A C310 PLT LOST BOTH ENGS DUE TO FUEL STARVATION; DURING APCH TO MDW. HE SWITCHED TO HIS FULL MAIN TANKS AND LANDED UNEVENTFULLY.

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I HAD BEEN WATCHING TSTMS DEVELOPING ALL THE WAY OVER FROM CLEVELAND (BKL). APCHING THE CHICAGO AREA; IT WAS OBVIOUS THAT IT WAS GOING TO BE QUESTIONABLE WHETHER I WOULD MAKE MDW BEFORE THE STORMS; APCHING FROM THE W; GOT THERE. I WAS PREPARED TO TURN AROUND AND HEAD BACK TO SBN; BUT IT LOOKED LIKE I WOULD BE ABLE TO MAKE MDW BEFORE THE WX GOT THERE. IT WAS A BUSY TIME; AS I WAS ASSIGNED A STAR THAT I HAD TO STUDY (GOSHEN3) AND WAS HAVING TROUBLE PICKING UP THE WX. I TRIED TO RUN MY PRE-DSCNT CHKLIST 3-4 TIMES BUT WAS INTERRUPTED BY TFC ON THE TCASII; OR CTLR DSCNT INSTRUCTIONS. AS I WAS BEING VECTORED ONTO THE FINAL APCH COURSE; I HIT A WALL OF HVY RAIN AND BEGAN TO LOSE THE R ENG AT THAT TIME. I ASSUMED IT WAS THE RAIN THAT WAS KILLING THE ENG (WRONG!) AND BEGAN TRYING TO DIAGNOSE THE PROB AND CTL THE AIRPLANE AT THE SAME TIME. AT THIS TIME; I RPTED THE PROB TO THE CTLR. THE RAIN AND WIND WERE FAIRLY STRONG AND COMPLICATING THE DIAGNOSIS AND KEPT ME FROM RUNNING THE EMER CHKLIST. ABOUT THIS TIME THE 2ND ENG FAILED AS WELL AND I BEGAN A STEEP DSCNT ABOUT 7-9 MI FROM THE ARPT; AS I ESTABLISHED BEST GLIDE. I TOLD THE CTLR I HAD NOW LOST BOTH ENGS AND HE TOLD ME THAT I WOULD NOT MAKE MDW AT THE CURRENT RATE OF DSCNT. FOR WHATEVER REASON (LUCK; TRAINING; OR ABJECT FEAR); I SUDDENLY REMEMBERED THAT I HAD BEEN ON THE AUX FUEL TANKS AND SWITCHED TO THE MAINS (WHICH EACH HAD 40 GALS IN THEM). BOTH ENGS CAME TO LIFE JUST AS MDW CAME INTO SIGHT. I TOLD THE CTLR THIS AND HE HANDED ME OFF TO THE TWR. THE TWR APPROVED RWY 4R AND I MADE A SOMEWHAT NORMAL LNDG (GIVEN MY STRESS LEVEL IT WAS FAR FROM PICTURE PERFECT). MDW HAD ALREADY SCRAMBLED THE FIRE TRUCKS. I WILL NEVER AGAIN BE RUNNING ON AUX FUEL WHEN I BEGIN MY DSCNT. I WILL FIND A WAY TO GET THROUGH THE PRE-DSCNT CHKLIST NO MATTER WHAT HAPPENS. FINALLY; THE FIRST PLACE I AM GOING TO LOOK ANYTIME AN ENG FAILS IS THE FUEL TANK SWITCHES. MY TRAINING PAID OFF; BUT I ALSO GOT LUCKY AND HAD EXCELLENT SUPPORT FROM THE CTLRS. THERE WAS JUST NO REASON FOR AN ALREADY CHALLENGING FLT; AND APCH; TO HAVE THE ADDED DRAMA OF A PLANE FALLING OUT OF THE SKY BECAUSE OF DRY AUX TANKS WHEN THE MAINS ARE SITTING ALMOST FULL. I AM A FANATIC ABOUT CHKLISTS AND YET; ON ONE OF THOSE RARE OCCASIONS WHEN I LET MY CHKLIST SCAN FALL THROUGH THE CRACKS; IT ALMOST COST ME. THERE IS JUST NO ROOM FOR ERROR FLYING SINGLE PLT IFR INTO BUSY AIRSPACE WITH CHALLENGING WX IN THE AREA. OBSESSING ABOUT THE WX AND ASSUMING IT WAS THE SOURCE OF MY PROBS WAS A MAJOR FACTOR IN THE INCIDENT.