Holy $h!t, a topic I actually know something about.
Nose forward and down - the board will act like an aerofoil, as previously stated, which will create lift - trying to remove surfboard from roof of car, and create drag - increasing fuel consumption. The fins will act just as they do in the water, creating lift - and drag - if they achieve an angle of attack due to swirling vortexes created by the car itself or by engaging in high speed cornering (boy racer?).
Nose rearward and down - the board is pure profile (parasite) drag creating no lift. The fins are not foiled in this orientation and cannot create and lift but will contribute to profile drag as well.
Nose forward and up - dumbass.
Nose rearward and up - see above, but not quite so much.
The shuttle rides piggyback on the Jumbo facing forward because it has foils (wings) that create lift so why not use them to help offset the weight of the shuttle? Neither the wings or the stabilizer (big sticky up bit at the back) of the shuttle were designed, built, tested or certified to fly backwards and I can only imagine the damage if it were tried.
If you’re thinking that the logic dictates that nose forward and up will create lift downwards, towards the roof of the car, helping to keep the board attached to the racks, sorry, the airflow is disturbed by the windshield of the car and will also stagnate because it cannot smoothly flow between the board and the roof. The racks themselves will also break up the airflow and prevent lift from being created.
Oddly enough, being born and raised on the Texas Gulf Coast (where the surf depends on the size of the last oil tanker that went by) boards always went nose rearward and down. I now live in the British Channel Islands where here, and in the UK, it would seem odd to not go with the nose forward and down (aerodynamic??) approach. Bizarre.
At the end of the day, does it really matter? How many of us have lost a board off of the roof? You’re just as well to go with the UK/Orange county - fins back, everywhere else fins forward theory.
Half-assed surfer, half-decent pilot.
Good night.
Buter