PA-28 pilot reported an near midair collision with another light aircraft while departing pao.

Attributes
ACN	1619759
Time
Date	201902
Local Time Of Day	1201-1800
Place
Locale Reference	PAO.Airport
State Reference	CA
Environment
Flight Conditions	VMC
Light	Daylight
Aircraft 1
Make Model Name	PA-28 Cherokee/Archer/Dakota/Pillan/Warrior
Operating Under FAR Part	Part 91
Flight Phase	Takeoff
Route In Use	Other leaving pattern
Flight Plan	VFR
Aircraft 2
Make Model Name	Skyhawk 172/Cutlass 172
Operating Under FAR Part	Part 91
Flight Phase	Takeoff
Route In Use	Other Pattern work
Flight Plan	VFR
Person 1
Function	Pilot Flying Single Pilot
Qualification	Flight Crew Flight Instructor Flight Crew Instrument Flight Crew Multiengine
Experience	Flight Crew Last 90 Days 25 Flight Crew Total 7000 Flight Crew Type 3000
Events
Anomaly	Conflict NMAC Deviation - Procedural Published Material / Policy
Miss Distance	Horizontal 100 Vertical 400

Narrative:

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.

Original NASA ASRS Text

Title: PA-28 pilot reported an NMAC with another light aircraft while departing PAO.

Narrative: 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.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.