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Or is there a “standard” that the auto pilot follows at all times?

By “standard” I mean the aircraft will bank at x amount of degrees each time regardless of the following mentioned? The more you bank, the sharper the turn is, correct?

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    $\begingroup$ A standard what? $\endgroup$ – J. Hougaard Nov 30 '19 at 19:50
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    $\begingroup$ I'm guessing what you're after is the formula between airspeed and bank angle for a standard rate turn, which is: std_bank_angle = arctan( pi / 60.0 * TAS[m/s] / 9.81[m/s/s] ) for a one minute (60 second) 360° turn $\endgroup$ – Jan Nov 30 '19 at 20:17
  • $\begingroup$ You may also read about close feedback loop. Here, you want to maintain heading controlling bank angle. $\endgroup$ – Manu H Dec 3 '19 at 15:31
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If your talking about standard rate turns, those are not really practical in large commuter aircraft. As true airspeed increases the maximum turn rate decreases when the bank angle is limited to a comfortable level of less than 30 degrees of bank. So please make this question more specific, which airplane category are you talking about?

Usually the autopilot uses the difference between the target heading and the current heading to generate a bank angle target, often just proportional by a linear factor but limited to, e.g. 25 degrees of bank or the minimum of a 30 degree bank turn and a standard rate turn bank angle or even manually selected like in the Boeing aircraft. The autopilot then calculates the difference between the target bank angle and the actual bank angle and generates a roll rate target. Based on the roll rate target and current roll rate the autopilot computes a roll acceleration target and finally an aileron deflection target, which could, for example, just be a factor times the roll rate deviation.

The computation from the deviation of any of these parameters to the next lower level control loop target can consider the true airspeed and altitude, yes. But this can't be said for all types of autopilots that ever existed and is too broad of a question.

For certification of an autopilot system it has to be demonstrated that the autopilot remains within a safe enveloped, as specified in the requirements. This could limit the roll acceleration, roll rate, maximum bank angle or demand a response within a certain time frame or a maximum deviation for any of these values, transient allowed overshoots, etc. Since the autopilot has to work throughout the flight envelope the parameters used in the computation of the bank angle, roll rate, roll acceleration, aileron deflection, etc. may require a look-up table for each airspeed and altitude to ensure a stable and safe operation. This can differ between aircraft types, e.g. a large passenger aircraft should fly less aggressive roll maneuvers because the people sitting on the outside far away from the center are being subjected to major g-forces as the aircraft rolls, which is uncomfortable and potentially hazardous.

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The amount of bank is that which is required to achieve the standard "Rate 1" or 2 Minute turn, being 3 degrees heading change per second, which takes you in a full circle in 2 minutes. This is a universal protocol for turns in the IFR world.

This varies with true airspeed (the faster you're going the higher the bank angle required to turn at 3 deg/sec) but you get a good ballpark number by dividing TAS by 10 and adding 7 (so at 180 kt, it's 18 + 7, or 25 degrees bank).

The pilot hand flying a light aircraft has the Turn and Bank or Turn coordinator to determine when the bank angle is correct for Rate 1 and flies whatever bank angle gets the indicator showing the correct rate. The pilot of a transport aircraft has the Flight Director to tell him/her the precise bank angle target required. (If the turn rate indication or Flight Director indication was not available, that's when the 10% of TAS + 7 formula comes in handy.)

The autopilot does the same thing. It uses whatever bank angle it needs to to achieve Rate 1, and it'll be programed to use a certain roll rate and roll out lead heading angle (normally quite gentle - several seconds to roll into a 25 deg banked turn). It'll start to roll out of the turn about 15 degrees of heading before the target and reduce the roll rate as it gets close to creep the last few degrees to avoid overshooting.

The amount of heading change doesn't really come into it, unless the heading change is so small that it's time to start rolling out before the turn rate even gets to Rate 1.

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In all the jets I fly, the autopilot will always bank at 25 degrees. It doesn't worry about standard rate turns. As others have pointed out or alluded to; a standard rate turn with airspeed above 180 KTAS requires larger than comfortable bank angles.

The autopilots also have a half bank feature to limit banks to 13 degrees. Most often pilots will use that feature on a single engine climb at V2.

Some FMS installations will also limit its bank angle above a certain altitude to half bank to limit the chance of an acceleration stall. The autopilot must be in NAV mode for that to work.

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