AN EXPERIENCED J5 PILOT REPORTS LOSING CTL OF THE ACFT AFTER A CROSSWIND LNDG AT A VERY SLOW SPD WITH FULL RUDDER. PROP DAMAGE RESULTED.

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I WAS FLYING MY J-5A CUB XCOUNTRY FOR ITS ANNUAL INSPECTION. I CALLED ZZZ1 WX. WINDS WERE 9 KTS AT 350 DEGS. I ESTIMATED WINDS ALOFT AT 2000 FT TO BE 15 KTS AND WITH THAT WIND CORRECTION ANGLE HIT ZZZ3 DEAD ON. I TUNED IN ZZZ2. ENRTE WINDS WERE LOWER THAN AT ZZZ1 (I DON'T RECALL WHAT). I MADE A ROUTINE APCH TO RWY 31. THE WIND WAS FROM THE N. THE 2 WINDSOCKS BILLOWED BUT IT APPEARED TO BE A 45 DEG XING FROM STARBOARD. I MADE A WHEEL LNDG ON THE NUMBERS IN THE CTR OF THE RWY. THE TAIL WAS DOWN; THE PLANE ON THE CTRLINE AT A POINT ABOUT 100 FT FROM THE TXWY INTXN WITH THE SPD SIGNIFICANTLY BLED OFF WHEN THE NOSE BEGAN TO VEER R. I CORRECTED WITH STEADILY INCREASING AMOUNTS OF L RUDDER. IT STOPPED FURTHER VEERING BUT DID NOT BRING THE NOSE BACK TO THE CTRLINE AT ALL. I BEGAN APPLYING BRAKES DURING THE VEER. I WAS SURPRISED THE NOSE DID NOT COME BACK. THE TIME INVOLVED WAS; AT BEST; A FEW SECONDS; DURING WHICH I BELIEVED I COULD CORRECT THE VEER. HOWEVER; ONCE FULL L RUDDER INPUT HAD BEEN MADE; I REALIZED THAT I WAS STILL A BIT TOO FAST TO MAKE THE TURNOFF BUT; REGARDLESS; THE PLANE WAS HEADING DIRECTLY AT A NEST OF TXWY AND RWY LIGHTS; AND I DIDN'T BELIEVE I COULD EITHER STOP OR AVOID THEM. I CUT THE SWITCH; KEPT FULL L RUDDER AND HARD L STICK. I EXPECTED TO ROLL THROUGH THE LIGHTS; BUT AS THE R GEAR LEG LEFT THE RWY AND FELL OFF THE 2-3 INCH LIP TO THE GRASS; THE TAIL CAME UP AND THE AIRPLANE NOSED OVER. IT HAPPENED VERY SLOWLY BUT THE PROP HAD NOT STOPPED WIND-MILLING WHEN IT HIT. THE NOSE DUG IN 3 FT SHORT OF THE LIGHT. BRAKES WERE NOT BEING APPLIED WHEN THE NOSE-OVER OCCURRED. AT THE TIME IT NOSED OVER; THE PLANE WAS GOING SLOW ENOUGH TO TURN SAFELY. IT JUST WOULDN'T GO L; AND THE LIGHTS WERE AHEAD AND TO THE R. IN RETROSPECT; I SHOULD HAVE ADDED SOME PWR WHICH WOULD HAVE GIVEN THE RUDDER THE AUTH I NEEDED TO SWING THE NOSE L. THIS WAS A VERY LOW SPD EVENT. I HAVE NEVER HAD A PROB CTLING THIS PLANE IN EVEN HIGH WIND CONDITIONS. I DID NOT EXPECT A SITUATION WHERE THE PLANE WOULD SWING R AT LOW SPD AND I COULD NOT CORRECT IT. I HAVE MADE 1458 TKOFS AND LNDGS IN THIS PLANE PRIOR TO THE INCIDENT. IT WAS A VERY DISCONCERTING LESSON AND A VERY HUMBLING EVENT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: REPORTER STATED THAT NO MECHANICAL PROBLEM CAUSED THIS EVENT. HE WAS SIMPLY GOING TOO SLOWLY TO CONTROL THE ACFT. THE PROP WAS DESTROYED AND THE LOWER COWLING WRINKLED BUT NO ENG DAMAGE WAS FOUND WHEN IT WAS DISASSEMBLED.