have to be mounted a known distance apart usually along or across the long axis of the aircraft. We use a system on ships with a 2 metre baseline and gives us a heading accurate to better than 0.1°. If you had the antennae on your wing tips your baseline would be 10 or 14 metres apart and the accuracy would be way better. Both position fixes have similar errors due to satellite mistimings and atmospheric errors but if the bearing is calculated between the two antennae then that is extremely accurate. Unfortunately no one makes the units for GA aircraft.

The principle is correct, but unfortunately one rarely knows the winds aloft to any accuracy, because the forecasts are pretty poor (at common GA altitudes).

The way one normally flies is that one flies a heading, and one adjusts the heading so that one's actual track (displayed on the GPS) lines up with the magenta line (the desired track) on the GPS.

Then, from the difference between the track and the heading, plus any difference between TAS and GS, one can see what the wind aloft is. Usually this is very very obvious, at a glance.

I'll not engage in the discussion on Heading, Track etc as this seems to have been done to death here with mostly the right answers.

For those who are interested in how GPS derives Course over Ground (COG, track or whatever you want to call it) and speed over ground (SOG, speed) here is a (over) simple explanation.

As far as I know all aviation units use position based information to derive COG and SOG. Every second for hand-held units and five times per second for IFR certified units, the GPS unit works out a best estimate of where it is. The problem is that this position is just that, an estimate. Even if you are not moving the GPS position will be constantly moving (even if it’s just by a small amount) due to a range of erorr sources. This noise in the position data is very variable and requires complex filtration to derive COG and SOG. If there was no filter, the COG and SOG output would be very noisy (giving a jumpy display). Simply using a moving-average type filter does not work well in this type of application.

Using a very clever piece of mathematics called a Kalman Filter the unit then works out in what direction and how fast it has moved over a recent time period.

More by way of interest, some survey-grade GPS units as used by civil engineers surveyors etc. give centimetre accuracy using phase shift measurements of the carrier phase transmitted by the GPS satellites. Similarly, there are commercially available GPS units that very accurately measure speed using Doppler shift measurements of the carrier phase.

Fright level

Well, sort of. It would appear that your model of GPS - of which I know nothing - is relying on a representation of a magnetic compass needle - albeit maybe a computer generated image of a needle - built in to it, which seeks Magnetic North just like the old E2B that hung from the windscreen pillar of the Boeing 747, and has actually nothing whatsoever to do with orbiting satellites, or obtuse mathematical equations ? Is this right ?

If so, then it is no better than the old alcohol filled compass bolted in front of the stick of the Harvard, or hung upside down from above the windshield of some aircraft, and read with a mirror, and I agree that it doesn't need to be actually bolted to the fore and aft axis of the aircraft, just occasionally aligned with it by holding it in a wavering hand, which might occasionally get it spot on. The heading it depicts is relative to its lubber line, as you correctly say, but only if the its lubber line and the aircrafts lubber line are parallel will you know the aircraft heading correctly. No ?

If this is not the case, then we are back to the the original question - How Does A GPS Work Out Heading ? and the question was HEADING, not Track Made Good. ?? HEADING is relative to North, either True or Magnetic, not movement over the ground, which is what the GPS computes.

Knowing ones heading, and track made good, and groundspeed and airspeed, then one can work out the wind.

A GPS uses the satellites to work out where it is, then a few milli-seconds, minutes or whatever units it is programmed to accept, it works out where it is again - then Bingo ! it now knows which way it was moving, and what speed it has achieved between the two points over the time it has taken to make the two points, i.e. groundspeed, and you know what airspeed you were flying,and what heading you were maintaining, and so the rest is just maths.

Using a sextant in a Boeing 707 I would fix a position using the stars, maybe half an hour later I would fix my new position by the same means, and providing the pilot had maintained a steady compass heading, the difference between where I now knew I was, versus the position where I had worked out that I would have been had there been no wind ( or more accurately the forcast wind that I has applied ) - the Air Plot - provided the correct wind vector to apply to the next required track to arrive at the next turning point ( 'waypoint' in Yuppiespeak )

The basics of navigation are no different now, the only difference is that I might slave away for 7 hours, producing a 'fix' by sextant every 30 minutes - and barely have time for a coffee - whereas the GPS does it in a nano-second, and continuously,whereas I drew a graphical representation on a chart - and actually created a visible triangle of velocities that could be seen, and measured.

Not a lot new under the Sun - all that's new is the means by way the information is derived.

Thanx.

P.s. Between the sextant and the GPS was INS ( inertial navigation ). The INS couldn't work out where it was, it had to be told where it was starting from, after which it used acceleration changes to work out where it was next - and hence calculated the same formulas to reach the same results. The Powers that Rule Our Lives could turn off the satellites at a whim - then where would you be ? INS was totally self contained, the World could be destroyed by a Nuclear Holocaust between leaving New York and arriving overhead London, and the INS would calmly continue to navigate blissfully unaware !! Happy Days.

This (the Americans turning off GPS) has for the most part been used for a decade or more to scare pilots from using GPS, and has been a part of the CAA campaign to keep a lid on GPS approach introduction.

What everybody pushing this line doesn't realise is that if this actually happened (WW3, basically) we would not be flying. GA would be banned on day 1 of any large scale hostilities - as happened in WW2 for example.

And if your airliner happened to be airborne on the N Atlantic route when the world comes to an end, you only have to fly a heading within about 10 degrees to find Europe :)

And your INS won't help you land on an IAP - far too inaccurate. You would have to descend over the sea and continue visually below cloud.

Of course, no contest. I wasn't suggesting that INS was better than GPS, just that navigation hasn't changed in principle since Pontius was a Pilate.

To assess W/V one started with sticking a wet finger into the air, then we had drift sights ( I was once told that I'd never make a navigator so long as I had a hole in my axxxe, until I'd had to fly a three-wind drift sight calculation over Berlin with the shells coming through the cockpit ) then sextants and an air plot on a chart, then Consol, then Loran, then Doppler, then INS and now GPS - to get the fixes required to apply the trigonometry - and I don't doubt someone will invent an iPod to do it next. The point being that all we are doing is inventing something new to evaluate the data we need to achieve the result. The trick is knowing how to use it - and keep in practice.

I was recently flying my microlight towards controlled airspace, and needed a cross bearing, and instead of pre-programming the panel mounted GPS ( yes, it is a microlight - LSA if you prefer ) I pulled a handheld GPS out of my pocket. I had to see the irony, having navigated 707's with a sextant, I was now navigating a microlight in VMC - with 2 GPS's !! How the World has changed ! But is it for the better ? Do the present pilots understand the principles, or do they just follow flashing LED's !

OK, I'll crawl back into my cave !!