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I recently encountered a situation where the autopilot was flying a right turn in FMS mode but would not make a left turn when switched into heading mode. This is a common occurrence flying the Teteboro 4 Departure if your route is to the south but you're departing on the north facing runway. That departure is the worse time to have the auto-pilot ignore your input given the amount of traffic and hard altitude restrictions from Newark International, which is very close.

The exacts steps are:

1. I departed Teteboro IMC on Runway 1 on the Teteboro 4 Departure. That requires an initial turn to a heading of 040 degrees and then a turn to a heading of 280 degrees at 2.3 miles from Teteboro. The auto-pilot will fly that in FMS.

2. While in the right turn to a heading of 040, the departure controller instructed me to turn left to a heading of 200, which is more than 180 degrees from the heading I was passing in the turn when I received the instruction. Normally a right turn would make more sense but given NY's airspace a sweeping left turn is demanded for separation from Newark Departures.

3. I turned the heading bug to left to 200 and hit heading mode. The auto-pilot continued the turn to the right seeing that right was the shortest turn to the 200 heading. I immediately turned the heading bug to less to 180 degrees from my present heading to attempt to lead the turn to the left, which did not stop the right turn. At that point, I disconnected the auto-pilot to hand fly, which is not a great time in these conditions and NY airspace.

I've been able to recreate the issue. It honestly make sense but I think the fact that the auto-pilot always turns in the direction you spin the heading bug when in heading mode, but that behavior can feel different when switching from FMS to heading mode is a bit unexpected even if it makes sense.

In retrospect, the easiest solution would have been to press the heading bug to center it, which would level the wings and then start the left turn again. But leaving Teteboro IMC in some of the world's busiest airspace there's not a lot of time to experiment.

I'm sharing because this is likely to occur if leaving NY in rain on a flight anywhere south of New York. Hope that helps. It might be a good training tip for Garmin 3000 users.

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I can't promise this explanation is accurate (I don't have internal garmin knowledge), but my guess is that the behavior you observed exists because they are trying to ensure the AP does the correct thing when you follow what they consider the "correct" procedure for a > 180 turn.

Specifically (and using a simple example where you are heading 360 and want a LEFT turn to heading 090)... they expect you to:
1. Sync heading bug (360)
2. Switch the HDG mode
3. Start spinning heading LEFT (which starts the turn to the left) until you hit 090 -- the plane will continue the long left turn to 090.

In this case, they want to make sure the plane doesn't suddenly reverse the direction of the turn once you've spun more than 180 from current heading.

In the case of your example, you spun the bug before switching to heading, so as you point out, the plane went the shortest direction (right) once you engaged heading mode.
Now you are in heading mode turning right, so the fact that then you spun to a heading < 180 to the left doesn't matter - the AP doesn't want to reverse directions in the middle of the turn -- in fact, it assumes what you are trying to do is initiate a long right turn to your (newly input) heading.

In short, I think the Garmin AP does not want to reverse direction once HDG mode is engaged and a turn is initiated.

Left to the reader if using something like CWS (without dropping HDG mode) and manually turning it the direction you want would convince it to turn the opposite direction, although I've experienced this behavior before and I think I tried that unsuccessfully.

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I totally agree with your comment. When I was in cruise climb it occurred to me leveling the wings before reversing the turn was the best thing to do. As you point out centering the heading bug accomplishes this. I think it's a good habit to adopt, especially if you're also switching auto-pilot modes at the same time. Thanks.