Alcon;
I work on a ship, as a photographer. Needless to say, my studio space is small, and has VERY low ceilings. (Think about 7' useable as there is a grid for the 1k's we use for video mounted to the overhead.) The space itself is about 15' x 20' (useable space).
50% of the time I'm shooting full-length portraits on white seamless, which is never a problem. Pop two strobes in umbrellas, and two with reflectors to make the background just about blow out, remove anything (wriinkles, dust, bad gradient, the edge of the plexi if someone got it in the shot...) you don't like in post. (The only time I'm allowed to touch something with the healing brush!)
The other 50% is a 'roster' shot. Sitting, forearms/hands on a posing bench, with two flags over the shoulder. I like to get the flags far enough back from the subject so that they start to blur just a bit at F/8 @ 50mm. (I'd love to go longer, but there just isn't the space!) Key and fill as high as I can get them, umbrella'd, approximately 45* off. (This is basic stuff. Has to look the same every time.) Pop a strobe on the background from behind the subject to get a bit of a vignette on the black seamless.
My problem is, even getting the flags as far away form the background as I can (generally, at most 4') I get a distinct, triangular shadow on the black background paper. If I move the background light farther away from the BG, I wind up illuminating the flags from the bottom and it just looks silly. (Unfortunately, I don't have a grid that will fit these strobes.)
Does anyone have suggestions? I can post examples tomorrow when I get back into work. I was trying to teach one of my new Sailors how to shoot studio today, and for some reason it was particularly bad.
Edit - I can think of several ways I'd 'like' to fix this. Get the flags farther away from the BG, get the lights higher, get a bigger light source, get a grid on the background light.... Just can't think of any I can actually do in such a small space with the gear I have!

