AN ACR CREW WITH AN MEL'ED FMS MISREAD A COMMERCIAL AIRWAY CHART AND TURNED AT 55 DME FROM A FIX INSTEAD OF AT A D55 FIX. CREW WAS FATIGUED.

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WE WERE WITHOUT OUR FMS (MEL'ED) FLYING THE HARDU TWO ARR INTO CINCINNATI. WE THOUGHT THAT WHEN WE GOT TO DME 55 FROM HMV VOR WE SHOULD TURN R TO INTERCEPT THE 011 DEG RADIAL FROM VXV VOR. WHEN WE TURNED R THE NEEDLE FROM THE VXV VOR WAS FULL SCALE L. WHEN THIS HAPPENED I CALLED ZID AND ASKED HOW FAR OFF THE AIRWAY WE WERE. HE RESPONDED WITH 'I SHOW YOU HDG N AT 240.' BOTH THE FO AND I WERE CONFUSED AND UNSURE OF OUR POS. WE LOOKED AT OUR CHARTS TO TRY TO FIGURE OUT OUR POS. ABOUT THE SAME TIME WE GOT A TCAS ALERT ('TFC; TFC') THAT DISTR US FROM FIGURING OUT OUR ERROR. WE THEN ASKED FOR A DEV AROUND WX AND THE CTLR STATED 'STAND BY; YOU ARE 35 MI OFF COURSE AND I NEED TO COORDINATE EVERY TURN.' ABOUT THAT TIME WE FIGURED OUT OUR ERROR. THE 55 DME WAS THE SEGMENT FROM PACKO AND CHEDA (THE TURN POINT); NOT THE TOTAL DME TO CHEDA. WE HAD SIMPLY MISTAKEN 55 FOR D55 ON THE CHART AND TURNED AT 55 DME INSTEAD OF THE 90 DME WE SHOULD HAVE. WE EVENTUALLY GOT OUR DEV AND THE REST OF THE FLT WAS UNEVENTFUL. I CALLED ZID QUALITY ASSURANCE WHEN WE ARRIVED AND EXPLAINED WHAT HAD HAPPENED. HE STATED THAT WHILE WE OF COURSE SHOULD NOT HAVE TURNED; THE CTLR 'DIDN'T DO YOU ANY FAVORS' WHEN YOU ASKED FOR HELP BY ASKING FOR YOUR POS. THE ROOT CAUSE WAS SIMPLY READING THE CHART INCORRECTLY. I BELIEVE THE CAUSES OF READING THE CHART INCORRECTLY INCLUDE: 1) FATIGUE (WE ARE TIRED; BUT NOT ENOUGH TO CALL OUT FATIGUED). 2) POOR CHART DESIGN. THERE SHOULD BE A 'D90' ON THE CHART FOR CHEDA; NOT JUST THE SEGMENT DISTANCES. 3) WE ONLY HAVE TO FLY 'GREEN NEEDLES' WITHOUT AN FMS MAYBE ONCE A YR AT MOST. WHILE OF COURSE WE SHOULD KNOW OUR CHARTS; SHOULD WE REALLY BE ABLE TO FLY WITHOUT AN FMS WHEN WE ONLY DO IT ONCE ABOUT ONCE A YR? IT DOES REDUCE SAFETY MARGINS.