On August 5, 2001, at 1315 eastern daylight time, a Grumman AA-5B, N4545T, collided with the terrain after over running the end of runway 35 (3,500 feet by 140 feet, dry grass) while landing at the Welke Airport, Beaver Island, Michigan. The private pilot and passenger were not injured. The airplane was substantially damaged. The 14 CFR Part 91 personal flight was operating in visual meteorological conditions and a VFR flight plan was filed. The flight originated from Harbor Springs, Michigan at 1230. The pilot included a typed statement with the NTSB form 6120.1/2 that he submitted. The statement reported that the pilot reported that he checked the weather prior to the flight and the winds in the general area of Beaver Island were from 270 degrees at 3 to 7 knots. He reported that they initially intended to land on runway 27 at the Beaver Island Airport. However, once arriving in the area, he decided to land at the Welke Airport, which was closer to the main town on the island. The pilot reported he flew over the Welke Airport and confirmed that the windsock was indicating that the wind was perpendicular to runway 35. The pilot reported, "On the turn to final it was observed that a stand of trees existed to the south of the field that required a higher than normal angle of approach to the runway." The pilot reported he used a slight crab to the left and "the power setting was sustained until the aircraft was clear of the treeline." He reported he closed the throttle after clearing the trees and the airplane touched down "500 feet beyond the south-most (entry) end of the runway." The pilot reported he maintained an airspeed that was 5 knots higher than normal due to the crosswind. The pilot reported that during the landing roll he applied additional braking when he realized that the runway had a down slope. The pilot reported, "While I am sure there was a moment that I could have aborted the landing, it passed due to my confidence that directional control and braking was sufficient to achieve this landing." The airplane continued off the departure end of the runway into a sand/gravel pit, which is 8 to 10 feet below the runway elevation. The right wing contacted a sand pile and the airplane rotated 20 degrees to the right prior to coming to rest. According to the 2001 Michigan Airport Directory and AirNav.com, there are 60-foot tall trees located 10 feet from the approach end of runway 35. Runway 35 has a 1,350 foot displaced threshold. Winds reported at the Charlevoix Airport (26 miles southeast of the Welke Airport) at 1315, were from 240 degrees at 6 knots.