AN A300 ON A NON-PRECISION APCH TO SDF DSNDS BELOW THE CHARTED ALT AND GETS GPWS 'TERRAIN' AND 'PULL UP' WARNINGS. CREW ADJUSTS ALT AND CONTINUES APCH.

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FLYING INTO SDF WHERE THE WX WAS RPTED AT 1200 FT AND 8 MI WE WERE EXPECTING THE LOC TO RWY 35L. WE BRIEF THE APCH COMPLETELY TO BE SURE WE WERE BOTH ON THE SAME PAGE FOR IT HAD BEEN SOME TIME SINCE EITHER ONE OF US HAD DONE A LOC APCH (NON PRECISION APCH). DURING VECTORS WE HAD NOTICED APCH CTL WANTED THE ACFT TO KEEP THEIR SPD UP UNTIL REACHING CARDINAL. WE DISCUSS THAT WE WOULD NEED A GREATER DSCNT RATE IN ORDER TO COMPLY WITH ATC. ESTABLISH INBOUND ON THE LOC ATC CLRS US FOR THE APCH. WE CONFIGURED THE ACFT TO CROSS CARDINAL IN LNDG CONFIGN AND PROCEEDED TO START DOWN TO OUR XING FIX; AND THEN DOWN TO THE MDA. AS WE BROKE OUT I IMMEDIATELY NOTICE THAT WE WERE LOW; AS THE PAPI LIGHT ALSO INDICATED. WE IMMEDIATELY LEVEL THE ACFT AND AT THE SAME TIME WE RECEIVE TERRAIN GPWS. WITH THE RWY IN SIGHT; WE INITIATED A SLIGHT CLB TO PUT US BACK ON THE PAPI. AT THAT SAME TIME WE RECEIVE A GPWS 'PULL UP' WHICH WE HAD ALREADY PREVIOUSLY INITIATED. WE WERE REESTABLISHED ON THE APCH IN SECONDS AND PROCEEDED WITH A VISUAL APCH AND LNDG ON RWY 35L. ONCE ON THE GND; AND THE ACFT SECURE WE TALKED ABOUT WHAT HAD JUST HAPPENED. WE BELIEVE THAT WE CONVINCED OURSELVES THAT DUE TO THE FASTER AIRSPD THAT ATC REQUESTED; THAT WE REALLY NEEDED TO HURRY DOWN DURING THE APCH IN ORDER TO COMPLY WITH BOTH THE APCH CRITERIA; AND ATC REQUEST. IN HINDSIGHT; EVEN THOUGH WE WERE VMC; WE SHOULD HAVE DONE A GAR; AND CAME BACK AROUND FOR ANOTHER APCH. A LESSON WELL LEARNED! SUPPLEMENTAL INFO FROM ACN 713472: I 'THINK' BOTH PLTS MISREAD DISTANCE BY READING DISTANCE ON TOP OF EHSI; INSTEAD OF READING DISTANCE FROM ILS DME AS WE BRIEFED. WE BEGAN DSCNT TO MDA OF 860 FT AT WHAT WE THOUGHT WAS 4.5 DME BUT WAS PROBABLY 4.5 MI FROM THRESHOLD.