Admiral346 - Well, I think the aircraft did just right. Cleard for the ILS 14R and deciding to go around, whatever else should they have flown? Assuming you were a controler there, you should have issued missed approach instructions with the ILS clearance if you wanted them to fly anything else.
For the general issue, I usually brief a visual pattern towards the circling side at 1500' AGL when cleared for a visual. But thinking about it, a word to ATC about the plan while the radios still work will be on my list from now on.
Nic
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Flying the published MAP, while on a visual, or when the airport is VFR/VMC, without ATC approval can.
AMS/FRA might have MAP procedures, due to airspace, that allow an aircraft on a MA/Go-around to fly the MAP in VFR/VMC conditions. Other airports, to increase VFR/VMC arrival traffic, don't have that luxury, due to other airports(ie EWR/LGA/JFK) or airport configuration (ORD).
For example, visual KJFK 31R. You go-around and decide to fly the MAP without communicating with ATC. That will turn you towards the departing traffic on 31L. Straight ahead isn't an option for long (KLGA 8 n.m. away).
JFK tower will typically give you "runway heading/2000' " and get any departure off of 31L to start a turn to the left. After the 31L aircraft starts turning JFK tower will give you a left turn to avoid LGA's airspace.
Been there, done that.