Pilot reported a loss of engine power and subsequent failure necessitated a return to the departure airport shortly after takeoff.

Narrative

This was a Ferry flight of a Yak-52. Uneventful runup and climb out from Runway XX. Winds approximately 340 at 8 kts. After liftoff; raised gear and adjusted prop and power to climb settings. Performed normal right pattern then exited airport traffic pattern to southeast heading. I had a chase plane following me; we exchanged calls about altitude (on discrete frequency). Then; my engine began running very rough. I informed chase aircraft and said I'm returning to the airport which was approximately 3 miles. I asked him to call ZZZ traffic and inform them. As I made a right turn to the airport the engine continued to lose power. I had to maintain mid to high power to keep the engine running. If I dropped below approximately 50%; it would appear to be shutting off. So; I continued to move the throttle back and forth. At this point; I had to consider priority landing procedure of the Yak for off airport priority landings which states to land with gear up due to the hazard of the aircraft flipping over.I continued to lose altitude and was able to get to the airport at a low and shallow approach. The engine was still running but I was continuously adding and reducing power to try to get my airspeed to a reasonable landing speed. When I was over threshold; I lowered the flaps and gear. At this point; I was low and fast. I landed the aircraft hard on the runway and either the gear collapsed or had not extended fully. As a result the aircraft landed with the gear only minimally extended. This broke the wooden propeller and minor damage to flaps with no other damage to the aircraft. I was able to add power to get the aircraft off the runway then it quit when I reduced power. Ground crews towed the aircraft to the hangar. Note about the Yak-52. The aircraft gear; when retracted the gear is different from most aircraft in that the gear does not retract in the wing. Instead; it is just pulled up to the wing and locked in place. This design permits the aircraft to be landed in that configuration for situation I described resulting in only damage to the propeller. Additionally; the gear and flaps are actuated by a compressed air system.