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1) For optimum performance on a 15 foot ceiling, typically the blades of the ceiling fans will be anywhere from 9 feet to about 12 feet above the floor level. You can go lower or higher, but I would not recommend to install the fan blades any lower than around 8 feet 6 inches or so above the floor line.
2) The down rods come in 12", 24", 36" 48" and 72" versions. For your application, I would recommend using a 36" (3 foot) down rod and you should be fine. This will provide you with approximately 12 feet above the floor level (give or take a few inches due to the fan canopy) and using a 60 inch diameter fan will provide a good air movement. The 48" down rod is also an adequate length if you want the blades lower, but I would recommend to not go any smaller than the 36" size.
3) Since the ceiling is somewhat taller than normal ceiling heights and you are also using a larger diameter fan (60 inch), I would go with the 36" down rod, since this height will blend in better with the ceiling height as well as the diameter of the fan. I think this height is more appealing to the eye versus if the fan were lower.
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