A common belief among amateur radio operators is that the radiation efficiency of a vertical monopole driven against the Earth is much less than that of an elevated, horizontal dipole of the same aperture (and other things equal). But is that belief correct?
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1$\begingroup$ This question may be ill posed, as useful radiation efficiency (to some set of possible targets) is different from theoretical efficiency (which includes radiation straight down through the planet from a horizontal dipole). And the term "same aperture" again depends on your choice of integration surface, which again might or might not include the portion of RF energy that warms up your lawn. $\endgroup$– hotpaw2Commented Aug 30, 2021 at 16:20
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Below is a graphic of a short monograph addressing this issue.
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$\begingroup$ Looking only at R_in and R_rad covers only losses like resistance in the antenna, ground rod and soil right there. What about all the power lost "near the horizon", outside of the near field where it can't affect the impedance? NEC's integration of the far field, if done right, is the definitive measure of efficiency. [In fact you can use the far field to "fix" the impedance which can be inaccurate because it depends on the current on a single segment, in this case at an interesting junction of the model]. $\endgroup$– tomnexusCommented Aug 29, 2021 at 14:56
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$\begingroup$ See the NEC4 theory manual page 101 "Prad is evaluated in NEC as Prad = Pin - Ploss" and "The code also will compute average power gain by integrating the far-field radated power ... will be the total radiated power obtained by integrating the far field. This evaluation represents a variational from for the radiated power, so is generally more accurate than Prad evaluated from the voltage and current at the source and ohmic losses. Comparison of these two evaluations of radiated power can provide a useful check on the accuracy of the solution, and particularly on the voltage source model. $\endgroup$– tomnexusCommented Aug 29, 2021 at 15:03
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$\begingroup$ To be fair to the monopole and finish the comparison asked in the question, you should simulate an inverted V dipole starting 60' high, over real ground, and report that efficiency too. Both will be quite sensitive to ground type, monopole more than dipole, perhaps try poor sandy soil and rich earth too. $\endgroup$– tomnexusCommented Aug 29, 2021 at 15:06
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$\begingroup$ Thanks for your comments, but true radiation efficiency does not include propagation losses — which losses are not intrinsic to the radiator, itself. Also note that space waves traveling on a path toward the ionosphere even at low elevation angles from a vertical monopole propagate with a decay rate of 1/r (e.g., they are unaffected by the conductivity of a ground plane sufficiently beneath them). $\endgroup$ Commented Aug 29, 2021 at 15:27
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1$\begingroup$ Sure, we need to define efficiency. For Hams what matters most IMHO is probably peak far field gain *anywhere below 20 degrees" or something. Peak not average, because you're not trying to contact any particular station. Below 20 or something for maximum range. Dipoles, high enough, win this one. But for average, total, or something, monopoles are pretty good. You should still do a comparison to a dipole, on the same axes. $\endgroup$– tomnexusCommented Aug 30, 2021 at 1:49