# Radio Propagation Simulator - Ionosphere, MUF, Skip Distance, Sky-Wave Ray Tracing

> Chapman-layer ionosphere and plasma frequency, sky-wave ray tracing with hops and skip zone, MUF, skip distance, D-layer absorption, radio horizon, path loss.

- URL: https://qilingtools.com/en/physics/radio-propagation
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Choose the local time, sunspot number and frequency, and the tool builds the D, E, F1 and F2 electron density profile from Chapman layers and works out each layer's critical frequency. It then traces rays through a two-dimensional ionosphere over a curved Earth, animating sky waves hopping between the ionosphere and the ground, rays above the MUF escaping into space, and the skip zone near the transmitter. Other tabs cover the secant-law MUF, D-layer absorption by frequency and time of day, the radio horizon, free-space path loss and how each band from LF to SHF propagates.

## How to use

1. Set the local time, sunspot number and frequency, or use a quick setting such as AM broadcast or 7 MHz shortwave
2. Under Sky-wave ray tracing, show a fan of elevations or a single ray to see reflections, hops, escapes and the skip zone; read foF2, the MUF and skip distance
3. Under Ionosphere & MUF, view the plasma frequency profile and layer table, and enter a path length to get the MUF and optimum frequency
4. Under D-layer absorption and Line of sight, compare day and night absorption, the horizon for given antenna heights and the link loss

## Features

- Chapman-layer electron density that changes with local time and solar activity; D and F1 vanish at night
- 2D spherical ray tracing (RK4) with animated multi-hop sky waves, escapes and the skip zone
- Secant-law MUF with Earth curvature, longest single hop, and ray-traced versus analytic skip distance
- Day and night D-layer absorption scaling as 1/(f + fH)², explaining long-distance AM reception at night
- Radio horizon with k = 4/3, an Earth-bulge sketch, free-space path loss and received power
- Band table from LF to SHF: ground wave, sky wave, line of sight and typical uses

## FAQ

### How can shortwave signals reach the other side of the world?

Solar UV and X-rays ionise the air from about 60 to 1,000 km, forming the ionosphere. There the refractive index n² = 1 − fp²/f² falls as electron density rises, so a wave entering at an angle is bent gradually back down. The ground reflects it up again, and after several hops it can travel thousands of kilometres. Higher frequencies need more electrons to bend back, and waves above the maximum usable frequency (MUF) pass through into space.

### What are the critical frequency, MUF and skip distance?

The critical frequency is the highest frequency reflected at vertical incidence, equal to the layer's peak plasma frequency fo = 8.98√Nm Hz. Oblique rays reflect more easily, so the maximum usable frequency is MUF ≈ foF2·sec i, typically about three times foF2 on a 3,000 km path. Above foF2, rays that are too steep pass through; the nearest landing point is the skip distance, and inside it, beyond the reach of the ground wave, nothing is heard. That region is the skip zone.

### Why do AM stations come in from far away at night?

By day the Sun ionises the D layer at 60–90 km. The air there is dense, electrons keep colliding with molecules, and wave energy turns into heat; absorption scales roughly as one over the frequency squared, so the AM sky wave is almost entirely absorbed and AM travels only a few hundred km by ground wave. After sunset the D layer quickly disappears, the higher E layer reflects AM back to Earth over a thousand km away, and distant stations appear on the dial.

### Why don't FM radio and mobile signals travel very far?

VHF and higher frequencies are far above the ionosphere's plasma frequency, so they pass straight through it, and their ground wave dies quickly. That leaves line-of-sight propagation. With normal atmospheric refraction (effective Earth radius 4/3 times larger) the horizon is about 4.12(√h₁ + √h₂) km with heights in metres, roughly 28 km from a 30 m mast to a receiver 2 m up. That is why TV towers are tall and mobile networks need many base stations.

### How accurate is the ionosphere model?

It is an illustrative mid-latitude, near-equinox model: Chapman-shaped layers whose parameters vary smoothly with local time and sunspot number, and ray tracing that ignores the geomagnetic field (ordinary and extraordinary waves) and collisions. The real ionosphere changes a lot with season, latitude, solar flares and geomagnetic storms, so radio operators should use real-time ionosonde data and propagation forecasts.

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