Narrative:

I was in a piper cherokee with a student departing from ZZZ to remain in the traffic pattern to work on pattern work and landings. My student and I conducted a thorough preflight inspection prior to flight and discovered no discrepancies or issues. My student and I conducted the before start; start; taxi; and run up checklists and procedures and detected no issues. Including a throttle to idle to check and return to power in the run-up with no detected discrepancies or issues. My student made a radio call on the ZZZ CTAF to announce our takeoff and that we were to remain in the pattern. We successfully conducted the takeoff with no abnormalities. We flew upwind and all system gauges checked out within limits. We then turned crosswind while still at full power on the way up to traffic pattern altitude. Upon turning downwind my student had reached the target pattern altitude for ZZZ and tried to reduce the power to maintain traffic pattern altitude. We both quickly realized that our engine was stuck at full power because even with reducing the throttle all the way to idle there was no response from the engine or the RPM gauge. No matter what we did with the throttle control the engine was stuck at full power. I took over control of the aircraft and announced on the ZZZ CTAF that we were departing the downwind for to the south. I switched over to approach and explained the situation and told them I was going to maneuver in the area and troubleshoot the issue. We climbed to 5000 MSL and circled in the vicinity of the airport in case we had further engine troubles. After checking the emergency checklist and the poh for the stuck at full power situation I realized we had no choice but to shut down the engine and execute an emergency landing. I told [approach] I needed to shutdown my engine and execute a landing. There was no guarantees I could have restarted after I shut down the engine. I requested the longest possible runway. ZZZ1 tower told me the winds were at 230 at 3 knots so I requested the longest runway and most favorable for the wind condition. I managed to descend the aircraft down to approximately 2500 MSL and set the aircraft up for right downwind of [the] runway at ZZZ1. A little past midfield downwind I pulled the mixture to full lean to consequently shutdown the engine. I maintained my altitude to allow my airspeed to decrease below vfe. Once I was below vfe I extended full flaps (40 degrees) and turned base. I was pitching for 80-85 knots and then turned final and executed a forward slip to a landing and then executed the power off landing at ZZZ1 successfully with no injuries or damage to the airplane whatsoever.[contributing factors] cowling of aircraft X is only removable by multiple people and a mechanic. Some cherokees have hinges on the cowling that allow the pilot to inspect underneath the cowling. In the case of aircraft X it does not have hinges so the whole cowling has to be removed. So in the future pilots could check the cable attachment to the throttle lever on the engine to ensure a secure attachment and that the cotter pin is intact and secure. After landing the mechanics discovered the cotter pin was missing and that the throttle cable had detached from the throttle lever in flight. Maybe a more secure attachment in the future might have helped.it was discovered by my student and I in flight when the power would not reduce. Also by mechanics inspecting underneath the cowling after the landing.corrective actions are that the mechanics are to put a better and improved attachment system to the throttle cable and lever attachment.

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Original NASA ASRS Text

Title: PA28 Cherokee pilot reported that during climb the engine was stuck at full power.

Narrative: I was in a Piper Cherokee with a student departing from ZZZ to remain in the traffic pattern to work on pattern work and landings. My student and I conducted a thorough preflight inspection prior to flight and discovered no discrepancies or issues. My student and I conducted the before start; start; taxi; and run up checklists and procedures and detected no issues. Including a throttle to idle to check and return to power in the run-up with no detected discrepancies or issues. My student made a radio call on the ZZZ CTAF to announce our takeoff and that we were to remain in the pattern. We successfully conducted the takeoff with no abnormalities. We flew upwind and all system gauges checked out within limits. We then turned crosswind while still at full power on the way up to traffic pattern altitude. Upon turning downwind my student had reached the target pattern altitude for ZZZ and tried to reduce the power to maintain traffic pattern altitude. We both quickly realized that our engine was stuck at full power because even with reducing the throttle all the way to idle there was no response from the engine or the RPM gauge. No matter what we did with the throttle control the engine was stuck at full power. I took over control of the aircraft and announced on the ZZZ CTAF that we were departing the downwind for to the South. I switched over to approach and explained the situation and told them I was going to maneuver in the area and troubleshoot the issue. We climbed to 5000 MSL and circled in the vicinity of the airport in case we had further engine troubles. After checking the emergency checklist and the POH for the stuck at full power situation I realized we had no choice but to shut down the engine and execute an emergency landing. I told [approach] I needed to shutdown my engine and execute a landing. There was no guarantees I could have restarted after I shut down the engine. I requested the longest possible runway. ZZZ1 Tower told me the winds were at 230 at 3 knots so I requested the longest runway and most favorable for the wind condition. I managed to descend the aircraft down to approximately 2500 MSL and set the aircraft up for right downwind of [the] runway at ZZZ1. A little past midfield downwind I pulled the mixture to full lean to consequently shutdown the engine. I maintained my altitude to allow my airspeed to decrease below VFE. Once I was below VFE I extended full flaps (40 degrees) and turned base. I was pitching for 80-85 knots and then turned final and executed a forward slip to a landing and then executed the power off landing at ZZZ1 successfully with no injuries or damage to the airplane whatsoever.[Contributing Factors] cowling of Aircraft X is only removable by multiple people and a mechanic. Some Cherokees have hinges on the cowling that allow the pilot to inspect underneath the cowling. In the case of Aircraft X it does not have hinges so the whole cowling has to be removed. So in the future pilots could check the cable attachment to the throttle lever on the engine to ensure a secure attachment and that the cotter pin is intact and secure. After landing the mechanics discovered the cotter pin was missing and that the throttle cable had detached from the throttle lever in flight. Maybe a more secure attachment in the future might have helped.It was discovered by my student and I in flight when the power would not reduce. Also by mechanics inspecting underneath the cowling after the landing.Corrective actions are that the mechanics are to put a better and improved attachment system to the throttle cable and lever attachment.

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.