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Can someone give a good and simple explanation about these three dynamics?

  1. Altitude Hold
  2. Attitude Hold
  3. Heading Hold
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These are generally 3 different auto pilot modes. The first two are related to pitch and the third to heading/roll a nice overview can be found here

Altitude Hold: Generally speaking setting an autopilot to altitude hold will cause the autopilot to maintain that altitude by varying the pitch of the aircraft. Depending on the system it may attempt to maintain the altitude even its not possible which can lead to a dangerous situation.

Attitude Hold: Is the autopilot setting that will hold the pitch of the aircraft constant when set to this mode. For example if you depart and climb out at an 8 degree nose up attitude, engage attitude hold, the aircraft will hold 8 degrees nose up until set otherwise or shut off. As noted in the comments this can create a very dangerous situation as the aircraft may continue to maintain pitch (generally for a climb) even if power does not allow this can cause a stall at high altitude. More sophisticated auto pilots allow for constant airspeed climbs which are far safer.

In my experience you are generally in either altitude or attitude mode at any given time.

Heading Hold: This is a roll control mode that holds the heading of the aircraft (keeps it on track). It will typically be slaved to a bug on the HSI where you can set the heading the autopilot flies.

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    $\begingroup$ Note that attitude hold is even more prone to inducing dangerous situations than altitude hold, especially in climb. Preferred mode for climb is “open climb”, which maintains speed with pitch. $\endgroup$ – Jan Hudec May 2 '18 at 14:09
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    $\begingroup$ As long as you are mentioning airspeed mode, vertical speed mode is also common as well. More detailed info is available here: Flight Level Change or Vertical Speed - When to use it? $\endgroup$ – Lnafziger May 2 '18 at 14:40
  • $\begingroup$ There is also GPSS, or GPS Steering, where an in-panel (typically) GPS or GPS Moving Map, controls the autopilot steering. In my plane, the GPS 'talks' to the DG/HSI which then connects to the autopilot. The DG/HSI is used to select between Heading and GPSS. $\endgroup$ – CrossRoads May 2 '18 at 18:51
  • $\begingroup$ @MichaelKjörling :-) Yeah, or maybe decreasing! $\endgroup$ – Richard May 3 '18 at 14:43
  • $\begingroup$ @Richard Even better. $\endgroup$ – a CVn May 3 '18 at 14:43

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