There are dozens (if not hundreds) of industry groups, including type-specific clubs and organizations for pilots with shared interests. They're full of experts on specific types of aircraft and activities, and some of them might be interested in contributing here. What would a good 'letter of introduction' (for lack of another way to describe it) look like to a group of pilots? Would it differ for online vs offline?
Some examples:
The best (or at least most convincing) publicity is usually word of mouth, so I would say that members of those organizations should just post something on their forums or whatever. Following any rules about publicizing other sites, of course.
For the larger organizations like AOPA I suppose an email to their news editor might be worth a shot, provided that it's well written and 'sells' SE effectively. "Q&A network StackExchange launches aviation site" could be good filler material for them. The only issue with that is establishing who actually represents SE and/or aviation.SE to the outside world? I don't know if there's already an established process or precedent for SE in general?
I'm an AOPA member and although I'm not active on their forums I considered posting something there along these lines:
Hello everyone,
If you already use any of the StackExchange Q&A sites you might like to know that they now have an aviation site in public beta. If you've never come across them you can read more about them here, but basically it's a bunch of Q&A sites on a lot of different (often technical) topics; their IT-related sites in particular are very well known. They focus on answers, not discussions, so the 'feel' of the site is a bit different from here.
Regards etc.
The main reason I haven't done it yet is that I have never posted on their forums so posting a "check out this cool new site" message might look a bit like spam, especially to people unfamiliar with SE. A post like that certainly wouldn't be considered useful here. On the other hand, only AOPA members can post there, so at least they'd know I'm not a bot!
EDIT: I just discovered that this point is addressed in the "7 essential questions" meta post. This suggestion is very interesting:
sharing links to great questions and answers is the best way to start
I think that sounds like a great way to introduce the site on other forums, and I'd never even realized that there are badges for doing it. I guess that a posting about an interesting question is likely to be much better received than a typical 'check this out' post.
On the other hand, only AOPA members can post there, so at least they'd know I'm not a bot! . . . is that a subtle reminder to Otto that he needs to renew his membership? :)
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In addition to Pondlife's suggestions, we should all try to make a point of visiting the various local aviation group meetings (a lot of them have monthly meetings that are open to the public/pilots) and look for opportunities to introduce the site to other people in aviation.
Listen for questions that people ask that we may have already covered here and you can chime in with "I just read about that on Aviation.SE. Let me see if I can pull it up....". Try not to push it too hard but let them become curious and ask questions on their own. If someone asks a question that would be a good fit and no one knows the answer, you can say "That would be a great question for Aviation.SE. Have you heard of it?".
Tell anybody that is involved in flight training about Aviation.SE. This will be a great resource for students, because they always have questions (and I only wish that we were around when I was working on my ratings). If you are a flight instructor, tell all of your students and the other instructors because both can use us as a resource (CRM!). If you aren't an instructor, tell people at your local flight school. It only takes one person (particularly an instructor) to get really interested and it will spread quickly throughout the organization!
Just like above, introduce the site as a resource, not something that you are trying to "sell"!
Keep an ear out for other pilots at these meetings and schools who are asking questions that haven't been covered here. If they would be a good fit, "borrow" the question and come back to ask here.
The best way to get more people involved is to have great content on the site to draw them in and make them want to be here!