An RV8 private pilot departed FHU into R-2300A while it was hot. He adjusted his departure path to maintain separation with a UAV which had departed ahead of him. Confusion existed between the pilot; the Tower; and the Departure Controller as to his presence in the hot restricted area.

Narrative

Departing from FHU; Tower Controller stated R-2303A & B [were] hot and to fly runway heading and expect a right turn north when requested. On initial climb; I maintained runway heading and was advised of a UAV aircraft turning from crosswind to downwind. I told the Controller I had the aircraft in sight. Tower Controller instructed to turn north and contact Departure Control. After turning north I had a 1;750 AGL hill in my direction of flight. I [turned] to 330 degrees to avoid direct overflight of the hill. Upon contact with Departure Control; the Controller vectored me to 020 degrees. The Controller asked if the Tower had advised me that R2303A & B were hot. I stated that he had advised me.Based on the Departure Controller's actions; I'm assuming I entered R2303A & B. Contributing factors was the extended upwind prior to turning due to the UAV in the pattern. I believe the Tower Controller should have stated 'turn to 360 degrees' and not 'turn north.' Also; I should have turned to the east side of the hill away from the restricted area to avoid overflight of the hill.