A PITTS S2B PILOT EXPERIENCED A NMAC WITH ANOTHER AIRCRAFT IN THE PATTERN AT LWM.

Narrative

I APCHED LWM FROM THE N FOR A FUEL STOP. I RPTED A 2 MI R BASE FOR RWY 23 AS INSTRUCTED BY THE TWR. THE PATTERN WAS VERY BUSY AND CHAOTIC WITH TFC GIVING AIRPLANE RIDES ASSOCIATED WITH A CHARITY EVENT (NOT RPTED IN A NOTAM DURING MY FAA PREFLT BRIEFING). THE TWR CTLR WAS HAVING DIFFICULTY GETTING THE OTHER ACFT TO TURN FROM L DOWNWIND TO L BASE AHEAD OF ME. THE CTLR ASKED ME TO TURN TO 110 DEGS; THEN TO A 90 DEG HDG TO AVOID THE TFC. DESPITE MY DILIGENT SCANNING; I COULD NOT LOCATE THE OTHER ACFT. I DID NOT SEE IT UNTIL IT TURNED BASE TO FINAL ABOUT 100 FT BELOW AND 100 FT AHEAD OF ME. I FOLLOWED THE ACFT IN FOR AN UNEVENTFUL LNDG. I SHOULD HAVE SEEN THE TFC EARLIER BUT DID NOT; DESPITE MY CONCENTRATED SEARCH. I SHOULD HAVE MANEUVERED MORE TO ENSURE I HAD A COMPLETELY UNOBSTRUCTED VIEW. I COULD ALSO HAVE ASKED THE CTLR FOR ADDITIONAL UPDATES ON THE TFC LOCATION; ALTHOUGH HE WAS QUITE PREOCCUPIED WITH THE OTHER TFC. A CONTRIBUTING FACTOR MAY HAVE BEEN MY LACK OF A DIRECTIONAL GYRO. AT TIMES THE COMPASS IS DIFFICULT TO INTERPRET WHILE MANEUVERING IN THE PITTS SPECIAL. IN ANY CASE; I BELIEVE I TURNED SUFFICIENTLY AWAY FROM MY ORIGINAL HDG TO SATISFY THE CTLR'S INTENT.