THE PLT WAS PARTICIPATING IN AN OPEN COURSE AIR RACE TO JACKPOT, NV. HE PLANNED TO MAKE AN EN ROUTE STOP AT ARCO, ID TO REFUEL. THE WX FORCAST CALLED FOR MARGINAL CONDITIONS. THE PLT MADE A TELEPHONE CALL TO ARCO & CONFIRMED THAT THE WX (AT THAT TIME) WAS VFR, SO HE PROCEEDED WITH THE FLT. FOR WEIGHT CONSIDERATIONS, HE TOOK OFF WITH ONLY 38 GAL OF FUEL ON BOARD. HOWEVER, AFTER ARRIVING IN THE AREA OF ARCO, A HEAVY RAIN SHOWER PREVENTED HIM FROM LANDING. HE CHOSE TO CONTINUE TO BURLEY, ID, BUT BEFORE REACHING HIS ALTERNATE STOPPING POINT, THE ENG LOST POWER FROM FUEL EXHAUSTION. SUBSEQUENTLY, THE ACFT WAS DAMAGED DURING A LANDING ON ROUGH TERRAIN. TOTAL TIME OF ENG OPERATION WAS APRX 4 HR & 50 MIN. ACCORDING TO THE OWNER'S MANUAL, 38 GAL WOULD HAVE PROVIDED ABOUT 4.9 HRS OF FLT TIME. LESS THAN 1 PINT OF FUEL WAS FOUND IN THE FUEL TANKS.