On July 29, 2003, about 1150 eastern daylight time, an Aeronca 11AC, N86233, owned and operated by a private pilot, sustained substantial damage when it exited runway 22 (3,120 feet by 24 feet, asphalt) at Brighton Airport (45G), near Brighton, Michigan, and impacted a construction vehicle. Visual meteorological conditions prevailed at the time of the accident. The private pilot and his flight instructor rated passenger reported no injuries. The 14 CFR Part 91 personal flight was not operating on a flight plan. The local flight departed 45G at 1100. The pilot stated: Doing pattern work, take offs and landings on runway 22, we were on our fourth landing attempt when the incident occurred. Each previous attempt ended with a go around after a couple of bounces on the runway. On this attempt the power was reduced to idle after the first touch and the second touch the airplane was in a 3 point attitude rolling on the runway and started to turn to the right and then was overcorrected to the left, then was corrected to the right. At this time the airplane continued to turn right between the runway lights and to about 80 degrees off the runway heading to the right and continued until kitting the side of a large earth mover. The earth mover was parked off the runway next to some bushes. We hit the side of the earth mover at about 10 mph. Even with full left rudder there was no change in the airplanes path in the turn to the right. A Federal Aviation Administration Inspector examined the airplane. He stated that the "left hand rudder cable forward attach point had separated from the torque tube, rendering the left hand rudder cable inoperative." At 1200, the recorded Livingston County Airport, near Howell, Michigan, weather was: Wind calm; visibility 10 statute miles; sky condition scattered 4,300 feet; temperature 19 degrees C; dew point 14 degrees C; altimeter 30.04 inches of mercury.