Small Aircraft; Low Wing; 1 Eng; Fixed Gear
Flight Crew Air Transport Pilot (ATP); Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 50; Flight Crew Total 20000; Flight Crew Type 6000
Communication Breakdown; Confusion; Distraction; Situational Awareness; Workload
Conflict NMAC
Air Traffic Control Issued New Clearance; Flight Crew Executed Go Around / Missed Approach; Flight Crew FLC complied w / Automation / Advisory; Flight Crew Took Evasive Action
Human Factors
My student was flying the aircraft; we were cleared to land #1 and were approximately 1.25 miles from touchdown on a stable approach when ATC alerted us to immediately go-around due an aircraft which had suddenly appeared on a tight right base to FPR Runway 32. I saw the aircraft immediately; about 50-100 feet below us; slightly right of our nose when we were alerted to go-around; I took control and executed an aggressive go-around climbing over the top of the other aircraft.  I estimate we avoided a certain collision by 50-100 feet.The circuit pattern was busy and I was aware that ATC had instructed this aircraft who was on the right downwind (we were on the left downwind) to extend downwind and follow us. I recall ATC having to pass this instruction 2 or 3 times as the other aircraft did not respond at first. I was naturally looking hard to locate the other traffic visually but failed to do so whilst on base leg and on initial final which we turned at approx 1.75 miles. No further ATC instructions were given to us or them and we were not alerted to any problem so; as with thousands of other approaches and landings I have undertaken; all seemed OK; we were number 1 to land with runway clearly in sight and positioned nicely on a short final. ATC's alert for us to go-around without doubt played a major role in avoiding an accident; nevertheless; I am very concerned and surprised that the aircraft was able to get into that position especially after ATC had at least twice instructed them to extend downwind to follow us.After landing; I heard ATC attempting many times to give the pilot of the other aircraft the telephone number for a possible pilot deviation which he seemed to refuse to take at first claiming some issue with the radio. There is little doubt that the other pilot was extremely negligent and in violation of the rules and proper procedures which could have led to a fatal accident. In my 40+ years as a pilot I have never witnessed such gross negligence first hand by another pilot. Short of ATC keeping complete focus on the other aircraft at all times and noticing that he had failed to obey the instructions given and giving us further heads up as to a developing problem; I cannot see how we can improve safety when such negligence occurs by any pilot.
An instructor took evasive action to a near miss and executed a go-around from his student's stable approach after another pilot departed FPR Runway 32; ignored ATC's instructions then climbed directly toward his aircraft.