This is a glitch that can't be used for anything (I think) but I'm sure some people will find it amusing.
Step 1. Have a ship "trained" as a work order by talking to Yanas Seastrike (for Alliance)
Step 2. Make sure the work order has completed. The new ship should be right-clickable and not greyed out.
Step 3. In midair, right click the ship (I got to midair with Throbbing Blood Orb. The Goblin Glider might work as well.) The short cinematic should play, showing the ship sailing out to sea. Skip it with esc.
Step 4. When you skip the cinematic, the game will resume, and you will be floating in midair.
Step 5. Find a use for floating in midair in the shipyard.
Step 6. Enjoy?
EDIT: You can fish from midair!