L1011 ACFT ON TKOF ROLL; FLC FELT BAD SHAKING AND CONTINUED. AFTER TKOF 'C' HYD SYS WAS LOST DISABLING RAISING THE GEAR AND NOSEWHEEL STEERING. FLC LEVELED AT 5000 FT; DUMPED 30000 LBS OF FUEL; DECLARED AN EMER AND RETURNED FOR AN UNEVENTFUL LNDG. NOSEWHEEL TIRE HAD BLOWN TAKING OUT THE HYD LINES FOR 'C' SYS.

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ABOUT 20 KTS BEFORE V1/VR WE FELT A BAD SHAKING. FELT LIKE WE BLEW A TIRE. GOT AIRBORNE AND DECIDED TO NOT RAISE GEAR. SO RPTED THAT WE LOST 'C' HYD SYS WHICH MEANT WE COULD NOT RAISE THE GEAR AND HAD LOST NOSEWHEEL STEERING PLUS PARTS OF OTHER SYS. CLB TO 5000 FT MSL AND DUMPED 30000 LBS OF FUEL TO PUT US BELOW MAX LNDG WT. TKOF WT WAS 379500 LBS. WE WERE NOT SURE IF A MAIN TIRE(S) HAD BLOWN. WE HAD A R 'TRUCK' LIGHT WHICH MADE ME SUSPECT A BLOWN R MAIN -- THE REASON FOR DUMPING AND PREPARING THE PAX FOR AN EMER LNDG AND POSSIBLE EVAC. WE DECLARED AN EMER WITH APCH AND REQUESTED THE LONGEST RWY AND EQUIP. UNEVENTFUL LNDG UNTIL NOSEWHEEL WAS LOWERED. THEN GOT THE SHAKING. WE THEN KNEW IT WAS A NOSEWHEEL TIRE(S). WAS ABLE TO CLR RWY WITH DIFFERENTIAL BRAKING AND PWR. A RECAPPED NOSE GEAR TIRE HAD COME APART AND TOOK OUT HYD LINES FOR THE NOSEWHEEL STEERING AND CAUSED THE TOTAL LOSS OF 'C' SYS. WX WAS 700 FT OVCST GOOD VISIBILITY. SUGGESTION: ATC SHOULD INFORM PLT OF MINIMUM DUMP ALT. IN ATL 5000 FT WAS A BIT TOO LOW; A FACT I FOUND IN OUR GENERAL OPS MANUAL; BUT NOT IN OUR ACFT OPS MANUAL WHICH HAD OUR EMER PROCS.