Air Corps/AAF Transition Insignia?

[Jennison]

Hi: I've got a repro 1939 Werber A-2 and I'm looking to add a shoulder patch from mid-1942. My questions are, was there an emblem in use between that of the Air Corps pinwheel and the Hap Arnold star & wings, or was the pinwheel used into 1942 until replaced by the Arnold emblem? Or no emblem?

Thanks, Jennison