111 lines
9.2 KiB
Markdown
111 lines
9.2 KiB
Markdown
+++
|
||
title = "Why signals bend (and why your 10 GHz signal sometimes goes through a hill)"
|
||
date = 2026-04-22
|
||
draft = false
|
||
+++
|
||
|
||
<link rel="stylesheet" href="/css/nlos.css">
|
||
|
||
<div class="nlos" data-nlos>
|
||
|
||
A line-of-sight microwave link is easy to reason about. Two antennas, straight line, if nothing touches the line the path works.
|
||
|
||
Ham radio doesn't cooperate with that story. People working the [ARRL 10 GHz and Up contest](https://www.arrl.org/10-ghz-up) log contacts over hundreds of kilometers where a string between the two stations would go straight through an Oklahoma mesa. The path profile looks broken. The contact happens anyway. The universe has, as usual, not consulted the path profile.
|
||
|
||
Below, one layer at a time, with scenes you can interact with. We start from the straight-line-and-obstacle model and break it four times.
|
||
|
||
## Start simple: a line between two antennas
|
||
|
||
Two antennas, flat ground, a hill in the middle. If the hill sticks above the line, you get nothing.
|
||
|
||
<div id="scene-los"></div>
|
||
|
||
That model is how nearly every commercial point-to-point microwave link is designed. WISPs, utility SCADA, carrier backhaul, all of it. It hides two small lies that the rest of this post is mostly about. The Earth isn't flat, and the signal isn't a line.
|
||
|
||
## Earth gets in the way too
|
||
|
||
Zoom out far enough and the ground curves. From an antenna of height *h* the geometric horizon sits at about √(2·R·h). Two 30-meter towers can each see a horizon roughly 20 km away. Push them 80 km apart and the Earth bulges more than 120 meters up between them.
|
||
|
||
<div id="scene-curve"></div>
|
||
|
||
No mast is tall enough to beat that on its own.
|
||
|
||
## The signal is fatter than a line
|
||
|
||
Here's the first thing in the geometry-only model that helps NLOS along a little. Radio energy doesn't ride a pencil-thin ray. It fills an ellipsoid between the antennas called the first Fresnel zone, and you want about 60% of that zone clear for the path to behave like free space.
|
||
|
||
The ellipsoid is fattest at the middle of the path. Its radius there is √(λ·d/4), so it grows with wavelength. A 40 km path on 50 MHz has a midspan radius around 24 meters. Same path on 10 GHz is 1.7 meters.
|
||
|
||
<div id="scene-fresnel"></div>
|
||
|
||
This is why microwave links behave so much worse than HF over the same obstructed path. Higher frequency, skinnier ellipsoid, easier to clip with a ridge that doesn't look like much on the path profile. The ridge does not care how it looks on the path profile.
|
||
|
||
## Ridges leak signal
|
||
|
||
When the line of sight is fully blocked, a sharp ridge doesn't eat everything. The wavefront hitting that edge keeps going, and some energy diffracts into the shadow. The usual way to describe it is the Fresnel-Kirchhoff parameter ν, which mashes together the geometry and the wavelength. ITU-R [P.526](https://www.itu.int/rec/R-REC-P.526/) gives the loss curve, shown on the right.
|
||
|
||
<div id="scene-knife"></div>
|
||
|
||
A knife edge grazing the LOS already costs 6 dB. Stick it one Fresnel zone above and you're down 20+. It's cheap power on VHF. On 10 GHz the same geometry is almost never workable on its own.
|
||
|
||
## Real hills are rounded, which costs more
|
||
|
||
Knife edges are a convenient fiction. A rounded summit scatters more energy away from the shadow zone, so actual loss is worse than the knife-edge baseline. P.526 tacks on an extra term based on the crest's radius of curvature.
|
||
|
||
<div id="scene-round"></div>
|
||
|
||
This is where path profile software starts lying to you, politely and with conviction. If it says a ridge clears by 5 meters and you'll be +3 dB over the noise floor, you can usually subtract another 5–10 dB once you account for the rounding. Most of the time that subtraction puts the link under water. Except the link works. So something else is going on.
|
||
|
||
## Air isn't empty
|
||
|
||
Air, it turns out, cares quite a bit about radio waves. Microwaves travel a hair slower through it than through vacuum, and the slowness changes with pressure, temperature, and humidity. Radio engineers express it as N-units:
|
||
|
||
> N = (n − 1) · 10⁶
|
||
|
||
where *n* is the refractive index. At sea level N is usually around 315. It falls off with altitude, and the slope of that fall is what bends rays.
|
||
|
||
<div id="scene-refractivity"></div>
|
||
|
||
The dashed line is the international standard atmosphere. Drag the slope and the regime label changes with it. Most of the useful ham band magic happens on the far left side of that slider.
|
||
|
||
## Rays follow the gradient
|
||
|
||
A horizontal ray in a medium whose refractive index falls with altitude bends downward. The tighter the gradient, the tighter the curve. Under the standard atmosphere the bend is gentle, about a quarter of Earth's own curvature, and engineers handle this by quietly pretending the Earth is 4/3 its real size and the rays are straight. Nobody points out that this is a slightly strange thing to do. That's the familiar k = 4/3 factor.
|
||
|
||
<div id="scene-raytrace"></div>
|
||
|
||
Push the slope below −79 N/km and rays start bending faster than standard. A lot of VHF/UHF tropo propagation lives in that regime. Push below −157 N/km and rays curve tighter than the Earth curves away. The ray can't climb out anymore.
|
||
|
||
## The signal gets trapped
|
||
|
||
Here's where a ham-friendly explanation helps. Propagation models talk about "rays" because the math is a lot easier when you treat a radio wave as a bundle of straight (or curving) lines, each representing the direction the wavefront is moving at that point. In practice, those lines are the actual paths your RF follows out of the antenna. When the atmosphere bends them, your signal goes where the lines go.
|
||
|
||
A *duct* is a layer of atmosphere where the refractivity drops steeply enough that any signal launched into the layer at a shallow enough elevation angle can't escape upward. Picture a slice of your antenna's radiation pattern between about −0.5° and +0.5° elevation. Normally that energy just keeps rising into space and is lost. Under a duct, it climbs into the layer, curves back down, hits the ground (or a lower boundary of the duct) and reflects, climbs again, curves back down again, and keeps repeating. The signal skips along inside the duct for hundreds of kilometers, losing very little on each bounce because the reflections are shallow and the layer is keeping the wavefront collimated.
|
||
|
||
<div id="scene-duct"></div>
|
||
|
||
Green paths in the scene are the rays (ray = the direction the wavefront is traveling) that stay trapped inside the duct. Orange ones escape. The "critical angle" is the elevation window that stays trapped, and it's tiny, usually a fraction of a degree. That's why ducting is so fickle. Your antenna has to be radiating useful power inside that window, *and* the duct has to exist above your station, *and* the station on the other end has to be inside it or close enough for its energy to enter. When all three line up, your 10 GHz rig works a contact 400 km away. When any one of them is off, the path behaves the way the terrain profile says it should, which is to say, not at all. The atmosphere is happy to support this arrangement, briefly, before rearranging itself into something less interesting.
|
||
|
||
## Flavors of duct
|
||
|
||
Three of these show up in the wild, all the same physics, different ways the atmosphere sets them up.
|
||
|
||
<div id="scene-ducttypes"></div>
|
||
|
||
Surface ducts form overnight as the ground cools faster than the air above it, and they collapse once the sun warms things back up. Elevated ducts sit aloft under a subsidence inversion, typical under a high-pressure ridge. Both ends of the link usually need to be inside the layer, or at least angled into it. Evaporation ducts are the interesting one: over warm oceans the humidity gradient in the first 5-40 meters is so sharp that a thin duct is there nearly 24/7. Every over-water microwave link above a few GHz lives inside one.
|
||
|
||
## A real path
|
||
|
||
This is the 65 km path I've been staring at: my QTH to the W5HN/B beacon on top of the TWU dorms in Denton. Terrain heights are the actual SRTM elevations along the great circle between the two antennas. Earth's curvature (using the standard k = 4/3 effective Earth) is added on top, which is why the middle of the profile bulges up about 62 m above the endpoints. The terrain is unambiguously in the way. On the right mornings the path works anyway, because an elevated duct parks over North Texas and both ends get into it.
|
||
|
||
<div id="scene-real"></div>
|
||
|
||
Figuring out whether that duct is there on any given day is the whole point of <https://prop.w5isp.com>. The app pulls HRRR at native hybrid-sigma levels, corrects against ASOS and radiosonde profiles, and computes the refractivity gradient along every path we track. When a duct is sitting on the path the score lights up. When it isn't, the path should behave the way the terrain profile says.
|
||
|
||
The part that keeps me working on it is how often it *doesn't* behave that way. Ducting, super-refraction, and enhanced tropo scatter combine in ways that still surprise people who've been operating these bands for forty years, which is both a bit humbling and a strong argument against ever finishing this project. The more verified contacts we log with good atmospheric data behind them, the better the model gets.
|
||
|
||
If you run 50 MHz or up, submit your contacts or beacons at <https://prop.w5isp.com>. A continuous, known-distance path is worth a lot more to the model than a pile of contest contacts.
|
||
|
||
</div>
|
||
|
||
<script src="/js/nlos.js" defer></script>
|