Cecil Moore wrote:

Dave, Your 2+ dBi gain is for a dipole in free space Vs an isotropic in
free space. Roy chose to compare the dipole over perfect ground to the
isotropic in free space. The ~3dB of reflections from the perfect ground
cause the additional gain due to constructive interference.

Art chose to compare his antenna to an isotropic antenna in free space
-- he reported the gain in dBi. So I compared a dipole at the same
height to an isotropic antenna in free space. This combination allows
comparison of Art's antenna in its position over ground to a dipole at
the same height above ground.

Roy Lewallen, W7EL