What was found
FULL TAKE OFF POWER WAS ACHIEVED AT 2500 + RPM, NORMAL TAKE OFF, AND ENGINE GAUGES IN THE GREEN NOTED. ROTATION AND CLIMB NORMAL UNTIL 3500 AND ENGINE SURGED, SPUTTERED, AND STUMBLED, LOOSING RPM TO 1600-1700 RPM, WITH EXCESSIVE VIBRATION FELT THROUGHOUT AIRCRAFT. GAUGES ALL IN GREEN EXCEPT RPM AT 1600-1700. CARB HEAT WAS IMMEDIATELY APPLIED WITH A SLIGHT SMOOTHING OF THE VIBRATION, YET THEN CONTINUED TO DECREASE IN TAKE OFF POWER. INSTRUCTOR TOOK CONTROLS AND RAN QUICK VISUAL CHECKS OF PRIMER, MAGS, TANKS R/L, MIX, THROTTLE, AND TRIED ADJUSTING MIXTURE RICH, LEAN THEN BACK RICH MIXTURE. SLIGHT CLIMB FROM 3750 MSL GAINED AT VX 65 MPH TO 3850 DURING TESTING UPWIND, AND EVALUATING RISKS AND LANDING SPOTS, ABOUT TO TURN CROSSWIND. CONTINUED TO TRY TO CLIMB 60-65MPH. POWER WOULD NOT INCREASE, AND ALTITUDE COULD NOT BE MAINTAINED. INSTRUCTOR TOLD STUDENT TO MAKE EMERGENCY CALL AND SAID TURNING BACK FOR THE RUNWAY LOSS OF ENGINE POWER, 2 SOULS ON BOARD. TOWER CLEARED 45Q LAND ANY RUNWAY. INSTRUCTOR MAINTAINED 30 DEGREE BANK TURN WITH BEST GLIDE AT 80 MPH. AIMED AND LANDED MID FIELD RUNWAY 12. BLED OFF SPEED JUST ABOVE RUNWAY WITH 15 KT TAILWIND, LANDED WITHOUT EVENT. TAXIED TO PARKING WITH EXCESSIVE VIBRATION THROUGHOUT PLANE. MX PERFORMED: COMPRESSION CHECK COMPLETED, NO DEFECTS NOTED. CHECKED TIMING ON BOTH MAGNETOS, NO DEFECTS NOTED. FOUND BOTH SPARK PLUGS ON #1 CYLINDER FOULED. REPLACED ONE SPARK PLUG, CLEANED AND GAPPED OTHER PLUG.