Date: 201704
Local time of day: 1201-1800
Location: VGT.Airport, NV
Flight conditions: VMC
Light: Daylight
Aircraft: Skyhawk 172/Cutlass 172
Operator: FBO
Operating under: Part 91
Flight plan: VFR
Mission: Personal
Flight phase: Climb
Airspace: Class B LAS
ATC / advisory: TRACON L30
Second aircraft: Commercial Fixed Wing
Reporter organization: Personal
Reporter function: Single Pilot
Reporter qualification: Flight Crew Instrument; Flight Crew Private
Human factors: Confusion; Situational Awareness; Training / Qualification
Anomaly: ATC Issue All Types; Airspace Violation All Types; Conflict Airborne Conflict; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural FAR; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Person Air Traffic Control; Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Took Evasive Action
Contributing factors: Airspace Structure; Human Factors; Procedure
Primary problem: Human Factors

Narrative: I received a VFR departure clearance from VGT ground: After departure; heading 220; departure on 133.95; squawk XXXX. Upon departure contact I must have missed 'remain clear of Class B'. In my defense; I was very conscious of the Class B airspace since by my chart the 220 heading already had me in Class B. During the climb departure gave me further instructions to go no further south than 210; I was on a 220-225 heading at the time. This reinforced the feeling that I was cleared through Class B with positive control. During the climb I heard the same controller clear a Heavy departing LAS (26R I believe) and then followed with a clearance from 4000 to 8000 and a turn northeast. The controller then asked me when I intended to turn on my intended course (213). I responded that I would turn once clear of the Class B airspace; she replied I was already in Class B. While she was talking I had been watching the heavy turn directly into my path and; realizing we would be on a converging course initiated an aggressive dive. I heard the Heavy pilot state that they would be filling a 'proximity' report; after which the controller came on the frequency and stated that she had told me to remain clear of the Class B.My failures were approaching the departure in the immediate vicinity of a Class B airspace much too cavalierly. I would have benefited with a 5 minute evaluation of the LAS departure procedures to give me a better situational awareness. My aircraft is having an engine replaced. This was a rental; I did not fully know how to show the Class B airspace on the Garmin 430. I also made no effort to monitor my DME position from the LAS VORTAC. Finally I should have been listening intently for the 'remain clear' instructions; if those were made. I do believe that ATC contributed to confusion; first by a departure turn that already had me in the Class B airspace; and; if giving supplemental heading advice; to also call out an altitude limit. Certainly not a requirement as far as the letter of the law; but would have reduced confusion. My transponder was reporting altitude and position. The developing conflict should have been as readily apparent on the radar screen as it was to my own two eyes. In the future I will be exceptionally cautious on departures near any active airspace; and certainly Class B.




Synopsis: Cessna 172 pilot reported a Class Bravo intrusion along with an airborne conflict.