AN SMA PLT FINDS MVFR WX ENRTE WHILE ON A NO FLT PLAN FLT. CLBING UP THROUGH A HOLE IN THE CLOUD LAYER; HE INADVERTENTLY ENTERS MKE CLASS C AIRSPACE.

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FLT INTO CLASS C AIRSPACE WITHOUT ATC PERMISSION; WHILE CLBING TO VFR ON TOP CRUISE FLT. AIRSPACE VIOLATION OCCURRED AS A RESULT OF CLBING TO 3000 FT MSL; THROUGH 2200/4200 CLASS C'S OUTER RING WITHOUT CONTACTING APCH. SEQUENCE OF EVENTS: DEPARTING UES; WI; TO INTERSECT 155 DEG RADIAL FROM BAE VOR ENRTE TO LAKESHORE; TO FLY S TO MIEGS FIELD; CHICAGO; ENCOUNTERED MVFR AT 2000 FT MSL. BEGAN CLB THROUGH 'HOLE' TO GO VFR ON TOP. IN PROCESS OF 'CHASING' HOLE; NEGLECTED TO TUNE PROPER VOR RADIAL UNTIL 'ON TOP;' AT WHICH TIME PIC REALIZED THAT POS WAS WELL NE OF INTENDED RADIAL TRACK. TURNED TO PROPER HDG; INTERSECTED LAKESHORE N OF INTENDED INTXN POINT; THEN CONTINUED S TO DEST. WHEN INITIAL CONTACT WITH MIEGS TWR WAS MADE AFTER 5-6 ATTEMPTS; PIC WAS INSTRUCTED TO CALL CHICAGO APCH. ATTEMPTS FAILED TO RAISE APCH DUE TO CONGESTION. AGAIN CALLED MIEGS TWR FOR PERMISSION TO ENTER CLASS D AIRSPACE. CLRNC RECEIVED. DURING ROLLOUT I WAS ASKED TO COPY PHONE NUMBER TO CALL CHICAGO APCH SUPVR. CALL WAS MADE FROM TERMINAL. CHICAGO INSTRUCTED PIC TO CALL MKE APCH SUPVR. AT THIS TIME IT WAS OBVIOUS A VIOLATION OF AIRSPACE HAD BEEN MADE. ROOT CAUSE: 1) PIC LOSS OF POSITIONAL AWARENESS AND PREFLT INST SETTINGS OF VOR FREQ AND RADIAL. 2) LACK OF COM BY PIC -- TO MKE APCH FOR FLT FOLLOWING; ETC. CORRECTIVE ACTION; LESSONS LEARNED: 1) USE ATC/LCL APCH/DEP SVCS AT ALL TIMES WHEN MANEUVERING AND/OR TRANSITIONING NEAR AIRSPACE. 2) ADHERENCE TO PERSONAL FLT PLAN AND MORE THOROUGH REVIEW OF RATE OF FLT AND SURROUNDING AIRSPACE TO UNDERSTAND PROX OF FLT PATH TO CLASS D; C; B; AIRSPACES.