Narrative:

The aircraft had three occupants; a private pilot in the left seat; a private pilot passenger in the rear seat and myself in the right seat acting as a supervising instructor. The intent of the flight was for the pilot in the left seat to refresh currency and proficiency prior to a cross-country flight planned for later in the day. The pilot in the left seat had completed one circuit in the traffic pattern and had departed upwind following a touch and go on runway xx. On initial climbout; I noted that the engine was not making full power; indicating only 2030 RPM. After checking with the pilot and verifying correctness of throttle position; I took control of the airplane with annunciation inside the cockpit; and promptly [advised ATC]. The aircraft was approximately 50 feet AGL at this point.the engine was running rough. I determined that we had a slight positive climb rate. I elected to climb while looking for possible landing sites straight ahead. After the aircraft was above the power lines to the right (~400 feet AGL); I turned the airplane slightly to the right and started a left teardrop back to the airport. I was simultaneously assessing whether there was anything to our left that was workable as a landing spot. I was also aware that the tower had cleared us to land on any runway; and was clearing airspace for us; directing traffic in the pattern away from and above our flight path. Once I knew we could glide to runway xy; I closed the throttle; deployed full flaps and started side-slipping and s-turning to lose altitude to make the runway.my attempts to lose altitude were insufficient to make a landing with adequate runway. At the time it was unclear to me why this was so; in spite of the relatively light tailwind (~5 kts) we were dealing with. After seeing that I had only one third of the runway xy remaining and we were still about 10 to 15 feet off the ground; I made the very uncomfortable decision to apply all available power from the engine and attempt to 'go-around.' due to the flaps still being fully deployed; and the airplane only running up to ~2000 RPM; the aircraft didn't accelerate or climb well; barely clearing the fence south of the airport boundary. In a moment of haste; I retracted all the flaps; and heard the stall warning horn chirp momentarily - a glance at airspeed indicator showed ~55 knots. Because the flaps are electric; I brought the flap switch down to a partial setting; which likely just paused the retraction I had commanded seconds earlier. I then retracted them fully after a few more seconds.I deviated slightly to the right on the shallow climbout hoping to put the airplane down near the bike tracks south of the airport. Because of rising terrain in this area; our AGL altitude was perceived to be no higher than 50 feet. I was weighing my decision-making between landing off airport straight ahead or returning to the airport because I was unsure how long the engine would continue running. The pilot-passenger in the back seat suggested heading to [an alternate airport] but it was unclear if we could climb past the power lines; so I discounted this.I started a left teardrop turn again to the airport for runway xx; maneuvering at the level of power lines that run along the east of the airport. Once we were oriented towards runway xx; I let the airplane continue climbing until just above the normal glide path indicator. I closed the throttle and applied flaps over the pond just short of runway xx. To the best of my recollection; airspeed was about 75 knots at this point. Best glide was expected to be just under 70; and I was intentionally keeping some margin above this airspeed.what all occupants remember is that during this power reduction; the engine was not idling. It was running at 1600 RPM and had smoothened out noticeably than when it was making partial power at the full throttle setting. Suspecting that the airplane's engine was not going to idle as expected and also noting that our glide path was causing us to approach the runway faster than desired at 70 to 75 kts; I anticipated needing to kill the engine upon touchdown. We touched down about on the runway in the vicinity [of] taxiway X. I had the left seat occupant turn off the ignition switch as soon as the wheels touched down. I applied maximum braking to stop the airplane about 50 feet short of the airport boundary fence; in the overrun area of the runway.no injuries or damage to the aircraft resulted. An airport service vehicle helped tow the airplane off the runway. At the time of writing; maintenance personnel had done diagnostic runups after our landing on the engine and indicated one of the magnetos may have been malfunctioning.factors affecting my decision making (beyond the inherently unexpected nature of the emergency):1. Rehearsing for engine failure after takeoff (efato) has always been 'full power loss' in my training; and my instructors have maintained that the best course of action is to try to land straight ahead if below pattern altitude. I had some rehearsal for efato was as recently as 2 months prior to this event; during checkout of another aircraft type with an instructor. The aircraft in the recent practice sessions was a high-drag two-seat biplane with far worse glide performance than the C172 being flown during the actual emergency.2. I was acutely aware during the emergency that the 'impossible turn' attempted by pilots after efato-type events usually don't work because of the altitude loss during the 180. In spite of all these points; I set myself up for it anyway; because the engine was making some power; and I was able to keep us high enough for an approach to the 'downwind' runway.3. I deliberately stopped at step 1 of the typical 'emergency checklist;' 'fly the airplane.' I reached an initial conclusion in flight that this was likely an induction or ignition issue; with mechanical failure being less likely because of the following: I had good fuel flow; good oil pressure; and engine vibration was not jarring. Because I didn't have the luxury of altitude; I did not touch the ignition switch in case I killed the engine without a landing spot to aim for.4. Other than the airport; it was very clear that there were no good options to ditch in the vicinity of the area I flew over. Power lines running north to south; along the east of the airport 'boxed us in' over marshes to avoid populated areas.5. During the second attempt at landing; I wondered if the throttle linkage was preventing me from truly idling the engine; and if this made a tailwind approach on runway xy impossible. Suspecting this; I anticipated needing to kill the ignition even on runway xx; where we landed much farther down the runway than is standard.6. It is entirely possible that the engine was running at 1600 RPM purely from the higher-than best glide airspeed I was maintaining. However; this was hard to accept in the moment since the engine had also 'smoothed out' when the throttle handle was pulled to the closed position. The others on board shared my surprise when I pointed this out on short final. The effect of tailwind on the glidepath was difficult to account for when most landings are attempted into the wind under normal circumstances.7. My assessment is that my relatively low time in C172s was a contributing factor in inaccurately anticipating how well the aircraft can glide; slip; and slow down with flaps. This was especially true for the attempt on runway xx. If I were to guess; I'd say that I was faster than recommended for both the approaches I attempted after [advising ATC]; likely overcompensating against the spectre of full engine failure; which could have been expected at any time.8. [The airport]'s runway is short; at only 2;400 feet; it is possible that I could have made it down on something about twice as long during the tailwind landing attempt on runway xy. It is also possible that; had this issue occurred on a longer runway; a landing straight ahead would have put us back on the runway.9. Because of task saturation associated with flying the airplane; it was very difficult to respond to all information from ATC. However; I was listening during the whole incident and aware that ATC was offering relevant information; helpful clearances; and clearing the airspace for us.10. I surprised myself with the near-subconscious decision to announce control of the aircraft and [advising ATC] within seconds of realizing the engine was not behaving. I stuttered a bit scanning for the tail number on the dash - it was my first time flying this airplane. Declaring was a call for help - one that tower effectively and professionally responded to. I hope that others finding themselves in such a situation are trained to do so without hesitation.

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Original NASA ASRS Text

Title: Cessna 172 pilot reported that the engine lost power right at liftoff.

Narrative: The aircraft had three occupants; a private pilot in the left seat; a private pilot passenger in the rear seat and myself in the right seat acting as a supervising instructor. The intent of the flight was for the pilot in the left seat to refresh currency and proficiency prior to a cross-country flight planned for later in the day. The pilot in the left seat had completed one circuit in the traffic pattern and had departed upwind following a touch and go on Runway XX. On initial climbout; I noted that the engine was not making full power; indicating only 2030 RPM. After checking with the pilot and verifying correctness of throttle position; I took control of the airplane with annunciation inside the cockpit; and promptly [advised ATC]. The aircraft was approximately 50 feet AGL at this point.The engine was running rough. I determined that we had a slight positive climb rate. I elected to climb while looking for possible landing sites straight ahead. After the aircraft was above the power lines to the right (~400 feet AGL); I turned the airplane slightly to the right and started a left teardrop back to the airport. I was simultaneously assessing whether there was anything to our left that was workable as a landing spot. I was also aware that the Tower had cleared us to land on any runway; and was clearing airspace for us; directing traffic in the pattern away from and above our flight path. Once I knew we could glide to Runway XY; I closed the throttle; deployed full flaps and started side-slipping and S-turning to lose altitude to make the runway.My attempts to lose altitude were insufficient to make a landing with adequate runway. At the time it was unclear to me why this was so; in spite of the relatively light tailwind (~5 kts) we were dealing with. After seeing that I had only one third of the Runway XY remaining and we were still about 10 to 15 feet off the ground; I made the very uncomfortable decision to apply all available power from the engine and attempt to 'go-around.' Due to the flaps still being fully deployed; and the airplane only running up to ~2000 RPM; the aircraft didn't accelerate or climb well; barely clearing the fence south of the airport boundary. In a moment of haste; I retracted all the flaps; and heard the stall warning horn chirp momentarily - a glance at airspeed indicator showed ~55 knots. Because the flaps are electric; I brought the flap switch down to a partial setting; which likely just paused the retraction I had commanded seconds earlier. I then retracted them fully after a few more seconds.I deviated slightly to the right on the shallow climbout hoping to put the airplane down near the bike tracks south of the airport. Because of rising terrain in this area; our AGL altitude was perceived to be no higher than 50 feet. I was weighing my decision-making between landing off airport straight ahead or returning to the airport because I was unsure how long the engine would continue running. The pilot-passenger in the back seat suggested heading to [an alternate airport] but it was unclear if we could climb past the power lines; so I discounted this.I started a left teardrop turn again to the airport for Runway XX; maneuvering at the level of power lines that run along the east of the airport. Once we were oriented towards Runway XX; I let the airplane continue climbing until just above the normal glide path indicator. I closed the throttle and applied flaps over the pond just short of Runway XX. To the best of my recollection; airspeed was about 75 knots at this point. Best glide was expected to be just under 70; and I was intentionally keeping some margin above this airspeed.What all occupants remember is that during this power reduction; the engine was not idling. It was running at 1600 RPM and had smoothened out noticeably than when it was making partial power at the full throttle setting. Suspecting that the airplane's engine was not going to idle as expected and also noting that our glide path was causing us to approach the runway faster than desired at 70 to 75 kts; I anticipated needing to kill the engine upon touchdown. We touched down about on the runway in the vicinity [of] taxiway X. I had the left seat occupant turn off the ignition switch as soon as the wheels touched down. I applied maximum braking to stop the airplane about 50 feet short of the airport boundary fence; in the overrun area of the runway.No injuries or damage to the aircraft resulted. An airport service vehicle helped tow the airplane off the runway. At the time of writing; maintenance personnel had done diagnostic runups after our landing on the engine and indicated one of the magnetos may have been malfunctioning.Factors affecting my decision making (beyond the inherently unexpected nature of the emergency):1. Rehearsing for engine failure after takeoff (EFATO) has always been 'full power loss' in my training; and my instructors have maintained that the best course of action is to try to land straight ahead if below pattern altitude. I had some rehearsal for EFATO was as recently as 2 months prior to this event; during checkout of another aircraft type with an instructor. The aircraft in the recent practice sessions was a high-drag two-seat biplane with far worse glide performance than the C172 being flown during the actual emergency.2. I was acutely aware during the emergency that the 'impossible turn' attempted by pilots after EFATO-type events usually don't work because of the altitude loss during the 180. In spite of all these points; I set myself up for it anyway; because the engine was making some power; and I was able to keep us high enough for an approach to the 'downwind' runway.3. I deliberately stopped at step 1 of the typical 'emergency checklist;' 'Fly the airplane.' I reached an initial conclusion in flight that this was likely an induction or ignition issue; with mechanical failure being less likely because of the following: I had good fuel flow; good oil pressure; and engine vibration was not jarring. Because I didn't have the luxury of altitude; I did not touch the ignition switch in case I killed the engine without a landing spot to aim for.4. Other than the airport; it was very clear that there were no good options to ditch in the vicinity of the area I flew over. Power lines running north to south; along the east of the airport 'boxed us in' over marshes to avoid populated areas.5. During the second attempt at landing; I wondered if the throttle linkage was preventing me from truly idling the engine; and if this made a tailwind approach on Runway XY impossible. Suspecting this; I anticipated needing to kill the ignition even on Runway XX; where we landed much farther down the runway than is standard.6. It is entirely possible that the engine was running at 1600 RPM purely from the higher-than best glide airspeed I was maintaining. However; this was hard to accept in the moment since the engine had also 'smoothed out' when the throttle handle was pulled to the closed position. The others on board shared my surprise when I pointed this out on short final. The effect of tailwind on the glidepath was difficult to account for when most landings are attempted into the wind under normal circumstances.7. My assessment is that my relatively low time in C172s was a contributing factor in inaccurately anticipating how well the aircraft can glide; slip; and slow down with flaps. This was especially true for the attempt on Runway XX. If I were to guess; I'd say that I was faster than recommended for both the approaches I attempted after [advising ATC]; likely overcompensating against the spectre of full engine failure; which could have been expected at any time.8. [The airport]'s runway is short; at only 2;400 feet; it is possible that I could have made it down on something about twice as long during the tailwind landing attempt on Runway XY. It is also possible that; had this issue occurred on a longer runway; a landing straight ahead would have put us back on the runway.9. Because of task saturation associated with flying the airplane; it was very difficult to respond to all information from ATC. However; I was listening during the whole incident and aware that ATC was offering relevant information; helpful clearances; and clearing the airspace for us.10. I surprised myself with the near-subconscious decision to announce control of the aircraft and [advising ATC] within seconds of realizing the engine was not behaving. I stuttered a bit scanning for the tail number on the dash - it was my first time flying this airplane. Declaring was a call for help - one that Tower effectively and professionally responded to. I hope that others finding themselves in such a situation are trained to do so without hesitation.

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.