arXiv:2610.24368v2 Announce Type: replace Abstract: High-frequency (HF) skywave radars require high gain at take-off angles of 3 degrees-30 degrees, where vertically polarized monopoles and Yagi-Uda arrays over lossy land suffer from pseudo-Brewster cancellation. This paper shows that curving the elements of HF monopoles and Yagi-Uda arrays converts radiation from this soil-limited transverse-magnetic route into a transverse-electric route that is nearly insensitive to soil conditions. Closed-form half-space bounds quantify both routes and yield design rules; a separability result extends the soil insensitivity to arrays. A hybrid design method combines Bayesian optimization on analytical and method-of-moments models with full-wave simulations of a screened site on moist soil; current extraction differs by at most 5.1% RMS, and Fresnel post-processing agrees with independent perfect-ground results within 0.16 dB in pointwise gain for four arrays. At 15 MHz, a self-matched 2-element curved Yagi-Uda array and a Bayesian-optimized 3-element array achieve realized forward-sector gains of 6.8 and 8.3 dBi over moist soil, 6.4 and 6.3 dB above straight quarter-wave Yagi-Uda arrays optimized by the same procedure, with 92%-95% efficiency. Their gain changes by about 1 dB from a perfect ground to very dry soil, whereas that of the straight arrays falls by 9 dB. Bayesian optimization, confirmed by full-wave simulation, identified a design 0.2 dB above the sweep optimum and a gain-bandwidth Pareto front that offers up to twice the matched bandwidth. The results also show that the native far field of full-wave solvers can overestimate the low-angle gain of vertical arrays over soil by more than 4 dB.