PA-28 Cherokee/Archer/Dakota/Pillan/Warrior
Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Communication Breakdown; Human-Machine Interface; Situational Awareness
Conflict NMAC; Deviation / Discrepancy - Procedural Published Material / Policy
Flight Crew Took Evasive Action
Human Factors; Procedure
I was in [an] Archer; Aircraft X; in the pattern at ZZZ with my student working on landings. After completing a touch-and-go at ZZZ we took off and began [an] out-crossing turn at 500 feet AGL. Upon reaching the crossing-to-downing turn; what looked to be some sort of Piper Cherokee cut directly ahead of us on downwind. We saw them cut us off and executed a turn to our right to avoid and then another turn once clear to follow them in the pattern. As we entered the downwind leg; I determined we were too close for a safe pattern and told the student to execute a right 360-degree turn for spacing. I announced this on CTAF and we did the turn.While this was occurring; the unknown Cherokee was proceeding down the downwind leg and failed to notice Cessna 172; Aircraft Z; on an extended downwind/base leg. Aircraft Z had announced its intentions of doing so once [it] joined its downwind leg in order to provide spacing for another aircraft already in the pattern to complete a full-stop landing. This unknown Warrior proceeded to turn a base leg too close to the runway and effectively cut off Aircraft Z on final. The unknown Cherokee then overflew final; turned its own final leg; and proceeded to fly final within 100 feet. wing tip-to-wing tip of Aircraft Z. Aircraft Z then proceeded to execute a go-around and depart the area to the south afterwards. The unknown Cherokee did not make another radio call and proceeded to go around; departing ZZZ's pattern to the north from what I could tell.After talking to the other pilot in Aircraft Z; we determined that when Aircraft Z was on its entry leg into ZZZ's pattern the unknown Cherokee was following Aircraft Z in trail very closely. To make spacing; he announced he would execute a left 360. However; in reality he turned into an opposite direction downing leg and made a 180-degree turn after to reenter downwind on the correct direction. In doing so he effectively entered right where I; in Aircraft X; was making my turn and cut us off. All of this could have been fixed by proper radio communication on the part of the unknown Cherokee. The Cherokee should have also used standard pattern procedures and not nonstandard ones. If he had completed the 360 like he said he was going to he wouldn't have cut us off and standard procedure usage wouldn't have led to Aircraft Z being cut off as well.
PA-28 flight instructor reported an aircraft in the pattern was not using correct procedures or communicating with other aircraft and caused near midair collisions with multiple aircraft.