"Airship: Over the last decade, House Cannith and House Orien have developed flying vessels that use bound elementals as a motive force. An airship is a large
craft, similar to a sailing ship, long and shallow, surrounded by a Huge fire elemental bound into the form of a fiery ring. The bound elemental propels the ship at a fly speed of roughly 20 miles per hour (poor maneuverability). An airship requires a crew of 15 and can carry 30 tons of cargo.
Strong conjuration; CL 15th; Bind Elemental, greater planar binding; Price 92,000 gp."
This doesn't help much, as according to the MM, no fire elemental possesses a fly speed.
However, according to the ECS page 124:
"House Lyrandar Airship: House Lyrandar operates elemental flying vessels (usually utilizing bound air or fire elementals) to make rapid air travel possible across Khorvaire. (...)"
Air elementals do have a fly speed, so these airships could actually stay afloat. However, consider the following:
One needs greater planar binding to build such an airship, so the largest elemental one could use is one of 18 HD, or a Huge air elemental. So with 18 Str and being Huge its light load is 600 lb (it was unclear whether or not to regard it as quadruped, so I gave it the benefit of the doubt)(remember that a creature with a fly speed can only fly when carrying a light load). Still not nearly enough to carry an airship with crew and 30 tonnes of cargo!
So, am I missing some obvious effect mentioned in the rules, is there some real-world law of physics that lets a huge ring of fire carry an airship, or are these airship just meant to look cool, and shouldn't I wonder how they actually work?
One of the key components of an airship is the hull, which is made out of soarwood, from Aerenal. Soarwood has a magical buoyancy, meaning boats made out of it practically skim over the water, so their water speed is faster. I think it has that quality because it grows in a manifest zone, but I don't remember off the top of my head. When used in an airship, it allows it to hang in the air, even with out an elemental powering it.
The elemental only provides the propulsion, to move it through the air in a speed that can actually get somewhere in a quick amount of time. When the pilot suppresses the elemental when they dock (so the elemental can't take control of the ship and plow into stuff), the natural buoyancy of the soarwood lets the pilot maneuver into the dock, at a speed of I believe 20 feet.
The reasoning behind the fire and air elementals is that fire can propel the vehicle, much the same way as actual vehicles can use fire as propulsion. The air elemental works because since you are moving through the air, the air elemental can maneuver. So the carrying capacity of the elemental doesn't matter, because the elemental isn't physically carrying it, it is just pushing it.
Also, the reason that a Huge sized elemental is needed is because you need one of that size to push such a large vehicle. IIRC, a smaller item that has an elemental in it, such as elemental armor or a smaller vehicle, can use a smaller elemental.
I think this is how they work, but this is all off the top of my head, so I could have some of it wrong. Hope this helps.
And if you have any other questions, I don't mind answering. :D