Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Flight Instructor; Flight Crew Commercial
Flight Crew Last 90 Days 95; Flight Crew Total 331; Flight Crew Type 250
Situational Awareness; Training / Qualification; Communication Breakdown
Conflict NMAC
Flight Crew Took Evasive Action
Airspace Structure; Human Factors
My student and I were conducting a dual XC (cross-country) training flight and were coming inbound to E63 for a full stop; taxi back. We monitored CTAF and heard over that frequency that Runway 4 was in use. We planned at approximately 12 miles to the east-southeast that we would conduct a teardrop entry for left downwind Runway 4. We planned on crossing the Runway at 2100 feet; which is 500 feet above the TPA of 1600 feet. We made radio calls and broadcast our intentions every 2 miles until we were over the field.We made visual contact with another airplane (an instructor and student) that was conducting the same entry to the traffic pattern. When [we] were approximately 2 miles out; we announced over the CTAF that we had that plane in sight and were about 1 minute to entering the traffic pattern behind him. At the same time there was another airplane using the [same] call sign [as the other aircraft; but different flight number] had been announcing that he was north of the field and would be inbound for a full stop. While we were approaching the runway at 2100 feet we heard this student pilot announce that he was coming from the north and would be entering a midfield crossing at 2100 feet and doing a teardrop and make left traffic for Runway 4. We were trying to make visual contact and were confused as to why he would be making a teardrop entry while coming from the north. Nevertheless; at this time I took over radio control and kept asking the student what his position was from the field. The other airplane ([same] call sign); was in the teardrop entry for Runway 4 said 'He is headed right for you'. At [that] time we saw the student pilot at our same altitude approximately 75 feet to the left and he was turning left. We made an abrupt steep turn to the left to avoid traffic.After the near collision; I did announce over CTAF '[Expletive]; that was close'; in which the student pilot responded; 'My bad; [call sign]'. The student pilot continued to fly over the field at 2100 feet. He executed a 360 degree turn and flew back over the field at 2100 feet and then executed the teardrop entry for a left downwind on Runway 4. I made sure to keep visual and radio contact with Aircraft Y until my student and I were safe on the ground. We performed our landing; taxied back and departed from the area.
Cessna 172 instructor pilot reported an NMAC with another light aircraft in the pattern at E63.