Date: 202005
Local time of day: 0601-1200
Location: ZZZ.Tower, US
Flight conditions: Marginal
Weather elements / visibility: Haze / Smoke; 5
Light: Daylight
Aircraft: Skyhawk 172/Cutlass 172
Operator: FBO
Operating under: Part 91
Flight plan: IFR
Mission: Training
Flight phase: Initial Approach
Airspace: Class D ZZZ
ATC / advisory: Tower ZZZ
Aircraft component: Engine
Component problem: Malfunctioning
Reporter organization: FBO
Reporter function: Instructor; Pilot Flying
Reporter qualification: Flight Crew Commercial; Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Flight Instructor
Human factors: Troubleshooting; Workload
Anomaly: Aircraft Equipment Problem Critical
Detector: Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Provided Assistance; Flight Crew Landed in Emergency Condition; Flight Crew Diverted; Flight Crew Requested ATC Assistance / Clarification; General Maintenance Action
Contributing factors: Aircraft
Primary problem: Aircraft

Narrative: I was on an instrument training flight with a rotorcraft rated pilot who was transitioning to fixed wing aircraft. After practicing basic IFR maneuvers in VMC conditions; we obtained a pop-up IFR clearance to practice an ILS approach. We obtained the clearance due to some scattered to broken low clouds on the final approach course. We obtained our clearance and were vectored to the final approach course for the ILS Runway X into ZZZ. The final approach course is directly above ZZZ1. After intercepting the final approach course and about 2NM outside the FAF; we were instructed to contact ZZZ tower. We complied and made our initial call. After completing this call the engine suddenly began running very roughly. As the flight instructor and PIC on board; I took the controls of the aircraft and began to try and remedy the situation through use of an engine failure checklist. After checking that the fuel selector was set to both; mixture set to full rich; carburetor heat turned on; magnetos confirmed to both; and engine primer was locked; the engine continued to run quite rough. The engine roughness continued to worsen; and a gradual RPM loss began. At this time I applied full throttle in an effort to continue to ZZZ as planned. With full power being applied; the engine was only producing between 1500 and 1700 RPM. With this amount of RPM the airplane was struggling to maintain altitude. It is then that I decided that we would not be able to make a safe approach and landing at ZZZ; and elected to divert to ZZZ1; (which was right below us). I contacted ZZZ1 tower; informed them of the situation; and obtained a landing clearance to land on Runway X. I did not [request priority handling] at the time. While turning base for Runway X I again increased the throttle to full; and could see the engine cowling shaking; and feel the aircraft shaking as well; as the engine roughness continued to get worse. We were able to taxi off of the runway and to the ramp under our own power. I believe the engine may have suffered a broken or stuck valve; as determined by pulling the propeller through once on the ground and noting little to no compression on one cylinder. Prior to the flight we conducted an engine run up; and all magnetos and carburetor heat worked as expected. The engine was running smoothly and producing the correct amount of power for the entire flight up until the initial indications encountered on approach.




Synopsis: C172 Instructor reported that a partial loss of engine power resulted in a diversion.