Small Aircraft; Low Wing; 1 Eng; Retractable Gear
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 17
Communication Breakdown; Confusion
ATC Issue All Types; Conflict Airborne Conflict; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Unstabilized Approach
Flight Crew Executed Go Around / Missed Approach
Procedure
Aircraft X was vectored on to the Runway 28R final approach course for a VFR approach to landing at SFO.  I cleared Aircraft X to land number 2 behind a regional jet which he reported in sight upon initial contact. The regional jet was approximately 4 to 5 miles ahead of Aircraft X.  Aircraft X was approximately 10 to 20 knots faster than the regional jet traffic he was following so I advised him to continue to slow as he was gaining on traffic ahead.  When Aircraft X was approximately 1 mile final I advised him that a long landing was approved and that he could plan to exit the runway at Taxiway K.  At approximately this same time; I told Aircraft Y to 'Line up and wait on Runway 28L.' I noticed that Aircraft X was still airborne at approximately 50 feet or so and slowly descending as he flew down the runway just past the approach end of Runway 28R.  I then cleared Aircraft Y for takeoff on Runway 28L. Aircraft Y was a Shoreline5 Departure which meant he would turn right crosswind after takeoff.  I turned to observe Aircraft Y make his right turn and realized Aircraft X was climbing and was at about 500 feet on a right crosswind; Aircraft Y was outside of and above Aircraft X at about 1;200 feet.  I asked Aircraft X what he was doing to which he replied; 'I started to porpoise on landing so I went around.'   I told him that he needs to advise me when he is on a missed approach to which he replied that he had announced it.  I never heard any such announcement and after listening to the recording later; there was no such announcement made. I asked him what he wanted to do and he said he wanted to go back to SQL so vectored Aircraft X downwind towards the San Mateo Bridge to get him headed towards SQL.As soon as the aircraft was under control the pilot of Aircraft X should have aggressively let it be known that he was climbing on a missed approach.  It was still early morning and the shades were down and the sun was shining bright from the east where Aircraft X was operating.  These conditions make operations challenging enough and add to that major airport construction and a very small aircraft; extra due diligence is called for.  I had no reason to expect nor did I see Aircraft X execute a missed approach. Had I observed or been told by the pilot of Aircraft X that he was executing a missed approach; alternate instructions could have been given to all aircraft involved.
Aircraft X was landing on Runway 28R; everything appeared normal.  The pilot was advised that they could land long and plan to exit Runway 28 right at Taxiway 'Kilo'.  The pilot acknowledged. In the mean time the Local Controller cleared Aircraft Y for takeoff on Runway 28L.  A little while later the Supervisor asked the Local Controller what type of separation was being used between Aircraft Y flight and Aircraft X. I looked at the radar scope to see the Aircraft Y flight tagged up and below that there was a VFR limited tag off the departure end of Runway 28R.  I know that the Local Controller did not launch another airplane; so I was not sure who the VFR tag was.  It soon became clear that Aircraft X had done a touch and go or low approach and was just flying around and not letting air traffic know what they were doing.  The Local Controller asked Aircraft X what were their intentions.  The pilot responded that they were going to go to San Carlos airport.I would report this incident to the NSA or FBI or CIA; because this was very unusual behavior by this pilot.  It was very dangerous and could have led to an aircraft mid air collision.
Pilot reports of porpoising on final and then having to execute a missed approach; while off his left an air carrier departing is turning towards him. Controllers report of pilot not advising the Tower that the aircraft was going around.