B737 ACFT ENCOUNTERS WAKE TURB BEHIND A B777.

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BEING VECTORED FOR THE APCH TO RWY 4R AT ORD WE APPARENTLY FLEW INTO WAKE OF AN ACR B777 6 MI AHEAD BEING VECTORED FOR THE SAME RWY. WE EXPERIENCED A HIGH RATE OF ROLL TO THE L WHICH REQUIRED MOST OF THE AVAILABLE AILERON AND SUBSTANTIAL RUDDER TO STOP THE ROLL. THIS WAS FOLLOWED BY (2) MORE ENCOUNTERS OF LESS MAGNITUDE. WE ASKED FOR MORE SPACING AND FLEW APCH 1 DOT HIGH ON GS TO RWY. NO OTHER PROBS NOTED. NO INJURIES TO FLC OR PAX. AUTOPLT WAS DISCONNECTED AFTER 1ST ENCOUNTER. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THIS RPTR PARTICIPATED IN THE STRUCTURED WAKE TURB CALLBACK STUDY. DSNDING AND CLOSE TO THE ARPT; THIS RPTR WAS FLYING WHEN HIS ACFT ENCOUNTERED WAKE TURB FROM A PRECEDING B777. HE HAD A ROLL L AND R OF 20 DEGS. MAX FLT PATH DISPLACEMENT WAS ONLY 50 FT. HE DID NOT HAVE FULL CTL DURING THE ENCOUNTER BUT HAD PARTIAL CTL. THE ENCOUNTER LASTED ABOUT 9 SECONDS. AS SOON AS THEY WERE ABLE TO FLY UP AND OUT OF THE WAKE; THE RPTR FLEW 1 DOT HIGH ON THE GS TO CLR ANY OTHER WAKE GENERATED BY THE B777. REMAINDER OF THE APCH AND LNDG WENT WELL. RPTR FEELS HE WOULD LIKE GREATER SPACING BEHIND A HVY ACFT. THE OTHER THING HE WOULD DO IS QUESTION TRACON WHERE A PRECEDING ACFT STARTED HIS DSCNT. HE WOULD LIKE MORE INFO AS TO THE PRECEDING ACFT GND TRACK AND VERT TRACK. THAT INFO WOULD HELP HIM PLAN TO BE ABOVE OR DISPLACED LATERALLY FROM ANY WAKE. SUPPLEMENTAL INFO FROM ACN 331996: WE HAD A HIGH RATE OF ROLL TO THE L WHICH REQUIRED MOST OF THE AVAILABLE AILERON AND A SUBSTANTIAL AMOUNT OF RUDDER TO STOP; AND THEN CORRECT THE ROLL. THIS WAS FOLLOWED BY 2 MORE ROLL EVENTS OF LESS MAGNITUDE. ASKED FOR AND WAS GIVEN MORE SPACING BEHIND THE TFC AND FLEW 1 DOT HIGH ON APCH TO RWY. CALLBACK CONVERSATION WITH RPTR OF ACN 331996 REVEALED THE FOLLOWING INFO: THIS RPTR PARTICIPATED IN THE WAKE TURB INCIDENT CALLBACK. THE RPTR HAS BEEN INVOLVED IN OTHER WAKE TURB INCIDENTS AND THIS WAS NOT AS SEVERE AS OTHERS; HOWEVER; IT WAS LONGER LASTING. HIS ESTIMATE OF THE DURATION WAS 9 SECONDS. DURING THIS TIME HE RPTED THAT THERE WAS PARTIAL CTL OF THE ACFT AVAILABLE. HIS AIRSPD AT THE TIME OF THE INCIDENT WAS 210 KTS WHICH HELPED THEM CLB UP AND OUT OF THE WAKE. RPTR SUGGESTION ON HOW TO AVOID WAKE IN THE FUTURE IS ASSIGN ADDITIONAL SEPARATION; DSND NARROW BODY ACFT ON A TRACK DIFFERENT FROM WIDE BODY ACFT; AND GIVE FOLLOWING ACFT AN OFFSET GND TRACK TO THE RWY. RPTR DID STATE THAT SINCE THE AILERON CTL WAS REDUCED WHEN IN THE WAKE; CTL WAS ESTABLISHED BY LARGE INPUT OF RUDDER CTL. RUDDER IS MOST EFFECTIVE IN STOPPING THE ROLLING ACTION OF THE WAKE.