Antenna pattern over ground

Reflections from the ground reshape every HF antenna’s radiation. Raise a dipole and watch its lobes and takeoff angle change, then compare a vertical.

Radiation pattern over ground

Frequency

MHz

Height above ground 0.5 λ (21 m, 68.8 ft)

Or enter your antenna's height

Elevation pattern from horizon (0°) through straight up (90°) to the other horizon, relative to the strongest direction, on a decibel scale down to −30 dB. The ground here is a perfect conductor. Real ground reflects less and absorbs the rest. For horizontal polarization it reflects most near the horizon: soil with a relative permittivity of 13 and a conductivity of 0.005 S/m on 7.15 MHz reflects 0.96 of the field arriving at 5° but 0.64 straight down, so real ground changes a horizontal antenna's pattern most at high angles.

At 0.5 wavelength (21 m, 68.8 ft) on 7.15 MHz, looking broadside to the wire, the lowest lobe leaves at 30° above the horizon. Launched at 30°, one hop off the F2 layer (modeled as a mirror 300 km up) lands about 934 km (580 mi) away; off the E layer (a mirror 100 km up), about 334 km.

Takeoff angle of the lowest lobe: 30°
One F2 hop at that angle: 934 km
Nulls between horizon and zenith: None
Peak gain over perfect ground: 8.42 dBi (6.27 dBd)

Looking down: the azimuth pattern

Elevation angle of the slice 30°

Seen from above at 30° elevation, with the wire drawn across the center. Low angles show the familiar figure eight; at high angles the pattern fills in. Over perfect ground the slice has the same shape at every height; height changes only how strong it is. Drawn relative to the strongest direction anywhere above the ground: this slice is at the level of the strongest direction.

Try this

At a quarter wavelength or less, most of the energy goes straight up: the high-angle radiation NVIS uses for regional contacts (G9D01, G3C10).
The lowest lobe drops to about 14.5° and a second lobe appears at 48.6°: the higher the antenna, the lower the takeoff angle (E9C13). In this broadside slice every lobe over perfect ground is equally strong.
The antenna and its image cancel straight up, leaving a null overhead and the main lobes at 30° on each side.
A half-wave dipole radiates nothing along its own axis, so off the ends its radiation is about 6 dB weaker than broadside at this height and peaks higher, near 42° instead of 30°.
Over perfect ground a quarter-wave vertical radiates most along the horizon. Over real ground the reflection cancels the direct wave at the horizon and the soil absorbs much of the low-angle radiation; over seawater more of it survives (E9C11, E9A11).
Seen 70° above the horizon, a horizontal dipole radiates almost equally in every direction: the slice varies by only 0.78 dB, and in this model its shape is the same at every height. Height changes how much goes out up there. At a quarter wavelength this slice is within 0.1 dB of the strongest direction and 64 percent of the power leaves above 45°, so the antenna is almost omnidirectional, as G9B05 says of dipoles lower than half a wavelength.
The 70° slice keeps its round shape but is now 8.6 dB below the strongest lobes, which sit at 14.5° and 48.6°. Lower the slice to 15° to see the figure eight of the low-angle radiation, about 14 dB deep off the wire ends.

Apply it

Heights that matter, in wavelengths
Band	1/4 wavelength	1/2 wavelength	1 wavelength
80 m (3.75 MHz)	20 m (65.6 ft)	40 m (131 ft)	79.9 m (262 ft)
40 m (7.15 MHz)	10.5 m (34.4 ft)	21 m (68.8 ft)	41.9 m (138 ft)
20 m (14.2 MHz)	5.28 m (17.3 ft)	10.6 m (34.6 ft)	21.1 m (69.3 ft)
15 m (21.2 MHz)	3.54 m (11.6 ft)	7.07 m (23.2 ft)	14.1 m (46.4 ft)
10 m (28.4 MHz)	2.64 m (8.66 ft)	5.28 m (17.3 ft)	10.6 m (34.6 ft)

For short-skip contacts on 40 m during the day, the exam's NVIS antenna is a horizontal dipole between 1/10 and 1/4 wavelength high (G9D01); for long-distance contacts, height lowers the takeoff angle (E9C13). The skip explorer shows where each launch angle lands.
Real ground is not a perfect conductor. Ground losses for a ground-mounted vertical depend on soil conductivity (E9A11), and the same vertical keeps more low-angle radiation over seawater than over soil (E9C11). Reflections from the ground around an antenna are what the exam calls ground gain (E9A05).
Cut the wire for your frequency with the antenna length tool.

How it works

Over a perfectly conducting ground, the field is the sum of the antenna’s own field and that of its mirror image, each in free space (image theory; Hum, University of Toronto).
A half-wave dipole’s field is proportional to cos((π/2) cos ψ) / sin ψ, with ψ measured from the wire, and its directivity is 1.64, or 2.15 dBi (Smolders, Visser and Johannsen, eqs. 4.86 and 4.95).
A horizontal wire’s image carries the opposite current, which multiplies the field by 2 sin(2π h sin α) at elevation α and height h in wavelengths (eq. 4.96). The lowest lobe peaks where sin α = 1 / (4h), so a higher antenna has a lower takeoff angle (E9C13). A vertical’s image carries the same current, and a quarter-wave vertical on the ground radiates above it like a half-wave dipole in free space (Hum).
In the broadside slice of a horizontal dipole every lobe reaches the same peak: the power relative to the same dipole in free space is 4 sin²(k h cos θ), with θ from the zenith (eq. 4.97). The tool counts lobes within 0.1 dB of each other as equally strong.
Peak gain comes from integrating the pattern over the sky, with no losses in the ground or the antenna. Real ground reflects less than a perfect conductor and absorbs the rest, by an amount that depends on soil conductivity (E9A11) and on polarization. The tool computes the reflection from the TE and TM formulas (Ellingson, sections 5.6 and 5.7) with the ground’s complex permittivity εr − jσ/(ωε0) (ITU-R P.527-6). Horizontal polarization is reflected most near the horizon: for soil with εr = 13 and σ = 0.005 S/m on 7.15 MHz, |Γ| is 0.96 at 5° and 0.64 straight down. Vertical polarization is reflected least at low angles, 0.23 at 10°, and at the horizon the reflection cancels the direct wave, so a real vertical has no lobe at 0°; over seawater it keeps more low-angle radiation (E9C11).
The one-hop distance uses the skip explorer’s single-layer model (NBS Monograph 80), with the F2 and E layers as thin mirrors 300 km and 100 km up. Those heights are assumptions: NOAA’s Space Weather Prediction Center says HF waves are typically reflected near the peak of the F2 layer, about 300 km up; NBS Monograph 80 puts the daytime peak electron density around 300 km (section 3.3.3.2); and the ITU-R ionosphere handbook places the E region at 90 to 130 km (section 2.2.3).

Learn more: Antennas and feed lines

Sources: Modern Antennas and Microwave Circuits, sections 4.4 and 4.5 (Smolders, Visser and Johannsen, TU Eindhoven) (arXiv); Image Theory / Monopoles (ECE422 course notes, S. V. Hum) (University of Toronto); Ionospheric Radio Propagation (NBS Monograph 80, K. Davies, 1965), sections 3.3.3.2, 4.2 and 4.3 (National Bureau of Standards); D Region Absorption Predictions (D-RAP) (NOAA Space Weather Prediction Center); Handbook: The Ionosphere and its Effects on Radiowave Propagation (1998), section 2.2.3 (ITU-R); Electromagnetics, Vol. 2, 5.6 Plane Waves at Oblique Incidence on a Planar Boundary: TE Case (Virginia Tech (S. W. Ellingson)); Electromagnetics, Vol. 2, 5.7 Plane Waves at Oblique Incidence on a Planar Boundary: TM Case (Virginia Tech (S. W. Ellingson)); Recommendation ITU-R P.527-6, Electrical characteristics of the surface of the Earth (section 2) (ITU-R); 2023-2027 General question pool, question G9D01 (NCVEC Question Pool Committee); 2023-2027 General question pool, question G9B05 (NCVEC Question Pool Committee); 2023-2027 General question pool, question G3C10 (NCVEC Question Pool Committee); 2024-2028 Extra question pool, question E9C13 (NCVEC Question Pool Committee); 2024-2028 Extra question pool, question E9C11 (NCVEC Question Pool Committee); 2024-2028 Extra question pool, question E9A11 (NCVEC Question Pool Committee); 2024-2028 Extra question pool, question E9A05 (NCVEC Question Pool Committee)

Practice the exam questions: G9 Antennas and Feed Lines (General), E9 Antennas and Transmission Lines (Amateur Extra)

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