PLT OF AN SMA SEL FLEW BELOW THE MINIMUM SAFE ALT DURING THE EXECUTION OF AN NDB INST APCH.

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DURING RECURRENT TRAINING WITH INST RATED PLT; WE WERE CLRED FOR NDB RWY 29R APCH AT SCK. HDOF TO TWR FROM APCH HAD OCCURRED OUTSIDE MARKER (LOM). STUDENT STRAYED SLIGHTLY E OF COURSE; CORRECTED. AFTER CORRECTION; DUE TO EQUIP (ADF) DISPLAY ERROR; HE APPEARED TO BE ON COURSE. (ACTUALLY; WE WERE NE OF COURSE; BASED ON MY VIEW OF ARPT). I ALLOWED HIM TO CONTINUE; WISHING FOR HIM TO 'SUCCESSFULLY' COMPLETE THE APCH; AND APPRECIATE THE LIMITATIONS OF ADF EQUIP. I CANCELED OUR IFR STATUS WITH THE TWR; SO THAT THEY COULD ALLOW US TO CONTINUE THE APCH 'OFF COURSE.' THE AREA AROUND THE ARPT IS MOSTLY UNDEVELOPED. HOWEVER; THERE IS A CORRECTIONAL FACILITY 2- 3 MI NE OF ARPT. WHILE I WAS VIGILANT FOR TFC IN VICINITY; I INADVERTENTLY ALLOWED ACFT TO OVERFLY THE FACILITY AT MDA (400 FT AGL). I BELIEVE THIS WAS IMPROPER; DUE TO MY KNOWLEDGE OF OUR OFF-COURSE STATUS; AND SINCE OUR LOW ALT WAS A RESULT OF MY DESIRE FOR REALISM IN TRAINING; NOT 'NECESSARY FOR TKOF OR LNDG' (91.119). AN ALT OF 500 FT AGL SHOULD HAVE BEEN MAINTAINED IN THIS SIT. I COULD HAVE SPECIFIED CIRCLING MINIMUMS; OR SIMPLY REVISED MDA TO 500 FT. I AM NORMALLY ALERT TO THIS SORT OF TRAINING EXCURSION INTO A POSSIBLE CONFLICT WITH A REGULATORY (OR COMMON SENSE SAFETY) REQUIREMENT DUE TO MY 3000 HRS AS CFI-IA-MEI. I AM NOT COMPLACENT. HOWEVER; ON THIS DAY; I WAS FATIGUED AND UNCOMFORTABLE FROM A MEDICAL CONDITION WHICH I THOUGHT WOULD NOT IMPACT MY JUDGEMENT OR VIGILANCE. ALSO; THIS PLT WAS ABSORBING MORE OF MY ATTN THAN USUAL DUE TO HIS PROBS WITH NDB PROCS. THE IMPORTANT CONSIDERATION OF WHAT WAS UNDERNEATH US ESCAPED MY SITUATIONAL AWARENESS. I WILL BE MORE ALERT TO THIS SIT IN THE FUTURE.