I fly both, sitting on the right works for me especially now that I have a side stick in the fixed wing and "point" it where I want it to go.
Sitting in the left seat and trying to fly with the left hand is a little conversion in itself I am told
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Why do Capt`s sit in the left on Fixed Wings? Maybe so the right hand was free to cuff the surly FO`s and or backhand the FE back in the 30`s. See - it all boils down to CRM
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So what was the first dual side by side and who sat where, Wright flyer?