Great project. I applaud your efforts. In the spirit of thinking outside of a different box, let me attempt to crystallize some of the apparent issues so far:
- Need larger panel area to get meaningful charge
- Optimize angle of incidence to make most of available panel area
- Ideal to avoid impact on vehicle aerodynamics
- And the usual, make it cheap, make it durable...
Picturing the solar sun racers, they extend the dimensions of the vehicle to get more panels on.
So, in the spirit of changing the rules to help assure a win, have you considered changing your expectations? My understanding of the current idea is that you plan to charge while parked and while driving, and this imposes some limitations (such as not being able to use the area of the windshield for PV, the need to withstand wind force at driving speed etc.). What if your plan was to drive somewhere, then charge while you are there, and then drive back?
In that light, I had this idea a couple of weeks ago while considering how one might use the cheap broken 4x6" solar cells that you can get on EBay. The cells are not mounted in a panel and so you are more flexible on overall shape, but now you must somehow protect the cells from further breakage. So I half-baked something like this:
String the cells together and stack them, picture a Venetian blind. This collapses and can stack into a box for transport, without taking up all of the trunk. Add some framing and a flip out leg (like an easel stand), and the whole thing stands on the ground. Offset the holes in the cells from center so they expose their surface when extended, and such that a wind blows the cells open and flows between them. You briefly lose proper incidence, but your easel doesn't blow over (fingers crossed). Perhaps the whole easel can yield vertical axis to the wind as well or you can design a deflector that allows the extended panel to stay facing the sun, or you can anchor them to the car in some way (thus shading it and avoiding high heat on battery). You make several of these "panels".
This gives you as much surface area as you care to store and assemble. It allows you to track to the sun if desired rather than fix mounted to the car. The whole kit is stored within the car without modification to the car, so no impact on aerodynamics.