Date: 201203
Local time of day: 0601-1200
Location: BJC.Airport, CO
Flight conditions: VMC
Weather elements / visibility: 30
Light: Daylight
Aircraft: Bonanza 33
Operator: Personal
Operating under: Part 91
Flight plan: None
Mission: Personal
Flight phase: Final Approach
Airspace: Class D BJC
ATC / advisory: Tower BJC
Second aircraft: Cessna Single Piston Undifferentiated or Other Model
Reporter organization: Personal
Reporter function: Single Pilot; Pilot Flying
Reporter qualification: Flight Crew Private
Anomaly: Airspace Violation All Types; Conflict NMAC
Detector: Person Flight Crew
When detected: In-flight
Result: Flight Crew Took Evasive Action
Contributing factors: Procedure; Human Factors; Environment - Non Weather Related
Primary problem: Ambiguous

Narrative: I contacted BJC Tower about 10 miles north of the airport at about 7;000 MSL. I was cleared to enter a right downwind for 29R. I had been following a Piper Dakota that was also told to enter a right downwind for 29R. During the descent to traffic pattern altitude and before entering the downwind; I heard Tower tell the Dakota they were number 2 and then tell a Saratoga to follow the Dakota and that the Saratoga was number 3. I was then told to follow the Saratoga and that I was number 4. I told Tower that I was behind the Dakota and didn't have the Saratoga in sight. Tower asked me to IDENT which I did. Tower then asked me to IDENT again a few moments later; which I did. I slowed my airspeed as much as practicable (landing gear and flaps down) and scanned intently for traffic while following what I believe to be the Dakota.While [I was] on downwind the Tower changed me to Runway 29L. The Dakota landed and was turned off at A7 from Runway 29R.As we were turning a wide right base for Runway 29L the Tower urgently told a Cessna (I believe) on short final for 29R to go around. I'm not sure whether an airplane made a runway incursion; the Cessna on short final was landing on the wrong runway or whether the Tower cleared the Cessna to land and cleared an airplane onto the same runway.I believe I was cleared to land on Runway 29L and was on a 2-3 mile final when I spotted a Cessna on a left base for 29L turning final directly in front of us and cutting off our final approach path to Runway 29L. It seemed pretty clear to me that the Cessna did not see me on final for 29L before the turn or during the turn. I estimate that we were no more than 200 FT horizontally and 10-20 FT below the Cessna turning in front of us. I took evasive action by starting a left 360 turn. I told the Tower that I was executing a left 360 to avoid the Cessna that turned in front of me and the Tower acknowledged. As I executed the left 360 back to a final for Runway 29L I watched a Challenger (I believe) on final approach to land on 29R. I assume this Challenger traffic was why the Controller switched me to 29L from 29R.From our very first radio call it was clear that traffic was busy at BJC and I believe the Tower Controller was a bit overwhelmed. While I realize it is my responsibility to see and avoid traffic in VFR conditions the Controller seemed to have a poor mental picture of the traffic in his airspace and offered very few traffic advisories. On two occasions before the near midair collision with the Cessna; I considered leaving the Class D airspace and coming back later as I was concerned that the Tower Controller was not on top of the traffic in his airspace. During this situation the Tower Controller did tell some other traffic to remain clear of Class D so at least he was trying to gain control of the situation.I should have had a better mental picture of the traffic as well and being surprised by the Cessna turning into my final approach path should not happen. I believe the factors that caused me to have a suboptimal picture of the traffic for 29L included my wife being upset by the Controller's frantic calls to have the Cessna go around minutes before and the switch from Runway 29R to 29L. I should expect to land on any runway and have a picture of all the traffic in the airspace. I should have also done a better job of scanning for traffic in the 29L pattern.




Synopsis: A BE33 pilot experienced an NMAC with a Cessna while maneuvering to final from opposite direction base legs at BJC.