Earl, according to the studies by L. B. Cebik, W4RNL, noted ARRL technical authority, modeling has shown this is NOT the case, adding ground radials under the half wave vertical does not materially add to its efficiency. This was borne out by our tests here at the research lab field sites, one on a salt water beach, (hardly a better ground) and one on rocky dry upland. 73, Stuart K5KVH