The Wright Flyer had two propellers driven from one engine. Aside from airworthiness issues, would an ASEL or AMEL rating be needed to fly it?
What about the opposite design, with two engines powering one prop?
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Well, it's in the name. Single ENGINE, not single propeller. It's the number of torque generators that matter, because that's what determines the performance hit if one goes south.
You can have two engines driving one propeller, but if one quits, you are still stuck with 50% power just as if you had two propellers, so it would be considered a multi-engine airplane (though it may get a unique designation as multi-engine-single-propeller for identification purposes).