This would be true of a 20 degree sonar beam, but that really depends on the actual size and shape of the side lobes as well as at what measurement point (db or decibel) that the sonar beam was actually spec’d at and how sensitive the sonar receiver is.
Units that have a more sensitive receiver can actually receive sonar returns from an area that is wider than the specified area. I would guess that this is the majority of the middle to high end sonar units sold today. Think of this as trying to see at night with a flashlight and slipping on a pair of light intensifying glasses. With or without the glasses the same light source is used, yet you can see farther and over a wider area with the glasses on (more sensitivity to light).
You can use a transducer that is spec’d at the -3db point and yet find out the actual area of coverage (sometimes called “effective coverage area”) is far beyond that -3db point (same goes for transducers spec’d at the -6db point). Humminbird uses the much wider -10db point as it is a more realistic measurement point. It closer approximates that area that is actually shown on the display of the sonar unit. So a 20 degree sonar beam measured at the -3db point is wider than a 20 degree sonar beam measured at the -10db point (I think that it would be a 24 degree beam at -10db). So your area of coverage would be closer to 0.43 X water depth versus 0.35 X water depth for the 20 degree beam. Not much of a difference in that example but it does not take into account those side lobes like are shown in the Vexilar information which are more prevalent at shallow water depths (the sonar beam shape does not change shape due to water depth). Humminbird tries to minimize these side lobes. In my opinion; manufactures that spec their transducers at a narrow db point and yet advertise that their transducer beams cover some huge area are playing numbers games with John Q. Public. Sorry, had to get up my soapbox there for a minute. So maybe that 20 degree beam is covering a 4 foot diameter area while you are in 12 feet of water and maybe it isn’t!
Just some food for thought…


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