From: Brussels, Belgium
The 20 hex range aircraft has the same chance of detecting something within 10 hexes irrespective of whether its search range is limited to 10 hexes or 20 hexes.
So the manual is outdated, and setting the max range to a lower range than the full extended range does not, in fact, improve chance to detect?
That is not the question you asked, and no the manual is not outdated on this.
You asked about two aircraft models, one with a 10 hex range, the other with 20 hexes. Both set to search only out to 10 hexes, ceteris paribus, they have the same chance. The longer legged plane is not superior to the shorter legged plane. Of course in AE ceteris paribus would not apply in practice as there will be some difference somewhere.
Suggest you search for my posts on the subject.
The manual says "Setting the max range to a lower range than the full extended range will improve the chance to detect, as this can translate to more flights by the same plane."
What you're saying makes it look like the reference to the plane's full extended range is meaningless, but improvements to the chance to detect ships is linked to the absolute range of the mission, not the range as a certain ratio of the full extended range of the plane doing the search. Right ?
So, it wouldn't be useful to use longer-legged patrols when you plan to limit the search range due to, for example, a heavy CAP on a nearby base.
And could you give a link to your prior posts ? I tried a google search, but to no avail... (although I found this interesting old tidbit https://www.matrixgames.com/forums/tm.asp?m=2884834 about AM search ranges being limited to an endurance of 4 hours)