Depending on what exactly you are looking for, the easiest way to do this would be to stage it - meaning not actually lay out. If you only want a close up of your face, arm, and disc, you could hook your legs into something heavy (like a picnic table) and lean out and down (like in this photo, but cropping off the legs). Your friend could repeatedly throw you the disc instead of you repeatedly laying out. When you do this, be aware of the shadows from the table, photographer, and thrower.

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From the other side, there is a famous one of Peter Read Miller (SI) doing this exact thing for a baseball player. I think in that one they glued the ball into the edge of the mitt to get exactly what they wanted and just had him layout onto a mattress. The camera was facing up so you could saw the dive and sky behind him - the mattress was out of sight. There was no doing it again and again until he caught the ball.