Line-of-sight_propagation

# Line-of-sight propagation **Line-of-sight propagation** is the transmission of a radio wave, of light, or of an acoustic wave along the unobstructed straight path joining a transmitter and a receiver, with no reflection, refraction, or diffraction needed to complete the link. [[Radio_wave|Radio waves]] above roughly 30 megahertz (the [[Very_high_frequency|very-high-frequency]] band and everything of shorter wavelength) depend on this direct path almost exclusively, because the [[Ground_wave|ground wave]] that carries a lower-frequency signal around the planet's curve has essentially died out within a few wavelengths of the antenna, and the [[Ionosphere|ionosphere]] no longer bends the wave back down as it does for [[Skywave|skywave]] propagation. A three.js sketch on this page, adapted from Wikitube's Aviation portal, renders the same curved-Earth geometry in three dimensions that this article works through by hand below. Even where geometry allows a straight path, buildings, terrain, and foliage often do not, and the lower atmosphere bends, absorbs, and reflects the wave enough to matter at the frequencies line-of-sight links use; the impairments below describe how much of a supposedly clear path is not, in practice, clear at all. Cellular telephone networks are built on these same high-frequency bands yet routinely serve handsets with no direct view of a tower, a contradiction that multipath resolves rather than merely tolerates. How far apart a transmitter and receiver can stand and still see each other is set by the Earth's own curvature, a limit called the radio horizon, worked out below first for a bare rock in a vacuum and then again for a planet with an atmosphere. ## Impairments to line-of-sight propagation Even a geometrically clear path attenuates a signal simply because the wave's energy spreads over an ever-larger wavefront with distance, the [[Free-space_path_loss|free-space path loss]] that sets the floor every other impairment adds to. Physical obstacles, such as a building, a hill, or a stand of trees, block or diffract the direct ray; diffraction lets some energy bend around a sharp edge, but only a fraction of what a clear path would deliver, and the loss grows sharply once an obstacle intrudes into the first Fresnel zone, the cigar-shaped volume around the direct ray that must stay largely clear for the received signal to reach close to its full unobstructed strength; link engineers commonly work to a rule of keeping at least sixty percent of that zone's radius open.[^fresnel60] Reflections off the ground, nearby buildings, or moving vehicles send the same transmission to the receiver by more than one path at once, and because the paths differ in length the copies arrive out of phase and combine constructively or destructively depending on the receiver's exact position, an effect described elsewhere on this site as [[Multipath_propagation|multipath]] and, statistically, as [[Rayleigh_fading|Rayleigh fading]]. Water vapour and oxygen absorb microwave energy at specific frequencies regardless of what stands in the way, and rain adds further loss as the wavelength approaches the size of a raindrop, so a nominally clear band can be far noisier on a wet day than a dry one. None of this is helped by the receiver's own limits: at these frequencies the sky and ground a beam looks at can radiate real thermal energy of their own, so it is often the external brightness a receiver stares into, not its internal circuitry, that sets the faintest signal it can recover.[^ell-los1][^ell-los2] Finally, the lower atmosphere's refractive index does not stay perfectly uniform: a temperature inversion or a sharp humidity gradient can bend a signal enough to duct it well past where the geometry below predicts it should fade out, or just as easily bend it away and shorten a link that normally works. ## Mobile telephones Cellular and personal-communications handsets work in the same [[Ultra_high_frequency|ultra-high-frequency]] and low-[[Microwave|microwave]] bands where line-of-sight propagation dominates, yet a phone deep inside a building or between city blocks routinely has no direct view of the tower serving it. A fixed point-to-point microwave backhaul link is engineered the opposite way, with two dish antennas raised and aimed so the first Fresnel zone between them stays genuinely clear; a cellular base station instead accepts that most of its handsets will not have that clear path and leans on the same reflections, diffraction, and scattering described above as impairments, since a copy of a signal reaching a receiver by an indirect route is still a usable signal rather than a failed link. Base-station antennas are still mounted as high as practical, because raising either end of a link is the cheapest way to push its geometric horizon outward, and coverage planning starts from that horizon distance before subtracting the losses clutter and buildings add on top of it. Millimetre-wave services built around very short wavelengths give back some of this tolerance for obstruction: at those frequencies diffraction is weak and a hand, a wall, or foliage can block the path outright, so a millimetre-wave small cell is deployed at short range and often steers its beam electronically toward whatever reflected path remains open once the direct one is lost. ## Radio horizon Two antennas can hold a clear line of sight only until the Earth's own curvature gets in the way, and the distance at which that happens, the radio horizon, is a matter of geometry before it is a matter of radio at all. The same limit governs an aircraft's [[Radar_horizon|radar horizon]], a satellite dish's view of a distant transmitter, and the reach of a coastal broadcaster's higher harmonics; only the numbers change. ### Earth bulge Over a path more than a few kilometres long, the ground does not stay conveniently flat: measured against the straight line joining two antennas, the Earth's own surface rises, or bulges, toward the middle of the path, by an amount that grows with the square of the distance between the ends. A path can be unobstructed by any building or hill and still lose signal if that bulge intrudes far enough into the first Fresnel zone at its midpoint, which is why a long microwave link is planned against the bulge's height directly rather than against a flat-Earth assumption that holds only for short hops. ### Vacuum distance to horizon Stripped of any atmosphere, the reach of a straight ray from an antenna at height h above a sphere of radius R is the length of the tangent line to that sphere, `d = sqrt(2*R*h)` once h is small next to R, which it always is for any antenna anyone has built. Putting in the Earth's mean radius of 6,371 km gives the working form `d(km) = 3.57*sqrt(h(m))`: an antenna 10 m up sees about 11.3 km of curved ground; one 100 m up sees about 35.7 km. Two antennas at heights h1 and h2 can see each other out to the sum of their individual horizons, `d(km) = 3.57*(sqrt(h1) + sqrt(h2))`. ### Atmospheric refraction A real atmosphere is not a vacuum, and its refractive index falls slightly with altitude as the air thins, bending a radio ray very gently back toward the Earth as it travels and letting it reach a little beyond the vacuum horizon above. Engineers fold this bending into the same flat geometry by pretending the Earth is somewhat larger than it really is (the effective-Earth-radius model) with a standard atmosphere corresponding to a factor `k` of about 4/3.[^k43] Unusually strong refraction, from a temperature inversion or a sharp drop in humidity with height, can trap a signal in a duct near the surface and carry it far past even this extended horizon; unusually weak refraction shortens the reach instead. #### Refracted distance to horizon Scaling the vacuum formula by `sqrt(4/3) ≈ 1.155` gives the standard working figure for ordinary VHF, UHF, and microwave links, `d(km) ≈ 4.12*sqrt(h(m))`, or for two antennas, `d(km) ≈ 4.12*(sqrt(h1) + sqrt(h2))`. An aircraft cruising at 10,000 m, a round number whose square root is exactly 100, has a vacuum horizon of 357 km and a refracted radio horizon of about 412 km — the extra reach the standard atmosphere's bending buys over pure geometry. Aviation and radar practice often restate the same relation using feet and nautical miles, `d(nmi) ≈ 1.23*sqrt(h(ft))`, a form familiar from air-traffic and shipboard radar-horizon tables.[^nmiformula] ## Microsims This article carries no p5.js sketch of its own. Its geometry is close kin to problems that neighbouring Wikitube pages do model interactively, and the horizon calculation above is the one a three.js companion, carried over from Wikitube's Aviation portal, renders as a curved-Earth scene rather than as a flat sketch. Two neighbouring sketches are built around a different kind of hard limit that nonetheless makes the same point as the horizon above: every radio or acoustic system has some built-in ceiling on range, geometric or otherwise, past which what arrives is not merely fainter but wrong. The Radar sketch enforces its ceiling through pulse timing rather than curvature, folding a distant target's echo back to a false, much shorter range once it is dragged past the receiver's unambiguous-range ring. The Sonar sketch makes a related point about a wrong assumption rather than a hard limit: biasing its assumed sound speed away from the true value slides every measured range off its true position by the same ratio, much as an atmosphere refracting more or less than the standard model biases a radio path's real horizon away from the textbook figure worked out above. The Doppler effect sketch speaks most directly to the mobile-telephone case: dragging its source to a higher speed bunches the wavefronts ahead of it, the same geometric bunching that adds a Doppler component to the fading a fast-moving handset picks up even on an otherwise open path. *Try:* in the [[Radar]] sketch, drag a target's range out past the dashed unambiguous-range ring and watch its echo reappear as a ghost at a short, false range — a timing limit standing in for the curvature limit above. *Try:* in the Sonar sketch, drag the assumed sound speed away from 1,500 m/s and watch every measured range slide off its true-range tick by the same ratio. *Try:* in the [[Doppler_effect]] sketch, raise the source speed and watch the wavefronts bunch ahead of it, the root of the extra fading a moving handset picks up on top of the multipath described above. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Line-of-sight_propagation) : [Wikitube](https://en.wikitube.io/wiki/Line-of-sight_propagation) Skeleton mirrored at revision 1339192660. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Free-space_path_loss]] - [[Multipath_propagation]] - [[Very_high_frequency]] - [[Ultra_high_frequency]] - [[Microwave]] - [[Radar_horizon]] - [[Ground_wave]] - [[Skywave]] - [[Ionosphere]] ## References The Earth-curvature and refraction geometry of the radio horizon — the tangent-line distance formula and the resulting `3.57√h` and `4.12√h` working figures — is standard textbook geometry and optics, not separately footnoted here, per the Wikitube style guide's §6.1. Page numbers below are PDF pages of the open edition linked in Further reading. [^ell-los1]: Ellingson, S. *Radio Systems Engineering, Revised First Edition*. 2023, pp. 99-101 (PDF pages). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. [^ell-los2]: Ellingson, S. *Radio Systems Engineering, Revised First Edition*. 2023, pp. 104-107 (PDF pages). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. [^fresnel60]: Citation needed: a current point-to-point microwave link engineering handbook or standard giving the customary first-Fresnel-zone clearance fraction would confirm the "60 percent" figure used here. [^k43]: Citation needed: the standard-atmosphere refractivity gradient and the resulting 4/3 effective-Earth-radius factor are traceable to a specific ITU-R recommendation or radio-engineering handbook, not yet pinned to a page in this pass. [^nmiformula]: Citation needed: a current aviation or radar-siting handbook giving the nautical-mile form `d(nmi) ≈ 1.23·√h(ft)` would confirm the figure quoted here. **Further reading** — the open textbook this article draws on, since the pair carries no separate Further reading heading of its own: - Steven Ellingson. *Radio Systems Engineering, Revised First Edition* (2023). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering ## External links This article carries no p5.js simulation of its own. The three.js companion named in Microsims above is reused from Wikitube's Aviation portal rather than hosted as a separate external resource here.