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If the box is ported at one end with the driver at the other the physical separation of the sound sources might prove problematic for the nearest seats.
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Speaking of tuning to 13Hz... is not the purpose of the port to augment the tuned frequency? If so, how is anyone going to localize 13Hz?
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It's not that you would localise port output, it's that due to the length of the sub and your proximity to the drivers, the driver output and port output may not have had enough space to mesh by the time the driver output gets to your seat, and the driver output would be louder in relation. You could solve it by placing the edge of the sub where the port opening will be the same space from your seat as the center point between the two drivers. I'd probably face the port side towards the side wall corner too, keep it about 1' away though. Ideally such a sub would be a good 6' or so away from you, like say, in the front of the room where some other ones are

, but I think you already covered that.
Keep in mind, 570 liters is pretty big
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I believe Stevecallas stated I would need at least 260 effective liters and a 6" diameter port that is 31" long. Would this be correct for a 13Hz tune?
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No, the 260 liter, 6" diameter port that is 31" long would be for the more common ~15hz tune design. You'd have to do something like 320 liters and a 6" diameter port that is 35" long to get it to work with a single driver sub. That's definitely doable, but I don't see what you are gaining, as the ports would still be best firing out the sides.