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Getting started in FAI competition seems (and is!) intimidating.  The models that show up at U.S. Team selection contests and at the World Championships probably weigh less than anything you've built before.  All of the duration events have MAX times that seem impossible to achieve with a wimpy A3-4T mini-motor.  Just how do those guys and gals get to that kind of building and flying skill?  Can you?

I'm going to relate a personal suggestion for how to get started.  This is only my opinion, and you can take it for what it is worth.  First, start with a simple duration model made for the rules of Streamer or Parachute Duration.  Here is one that fits the bill:
If it looks familiar, it should.  That is the good old Estes "Big Bertha" modified to improve performance.  This model has had the number of fins reduced from 4 to 3.  The plastic nose cone was replaced with a balsa cone from BMS (Balsa Machining Service) that was aggressively hollowed out.  The launch lug, motor hook and motor block were all discarded.  With some other modifications such as lighter balsa for the fins, and peeling the body tube, the finished weight is right over one ounce! (29.5 g on my scale). When flown in its only contest flight, this model made a 4+ minute flight using an A8-5.

One reason I suggest this type of starter model is that it can be light enough to perform well and can be durable enough for repeated practice flights.  IMO, this is a great way to start flying S3A Parachute Duration.

If that model is too simple, then I suggest going a little farther.  If you have the skill and want to try a more conventional FAI style, how about building something like the NLBC (Not Light, But Cheap)?
This was my introduction to FAI competition in 2011.  Ed LaCroix and I designed these models to meet the requirements (500mm length x 40mm diameter) and not have to get messy with fiberglass and epoxy.  The body and motor tubes are standard BT-60 and BT-5 peeled for lightness and the fins are good old balsa.  The tail-cones are rolled 20# bond paper.  The only stretch might be the vac-formed nose cones.  You will have to come up with your own.  These were made by George Gassaway years ago and had ended up in Ed's parts bin.  They worked perfectly for these models.  Though slightly different in dimensions, these models are very close in weight at right around 15g.  Back then I posted this video of NLBC#2 flying on a 1/2A3-2T.

Before dismissing BT-60 as a viable body tube, remember that it is only 2mm greater in diameter than a typical FAI body tube.  This small difference means that you can build a model substantially similar to a "real" FAI model.  I highly recommend trying to design your own model along these lines if you have moved beyond the Big Bertha phase.

Finally, you may want to go all in.  You can try your hand at making an even lighter and more competitive model.  Explore what others have done.  Look at the construction tips posted here and on the NAR website.  Try making models from velum, Kapton film, etc.  Follow links in the FAI section of this forum under each of the events.  For me, I ended up building models like this:
The model above was a final version of what I took to Bulgaria in 2014.  Though I did not do well at that contest, it wasn't the model's fault.  The model above has a vac-formed nose cone, epoxy/fiberglass body, and 1/32 balsa fins.  It weighs just under 8g.  I had great success with this type of model in several contest, but I continue to try new methods and to get better at building and flying.  With practice and patience, you can build models that are easily as good and probably better!

I learned to build and fly FAI progressively over several years.  Many members of the U.S. Team helped me with tips and techniques.  If you'd like to learn more, please post your questions here or contact one of the FAI mentors listed on the NAR website under the FAI Spacemodeling page in the Competition section.  Link:US FAI Spacemodeling Advisors (Jan 2017)

Best of luck,