A DA40F ON A XCOUNTRY TRAINING FLT LOST THE ACFT DOOR AND DIVERTED TO NEAREST ARPT.

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A STUDENT AND I WERE ON A NIGHT XCOUNTRY FLT. WE HAD SET UP A CRUISE FLT AND DECIDED TO OPEN THE FLT PLAN AND AMENDED THE DEP TIME FROM XA00 TO XA41. WE WERE ABOUT 10 MILES TO THE NW OF ZZZ WHEN I NOTICED A BREEZE. SO I CHKED ALL OF THE VENTS IN THE PLANE TO MAKE SURE THEY WERE CLOSED. I LOOKED AND NOTICED THAT THE DOOR WAS NO LONGER CLOSED ALL THE WAY. I INSPECTED VISUALLY THE DOOR LATCH AND NOTICED THAT IT WAS SECURED PROPERLY. BUT THE DOOR WAS NOT DOWN ALL OF THE WAY. I SAW THE DOOR POP OPEN MORE AND TRIED TO GRAB IT; BUT JUST BEFORE I TOUCHED THE DOOR; IT GAVE AND THE DOOR WAS IMMEDIATELY RIPPED CLEAR OFF THE PLANE. I CONTACTED LOCAL RADIO AND INFORMED THEM THAT WE WERE GOING TO FLY DIRECT TO ZZZ1 AND WANTED THE FLT PLAN CLOSED. HE SAID HE WANTED TO OPEN A FLT PLAN TO ZZZ1 FOR US AND ASKED FOR OUR ETA. AFTER COMPUTING OUR ETA ON THE G1000 FOR A DIRECT TO ZZZ1 I TOLD HIM IT WOULD BE ABOUT 13 MINUTES. HE SAID TO MAKE SURE THAT WE CONTACTED HIM UPON ARR AND THEY WOULD KEEP AN EYE OUT FOR US. WE RETURNED BACK TO ZZZ1 AND HAD ANOTHER FLT INSTRUCTOR FOLLOW US BACK TO THE ARPT TO MAKE SURE THAT WE MADE IT SAFELY. THE REST OF THE FLT WAS -12 DEGS AND COLD; BUT LUCKILY; UNEVENTFUL. IT LOOKED LIKE THE DOOR WAS A PRETTY CLEAN BREAK RIGHT AT THE HINGES. WE LOOKED AT TWO OTHER DIAMONDS AND NOTICED THAT THE HINGES LOOKED LIKE THEY MIGHT HAVE CRACKS ON THEM ALSO.CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATES THE DOOR WAS FOUND RECENTLY AND INSPECTION REVEALED THE AFT LOCKING PIN HAD COME ADRIFT AND WAS FOUND WITHIN THE DOOR ITSELF. THERE IS NO WARNING LIGHT ASSOCIATED WITH THE AFT PIN; UNLIKE THE FORWARD PIN WHICH; IF NOT LOCKED; WOULD ILLUMINATE THE MASTER CAUTION LIGHT. RPTR'S EMPLOYER; A FLT SCHOOL; IS IN CONTACT WITH MANUFACTURER AND IS INSPECTING THE BALANCE OF THEIR FLEET TO DETERMINE IF OTHER POTENTIAL PROBS EXIST.