Narrative:

The purpose of the flight was leisure flight to attend an airshow.this was my second flight in aircraft X; I had been previously checked out as required by the flight school's 141 standardization. During the preflight inspection; I found no abnormalities with the aircraft; and deemed it to be in airworthy condition. During the before takeoff checklist and engine run up; the engine performed normally; all engine instruments were in the green and controls acted properly. I departed and climbed via the class B transition route; leveling off at 10;500 MSL. The aircraft and engine performed normally during the flight up to ZZZ1; all engine instruments were in their green arcs; and the aircraft made the calculated cruise performance. During the climb; I changed fuel tanks every 15 minutes to maintain fuel balance; by turning the fuel pump on; waiting a few seconds; then changing tanks; waiting a few seconds; then turning the fuel pump off. I descended into ZZZ1 and made a normal landing; I parked the aircraft at the ramp and attended the airshow.when the airshow finished; I returned to the aircraft and performed an inspection focusing on flight controls; landing gear; fuel; engine oil; and the propeller; all components showed no damage. The engine oil showed eight quarts; the right-wing tank was fuller than the left; I departed and initially climbed on the left tank. Both my passenger and I boarded aircraft X; I performed the appropriate checklists; and started the engine on the right-wing tank. No abnormalities were noted; I received my taxi clearance; and taxi clearance to runway xy. In the run up area I performed the before takeoff checklist and engine runup on the right-wing tank. I performed the engine runup at full power and leaned the mixture until the peak power was reached; I then enriched the mixture slightly to be rich of the peak. The engine instruments all read within their green arcs and no abnormalities were noted. I have a fair amount of experience operating in high density altitude because I conducted my private; instrument; commercial single and multiengine training at ZZZ1 [a high altitude airport]. I elected to do a short field takeoff to give me the best climb performance; I received the takeoff clearance from ZZZ1 tower and took from runway xy. During the takeoff roll I noted the engine RPM and manifold pressure were indicating full power; the engine instruments were in the green; and the airspeed indicator was alive. After rotation; the aircraft climbed at approximately 700 feet per minute; I was then cleared for a left crosswind departure be ZZZ1 tower. I elected to extend the upwind leg; I turned crosswind over. At 500 feet AGL I reduced power to the climb power setting and at 1;500 feet AGL I performed the after takeoff checklist; and changed radio frequencies to contact approach to receive VFR flight following.while climbing through 7;500 feet MSL five miles southeast of ZZZ1; I heard and felt the engine reduce in power and begin to vibrate; also I noticed a reduction in airspeed and climb rate. I started the engine troubleshoot checklist by memory and initiated a left turn towards ZZZ1. I called and [notified ATC] initially on approach by mistake; then I changed back to ZZZ1 tower. I stated I had an engine failure and would enter left traffic for runway xy. The engine continued to run rough with all corrective action until I changed fuel tanks form right to left. After I changed fuel tanks the engine regained normal power output and the vibration ceased. I entered the traffic pattern completed the before landing checklist and landed on runway xy. I was followed by emergency vehicles and exited the runway and taxied to the FBO ramp. I performed the engine securing checklist and shut down the engine. I performed a post flight inspection and found no abnormalities on the exterior of the aircraft. I was met with ZZZ1 airport officials and provided a statement; they deemed that no further information was necessary.in the days following the company drove a mechanic and flight instructor up to ZZZ1 to inspect aircraft X. The mechanic drained fuel from both fuel tanks; drained and cleaned the fuel strainer. The mechanic found an unreinforced duct connecting the engine air intake on the cowling and the carburetor. The unreinforced duct was replaced. As far as I know no abnormalities were found in the fuel system; no cause was found for the engines reduction in power; nor why changing fuel tanks alleviated the power loss. A flight instructor flew aircraft X from ZZZ1 back to [departure airport] with no problems noted.

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Original NASA ASRS Text

Title: A Piper PA28 Pilot reported that during climb the engine began to lose power and vibrate. Pilot performed a succesful precautionary landing at the departure airport.

Narrative: The purpose of the flight was leisure flight to attend an airshow.This was my second flight in Aircraft X; I had been previously checked out as required by the flight school's 141 standardization. During the preflight inspection; I found no abnormalities with the aircraft; and deemed it to be in airworthy condition. During the before takeoff checklist and engine run up; the engine performed normally; all engine instruments were in the green and controls acted properly. I departed and climbed via the class B transition route; leveling off at 10;500 MSL. The aircraft and engine performed normally during the flight up to ZZZ1; all engine instruments were in their green arcs; and the aircraft made the calculated cruise performance. During the climb; I changed fuel tanks every 15 minutes to maintain fuel balance; by turning the fuel pump on; waiting a few seconds; then changing tanks; waiting a few seconds; then turning the fuel pump off. I descended into ZZZ1 and made a normal landing; I parked the aircraft at the ramp and attended the airshow.When the airshow finished; I returned to the aircraft and performed an inspection focusing on flight controls; landing gear; fuel; engine oil; and the propeller; all components showed no damage. The engine oil showed eight quarts; the right-wing tank was fuller than the left; I departed and initially climbed on the left tank. Both my passenger and I boarded Aircraft X; I performed the appropriate checklists; and started the engine on the right-wing tank. No abnormalities were noted; I received my taxi clearance; and taxi clearance to runway XY. In the run up area I performed the before takeoff checklist and engine runup on the right-wing tank. I performed the engine runup at full power and leaned the mixture until the peak power was reached; I then enriched the mixture slightly to be rich of the peak. The engine instruments all read within their green arcs and no abnormalities were noted. I have a fair amount of experience operating in high density altitude because I conducted my private; instrument; commercial single and multiengine training at ZZZ1 [a high altitude airport]. I elected to do a short field takeoff to give me the best climb performance; I received the takeoff clearance from ZZZ1 tower and took from runway XY. During the takeoff roll I noted the engine RPM and manifold pressure were indicating full power; the engine instruments were in the green; and the airspeed indicator was alive. After rotation; the aircraft climbed at approximately 700 feet per minute; I was then cleared for a left crosswind departure be ZZZ1 tower. I elected to extend the upwind leg; I turned crosswind over. At 500 feet AGL I reduced power to the climb power setting and at 1;500 feet AGL I performed the after takeoff checklist; and changed radio frequencies to contact Approach to receive VFR flight following.While climbing through 7;500 feet MSL five miles southeast of ZZZ1; I heard and felt the engine reduce in power and begin to vibrate; also I noticed a reduction in airspeed and climb rate. I started the engine troubleshoot checklist by memory and initiated a left turn towards ZZZ1. I called and [notified ATC] initially on Approach by mistake; then I changed back to ZZZ1 tower. I stated I had an engine failure and would enter left traffic for runway XY. The engine continued to run rough with all corrective action until I changed fuel tanks form right to left. After I changed fuel tanks the engine regained normal power output and the vibration ceased. I entered the traffic pattern completed the before landing checklist and landed on runway XY. I was followed by emergency vehicles and exited the runway and taxied to the FBO ramp. I performed the engine securing checklist and shut down the engine. I performed a post flight inspection and found no abnormalities on the exterior of the aircraft. I was met with ZZZ1 airport officials and provided a statement; they deemed that no further information was necessary.In the days following the company drove a mechanic and flight instructor up to ZZZ1 to inspect Aircraft X. The mechanic drained fuel from both fuel tanks; drained and cleaned the fuel strainer. The mechanic found an unreinforced duct connecting the engine air intake on the cowling and the carburetor. The unreinforced duct was replaced. As far as I know no abnormalities were found in the fuel system; no cause was found for the engines reduction in power; nor why changing fuel tanks alleviated the power loss. A flight instructor flew Aircraft X from ZZZ1 back to [departure airport] with no problems noted.

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.