C172 instructor reported that a partial loss of engine power resulted in a diversion.

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.

Original NASA ASRS Text

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

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.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.

Attributes
ACN	1742745
Time
Date	202005
Local Time Of Day	0601-1200
Place
Locale Reference	ZZZ.Tower
State Reference	US
Environment
Flight Conditions	Marginal
Light	Daylight
Aircraft 1
Make Model Name	Skyhawk 172/Cutlass 172
Operating Under FAR Part	Part 91
Flight Phase	Initial Approach
Route In Use	Vectors
Flight Plan	IFR
Component
Aircraft Component	Engine
Person 1
Function	Instructor Pilot Flying
Qualification	Flight Crew Commercial Flight Crew Multiengine Flight Crew Instrument Flight Crew Flight Instructor
Experience	Flight Crew Last 90 Days 200 Flight Crew Total 1150 Flight Crew Type 600
Events
Anomaly	Aircraft Equipment Problem Critical