Date: 202104
Local time of day: 1201-1800
Location: ZZZ.Airport, US
Flight conditions: IMC
Weather elements / visibility: Rain; Turbulence; 2
Light: Daylight
Aircraft: Skyhawk 172/Cutlass 172
Operator: Personal
Operating under: Part 91
Flight plan: IFR
Mission: Training
Flight phase: Initial Approach
Airspace: Class E ZZZ
ATC / advisory: TRACON ZZZ
Reporter organization: FBO
Reporter function: Pilot Not Flying; Instructor
Reporter qualification: Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Human factors: Workload; Training / Qualification; Situational Awareness; Fatigue; Distraction; Confusion
Second reporter function: Pilot Flying
Anomaly: Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Weather / Turbulence; Inflight Event / Encounter CFTT / CFIT
Detector: Automation Air Traffic Control; Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Issued New Clearance; Air Traffic Control Issued Advisory / Alert; Air Traffic Control Provided Assistance; Flight Crew Became Reoriented; Flight Crew FLC complied w / Automation / Advisory
Contributing factors: Airspace Structure; Chart Or Publication; Environment - Non Weather Related; Human Factors; Procedure; Weather
Primary problem: Human Factors

Narrative: I was acting as a flight instructor on board Aircraft X; a Cessna 172S on a local IFR flight practicing approaches. My student is a Certified Flight Instructor (CFI) candidate who was gaining instrument currency and proficiency. We began with an ILS approach at ZZZ1 with my student flying the aircraft and me handling ATC communications to reduce his workload in the hard IMC conditions. We crossed a cold front while receiving vectors for the ILS approach where we encountered light to moderate turbulence and precipitation. We completed the ILS approach without incident and proceeded to the VOR for the VOR-A approach into ZZZ; planning to complete a Low Approach Only. We experienced severe turbulence which forced the autopilot (GFC700) to disconnect and I took the controls of the aircraft and requested deviations to the north as necessary to track clear of the progressing cold front. Once we got into smoother air; I gave my student the flight controls and we proceeded direct ZZZ2 [VOR] for a procedure turn. Our plan was to complete the VOR-A approach and then receive radar vectors for the RNAV 01 at ZZZ. My student had proclaimed that he wanted to avoid going back through the cold front while getting vectored for the RNAV 01 approach and suggested we circle to land at ZZZ and cancel the IFR flight plan. When my student suggested this; we had passed the Final Approach Fix inbound and began a descent to the Minimum Descent Altitude and were switched over to advisory frequency. I switched frequencies back to Approach to tell them our intentions to try and circle to land since they were expecting us to go missed on the practice approach. When I told ATC of our intentions; they replied in the affirmative and added 'Aircraft X; low altitude alert; check altitude immediately; altitude indicates 1;800.' I replied the altitude checks and requested an altimeter setting. ATC replied with an altimeter setting of 29.58 and we had a setting of 29.67 set in. I figured this was why they gave us the low altitude alert but then quickly realized that the Minimum Descent Altitude for the segment of the approach we were on was 2;020 feet and we were at 1;720 feet with the new altimeter setting. I informed my student to return to 2;020 feet and we continued on the approach without issue and proceeded with the missed approach with vectors to the RNAV01 at ZZZ. During the missed approach; I was surprised at myself that I did not catch that the student had descended below the Minimum Descent Altitude and I assessed why that had happened during a period of smooth flight and during the post flight discussion with my student. During the lead up to the approach; the encounter with the severe turbulence had shaken both me and my student. We also had a back seat passenger who was an instrument student who had never been in IMC before. I was concerned with the safety of my student and the back seat student and began thinking about the circle to land approach and how we would request vectors for the RNAV Approach if we were unable to circle to land in order to stay away from the front line. I had determined from the weather when we departed ZZZ that circling for the runway at ZZZ would have been nearly impossible with the current ceilings. I told my student this and informed him we would need to execute the RNAV Approach in order to make it back into the airport.The workload at the moment was very high and the effects of the turbulence certainly could have impaired multitasking skills for both my student and I. When we began the descent on the approach; we left 3;000 feet for 2;020 feet which is the Minimum Descent Altitude until a fix which then the Minimum Descent Altitude decreases to 1;760 feet. My student did not reset the altitude select when we ran our Final Approach Fix check and the altitude select remained at 3;000 feet. Additionally; when I recognized we were below the published Minimum Descent Altitude; I should have instructed my student to execute the missed approach as 91.175(E)(1)(i) states; rather than just climbing back up to the Minimum Descent Altitude.This flight was also my third flight in hard IMC this day; and this VOR approach was my 8th approach in IMC in a span of 6 hours. I am an experienced Flight Instructor with over 45 hours in actual instrument conditions and over 150 approach logged; but never before had I completed so many IMC flights in such a time span with the challenging conditions of the frontal passage. My self-assessment prior to this flight determined I was able to complete the flight successfully with good quality of instruction to the student; but the extraordinary conditions we experienced during the flight quickly eroded that ability for me; in addition to the highly divided workload situation we found ourselves in while inbound on the VOR Approach which led to the descent below Minimum Descent Altitude and failure to execute the missed approach immediately after. I think also a more comprehensive briefing of the approach would have aided in my student's short term memory of the initial difference of Minimum Descent Altitude. Even though I briefed the Minimum Descent Altitudes; I do not think they were retained due to the stress and workload of the situation. If this event were to occur again; I would better instruct my student to execute the missed approach rather than working to reclaim the missed Minimum Descent Altitude.


Second narrative: The aircraft had 3 people on board for a local approaches flight in IMC conditions in Aircraft. This flight took place while a stationary front was passing through the area. This caused for almost constant moderate turbulence at times during the flight close to the frontal passage. The flight started with an ILS approach into ZZZ1. After the ILS approach we were vectored to go to the ZZZ2 VOR . Along the way; we had to deviate twice for turbulence. This; as well as IMC conditions; was causing a good amount of sensory overload for myself and the flight instructor with me. At times during the flight the autopilot was being used; but at one point; the amount of turbulence actually caused the autopilot to disengage. Because of this; at the time of the deviation; I was hand flying the aircraft while the other pilot was loading the VOR Approach. When we proceeded inbound on the approach; there is a step down to a minimum of 2;020 feet until an 8 DME fix. Then the minimum goes lower to 1;760 feet. With the sensory overload that both I and the other pilot were experiencing during the IMC flight; we ended up descending below the altitude minimum below the fix. ATC had not updated our altimeter setting in a decent amount of time. We were called by ATC letting us know for a low altitude and to immediately recover. They gave us an updated altimeter and our altitude after the correction showed it being right at the approach total minimum. Instead of executing an immediate missed approach we climbed back up to 2020 feet then re-descended to the 1;760 minimums. By doing this we unfortunately broke 14 CFR 91.175 (c) 1; 3 and (e) 1. The proper action would have been to either; not conduct the flight in the first place or; to immediately execute the missed approach once realizing the descent below the step down. We also could have stopped the flight after the ILS approach into ZZZ1. The rest of the flight utilized great CRM; but during this approach; a better action to even ask as the approach started would have been to double check the approach and its minimums including each step down.


Synopsis: Instructor and student reported descending below Minimum Descent Altitude; which they attributed to an incorrect altimeter setting; and turbulence.