OFF ARPT LNDG PLANNED WHEN A BEECH A-36 PLT FALTERS IN HIS FIRST APPLICATION OF HIS FUEL EMER CHKLIST OVER NANTUCKET SOUND; 10 MI S OF HYA; MA.

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I HAD JUST DEPARTED CHATHAM (CQX) AFTER A XWIND LNDG IN MY BE-A36 AND CLBED UP TO 3000 FT MSL ENRTE BACK TO EWB. I WAS HDG ABOUT 310 DEGS AND WAS OUT OVER NANTUCKET SOUND AND DURING THE COURSE OF THE LEANING PROC NOTED THAT WHEN I ENRICHED THE MIXTURE; THE FUEL FLOW ACTUALLY BEGAN DECREASING INSTEAD OF INCREASING. I IMMEDIATELY BEGAN A CLB ON COURSE AND AT APPROX 5000 FT MSL THE ENG WAS NO LONGER PRODUCING ANY PWR. THE NEAREST ARPT WAS HYA; APPROX 10 MI N OF MY POS. I ATTEMPTED BEST GLIDE; AND CHANGED FUEL TANKS; MADE SURE THROTTLE; PROP AND MIXTURE CTLS WERE FULL FORWARD; MAGNETOS ON 'BOTH;' DECLARED AN EMER AND BEGAN THE DSCNT INTO HYA. AT APPROX 3000 FT I WENT THROUGH IT AGAIN AND THIS TIME TURNED ON THE FUEL BOOST PUMP WHICH CAUSED THE ENG TO REGAIN PWR AND I INFORMED HYA TWR OF THAT AND TOLD THEM I'D LIKE TO PROCEED TO EWB AT THAT TIME. THEY ASKED ME IF I WAS SURE; AND I STATED THAT I WOULD LAND AT HYA AND HAVE THINGS CHKED OUT; AND I MADE AN UNEVENTFUL LNDG AT HYA. THE FOLLOWING ARE WHAT I THOUGHT I MIGHT HAVE DONE BETTER ON THIS FLT: 1) I DID NOT OBTAIN A COMPLETE WX BRIEFING (IT WAS SOLID VFR OVER MY RTE OF FLT) AND I HAD DONE A COMPUTER WX BRIEF FOR THE AREA BUT I HADN'T OBTAINED THE WINDS ALOFT; NOTAMS; ETC. I KNEW FROM MY FLYING THAT DAY THAT THE WINDS ALOFT WERE FROM THE NNW AND THAT WHEN I HEADED TO HYA I WAS BUCKING A FAIRLY STRONG HEADWIND. IT BECAME APPARENT THAT DURING MY DSCNT WITHOUT PWR THAT I WAS NOT LIKELY TO MAKE THE ARPT AND THAT I WOULD HAVE TO LAND OFF ARPT. A BETTER CHOICE MIGHT HAVE BEEN TO TURN S AND LAND ON THE BEACH AT NANTUCKET. 2) I HAD DIFFICULTY HOLDING BEST GLIDE SPD IN MY AIRPLANE OF 110 KIAS AND INSTEAD FLUCTUATED BTWN 90-100 KIAS. 3) I DID NOT GO THROUGH THE ENG OUT CHKLIST IN AN ORDERLY FASHION. THIS LED TO A DELAY IN SELECTING THE ELECTRIC FUEL BOOST PUMP AND NEEDLESS GLIDING ALONG WITHOUT PWR; AND 4) ONCE THE PWR HAD BEEN REGAINED; IT WAS POOR JUDGEMENT TO EVEN THINK ABOUT GOING TO ANOTHER ARPT UNTIL THE ENG HAD BEEN CHKED OUT. TO RECTIFY THIS SIT; I WILL RECEIVE ADDITIONAL EMER PROC TRAINING; OBTAIN COMPLETE WX BRIEFING AND TRY AND EXERCISE BETTER JUDGEMENT. I DON'T THINK THAT THE FAA WILL HAVE ANY ISSUES THAT MAY LEAD TO AN ENFORCEMENT ACTION; HOWEVER; I AM SUBMITTING THIS IN HOPES THAT OTHERS MAY LEARN FROM MY EXPERIENCE.