A SIGHT SEEING FLT TO MOUNT RUSHMORE FOLLOWED BY A VOR APCH TO RAP ENDS IN A LNDG TO RCA. A RECURRING NAV EQUIP PROB CONTRIBUTES TO THE EVENT.

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I MADE AN UNAUTH LNDG AT RCA; RWY 13; INSTEAD OF MY INTENDED LNDG AT RAP. IN SUMMARY; I WAS ON AN IFR FLT FROM FUNY TO FRAP TO VIEW THE MOUNT RUSHMORE AND CRAZY HORSE MONUMENTS; WHEN ON FINAL APCH TO RAP; I EXPERIENCED A SANDEL/DIRECTIONAL GYRO MALFUNCTION; WHICH CAUSED ME TO BELIEVE THAT I WAS INBOUND ON THE VOR RWY 14 APCH TO FRAP. BOTH ARPTS ARE QUITE CLOSE TO EACH OTHER (APPROX 6.2 MI APART; AND THE RWYS ARE ROUGHLY ALIGNED (RRAP IS RWY 14; AND KRCA IS RWY 13). I WAS CLRED FOR THE RAP RWY 14 VOR APCH; GIVEN A RADAR VECTOR FOR AN INTERCEPT COURSE TO TRACK THE COURSE INBOUND; AND CLRNC TO DSND; AND THEN FOR THE APCH; ONCE THE COURSE WAS INTERCEPTED; I INTERCEPTED THE RADIAL (THE DIRECTIONAL GYRO AND OBS NEEDLE SEEMED PROPERLY ALIGNED); BUT MY DME IN THE SANDEL BECAME INOP; AND WHEN I SAW THE RWY IN FRONT OF ME (LINED UP WITH MY DIRECTIONAL GYRO AND OBS); I WRONGLY BELIEVED I WAS LNDG AT RAP. I CHANGED FREQ TO THE TWR; IDENTED MYSELF AND I WAS CLRED TO LAND ON RWY 14. THERE WAS A VERY STRONG XWIND; SO I WAS CRABBED SIGNIFICANTLY TO THE R; AND I WAS NOSE HIGH; SO I DID NOT SEE ANY INDICATION THAT I WAS LNDG OVER A PORTION OF A CLOSED RWY. I BELIEVE THE SANDEL PIN CONNECTORS MUST BE FULLY SEATED TO THE PANEL CONNECTORS OR THIS PROB MAY RECUR WITH OTHERS. ALSO; GIVEN HOW CLOSE THESE ARPTS ARE; I BELIEVE THAT ATC SHOULD MONITOR PLTS IN THIS AREA TO ENSURE THAT THEY ARE NOT ON APCH TO THE WRONG ARPT. I THINK IT WOULD BE A GOOD IDEA FOR ELSWORTH APCH TO MONITOR THE RAP TWR FREQ TO INSURE THAT PLTS DO NOT MISTAKE THESE 2 ARPTS. AS I ALSO MENTIONED TO YOU YESTERDAY; OVER THE PAST 2 YRS I HAVE HAD A NUMBER OF INTERMITTENT PROBS WITH MY SANDEL THAT HAS REQUIRED VARIOUS REPAIRS. THIS PROB FIRST OCCURRED ABOUT 2 YRS AGO (AND MY MECH RESEATED THE SANDEL); AND THEN ABOUT 12-14 MONTHS AGO; THE PROB RECURRED TWICE; AND SANDEL AUTH REPAIR AND REPLACEMENT (FREE OF CHARGE) THE MOUNTING BRACKET FOR THE SANDEL.