Pilot reported a runway excursion during gusty wind conditions while receiving training in a tail-wheel aircraft. The instructor took over the controls as the aircraft rolled into a grass area undamaged; then taxied to the hangar.

Narrative

As a 2900+ hour CFII who had always flown tricycle gear aircraft; I decided to receive training towards a tailwheel endorsement. I proceeded to receive training in a PA-11 at ZZZ. From the beginning I had difficulties with rudder control; resulting in overcorrections. With practice; these became less troublesome; but I still had difficulties making consistent wheel landings. On the morning of the incident; we had a left crosswind of about 40 degrees with winds gusting up to 15 kt. I questioned the [instructor] if it would be appropriate at my stage of training to fly. The instructor said we could proceed. The initial takeoff was uneventful; but on climb out I noticed moderate turbulence. We remained in the pattern to practice wheel landings. On my first approach and landing; the gusty crosswinds were difficult to deal. My rudder control was adequate but I bounced the landing and finally settled it on the runway further down before adding power for the touch and go. The second landing attempt was better but I still bounced slightly and had difficulty getting the stick forward to keep the airplane on the ground. On the third attempt; I succeeded in maintaining good runway alignment; was able to plant the airplane on the ground without bouncing and continued to track down the runway. I decided that I should declare success; added power for the touch and go and lifted off the runway. The instructor thought otherwise and pulled the power back so that I could make a second touchdown. The change in plans took me by surprise. We touched down and as I was trying to get the tail back up; I must have inadvertently added too much right rudder. The airplane started to head for the side of the runway; so the instructor yelled for me to let go of all the controls. He added power but the aircraft veered further right towards the the edge of the runway. He pulled the power back and we rolled across the grass area and slowly reentered the taxi ramp. We requested taxi clearance back to hangars to inspect the aircraft. I taxied the aircraft back with no further problems. We detected no damage to the aircraft. As we approached the parking area Ground Control asked us to contact them or Tower about the runway excursion The instructor thought that I may have inadvertently applied the right brake as he was adding power. I told him I didn't think I had because since the aircraft has heel brakes; I always have to work hard to reposition my heels to apply the brakes. I suspect the problem was a combination of an already deflected rudder; a gust of wind; and the yaw from suddenly adding power. On reflection; it probably wasn't a good decision to attempt training in gusty wind conditions without first having mastered tailwheel flying under normal circumstances. The instructor said he would contact the Tower.