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Other than the admonition and expectation of using standard rate turns under IFR, I don't think there's anything official on what a "normal" bank angle it.
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Funny thing is ATC doesn't know/can't tell what a "standard rate turn"
is, nor do they really care, from their scopes. Further more, most transport category aircraft do not even
have a turn coordinator of any kind, much less anything with a "standard rate" demarcation.
And further yet, a new ruling is now in place for part 91 ops that states if you have two Attitude Indicators (powered seperately) you do
not need a Turn Coordinator installed in the aircraft. Hence there really is no such thing as a "standard rate" turn anymore (if there ever really was to begin with).
Fun facts.
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I'm not an air traffic controller, so can't say for sure, but I would probably guess that they do somewhat plan for aircraft making somewhat of a standard rate. For instance, if flying IFR and you made all your turns at 3 degrees of bank (exagerating for effect) you'd probably eventually hear something from a controller.
Also, one of the reasons why transport category aircraft do not do standard rate turns is due to the speeds at which they fly. As you know, the bank angle for a standard rate turn increases with speed. A common rule of thumb is 15% of your airspeed. So for a cessna cruising along at 100 knots, you can expect about a 15 degree bank to achieve a standard rate turn. For an airliner cruising along at 400 knots, it would take about 60 degrees of bank, which is quite significant. So for those reasons, airliners do not tend to use a standard rate turn (but s ometimes you'll hear about 1/2 standard rate).
Just because you don't need a turn coordinator doenst mean a standard rate turn doesnt exist. A standard rate turn means a turn at 3 degrees per second. A turn coordinator is calibrated to "do the math" for us. But you can easily figure it out using the formula above. I don't think the FAA's intent in that regulation was to do away with standard rate turns, indeed, I think the concept will probably be around in GA for a long time, but just to allow greater flexibility in terms of redundancy. For aircraft with limited panel space, a pilot may choose to have two AI instead of one AI and a TC because an AI provides more information than a TC can.
Just some friendly remarks.