>> “Why does the coil have to be oriented East-West?” <<
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That was taken from a paper by an EE student from Stanford, around 1959, he stated that the power yield was measurably greater if E-W orientation was used. We took him at his word, being mere High School punks working on a class assignment. The crystal radio is working from broadcast power which has various polarities and alignments, not natural magnetism.
I don’t think that using a core should be a problem except with a boxed transformer, just not necessary. None of the surplus radar coils had cores, and they worked.
Did you ever move the coils orientations to see which direction was strongest?