Hi all,
Thought I'd chime in here since I did a lightweight sandwich construction on my trailer back before I could find much information on it on the teardrop boards. Tom Matheson did provide me with lots of good information in some private e-mails.
First some basics: I used 5/32" (4mm) Finland Birch plywood sandwiching 3/4" Styrofoam (for the floor, sidewalls, bulkhead, galley counter, etc.) and 1.5" Styrofoam (for the roof, front wall, and galley hatch). I used 3/4" x 1.5" poplar for the framing laid flat, or on-end, respectively.
What I can tell you is that the construction technique I used is way stronger than possibly required by this trailer (for example, I can jump up and down in the middle of my 5-foot wide roof with no worries ). The panels were very strong by themselves and when attached together, you get a large, incredibly strong torsion box. However, the technique is also very labor intensive and costly (if using epoxy to do glue-up). And that was without vacuum-bagging (which I seriously considered and then decided against for reasons that I'll discuss below).
My opinion is that as long as you are gluing the whole surface of the foam, 1/8" plywood on each side is plenty strong for a sandwich panel, even for the floor. Larry Messaros' experience using a framed panel with 1/8" plywood on the inside and no outside panel suggests that even that technique is plently strong, at least for side walls. Plus, most commercial trailers were made this way in the past.
Also a word about plywood: A lot of luan plywood is really low quality stuff. Full of voids and knots in the interior core. And paper-thin (and brittle and easily cracked) exterior skins Also, the reason that it is so cheap is that it is coming from impoverished countries with few environmetal safeguards that are decimating their rainforests to produce it (luan is not made out of mahogany. It is made from 15-20 hardwood rainforest tree species that are being unsustainably logged). So, there are a few reasons to avoid using it if possible.
Using my method, my panels ending up weighing about as much as 1/2" to 5/8" plywood (sometimes more, sometimes less, depending on how much framing I used). The side panels, for example have a lot of poplar framing, but still weigh only 1.8 lbs./sq. ft., which is a bit more than 1/2" (nominal, actually 15/32") plywood at 1.5 lbs./sq.ft., equivalent to 5/8" (nominal, actually 19/32") plywood at 1.8 lbs./sq. ft., and less than 3/4" (nominal, actually 23/32") plywood) at 2.2 lbs./sq. ft. However, the side panels have about 3.3 times the stiffness of 3/4" plywood, and almost 12 times the stiffness of 1/2" plywood.
The basic process I used for gluing the sandwich panels typically was this (first I built a large
flat, strong table to glue down everything - any curve you impart to the panel is going to be hard to correct):
1. glue framing to "outside" skin using Titebond II glue- clamp using clamps (of all things) and by screwing through the framing into the table. Framing was also pocket-screwed together, though this probably wasn't necessary.
2. cut Styrofoam fit into the spaces in the frame with an X-acto knife. I tried a lot of techniques and a sharp (change blades often) X-acto, did the best, most precise job. Hint: press an oversize piece of foam hard onto the framing and you will get indentations that will show you where to cut the foam.

[this is my floor before the inside sking was put on; notice hole for footwell]
3. lightly sand both sides of the Styrofoam (I used both a ROS and a long-board with 120 grit) to give some "tooth" for the adhesive to grab onto. Also the 3/4" foam was slightly thicker than this, so this gave it the right thickness.
4. apply a thin wet-out coat of "neat" (unfilled) epoxy mixture to the inside of the outer skin, the frame members and both sides of the styrofoam pieces. I used System Three epoxy. I applied it with a foam roller (large areas) and a small brush.
5. apply a thickened epoxy mixture to the inside of the outer skin and the frame members. I used System Three epoxy mixed with plastic minifibers. I applied the mixture with a 1/32"notched trowel that provides about a 16 mil thickness or so.
6. squeeze Styrofoam pieces into frame spaces
7. apply a thickened epoxy mixture to the styrofoam and frame using the notched trowel
8. Place "inside" skin on top and line up. I then clamped the entire sandwich together using a combination of clamping the panel to the table on the edges, using clamps across the table, screwing into the table where the screwholes would be hidden later, and weights (containers filled with water).
9. Let epoxy cure overnight
That's it! Easy, right?!
I have some thoughts about vaccum bagging:
Vacuum bagging would have been a little more tricky and would have added some more complication to an already complicated process. It's hard enough to be able to do everything you need to on a large panel before the epoxy starts kicking off.
Vacuum bagging allows you to use a thinner glue line and thus theroretically use less epoxy and save money (and a little weight). However, you still need a way to spread the epoxy evenly at the thickness that you want. In the System Three literature, I found that 20 mils was the minimum recommended glues line thickness using clamping, and 8 mils if using vacuum bagging. Since it would be hard to spread the thickened epoxy at an 8 mil thickness, there would be a lot of waste as the excess epoxy squeezed out of the panels, and practically speaking, you might not use much less epoxy that way. Plus, you do have to worry about too much epoxy squeezing out and "starving the joint" if vacuum bagging is used.
When it came down to it, I used some makeshift clamping methods in lieu of vacuum bagging. Since the glueline was so thick, I was not worried about gaps. Using my wet-out and 1/32" notched trowel method, I got about 60 sq. ft. of coverage per gallon of neat epoxy (about 20 mil thickness - 5 for wet-out coat and 16 for thickened mixture), But remember, that's spread out on both sides of the sandwich panel, so the epoxy use really adds up!
If I wanted to go really lightweight and insulated, and I didn't care about having smooth sides: I'd do something similar to "standard" trailer construction techniques (also see Larry Messaros', Glen-L plans), etc. I'd cut a profile out of 3/4 plywood and then cut out holes for insulation, leaving only a little framing left. Then I'd glue the interior 1/8" plywood panel to it. Then cut Styrofoam insulation to fit. And cover exterior in overlapping, stapled, aluminum panels like Grant Whipp does on his Lil' Bears.
Hope this helps some of you in your construction efforts.
Rik