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Google produced this curt explanation:

Course is the direction in which the aircraft is flying over the ground. Heading is the direction in which the aircraft is pointing.

1. Is there a better yet equally pithy explanation, in fewer than 50 words?

The above motivated me to question this:

See it like this... When Tomtom directs you from Amsterdam to Barcelona via Paris, Barcelona is your final 'course', but for now... you're 'heading' towards Paris... (taking in mind that you just left from Amsterdam...)

Other example: If you're doing an approach for landing at, let's say, LEBB (Bilbao) Airport on RWY 30, your Course is 300 but you can have various 'headings' TOWARDS your final course, Course 300 for RWY 30.

2. Why would you need to control and manage heading and course separately? If I'm flying to Paris first, then wouldn't I just enter the heading to fly to Paris? Only after reaching Paris, would I then change the heading to Barcelona? Isn't 'course' redundant here?

3. Same question as 2, but isn't 'heading' redundant here? I just need to steer the plane to the runway's course (or heading?)? Why agonize over the headings on the short segments of vectors?

4. Does any of the above explain this picture, in which the crosswind requires the plane to angle its nose to land?

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First, I'll try for the 50 words or less: Course is the line across the ground that you want to go. Heading is where you have to point the aircraft to fly that line.

That's less than 50 words, but I'm not sure it's any better.

Let's look at the obvious first. Let's say, over a short distance, you want to fly a course of 270 degrees true. If you fly the airplane on a heading of 270 degrees, you will fly that course ONLY if there is no wind, which for all practical purposes is never the case. If there was a wind from the north, you would have to maintain a heading greater than 270 degrees to make good a course of 270 degrees.

Actually, you can never say that the course between point A and point B is a single value in degrees unless those two points are very close together. If you draw a line between point A and point B and those two points are not close together, and then measure the course leaving point A (the angle between north and the line as it leaves point A) you will find that it is different from the course as you arrive at point B.

You can, however, tell the autopilot to fly a direct course from point A to point B and it will do it, changing the heading as necessary to account for the wind and fly that course.

So, why does an autopilot need to have a "course" function and a "heading" function. In my experience, the greatest single use of the heading function is when a controller is vectoring you and tells you to fly heading so and so. The second is when a reroute from your existing course is necessary, and you use the heading function to keep the airplane going straight ahead for a bit while you redo the revised course setting you want to use.

If you forget to again use the course function after putting in the revised course, the airplane will continue on the heading it was on while you were updating the course, and you will shortly be off course. That mistake has been responsible for aircraft being hundreds of miles off course.

During the first Gulf War, I heard a Canadian controller inform a USAF aircraft that they were over 300 miles off course when Canadian radar picked them up prior to landfall coming in from Europe.

A captain at the first 747 carrier I flew for got over 50 miles off course and was demoted to First Officer. He had forgotten to switch from the heading function to the course function.

Finally, as an added problem, if you choose to define your course in degrees magnetic, you must also account for the change in magnetic variation as you proceed along that course.

Insofar as item 4 is concerned, you (or the autopilot) is going to change heading as necessary to keep the airplane proceeding along the course as defined by the runway centerline. There's a bit of confusion of terms here in that runway directions are typically referred to as the runway heading rather than the runway course.

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Wow that's interesting. Is 50 miles all that much to justify demotion? For a 747 that's just 5 minutes' worth of flight, right? I feel like airport delays take way longer than that and no one gets demoted... – Mehrdad Aug 4 '14 at 11:37
Depending on where those 50 miles were pointing, he might have ended up over Russian airspace with nasty consequences (en.wikipedia.org/wiki/Korean_Air_Lines_Flight_007) – Radu094 Aug 4 '14 at 11:43
@Mehrdad: or even if you are still in safe airspace, you are going to make serious mess for the air traffic controller. – Jan Hudec Aug 4 '14 at 12:57
@Mehrdad In todays GPS environment I don't know what the rules are, but back in the pre-GPS environment of the North Atlantic MNPS airspace of the 1990s you were allowed a max error of 10 nautical miles. I believe the demotion was appropriate. As I remember he was eventually allowed to requalify as a captain. – Terry Aug 4 '14 at 16:34

While the wind correction angle is the main difference that comes to peoples mind, this has nothing to do with the reason the autopilot is providing these two operating modes:

One is a stabilization mode (heading), the other is a guidance function(course).

An autopilot can very easily fly a constant heading without external inputs or guidance. It might not even need a compass in some cases, just a turn coordinator to provide it with yaw rates. This makes the heading mode available in all but the direst failures. Easy to implement, easy to use, and available practically in any autopilot.

Flying a course requires guidance. Autopilot flies this mode (in an outer-feedback loop) by setting a desired heading (on the inner feedback loop). You might say the course mode runs on top of the heading mode. But it needs a lot of external data: groundspeed, windspeed, navigational signals wether GPS or a combination of VOR/DME. It'll be one of the first functions to lose when the autopilot goes into a degraded mode, it will be more complicated to build (ie. expensive) and more complicated to use (course from where? to where? on what NAV? )

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For course, position (from GPS or INS) or lateral guidance is enough. Ground and wind speed can be derived from that, but usually the outer controller will just keep adjusting heading depending on course deviation without explicitly calculating them. With lateral guidance only the direct course to/from the navaid can be flown, of course. – Jan Hudec Aug 4 '14 at 12:49

I will try to answer the question itself leaving out the heading/track discussion:

Because these are 2 different things.

Heading hold "simply" holds the aircraft on a specific heading. If you continue this heading for a long time, you will most probably follow a loxodrome.

Course hold function on the other hand will be used in conjunction with a navaid to follow a specific path to a specific navaid. FAA advanced avionics handbook chapter 4 under "Course Intercepts" in page 4-11 describes the concept itself. Note that the exact procedure of engaging a course might be different for each aircraft type.

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Its simple. Its all about the wind (and to a lesser degree magnetic variation).

Everything else you've mentioned is completely irrelevant, air traffic control, waypoints etc..... all completely irrelevant.

You calculate your correction angle and you fly that heading.

If ATC ask you to temporarily fly a new heading for traffic avoidance purposes, then its still up to you to figure out how you're going to rejoin your original course (i.e. the headings you'll need to fly taking into account wind) when they are done with you.

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