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I am looking to buy a wifi antenna for a boat to connect to shore based wireless hotspots that may be "far" away. Due to the waves, I am assuming that the antenna mast sways +-15° from vertical. The antenna will be mounted approximately 18m above the water.

Clearly if I choose an omni-directional antenna with too high gain, the swaying mast will lead to periodic drops of the the connection.

If I choose the gain too low, I will not reach shore based access points.

Can somebody advise me, what gain of an omni-directional antenna corresponds to an opening angle of 30°?

In principle it should be possible to define a relationship between gain and opening angle but all my internet searches for a graph showing this relationship have been in vain.

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    $\begingroup$ Welcome to SE. If you find the answer you need below, please use the green check mark so we can move your question out of the "unanswered" column. $\endgroup$ – Brian K1LI May 2 at 12:16
  • $\begingroup$ I use a 8 dBi omni antenna with good results, but it has only 15° beamwidth. see the specs here: [wifi-link.com/… $\endgroup$ – Jean-Marie May 3 at 18:20
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According to Kraus$^1$, the directivity of an antenna with a given beamwidth can be approximated by: $$D\approx\frac{4\pi}{\theta_{HP} \phi_{HP}}$$ where $\theta_{HP}$ and $\phi_{HP}$ are the half-power beamwidths (in radians) in the azimuth and elevation planes. Simply put, this approximates the solid fraction of a sphere that is subtended by the antenna's half-power beamwidth. The approximation ignores the antenna's minor lobes and should be used in that context.

When the beamwidths are expressed in degrees, $$D\approx\frac{41000}{\theta^{\circ}_{HP} \phi^{\circ}_{HP}}$$ Thus, for an omnidirectional antenna with 30$^\circ$ elevation beamwidth, $D\approx 3.8$ or about 5.8dB gain over an isotropic source.

This gain can be provided by a simple homemade collinear vertical antenna. Simulation indicates that such an antenna must be fed against a ground plane to provide low SWR to the WiFi radio.

  1. John D Kraus, Antennas, McGraw-Hill, any edition
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    $\begingroup$ I wonder if the gain of such an antenna is a net benefit in practice over what you'd get from a good AP with 6 simple dipole antennas. $\endgroup$ – Phil Frost - W8II May 2 at 12:11
  • $\begingroup$ @PhilFrost-W8II Good question, Phil. It doesn't seem as though this would provide much benefit unless the signal was right on the margin of the link budget. Especially since the signal is 3dB down at the extremes of mast travel away from the horizon. $\endgroup$ – Brian K1LI May 2 at 12:14
  • $\begingroup$ notice that if you're operating that wifi in an amateur radio fashion, you might (assuming typical legislation, no idea where OP is) use rather arbitrarily high-gain antenna systems. However, Europe for example severily restricts EIRP of ISM operation – ie. by adding gain, you reduce the maximum power your transmitter might emit by the same amount, which means that in transmit direction, getting a higher-gain antenna than the default has no advantage – in RX, it does. $\endgroup$ – Marcus Müller May 3 at 18:16
  • $\begingroup$ That goes to say that a single high-gain antenna onshore and a low-gain antenna aboard will probably not be much better than two low-gain antennas; after all, wifi needs the bidirectional communication. About a MIMO AP: that thing will inherently have antenna directivity × array directivity as directivity, and that is as good as getting a larger antenna, but unlike that, automatically finds the right direction, at least when communication without the array factor (i.e. as if you had a single antenna) still allows for basic detection. That's really the limiting factor here. $\endgroup$ – Marcus Müller May 3 at 18:23
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    $\begingroup$ @MikeWaters heh, but my comment did! ;) $\endgroup$ – Marcus Müller May 3 at 20:10
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I used a loop yagi, rated at 15 dB gain, on my boat. It had about a 30 degree beamwidth in both horizontal and vertical planes. It had plenty of gain when used with an amplifier, as it still had lots of signal at TCP-IP drop out (at a distance of about a mile, the nanosecond propagation delay seems to be too much for typical WIFI) I used it at a height of about 10 feet on a pole, since below that sihgnals die rapidly.

I would use trial and error to find a connection. I'd point it in a likely direction, see if there was service, then swing it 30 degrees, and try again. Also, I'd put the amplifier at the antenna and use USB cable to get to the cabin, avoiding coax loss (which is considerable at 2 Gigs.)

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