The pilot reported that the purpose of the flight was an orientation for two potential student pilots. The pilot said that he completed a visual inspection of the fuel tanks and that he estimated that the fuel tanks contained 10 gallons of fuel, which he determined, would have been adequate for the flight. The pilot completed two traffic patterns, and as he climbed the airplane to the downwind leg of the third pattern, the engine lost power and "surged" during the subsequent forced landing. The pilot requested an emergency landing to runway 13 but amended his request to runway 8 because the airplane was "too high." He subsequently determined the airplane was "too low" for runway 8, and the airplane touched down hard on a taxiway and skidded to a stop in the grass infield. The airplane sustained substantial damage to the cabin floor structure. Examination revealed that the airplane contained no fuel, and the pilot reported that he had exhausted his fuel supply.