Pilot reported engine failure on a touch and go resulted in an off airport landing with damage to the aircraft.

Narrative

This was my first time flying this aircraft; it was a checkout flight to then perform aerial glider tows. I started off in the morning with basic maneuvers at 3;000 ft. AGL. Descended down to perform touch and goes at the airport. During the 5th or 6th touch and go; on initial climb out about 50-100 ft. off the runway I heard a sputter of the engine and noticed my rpm dropped and I was not climbing anymore. I checked to make sure I had full power and everything was properly configured and I was still not climbing. I pushed on the stick to drop the nose down and noticed I was blown to the right side of the runway due to the crosswind. I had to make a landing and the engine was not providing performance. I did what I could to keep the airplane as straight as possible with the nose still down and flew the best I could into the ground. Without much time or altitude to make a decision I responded with what I could do. Upon making contact with the ground the landing gear collapsed and the prop struck the ground. Prior to this the airplane was showing no signs of any engine problems and I had a healthy engine performance up until then. I had full fuel and was only flying for about 30 minutes prior to the incident. A few weeks before this incident the annual had also been completed on this aircraft.