C150 DEPARTING ADS HAS NMAC WITH SUCCEEDING FASTER C172.

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THE PREFLT; TAXI AND TKOF WERE UNREMARKABLE. I BELIEVE I WAS SITTING AT TXWY C (ON THE E SIDE OF THE RWY); WAITING FOR TKOF CLRNC. I WAS SEQUENCED FOR WHAT APPEARED TO BE THE #5 POS FOR TKOF. WHAT APPEARED TO BE THE INCIDENT C172; WAS DIRECTLY ACROSS FROM ME ON THE OPPOSING TXWY. THE OTHER ACFT IN FRONT OF ME WERE QUICKLY SEQUENCED AND DEPARTED. THIS LEFT ME AND THE C172 -- WHICH I WAS SEQUENCED AHEAD OF. I WAS CLRED FOR TKOF AND THE C172 WAS CLRED FOR TKOF IMMEDIATELY BEHIND ME. KNOWING THAT HE WOULD OVERTAKE ME; I TURNED TO THE E MORE THAN USUAL; BEFORE HEADING N TO THE PRACTICE AREA. I WAS UNDER THE IMPRESSION HE WAS A NORTHERLY DEP AND I WANTED TO GIVE HIM PLENTY OF ROOM TO PASS AHEAD OF ME. AS WE LEFT ADDISON'S AIRSPACE; THE CTLR CALLED THE C172 AND TOLD HIM THERE WAS A C150 IN FRONT OF HIM. AS I RECALL; THE PLT SAID; 'HE HAD THE TFC IN SIGHT.' I CLBED AT ABOUT 500 FPM TO 2000 FT MSL AND TURNED SLOWLY TO A HEADING OF ROUGHLY 360 DEGS. FROM TKOF; I HAD TRAVELED APPROX 8-10 MI WHEN THE INCIDENT OCCURRED. THE C172 SUDDENLY APPEARED OFF MY L WING; AT A DISTANCE OF WHAT APPEARED TO BE ABOUT 40 FT. MY ALT WAS 2000 FT MSL AND HIS WAS 2000 FT MSL. MY HEADING WAS 360 DEGS AND HIS WAS 350 DEGS. WE WERE WINGTIP TO WINGTIP. THE OTHER ACFT WAS ALSO BOUNCING IN TURB ABOUT 10 FT UP AND DOWN. THE TURB WAS LIGHT WITH OCCASIONAL MODERATE. THE OTHER ACFT WAS MOVING FROM R TO L AND HE WAS IN A VERY SHALLOW L-HAND TURN MOVING THROUGH ABOUT 350 DEGS AND PULLING AHEAD OF ME. THE WAY ACFT SUDDENLY 'APPEARED SO CLOSE' WAS VERY STARTLING. ALSO; THE WAY HE JUST 'APPEARED' OFF MY L WING; GAVE ME THE IMPRESSION THAT HE CAME DOWN OR BOUNCED DOWN; FROM A SLIGHTLY HIGHER ALT. I COULD SEE THE PERSON IN THE COPLT SEAT; HE WAS LOOKING STRAIGHT AHEAD. THE OTHER ACFT CONTINUED ON SOMEWHAT OF A NW HEADING OVER TO LAKE LEWISVILLE; AND MOVED OUT OF SIGHT. I ABORTED THE TRAINING MISSION AND RETURNED TO MY HOME BASE. AFTER LNDG; I CONTACTED ADDISON TWR BY PHONE AND TOLD THE TWR SUPVR WHAT HAD HAPPENED. THE CAUSE OF THE NEAR MISS WAS THE FAILURE OF THE PLT OF THE OVERTAKING ACFT TO KEEP ME IN SIGHT EVEN AFTER ATC SPECIFICALLY ALERTED HIM TO THE TFC. ANOTHER FACTOR MAY HAVE BEEN CONVECTIVE TURB. IT IS PUZZLING THAT SINCE HE WAS TURNING FROM R TO L; HE POSSIBLY COULD HAVE SEEN ME IN HIS 10 OR 11 O'CLOCK POS BEFORE HE INITIATED HIS TURN. THE REASON FOR HIS FAILURE TO SEE AND AVOID IS UNKNOWN.