Directivity of omni-directional pattern in the horizontal plane given beamwidth. 

The lower scale gives the increase in gain as the beam is scanned above the horizon.  Note that the same aperture length was used for both patterns and the scanned pattern has a larger beamwidth since gain = L/λ independent of scan angle until the two sides join into a single beam.  Download program omnidir (Linux version) and run in DOS window.