Calculate Size of Side Airboxes
The way airboxes work, is they are kinda air tight and displace water. That makes them less dense than water, and therefore they float.
How To Make Airboxes
Air boxes are made just like your hull is made. So if you use the chine log and framing log construction technique, then you would simply do the same when building your airboxes. There are many other boat building techniques, and so many ways to make air boxes.
Your air boxes should be sealed so water won't get in there, but have access inside so you can remove any water that splashes or leaks in, and also air out the tank when not using the boat. The simplest solution is to mount "deck plates" which are round screw caps, see the materials page for more info. Some people re-purpose lids from other containers, and sometimes people make a simple plywood hatch cover. Whatever you do, the point is to keep the water out when the boat is laying on her side, or upside down.
Where To Place Airboxes on your boat
There are many different places and combinations of airboxes that work. Most people place them so that when your boat is knocked on it's side, that the hull will float high enough so when righted, there will not be too much water left inside. When you climb back in, you then bail out the rest of the water.
How Big Should You Make Airboxes
Typically full length side airboxes are made about 7" wide, and the full length & height of the side. This makes them wide to sit on, and will float the hull high so almost no water is inside when righted. This is a great configuration for racing, however you may want to make smaller boxes, or configure them differently, so lets look at how to calculate their size.
Water weighs about 62 lbs per cubic feet. Since the way airboxes work is to displace water, it makes it a simple matter of figuring how big (volume) the air box is.
Lets say you had a single airbox that was a cube, that was 1 foot x 1 foot x 1 foot. That box would displace exactly 1 cubic foot. If pushed under water, it would lift about 62 lbs by itself.
Now lets say you had 2 of those, one attached to the bow corner, and one attached to the stern corner. Together they would lift about 124 lbs, which happens to be about the same weight as an average hull, so the hull will probably be lifted out of the water when on it's side.
This is bare minimum for just the hull. Most of us carry gear, sail rig, rudder, leeboard etc, so you probably want more flotation on the side of your boat.
Example 2:Now lets look at calculating a full length, full heigh side airbox.
A 16" tall side hull side panel has about 9 square feet.
So a 1" wide airbox has about 0.75 cubic feet, and will displace (lift) about 46 lbs.
And a 7" wide airbox will displace (lift) 325 lbs.
So as you can see, the 7" airbox will lift all sorts of weight, that is why it is so popular on a duck that is used for racing.