A TRACON Controller reported a corporate jet on departure did not fly the SID as published and flew below the Minimum Vectoring Altitude.
Synopsis
A TRACON Controller reported a corporate jet on departure did not fly the SID as published and flew below the Minimum Vectoring Altitude.
Narrative
I was the instructor at position X; training a CPC-IT on his first day at the sector. This was our third session of the day; and we had previously discussed the fact that position X has frequent pilot deviations; mostly with the ZZZ1 departure. We discussed the importance of issuing the BRASHER statement; not to get pilots in trouble; but to educate the pilots and ensure the unsafe situation isn't repeated. ZZZ Tower called to request a release from Runway XX for a ZZZ One departure. Off Runway XX; the aircraft should turn northbound to heading XXX once they are through 5000 ft. The aircraft was released and departed shortly thereafter. The aircraft checked in climbing to 10;000 ft. on the ZZZ One and was radar identified.After some time and additional transmissions to other aircraft; we noticed the aircraft was still westbound as if on runway heading. The CPC-IT asked the pilot to verify they were on the ZZZ One departure; to which they responded 'affirmative; vectors to ZZZZZ.' I understand the intent behind asking if the pilot was on the departure. An expected possible response could've been 'Affirmative; in the right turn now;' as some pilots don't make this turn right away. Unfortunately; this aircraft continued into higher MVAs and a low altitude alert was never issued. The next departure from Runway XX; also on the ZZZ One; went into a higher MVA; but they were following the departure procedure correctly and made the turn appropriately. In most cases; 'appropriately' still leads to the aircraft getting into a higher MVA before making the turn northbound. I believe it could help to have ZZZ Tower reiterate what the departure procedure is read it line by line if necessary.
Second reporter narrative
Aircraft X was released from ZZZ on an IFR flight plan coordinated from Runway XX on the ZZZ 1 departure; which required a turn to heading XXX after crossing 5000 ft. Aircraft continued straight on runway heading; when queried leaving 7400 ft. as to the departure procedure assigned; pilot responded that he was assigned a heading to expect direct ZZZZZ; which is the normal route assigned for Runway XXL. Aircraft climbed and was turned on course upon reaching a higher altitude above the MVA (12000). Due to the issues related to giving or implying a heading below the MVA; I opted to allow the aircraft to climb above the MVA before issuing a turn on course. I hesitated giving the pilot deviation advisory due to the aircraft still being in a climb underneath the flight levels but was instructed to by my trainer. It is still my belief that such instruction should be delayed until the aircraft is in level flight and on course or already on the ground. Unknown what communication error upon departure allowed the pilot to believe he was supposed to fly runway heading instead of complying with the issued departure procedure.
Source: NASA Aviation Safety Reporting System (public domain). Reports are voluntary submissions and are not verified by NASA.