If one writes the equation, for elevation angles of nulls and maximums, in
terms of free-space wavelength instead of frequency, an even more simple
equation is obtained :

Beta = ArcSin( N * Lambda / 4 / Height ) degrees.

Where Lambda is free-space wavelength
and Height is height above ground.

When N is odd, Beta corresponds to a maximum in the pattern.
When N is even, Beta correspnds to a null in the pattern.
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Reg, G4FGQ