Date: 201711
Local time of day: 0601-1200
Location: ZZZ.Airport, US
Flight conditions: VMC
Weather elements / visibility: VFR; 10
Light: Daylight
Aircraft: Bonanza 36
Operator: Personal
Operating under: Part 91
Flight plan: IFR
Mission: Personal
Flight phase: Final Approach
Airspace: Class D ZZZ
ATC / advisory: Tower ZZZ
Second aircraft: PA-28 Cherokee/Archer/Dakota/Pillan/Warrior
Reporter organization: Personal
Reporter function: Pilot Flying
Reporter qualification: Air Traffic Control Fully Certified; Flight Crew Air Transport Pilot (ATP); Flight Crew Flight Engineer; Flight Crew Multiengine; Flight Crew Instrument
Human factors: Situational Awareness
Second reporter function: Instructor
Anomaly: Conflict NMAC; Deviation / Discrepancy - Procedural FAR
Detector: Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Flight Crew Executed Go Around / Missed Approach; Flight Crew Took Evasive Action
Contributing factors: Environment - Non Weather Related; Human Factors; Procedure
Primary problem: Human Factors

Narrative: Approach Control had cleared me for a visual approach to follow a Cherokee on a practice ILS approach short final; and to contact Tower. I was cleared to land on [Runway] XXR and heard Local Control tell a Cherokee on right downwind for [Runway] XXR; to follow a Bonanza (me) on Final. The next thing I heard was Local Control ask the Cherokee if he was on base leg. Before there was a reply; my passenger yelled that an airplane almost hit us under our wing. I saw the Cherokee; number 3 for landing; disappear under our airplane. At the same moment this all happened; Local told me to maintain altitude. He told the Cherokee to continue north; if there was an instructor on board and to call the Tower; that he had a pilot deviation. It was one of the local training school airplanes doing pattern work. He; Local; then cleared me to land; again.I fly into this airport every month; and I am also a former controller and a recently retired airline Captain. I am very keen to listen to all traffic; and keep an awareness of the traffic. This day; I was busy looking for my short final Cherokee traffic to make sure I was not catching up to him. I have an iPad with WingX Pro; that displays traffic; but neither of these Cherokees have ADS-B; so they do not show up. My passenger was also trying to find the Cherokee short final with me; while also checking the iPad. The one drawback; Local was also working ground control and never issued a timely alert to me about the errant Cherokee and conflict alert that I am sure was going off in the cab. I was a flight instructor many years ago; so I know how it can be distracting to try and teach while also maintaining safety. This flight school needs to have a review of their procedures and standards.


Second narrative: CFI was giving instructions to student pilot and coming into [airport] for full-stop landing. Instructor's plane was on right downwind for right traffic pattern of Runway XXR. When Tower instructed/said; '[Call sign]; you will follow Bonanza off your right side; 2 miles.' Student pilot and instructor spotted aircraft 2 miles on final approach path and started the base turn to follow as per ATC's instruction. However; instructor missed Tower's radio call to the Bonanza afterward. (According to the record) Tower said; 'Bonanza; you will be following traffic 3 miles ahead; number 2; Runway XXR cleared to land...' It turns out that instructor was supposed to follow the traffic on final leg 5 miles off the airport; not the one on 2 miles straight in for Runway [XXR]. And; instructor's plane was number 3 for landing. Because instructor couldn't constantly monitor other conversations; instructor was staying on right base leg while Bonanza was approaching for final leg. Instructor and student couldn't spot Bonanza aircraft; and Bonanza aircraft also couldn't spot our airplane until instructor's airplane crossed/passed their final path 700 feet below (based off ATC's radar altitude encoder). After near miss; instructor followed Tower's instruction to continue inbound for landing on final leg. Pilot understood the mistake/deviation made from ATC's instruction that caused the near miss. Instructor should have paid more attention on radio for better situational awareness to avoid any kind of incident/accident [from] happening. Instructor went over the voice records after landing to review/check own performance and mistake to prevent the same situation in future.


Synopsis: A Bonanza pilot and a Piper PA28 flight instructor reported that misunderstanding of ATC instructions caused a NMAC.