PA-28 Cherokee/Archer/Dakota/Pillan/Warrior
Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 25; Flight Crew Total 7000; Flight Crew Type 3000
Communication Breakdown; Situational Awareness
Conflict NMAC; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented
Human Factors
Airport and pattern was in slight chaos; construction on the taxiways had 5 airplanes holding for take off with lots of aircraft in the pattern. ATC was moving fast with quick instructions. I was told to taxi onto runway and be ready to go. He had just released what I think was a training C-172; he then released me. I quickly lost sight of aircraft in front. I was departing the pattern to the east and we both were going to a certain point in the pattern. I thought the pattern aircraft had already turned downwind and I turned crosswind and was climbing at Vy and saw the pattern aircraft pass under me. I don't think he saw me. I did not need take any evasive action as I was a lot higher than he was.ATC came on the radio and asked if I had him in sight; I said yes and then ATC wanted to know if I was climbing and I said yes. No further transmissions were addressed to me and I left the pattern.The radio was nothing but non-stop radio calls; to and from the Tower by all the other aircraft. There were two tower operators working the same audio channel; maybe a training situation. I lost my departing traffic until I turned crosswind. I should have stayed on the upwind heading until I found the pattern traffic but I was getting very close to San Carlos airspace and I could [not] get an word in edge-wise to ask where my traffic was.I will be much more vigilant at this airport when it is so busy.
PA-28 pilot reported an NMAC with another light aircraft while departing PAO.