Date: 201905
Local time of day: 1801-2400
Location: ZZZ.Airport, US
Flight conditions: VMC
Weather elements / visibility: Dirty windscreen; 10
Light: Daylight
Aircraft: Skyhawk 172/Cutlass 172
Operator: Personal
Operating under: Part 91
Flight plan: None
Mission: Training
Flight phase: Initial Approach
Airspace: Class G ZZZ
ATC / advisory: CTAF ZZZ
Second aircraft: Cessna 150
Reporter organization: Personal
Reporter function: Instructor; Pilot Not Flying
Reporter qualification: Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Human factors: Situational Awareness
Anomaly: Conflict NMAC
Detector: Person Flight Crew
When detected: In-flight
Result: Flight Crew Took Evasive Action
Contributing factors: Procedure
Primary problem: Procedure

Narrative: This is a revised/updated report from one I filed [previously]. Of particular interest is the difference in estimated miss distance in this report vs the [previous] report. The [previous] report said separation was 1000 ft horizontal and 1000 ft vertical. This updated report lowers my estimate to 100 vertical and horizontal; although I never saw the other airplane (C150) until after we both landed. For all I know; we were within a wingspan of each other. The pilot of the C150 said he did not see us either; so we don't know for sure what the separation was.Returning from a training flight from the east to home airport ZZZ in FBO's C172 with student in the left seat. I was PIC instructor pilot in right seat. Pattern entry to ZZZ from the east is either crosswind entry; or 45 to the upwind; for landing rwy XX. I chose xwind entry because of our position.I was about to make a radio call advertising 3 miles east for xwind entry left traffic rwy XX when I heard a C150 pilot say he was turning (or entering; I'm not sure which) upwind for rwy XX. I *thought* had previously heard him announce his takeoff so I *thought* I knew where he was. ADS-B In confirmed a target just starting the upwind leg; 900 feet below us... except in retrospect he was 900 feet above us (and 1-2 miles off our 10:00 position). Unfortunately; expectation bias kicked in and I recognized the number '900' but somehow ignored the plus sign and interpreted it as a minus sign; 900 feet below us. It's the only thing that made sense to me at the time. After all; I thought he had called his takeoff; announced turning upwind; and that's about where he would be if my expectations were correct. Trouble is; they weren't. Add to that the fact that no one should be descending into the upwind leg; so the 'plus' in front of the '900' simply did not compute.A frightening NMAC occurred as he got closer and closer to us; much faster than I would expect a 100-hp C150 to climb; and 'climbing' much faster than a 100-hp C150 could possibly climb; based on the numbers on the ADS-B getting smaller (900...800...700... feet below us; or so I thought). Here's the catch. He wasn't entering upwind following a takeoff; he was returning from the south and descending into the upwind. Want proof? I looked at [website] and found the C150's ADS-B track. The hits show him at 1800 MSL and then 1600 MSL descending into the upwind. A minute later; he was at [pattern altitude] for the upwind-to-crosswind turn.Meanwhile; we were level at [pattern altitude] entering crosswind at the same time as the C150's upwind-to-crosswind turn. [Expletive].Sadly; our data (C172) was not captured by the online system. Our C172 was ADS-B Out and In equipped and was displaying other traffic including the nearby C150; so why our data is not visible on the above website is a mystery to me.Due the distraction and subsequent focus on finding the other aircraft visually in order to determine my next move (continue into the xwind vs. wave off); I failed to make a radio call. Big mistake.Usually; an airplane at pattern altitude; which we were; can continue from the east and enter the xwind well before a climbing aircraft in the C150's 'entering upwind' position becomes a threat. Since I had instructed my student to slow the airplane down prior to pattern entry (2300 RPM; 80-85 kts); it appears we approached the upwind/crosswind corner at the same time as; and very close to; the C150. However; despite seeing his position on our ADS-B display; neither my student nor I was able to make visual contact. We were pointed almost directly at the sun looking through a dirty; bug-smashed windscreen (photos available on request.) Finding the target was proving to be impossible; so I kept some of attention on the ADS-B display while instructing my student to keep looking for the C150.Note: The C150 was being piloted by a fellow CFI with a student. This may be significant in the sense that both instructors were busy teaching/demonstrating/explaining things to our respective students and allowing them to manipulate the controls while attempting to do everything else needed to operate close to an uncontrolled field.After a few seconds; I decided that the only way to resolve the developing conflict was to turn to the north and begin a right 360 in order to get out of the C150's way. We did not have him in sight and there was no indication he had us in sight; so I figured we needed to yield. Based on the ADS-B display showing the C150 catching up to us surprisingly fast; I hastened the right turn; added power for speed knowing we can outrun the C150; and climbed 100-200 feet. Still; the ADS-B target was frighteningly close to us and within 100 feet of our indicated altitude. For all I know; my turn to the right (north) and shallow climb may have put us even closer to the C150 instead of farther away. Even though I know there is a 10-15 second delay between an aircraft's actual position and its target on our ADSB-GPS; I could not help turning 'away' from him. That's why I say I may have turned toward him instead of away from him. Had I been thinking more clearly; once his target is on top of ours; he is 10-15 seconds past us. I probably should have just stayed my course.After finishing our 360 and landing with proper radio calls and without further stress; I noticed that the C150 had already landed. I approached the instructor and asked him if he ever saw us; his answer was; 'no.' Now; while I made a number of decisions I would like to re-do and take full responsibility for; I am at a loss to explain why the other instructor (or his student) did not see us. We had ALL our lights on well in advance of our approach from the east. Further; we were 'downwind;' so to speak; from the sun as viewed from the C150. In other words; we were all lit up by being self-lighted (wing tip lights; taxi light; nav lights; strobes; flashing beacon) and we were lit up by the sun. He would be looking away from the sun in order to see us; while we were looking towards the sun while attempting to see him. Just sayin'.Why we couldn't see him is more explainable -- looking into the sun through a dirty windscreen; and he was above us while we were in a high-wing airplane.Feel free to contact me with any questions. Sorry for the overly verbose report. Thank you.




Synopsis: C-172 Instructor submitting updated previous NMAC report after reviewing additional data.