About one hour before you plan to start grilling, make the rub: In a small bowl, combine the brown sugar, sweet paprika, salt, pepper, chili powder, onion powder and garlic powder. Pat the ribs dry with paper towels, then sprinkle both sides of each rack with the rub. Set aside at room temperature for one hour.
Preheat the grill for indirect cooking at 250 to 300ºF. Add the drained wood chips, if using.
Place the ribs, meaty side down, over a drip pan, close the grill, and cook for 2 hours, spraying on both sides with the apple juice every 20 to 30 minutes, and adding about 12 coals to a charcoal grill every 45 minutes or so to maintain the heat.
Remove ribs from the grill. Double-wrap each rack in heavy-duty aluminum foil. Return wrapped ribs to the grill and cook until very tender and meat has shrunk from ends of bones by about 1/2 inch (open packet to check), 2 1/2 to 3 hours more, adding more coals as needed to charcoal grill.
Remove ribs from grill. Being careful of hot juices, unwrap ribs. Return unwrapped ribs to grill and brush the ribs with the barbecue sauce and continue to cook for about 5 minutes, until the sauce is set. Turn ribs and repeat with more sauce. Remove from the grill and let stand for 5 minutes.
Cut the racks into 3- or 4-rib sections and serve.