Roger Roger
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Some of the Cherokee family is sort of marginal when it comes to vapor suppression in the fuel system. A lot of them actually require an extra fuel pump to be run on avgas. So I would guess that with the low airspeed and attendant high temperatures in the cowling, you got vapor lock in the fuel system up there. I would hazard a guess that if you run the boost pump during maneuvers you won't have this trouble. As a side note, as a new Piper driver coming from Cessnas your first reflex after an engine failure (or even hiccup) now should be switch tanks, pump on. That will serve you well if you ever fly the Big Six, four fuel tanks feeding one engine.It was relatively cool so I dont think the engine overheated, the oil was at about 6 but the student noted it was practically BLACK as he checked it... i think they changed it after the incident though.
You nailed it on the head with the fuel pump though, I dont believe we had turned it on for maneuvers and another instructor asked me the same thing. He said the fuel pressure falls pretty noticeably during maneuvers if the pump is not on. All my single engine time has been 99% cessna (all twin time was in the seminole though) so learning the quirks of the piper will be interesting.