TXWY EXCURSION ATTEMPTING 180 DEG TURN.

Narrative

TAXIING AT NIGHT WITHOUT ANY ACFT PRECEDING US; WE HAD JUST STARTED L ENG AFTER SINGLE ENG TAXI TO RWY 21C AT DTW. APPROX 100 YARDS PRIOR TO TKOF END OF RWY 21C WHILE ON PARALLEL TXWY; TWR ASKED US IF WE WERE READY FOR TKOF. WE ADVISED THAT WE WOULD BE 'READY AT THE END.' TWR THEN CLRED US FOR TKOF AND ADVISED US OF LNDG TFC ON 4 MI FINAL. WE HAD COMPLETED AFTER-START CHKLIST AND HAD STARTED TAXI LIST WHEN I REALIZED LNDG TFC WAS TOO CLOSE TO LNDG AND WE ADVISED TWR THAT WE WOULD WAIT FOR LNDG TFC. TWR THEN CANCELLED TKOF CLRNC. IN THE MEANTIME; WE HAD TAXIED PAST THE APCH END OF RWY 21C AND ADVISED TWR. THEY SWITCHED US TO GND AND GND CLRED US TO MAKE 180 DEG TURN AT END OF PARALLEL (PAD AREA) PLT'S DISCRETION. WHEN ATTEMPTING TURN (R 45 DEGS; L 315 DEGS) R MAIN GEAR LEFT TXWY/PAD AND CAME TO A HALT. ENGS WERE SHUT DOWN; TWR ADVISED AND COMPANY RAMP WAS CALLED TO SEND A TUG. GND CREW ATTACHED TOW BAR AND PUSHED US BACKWARD ONTO PAVED AREA. GND CREW ADVISED THAT TXWY BLUE LIGHT AT THE AREA WHERE ACFT LEFT PAVEMENT WAS APPROX 10 FT OFF TXWY IN THE GRASS. WHEN FO CLRED R TURN; HE SAW ONLY PAVEMENT AND BLUE TAXI LIGHTS. PAX (NAVY PLT) SAID THAT AFTER WE CAME TO A STOP; HE KNEW WHAT HAPPENED BUT COULDN'T UNDERSTAND IT BECAUSE OUT HIS R WINDOW THE BLUE TAXI LIGHTS WERE STILL TO THE R OF THE ACFT. I FEEL THAT THE POS OF THE TAXI LIGHTS WERE MISLEADING CAUSING US TO THINK THAT WE HAD PLENTY OF ROOM TO MAKE TURN.