You might want to consider stitching the screen with something like nylon string and a needle (fishing line?), instead of a few zipties
Oh, oh, oh! I work at a rigging shop, and I have one thing better for that:
galvanized wire. At our shop we have 1/16" galvanized steel wire, and it'd be ideal for "stitching" up screening like that. From what I remember, it sells at our shop around $0.80/foot; a small mom & pop store might likely sell it for more.
Such wires are often sold at hardware stores as well (look in the section where they sell ropes and chain by the foot). The only issue would be tying off the ends -- normally we use aluminum oval sleeves.
Hrm, this is making me think that I should try out the screening on the bottom of the car here...
Forget the paint near any heat source and stay with plain aluminum screen, which is fireproof and a superb conductor of heat, good where the screen touches a hot exhaust pipe or muffler. You want it to breathe so as not to trap heat under the car.
Use several pieces of ~1/8" wall thickness 90 degree aluminum "L" angle stock as stringers under the screen to hold it taught and in place, with the stuff oriented parallel to the long axis of the car. This will act as flow fences, channeling the flow rearward and lessening turbulence. In effect, this will act the same way as the channels seen on the roof sides of NASCAR racers.
Flow fences, btw, are an excellent, simple, and cheap way to keep the airflow rearward rather than degrading into eddies or backflow. Old MiG fighters used this trick a lot.
Another possibility for areas free of heat and fire hazard would be to use dacron or mylar, fitted and stretched tight. Once so fitted, use a heat gun to shrink the dacron or mylar to an exact, smooth and tight fit. That's how they do it on modern fabric-covered aircraft wings and fuselages. Once the dacron is taught, they dope it to preserve, waterproof, and seal. Kayaks and some canoes also use this method. However, it's flammable. Being tight, it will probably be drum-like, and make a booming noise.
Just thinking about how I'd attach screen and came up with the following...
cut the screen about 1/2" oversize all round...
Unbend some wire coathangers, and wrap them around a nail every 6" or so to make loops..
Wrap the edge of the screen over the coathangers and sew it down with wire..
Use the loops in the coathanger to fasten screen on with self tapping screws or zipties.
Methinks that would be fairly durable.
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