Actually no German fighter had compressibility issues or suffer from "Mach tuck" like the 38 or 47. The 38's controls became ineffective because shock waves from the wing roots disrupted airflow over the tail surfaces. The 47's stick would flail about wildly in the cockpit often injuring the pilot. Neither aircraft could trim out of the dive since the airflow over the elevators was disrupted. Trimming was actually expressly forbidden since it could lead to over stressing the structure when the aircraft got low and slow enough for the control surfaces to suddenly become effective again.
The Germans knew about these transonic effects and equipped their fighters with flying-tail trim systems. They designed the 109, 190 and 262 with control surfaces that were out of the way of any shock waves and had trim that moved the entire tailplane, thus remaining effective even if control forces became excessive at extremely fast dives. Several P-51 pilots expressed surprise (and naturally a great deal of fear) when 109's pulled out of dives while they were still uncontrollable from compressibility effects, like Thomas L. Hayes, Jr., a P-51 ace of the 357th Fighter Group with 8 1/2 victories, recalled diving after a fleeing 109 until both aircraft neared the sound barrier and their controls locked. Both pilots took measures to slow down, but to Hayes' astonishment, the 109 was the first to pull out of its dive. As he belatedly regained control of his Mustang, Hayes was grateful that the German pilot chose to quit while he was ahead and fly home instead of taking advantage of Hayes' momentary helplessness.
