Here is a foam built ship named the Penguin, a design I borrowed from the http://www.starfleet-museum.org/penguin.jpg . It is 1/72 scale and was a fun build.
Penguin: RENFOAM 40 lb. foam board, cyanoacrylate glue, 2 part 5 minute epoxy, Tamiya Black and White acrylic paints, Grey Laquer spray can primer, decals (printer), hollow and solid brass rod, Garnet and Wet and Dry sandpaper.
Photon torpedo: Aluminum rod, brass shim, Tamiya Clear Blue.
Roughing/Shaping: pneumatic die grinder with 80 grit disc pads
Painting: Iwata airbrush and air compressor
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Step 1: Templates
I used this 4 view design and blew it up to 1/72 scale. The sheet was cut up and used as templates for the foam pieces. Once the pieces were band sawed, I prefit them together before contouring shaping each piece. The wings and fins were positioned with 3/32" dia. brass rods inserted. These were worked separately and bonded on later.
Step 2: Contouring and Shaping
.Here you can see each piece shaped close to finish. Shaping each piece separately sped up the build and made thing much easier. You can see pencil lines used as a reference for center lines, etc. For the 6-3/8" dia. exhaust hole at the rear, I left the back end square. The holes were drilled perpendicular to the back face, then sloped to match the 4 view angle. The 3/4" dia. hollow brass rod was also drilled into foam and fit. I used 80 grit and 120 grit garnet sandpaper for working down the parts, along with a pneumatic air grinder with 80 grit pads to do the initial roughing. Final smoothing was done with 220 and 320 grit garnet sandpaper.
Once the contouring was complete, all pieces were bonded with 5 minute epoxy.
Step 3: Priming and Adding Line Details
Next up is priming the model. I used quick a drying lacquer grey and was able to wet sand between coats with 400 Wet and Dry sandpaper. Total coats - 3.
Once dried, I stood it vertical and used a height gage to mark panel lines. Once the windows were marked, they were worked in.
Step 4: Painting
Tamiya acrylics were thinned and prayed with an Iwata Micron CM airbrush. The white was fogged on so that areas of primer show through to simulate wear.
The Photon torpedo is a piece of 1/2" aluminum rod with the ends turned down on a lathe. .010" thk. brass shim was bent and shaped as fins, then bonded with CA glue. It was masked then sprayed with Tamiya Clear Blue.
The base is a chunk of RENFOAM carved rough and installed with 1/8" dia. and 3/16" dia. solid brass rods to suspend the torpedo and Penguin.
Step 5: Finishing Up
Decals were added to the Penguin during the final step. My friend Steve graciously used his ALPS printer to make these beautiful decals. The windows were filled in with 5 minute epoxy tinted with Tamiya Clear Blue. Both Penquin and torpedo were bonded on with 5 minute epoxy.