A C177 TFC WATCH PLT EXPERIENCED A RAPID DETERIORATION IN WX; CAUSING HIM TO SCUD RUN AND THEN ENTER IMC.

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I DEPARTED AT XA30 FROM LUK ON A ROUTINE TFC WATCH FLT WITH 1 RPTR ON BOARD. I TOOK OFF ON RWY 3L WITH THE MOON AND STARS CLRLY VISIBLE. AS I CLBED TO OUR CRUISING ALT OF 2000 FT MSL; I NOTICED SOME VERY LIGHT; WISPY SCUD ABOUT 1 MI N OF THE ARPT. I TURNED W TO GO OVER DOWNTOWN WHICH WAS ABOUT 4 MI AWAY. THEN AS WE PROCEEDED N ALONG THE INTERSTATE (71N) AT 2000 FT; I NOTICED THAT AN UNDERCAST WAS BEGINNING TO FORM BELOW US AT AN ESTIMATED 1500 FT. THIS WAS ABOUT 10 MINS INTO THE FLT AND I TOLD MY PAX THAT THE WX WAS NOT AS FORECAST AND THAT WE WERE GOING TO GO BACK INTO LUK BEFORE CONDITIONS DETERIORATED ANY FURTHER. THERE WERE SOME BREAKS IN THE UNDERCAST AND I DSNDED THROUGH ONE OF THEM TO 1500 FT; AS I TURNED TOWARDS THE ARPT. AT THIS POINT; I RPTED TO THE LUK CTAF (118.7) THAT I WAS ON A 4 MI FINAL TO RWY 21L. I HAD GOOD GND VISIBILITY AT THIS POINT; BUT FORWARD VISIBILITY WAS LESS THAN 1 MI. I HAD TUNED IN THE RWY 21L LOC FOR COURSE GUIDANCE BUT WAS NOT ON AN IFR APCH CLRNC. I DID NOT HAVE A GS RECEIVER; SO I DSNDED TO 1100 FT FOR THE STRAIGHT-IN RWY 21L LOC MINIMUMS. AT APPROX 1300 FT; AND ABOUT 2 MI NE OF THE ARPT; I ENTERED IMC WHICH LASTED ABOUT 30 SECONDS. WE BROKE OUT INTO MARGINAL VMC ABOVE THE ARPT; AT WHICH POINT I MADE AN UNEVENTFUL LNDG ON RWY 3L AT APPROX XA50. THE TWR OPENS AT XB00. FORECASTS AND CURRENT CONDITION RPTS INDICATED GOOD VFR CONDITIONS FOR THE DURATION OF THE PROPOSED 2 HR FLT. A RAPIDLY FORMING CLOUD LAYER OVER LUK AND THE SURROUNDING AREA DROPPED CONDITIONS FROM VFR TO IFR IN A PERIOD OF APPROX 10 MINS. I DID THE RIGHT THING BY TURNING TO THE ARPT AS SOON AS I SAW CONDITIONS DETERIORATING. I SHOULD HAVE ENLISTED THE HELP OF CVG APCH AND FILED AN IFR FLT PLAN. I BROKE THE FARS BY CONTINUING VFR INTO IMC. I WAS AIDED BY BEING INST CURRENT AND HAVING AN IFR EQUIPPED ACFT. THE SPD OF THE DEVELOPING CLOUDS WAS UNUSUAL AND NOT SOMETHING I HAD EXPERIENCED BEFORE. IN THE FUTURE; I WILL MAINTAIN VFR ON TOP; IF NECESSARY; UNTIL AN APPROPRIATE CLRNC CAN BE OBTAINED FROM ATC. MY MISTAKE WAS TO TRY AND 'DUCK UNDER' BEFORE THINGS GOT ANY WORSE. I REALIZE THAT COULD HAVE BEEN FATAL; AND WAS CERTAINLY A FOOLISH MISTAKE. I WILL NOT MAKE THE SAME ERROR IN THE FUTURE AND WILL USE THIS AS A LESSON OF WHAT NOT TO DO WITH MY STUDENTS.