Keeping this answer limited to riding photos, I would have two preferred setups, one digital and one film. For film, it would be on my 6×6 Bronica SQ-a loaded with Provia 100 which I would push a stop at the lab. It would be either in the shadows or early/late light so that my strobes could balance well with the ambient at a decent f/stop (no lower than f5.6) while still at the action-freezing 1/500 shutter (remember leaf-shutters don’t have a flash sync). I only have an 80mm lens for it, but I’d prefer either the 30mm fisheye, or 150mm tele – I love seeing fisheye photos on square format over digital. Ideally, I’d have a filmer on hand so that I could watch the clip and make absolutely sure I timed the photo correctly- this has saved me a few times.
For digital, it would be on my Canon 1D mkIII – which I love – and with my 85mm 1.8 prime lens. It’s my sharpest lens by far, and using the long lens makes you really consider your surroundings and put extra time framing the shot perfectly. I’d strobe it, and the rider would be at the top half of the frame so that I could cheat the sync over 1/500s to freeze the action. Consequently, the flash would be eliminated on the ground making light source less obvious, which a lot of the time makes the photo look more polished while at others looking unnatural. I’d use a tripod since long lenses can be shaky and unstable hand-held.
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