How To Build A Teardrop Trailer/Assembling the Body
Attaching the Sidewalls 
The sidewalls will sit on the trailer frame and will be bonded to the wooden bed that is already bolted to the frame. Polyurethane glue is used to glue the sidewalls to the bed. Some builders use wood screws mainly to hold the sidewall while it dries.
However, the polyurethane glue, as good as it is, is really only gluing the top ply of the plywood. It is unlikely the glue will fail, but the plywood could fail. It does not take that much force to strip the top ply off plywood, especially if the plywood has been compromised by the elements.
So in addition to having the sidewall sit on top of the frame and polyurethane glued to the bed, it is a good idea to put 3.5 inch bolts through the sidewalls and through the wooden bed's wooden frame (made from 2x2s) with some big flat washers. Position the bolts about a foot apart.
Its really just a matter of having someone help you position the sidewall, drill the holes for the bolts, then take the sidewall down and coat the mating surfaces with polyurethane glue, and reposition and assemble with the bolts. Let dry overnight. You can use the wooden scraps cut off the sidewall profile as temporary bracing to hold the sidewalls up.
The Spars 
Spars are simply the 2x2 pine wooden braces that will be placed across the roof line. These are polyurethane glued in place and held with wood screws. Standard 2x2s that you get from the lumber yard are usually pretty ugly and rough, so you might want to take the time to rip the sides of the 2x2s with a table saw so that you have nice looking spars. This is especially true if decide not to have an interior ceiling.
You need to take a few items into consideration when locating the spars:
- Roof seams - The 5.2mm luan only bends well across the narrow dimension (across the 4 ft dimension on a 4x8 sheet). So you are looking at a seam every 4 feet. You should plan on attaching your first sheet to the front of the wooden bed frame (front of the trailer), so from the bottom of the wooden bed up 4 feet is the end of your first roofing sheet. A spar has to run under the center of this spot. Continuing up and back, you'll need spars centered under each seam.
- Curves - There needs to be multiple spars to support the front curve. This is a tight curve and even though the edges of the roofing luan will be attached to the sidewall's curved profile, the luan will tend to flatten out in the middle if there is not enough support. So going around the curve you want spars about every 6 to 8 inches. Spars can be farther apart on the flatter parts of the roof.
- Roof Vent - You need a couple of spars to support the edges of the roof vent and you might as well frame it in at this point.
- Hatch Hinge - Finally, at the rear you want to put 2 spars adjacent to each other to support the hatch hinge.
So the process is to carefully measure and mark where your spars should be. Then counter sink holes through the sidewalls. Finally, apply polyurethane glue and screw the spars in place. You can then fill the counter sinks with wood filler.
Laying the Luan 
This is actually one of the easier jobs. Unfortunately you will not be able to use the full 4'x8' sheet of luan for your roof unless your trailer is really narrow (like 46"). The reason is that the luan bends in the narrow direction not the long direction. This means cutting a 49" or 50" piece from the 4'x8' sheet and wasting the rest. You want the luan to overhang the sides. Unless you are a top notch woodworker and cut the sides perfectly identical and attached them so they are perfectly square, there is little chance of cutting a piece of luan such that it will line up on the sides - so we won't even try. Not to mention the glue and bending will consume all of your attention; you don't want to have to focus on lining up the sides too.
If you recall in the previous section, the front radius should not be smaller than 20" in order to bend the luan around it. The larger the radius, the easier time you will have with the roof. At exactly 20" radius, the Author did actually snap a piece of 5.2 luan in half. The Author ended up fastening the luan at the top with screws then "just" starting the next row of screws and carefully tightened the entire row of screws incrementally (in a round-robin fashion) to slowly bend the luan over the curve. Hence the recommendation to consider a 25" or even a 30" diameter curve if you want to avoid any issues.
You can cut the first piece of luan and start from the bottom front and work up and around to the back. Dry fit the first piece. The luan should line up square on the bottom front and the top of the luan edge should fall squarely in the middle of one of the spars - because that's how you planned it when fastening the spars. We don't care about the side edges of the luan as long as they are overhanging.
If everything looks good, remove the luan and apply polyurethane glue to the edges of the side walls and to the spar faces that contact the roof. Again place the luan so that it is lined up on the bottom and start a screw in the middle of the bottom spar. Check that the top still lines up to fall in the middle of the spar, then put in the remainder of the screws horizonally across the bottom. I used 7 screws across for each spar including two edge screws that went into the side walls.
You repeat this process to cover the entire roof. Clean off any excess glue and let dry. You can then use a router with a laminate trimming bit (with flush ball bearing guide) to trim off the over hang.
Other Options 
There are other ways of constructing the roof. Many builders will install the interior roof paneling prior to the external roof. This allows them to easily slide the interior paneling through the spars to get it inside the trailer - a necessity on teardrop trailers constructed with a permanent galley. In addition they may join (glue) the entire interior paneling set together on a flat surface first. This is done to avoid seam covers on the inside and to facilitate bending around the interior curves. Also, once the interior is attached, builders may run wiring and insulate the cavities prior to putting on the roof.
Another alternative is to use 1/8 inch luan (hard to find) or paneling for the roof and apply 2 layers. This is typical on some styles where the curves are tight.
Furthermore, many woody builders take up the challenge of not using screws. They use lots of clamps and nylon straps to hold the luan as the glue dries. This has the advantage of a smoother outer skin.
With the build method we are using, the areas in-between the screws will not be perfectly flush with the area around the fastener and there is no built-in galley so getting materials inside the trailer through the back is not an issue.