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While examining FAA's TERPS manual (Order 8260.3D) and PBN manual (Order 8260.58A), I noticed two seemingly contradictory statements.

TERPS 8260.3D Chapter 14. Departure Routes, 14-3-4 . Construct turning segments when the course change is more than 15 degrees

(emphasis mine)

Whereas in PBN manual, it seems that a deviation of 10 degrees is considered a turn.

PBN 8260.58A 1-2-5,b,(1)a . [...] Not applicable for FB turns of 10 degrees or less.

(emphasis mine)

Am I missing something. Is there any consistent rule that states when a transition between legs of an Instrument Procedure is considered a turn or a straight flight?

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    $\begingroup$ I believe the question might need to be restated. Whether a change in heading is "considered a turn" or not isn't really the issue. The documents you reference provide guidance for constructing a flyable procedure. If a turn was an acute angle the question of fly-over vs lead turn, as well as turn radius, play a very large part in the path the aircraft takes over the ground, and hence dramatically affect the design of the procedure. At angles less than 10 degrees it matters little whether you lead the turn or fly over it before changing heading. $\endgroup$ – Michael Hall Dec 12 '18 at 0:27
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    $\begingroup$ More specifically, PBN 8260.58A 1-2-5,b,(1)a describes how to calculate DTA, (Distance Turn Anticipation). It is not saying that turns less than 10 degrees are not officially considered turns, only that calculating the DTA is not applicable or necessary. $\endgroup$ – Michael Hall Dec 12 '18 at 0:38
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    $\begingroup$ @MichaelHall thanks I really appreciate your input. $\endgroup$ – Vector Zita Dec 12 '18 at 20:54
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I will have to answer my own question, since I have noticed that in FAA's PBN Manual it states:

PBN 8260.58A 1-2-5c . Turn parameters. For OEA construction, a turn is indicated when the course change exceeds the alignment tolerance of 0.03 degrees.

So, at least as far as route design is concerned, the alignment threshold for turn indication is 0.03 degrees.

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