HAMIOS v5.8.3
HF PROPAGATION GUIDE

The Science Behind Every QSO

Why can you sometimes work Australia with 100 watts and a wire, while on other days the next country is hard to reach? The answer lies 60 to 500 km above your head. This guide explains how radio signals travel around the world, what the Sun has to do with it, and how HAMIOS turns live measurements into band advice.

The Words You Will Meet

Radio propagation has its own vocabulary. Here are the terms this guide uses, each in one sentence — come back here whenever a word is unclear.

Band
A range of frequencies for radio amateurs, named after its wavelength: 20 m is around 14 MHz. Rule of thumb: MHz ≈ 300 ÷ metres, so fewer metres means a higher frequency.
DX
A contact over a long distance — usually another continent.
Ionosphere
The layer of electrically charged air 60–1000 km up, created by sunlight. It works as a mirror for shortwave.
Hop
One trip of the signal up to the ionosphere and back down to Earth.
Take-off angle
How steeply your signal leaves the antenna, measured from the horizon. Low angles reach far; high angles stay close.
Critical frequency (foF2)
The highest frequency the F2 layer still sends back when you transmit straight up. It is the “strength” of the mirror.
MUF
Maximum usable frequency: the highest frequency that still gets through on a particular path. Higher than that, the signal goes into space.
LUF
Lowest usable frequency: below it the signal is absorbed on the way and arrives too weak.
Skip zone
The ring around your station where the bounced signal does not come down: stations there cannot hear you via the ionosphere.
Absorption
Signal energy lost on the way — mainly in the D layer, by day, on the low bands.
Ionosonde
A measuring station that sweeps through the frequencies straight up, like a radar, and so measures the ionosphere above it every few minutes.
Geomagnetic storm (Kp)
A disturbance of Earth's magnetic field by the solar wind. It weakens the mirror; Kp measures how strong it is (0 = quiet, 9 = extreme).
Gray line
The moving boundary between day and night. Along it, low-band signals travel especially well.
Solar flux (SFI)
A daily measure of how active the Sun is. Higher means a stronger mirror and more open high bands.

The Atmosphere & the Ionosphere

The atmosphere tells two stories. The lower one — weather, temperature, the ozone layer — matters for VHF and UHF. The upper one, the ionosphere, is where shortwave (HF) propagation happens: a thin plasma of free electrons, created by the Sun, that bends radio waves back to Earth.

In short

High above the weather, sunlight turns a thin layer of air into a kind of mirror for radio waves: the ionosphere. Shortwave signals bounce off it and come down hundreds or thousands of kilometres away. The weather layers below it only matter for VHF and UHF.

TroposphereStratosphereMesosphereThermosphere= ionosphereozone layerVHF/UHF ducting (inversions)meteorsauroraISS 420 km→ 500–1500 °Ctemperature (°C)-80-4000 km10 km20 km50 km85 km100 km150 km200 km300 km400 km500 km600 kmATMOSPHEREDEF1F2day · foF2 ≈ 9.4 MHznight · foF2 ≈ 4.8 MHz108109101010111012electron density N (per m³)1 MHz2 MHz5 MHz10 MHzIONOSPHEREplasma frequency f = 9·√N
Left: temperature and the layers of the atmosphere. Right: electron density in the ionosphere by day and by night (logarithmic scale). The top scale gives the matching plasma frequency f = 9·√N — the highest frequency a layer reflects straight up. Altitude on a square-root scale.

Weather layers: troposphere and stratosphere (0–50 km)

All weather happens in the troposphere, the lowest 10–15 km. Shortwave passes straight through it, but for VHF and UHF it matters a great deal: a temperature inversion — warm air on top of cold air, typical of high-pressure weather — can trap 2 m and 70 cm signals in a duct and carry them hundreds, sometimes over a thousand kilometres (“tropo”). The stratosphere above it, with the ozone layer, plays no role in radio propagation.

The ionosphere (about 60–1000 km)

Above roughly 60 km, extreme ultraviolet (EUV) and X-rays from the Sun knock electrons loose from atoms and molecules. The free electrons form a plasma that refracts radio waves: the denser the plasma, the higher the frequency it can bend back. A layer with peak density N reflects frequencies up to f = 9·√N hertz when you transmit straight up — its critical frequency (foF2 for the F2 layer).

Because the ionisation comes from the Sun, the ionosphere changes all the time: with the time of day, the season, the 11-year solar cycle, and sudden events such as solar flares and geomagnetic storms. Reading those changes is what lets you find an open band instead of calling CQ into silence.

The Ionospheric Layers

The ionosphere is not one uniform mirror but a stack of regions at different heights, each created by a different part of the solar spectrum and each with its own effect on your signal.

In short

The mirror has floors. The lowest one (D) is a sponge: by day it soaks up signals on the low bands. E and F1 are small mirrors. F2, the highest, is the big mirror that makes long-distance (DX) contacts possible — day and night.

D

D Region

60 – 90 km
Day only
D region · 60–90 kmday: absorbednight: no D → up to F2

The D region forms at sunrise and fades within an hour or so after sunset. It is ionised mainly by the Sun's Lyman-alpha line (acting on nitric oxide) and by hard X-rays. The air there is still dense, so the free electrons keep colliding with molecules: instead of refracting a radio wave they absorb its energy. The D region does not reflect — it absorbs.

Absorption falls with the square of the frequency, so the low bands are hit hardest. By day, 160 m and 80 m barely reach beyond ground-wave and NVIS range; 40 m is limited to shorter distances; from 20 m upward the loss is small. After dark the D region disappears and the low bands open for DX. A strong solar flare can make it so dense that even 20–10 m fade out on the sunlit side of the Earth.

Effect on HFAbsorption ∝ 1/f² — hardest on 160 / 80 / 40 m
PresentSunrise to shortly after sunset
Operator tipWork 160 / 80 m DX at night and around the gray line.
E

E Region

90 – 130 km
Day (weak at night)
E region · 90–130 kmE hop ≤ 2000 kmsporadic E6 m / 10 m

The E region peaks at about 105–120 km and is ionised by soft X-rays and EUV. It follows the Sun closely: strongest at local noon, weak at night. Its critical frequency foE is typically 3–4 MHz at midday — enough for single hops of up to about 2000 km on 40 m and sometimes 20 m.

Sporadic E (Es) is its famous exception: thin, very dense clouds of ionisation at 100–120 km that come and go within minutes to hours. They form when wind shear in the upper atmosphere squeezes long-lived metal ions — left behind by meteors — into a thin sheet. Es reflects 10 m, 6 m and sometimes even 2 m over 500–2300 km. It peaks from May to August in the Northern Hemisphere, with a smaller peak around midwinter. HAMIOS detects Es from the measured foEs at ionosondes and from short-skip spots on 10 m and 6 m.

Effect on HFRefraction — single hop up to ~2000 km
Sporadic E10 m / 6 m (and 2 m) openings of 500–2300 km
Operator tipIn summer, watch 10 m and 6 m for short-skip spots.
F1

F1 Layer

150 – 220 km
Summer days
F1 layer · 150–220 km (summer days)occasional 1500–3000 km hop

On summer days — and more often in years of low solar activity — a ledge appears below the F2 peak: the F1 layer. It is ionised by EUV and follows the Sun like the E region. At night and in winter it merges into a single F layer.

For most operators the F1 layer is a side note: the F2 layer above it usually sets the MUF. Occasionally, on medium-distance paths, the F1 layer is the one that reflects.

Effect on HFOccasionally reflects paths of 1500–3000 km
PresentSummer daytime; merges with F2 at night
F2

F2 Layer — The DX Layer

220 – 400 km
24 h
F2 layer · 220–400 km — the DX layermulti-hop · up to ~4000 km per hop

The F2 layer is the one DX depends on. It is the densest layer, peaks at about 250–350 km and, because the air up there is so thin, electrons recombine slowly: the layer survives the night, weakened. Its critical frequency foF2 ranges from 2–4 MHz on a quiet night to 8–13 MHz on a sunny day near solar maximum.

One F2 hop covers up to about 4000 km (at very low take-off angles); longer paths use several hops. Every hop costs a few dB — the ground reflection most of all — so CW and digital modes such as FT8, with 10–25 dB more margin than SSB, reach much further with the same station.

It is also the most variable layer. It follows the solar cycle (higher sunspot number, higher foF2), the season (in winter, daytime foF2 at mid-latitudes is often higher than in summer — the winter anomaly) and geomagnetic storms, which can lower foF2 by 30–50 % for a day or more.

Effect on HFRefraction — long-haul DX, day and night
Skip distanceUp to ~4000 km per hop; multi-hop worldwide
Operator tipAt night the MUF drops: move down in frequency as the evening goes on.

Propagation Modes

A signal can reach another station in several ways. Which one works depends on the frequency, the take-off angle, the time of day and the state of the ionosphere.

In short

Your signal can reach the other station in different ways: by hugging the ground, by bouncing once or several times off the ionosphere, by going almost straight up and down for regional contacts, or through special effects such as sporadic E, aurora and meteors.

DEF2skip zone (20 m)NVIS 80 mtoo steep → into space1 hop F2 · 20 m · ≈ 3200 km2 hops · ≈ 4600 kmyouground waveheights exaggerated 2.5×
Ground wave, NVIS on 80 m, a ray that is too steep for 20 m and escapes, a single F2 hop on 20 m with its skip zone, and two F2 hops — on a curved Earth with realistic layer heights (vertical scale exaggerated).

Ground wave

The wave follows the Earth's surface. Its range drops quickly with frequency and depends on the ground: on 160 m it covers 100–300 km (much more over seawater), on 80 m a few tens of kilometres, above 10 MHz only a few. Mainly useful on the low bands during the day.

In practice: Local and regional contacts on 160 m and 80 m during the day, from tens to a few hundred kilometres.

Sky wave

The ionosphere bends a signal launched at an angle back to Earth, hundreds to thousands of kilometres away. For every frequency above the critical frequency there is a steepest angle that still comes back; closer in lies the skip zone, which you cannot reach by sky wave — and often not by ground wave either.

In practice: Every DX contact on shortwave. A station 300 km away that cannot hear you while one 3000 km away can? It is in your skip zone.

NVIS

Near Vertical Incidence Skywave: transmit almost straight up on a frequency below foF2 and the signal comes down in a circle of 0–400 km around you, with no skip zone. Ideal for regional contacts on 80, 60 and 40 m with a low horizontal dipole (0.1–0.25 λ high). It works only while foF2 is above your frequency — at night often only on 80 m.

In practice: Contacts 50–400 km away on 80 m or 40 m, for example a regional net. Hang your dipole low — a few metres is enough.

MUF, LUF and FOT

The MUF (maximum usable frequency) is the highest frequency the ionosphere returns on a given path. It is a median: on half of the days the band goes a little higher, on the other half not. The LUF (lowest usable frequency) is set by D-layer absorption and by your station — more power or a weak-signal mode lowers it. The best frequency, the FOT, is about 85 % of the MUF: open on roughly nine days out of ten.

In practice: Pick a band just below the MUF that HAMIOS shows. MUF 18 MHz? Then 20 m (14 MHz) is a good choice and 15 m (21 MHz) is closed.

Gray line

Along the day/night boundary the D layer is weak on both sides — not yet formed on the sunrise side, already gone on the sunset side — while the F layer is still dense. Paths along this line, at sunrise and sunset, often give the best low-band DX of the day on 160, 80 and 40 m. HAMIOS draws the gray line from the Sun's exact position.

In practice: Around sunrise and sunset, look at the gray line on the HAMIOS map: stations on that line are the ones to try on 80 m and 40 m.

Short path and long path

A signal can go the short way around the globe or the long way — the other side of the great circle, 40 000 km minus the short-path distance. When the short path is closed, or runs through darkness or the auroral zone, the long path through daylight or along the gray line is sometimes much stronger: Europe to New Zealand on 20 m in the morning is a classic.

In practice: Is a station weak? Turn your beam 180° and try the long path.

Sporadic E

Dense Es clouds reflect 10 m, 6 m and occasionally 2 m over 500–2300 km, far above the normal MUF. Openings appear suddenly and can move quickly. Two hops (Es + Es, or Es + F2) occasionally connect continents on 6 m.

In practice: If 10 m or 6 m suddenly fills with stations 1000–2000 km away on a summer day, that is sporadic E — be quick, it can close again within minutes.

Transequatorial propagation

On both sides of the geomagnetic equator the ionosphere forms two dense crests (the equatorial anomaly). Paths crossing the equator roughly north–south — Europe to southern Africa, Japan to Australia — can carry 10 m and 6 m in the afternoon and evening, even when F2 elsewhere is closed. Best around the equinoxes.

In practice: In the afternoon and early evening, try 10 m towards southern Africa or South America.

Aurora

During geomagnetic storms charged particles pour into the auroral zones. On HF that means extra absorption and a distorted ionosphere: polar paths (Europe–Japan, Europe–western North America) weaken first. On 6 m and 2 m the aurora itself can reflect signals, with a typical rough, buzzing sound — point your antenna north.

In practice: When Kp is high, avoid paths over the pole. On 6 m and 2 m, try pointing your antenna north.

Meteor scatter

Meteors leave short-lived trails of ionisation at 80–120 km that reflect VHF for a fraction of a second up to a minute. With MSK144, contacts of 800–2200 km on 6 m and 2 m are routine, especially during showers such as the Quadrantids (January), Perseids (August) and Geminids (December).

In practice: Use MSK144 during a meteor shower; the early morning hours are best.

Multi-hop and chordal hop

Longer paths use several hops. Every ground reflection costs a few dB — less over sea than over dry land. On a chordal hop the signal skips from one ionospheric point to the next without touching the ground, which gives surprisingly strong signals on long paths, typically around the equator and in the evening.

In practice: The more hops, the weaker the signal — that is where CW and FT8 make the difference.

Distance, Angle & Frequency

Whether a band “is open” is largely a question of geometry: the steeper a signal meets the layer, the lower the frequency the layer can still return. That single fact explains the skip zone, NVIS, and why a long DX path supports higher frequencies than a short one.

In short

Think of skimming a stone on water: thrown flat it bounces, thrown steeply it sinks. A radio wave that meets the ionosphere at a flat angle is sent back even at high frequencies; one that meets it steeply comes back only at low frequencies. That is why a long path often works on a higher band than a short one — and why there is a zone around you that sky waves skip.

F2 · foF280° · ≈ 100 km · MUF ≈ 1.0 × foF230° · ≈ 930 km · MUF ≈ 1.8 × foF25° · ≈ 2900 km · MUF ≈ 3.2 × foF2virtual height 300 km · heights exaggerated 3×
The same F2 layer, three take-off angles. Straight up, the layer returns at most foF2; at a lower angle it returns higher frequencies over a longer hop. HAMIOS uses the same relation for short paths.

The secant law

A wave that meets a layer at an angle of incidence φ is returned up to f = foF2 / cos φ — the secant law. The longer the hop, the flatter the incidence and the higher the maximum frequency. On a round Earth the factor for a 3000 km hop is about 3 to 3.5: that is the M(3000) factor ionosondes publish, and MUF(3000) = foF2 × M(3000).

Take-off angle F2 hop (300 km) MUF / foF2 E hop (110 km) MUF / foE
3°3,225 km3.3 ×1,776 km5.2 ×
5°2,877 km3.2 ×1,486 km4.9 ×
10°2,193 km2.9 ×1,004 km4.0 ×
15°1,714 km2.6 ×730 km3.2 ×
20°1,374 km2.3 ×561 km2.6 ×
30°934 km1.8 ×366 km1.9 ×
45°561 km1.4 ×214 km1.4 ×
60°328 km1.1 ×125 km1.1 ×

How to read it: a signal leaving your antenna at 10° comes down about 2200 km away after one F2 hop, and on that path the band can go up to 2.9 times the critical frequency. With foF2 = 7 MHz that is about 20 MHz — so 20 m works, 15 m does not. (Single hop on a round Earth, reflection at the given height.)

Your antenna sets the angle

A horizontal dipole radiates most strongly at an angle set by its height above ground: at about λ/2 high the main lobe points about 30° up, at 1 λ about 14°. Low antennas (below λ/4) radiate mostly straight up — perfect for NVIS, poor for DX. Verticals radiate at low angles, but over average ground they lose the very lowest ones. The HAM Antenna Designer computes this pattern for your height and ground.

Day, Night & Seasons

The ionosphere breathes with the Sun. Over a day the MUF rises after sunrise, peaks in the early afternoon and falls in the evening; the LUF follows the Sun even more closely. The window between the two curves is where the bands are open.

In short

Sunlight charges the mirror. By day the higher bands (20–10 m) open; at night the lower bands (80–40 m) take over. Summer and winter, and the Sun's 11-year cycle, shift that picture.

sunrisesunset160m80m40m30m20m17m15m12m10m000306091215182124051015202530MHzUTC (Netherlands, equinox)MUF (3000 km)FOT = 0.85 × MUFLUF (typical station)
MUF and LUF over one day for a 3000 km path whose midpoint lies over the Netherlands (52°N 5°E), at the equinox with a sunspot number of 100 — computed with the same model HAMIOS uses (before calibration on an ionosonde). A band is open where it lies between the curves: at midday up to 12 m (MUF ≈ 25 MHz), at night up to 30 m.

The daily rhythm

Before sunrise the MUF is at its lowest and the DX is on 80–30 m. After sunrise the higher bands open one by one, while the D layer builds up and closes 160 m and 80 m for long distances. In the afternoon 20–10 m are at their best; after sunset the process reverses. The ionosphere lags the Sun by roughly an hour, so the MUF keeps rising a little after local noon.

Seasons

Summer brings long days and sporadic E, but at mid-latitudes the daytime MUF is often lower than in winter: the summer upper atmosphere contains more molecules, which speed up recombination (the winter anomaly). Winter brings short days, long nights and the best low-band season. Around the equinoxes, in March and September, both hemispheres are lit alike — the best time for north–south DX and transequatorial propagation.

The solar cycle

Every 11 years or so the Sun goes from quiet to active and back. Near solar maximum the daytime MUF can exceed 35 MHz and 10 m is open worldwide; near minimum 20 m is often the highest reliable DX band and 10 m opens mainly through sporadic E. Cycle 25 peaked in October 2024 (smoothed sunspot number 161) and is now in its declining phase — still good years for the high bands, but less often and less long each day.

The Sun & Space Weather

HAMIOS shows a handful of numbers from the Sun and the magnetosphere. Here is what each one means for your bands.

In short

Two kinds of numbers. The first tells how strongly the Sun charges the mirror: solar flux (SFI) and sunspots — higher is better for the high bands. The second tells how disturbed Earth's magnetic field is: Kp, Bz and the A-index — lower is better. Solar flares (the X-ray class) can knock out shortwave for minutes to hours.

05010015020025030019962000200420082012201620202024cycle 23180 · 11/2001cycle 24116 · 04/2014cycle 25161 · 10/2024minimumminimumnow13-month smoothedmonthly meansunspot number · source: SILSO, Royal Observatory of Belgium
Sunspot number since 1996: monthly means and the 13-month smoothed curve. Cycle 23 peaked in November 2001 (180), cycle 24 in April 2014 (116) and cycle 25 in October 2024 (161). Source: SILSO, Royal Observatory of Belgium.

Typical daytime DX by Solar Flux Index (mid-latitudes)

< 70
70–100
100–130
130–160
> 160
160m
G
G
G
G
G
80m
G
G
G
G
G
40m
G
G
G
G
G
30m
G
G
G
G
G
20m
G
G
G
G
G
17m
F
G
G
G
G
15m
P
F
G
G
G
12m
P
P
F
G
E
10m
P
P
F
G*
E*
6m
P
P
P
P*
F*
P = Poor F = Fair G = Good E = Excellent Rule of thumb for daytime DX. 160 m and 80 m are night bands at every SFI — a low SFI even helps them (less absorption). * Sporadic E and TEP also open 10 m and 6 m at a lower SFI.
SFI

Solar Flux Index

Measured daily at 2800 MHz (10.7 cm) by the Dominion Radio Astrophysical Observatory in Penticton, Canada. The radio flux itself ionises nothing, but it tracks the solar EUV that creates the F2 layer: a higher SFI means a higher MUF. It runs from about 65 at solar minimum to 200–300 on the most active days.

< 70 — low bands and 20 m
70–100 — DX up to 17 m, 15 m now and then
100–150 — 15 m open by day, 12 / 10 m regularly
> 150 — 10 m wide open; 6 m F2 possible above ~200
SSN

Sunspot Number

The International Sunspot Number counts sunspot groups and individual spots (R = 10 × groups + spots) and is maintained by SILSO in Brussels. Averaged over a month or more it is the best single predictor of foF2 — which is why HAMIOS's model is built on it. Daily values jump around; for propagation the trend matters more.

Kp

Planetary K-index

Kp sums up geomagnetic disturbance over 3 hours on a scale from 0 (quiet) to 9 (extreme storm), from magnetometers around the world. HAMIOS uses NOAA's minute-by-minute estimate, so you see a storm while it develops. A storm hits HF twice: first extra absorption at high latitudes, then — often for a day or two — a lower foF2 and MUF (the negative storm phase).

0–2Quiet — normal conditions on all paths
3–4Unsettled to active — high-latitude and polar paths weaken
5G1 minor storm — polar paths poor, the MUF starts to drop
6–7G2–G3 moderate to strong storm — HF degraded at mid-latitudes, aurora on 6 m
8–9G4–G5 severe to extreme — HF often unusable for hours to days
Bz

Interplanetary Magnetic Field — Bz

The north–south component of the magnetic field carried by the solar wind, measured by DSCOVR and ACE at the L1 point, 1.5 million km sunward. When Bz turns south (negative) it couples to Earth's field and lets solar-wind energy in; a Bz of −10 nT or lower that lasts for hours drives storms. The solar wind needs 30–60 minutes from L1 to Earth, so Bz is the earliest warning you get. HAMIOS shows Bz live and raises an event when it is strongly southward.

X-ray

Solar X-ray Class

Flares are classified by their peak X-ray flux: A, B, C, M and X, each ten times stronger than the previous. The X-rays arrive in about 8 minutes and suddenly boost the D layer on the sunlit side — a short-wave fade-out, lowest bands first. NOAA's R scale links the classes to their radio impact:

A / BBackground — no HF effect
CSmall flare — rarely noticeable
MR1–R2 — minor to moderate fade-outs on the sunlit side, up to tens of minutes
XR3 (X1) to R5 (X20) — HF blackout on the sunlit side, from about an hour up to several hours
A

A-index

The daily A index sums up a whole day of geomagnetic activity. It is the average of the eight 3-hourly a indices — the linear equivalents of Kp (Kp 3 ≈ a 15, Kp 5 ≈ a 48). Below about 8 the day was quiet, 30–49 means a minor storm, 50 and above a major storm. A high A in the morning means the bands may still be recovering — high latitudes last.

R S G

NOAA space-weather scales

NOAA sums up space weather in three scales, each from 1 (minor) to 5 (extreme). HAMIOS shows them as events in its advice.

Scale Caused by Effect on HF
R1–R5Radio blackout: X-rays from a flare (M1 … X20) Minutes to hours of fade-out on the sunlit side; low bands first
S1–S5Solar radiation storm: energetic protons (≥ 10 MeV) Polar cap absorption: polar paths blacked out, often for days
G1–G5Geomagnetic storm: Kp 5 … 9 Absorption at high latitudes, then a lower MUF for a day or more

How HAMIOS Uses All of This

HAMIOS combines a physical model with live measurements: the model fills in what is not measured, the measurements keep the model honest.

In short

HAMIOS works out what should be open, checks that against live measurements and real reports from other stations, and then tells you in plain words which band to use, which way to point and for how long.

01

One calibrated propagation model

Every panel — the band bars, the 24-hour heatmap, the advice and the propagation map — uses the same model. It starts from the sunspot number and the Sun's position, then calibrates itself on the nearest ionosonde's live foF2 and MUF (KC2G / GIRO network, refreshed every 15 minutes). Across 27 ionosondes worldwide the calibrated model matches the measured MUF with a median ratio of 1.00.

02

Measured absorption

NOAA's D-RAP map shows where a flare or a proton event is absorbing HF right now. HAMIOS raises the LUF there, so after a flare the low bands drop out of the advice exactly where they are really closed.

03

Smart advice

Up to five recommendations — band, mode, frequency, direction and time window — checked against real WSPR, DX-cluster and PSKReporter spots. When real spots show a path the model does not expect (TEP, sporadic E), the spots win.

04

Propagation map

For the chosen band the map shows the probability that each point on Earth can be reached from your QTH, including the skip zone around you. Click anywhere for the great-circle path and the distance.

05

Gray line, Sun and aurora

The day/night boundary and the gray line come from the Sun's exact position (NOAA solar calculator, within about 1° on the map). The aurora layer shows NOAA OVATION's measured probability of aurora, updated every few minutes.

06

Ionosondes and space weather

The ionosonde panel shows your measured ionosphere: foF2 (the highest NVIS band) and MUF(3000) (the highest DX band). NOAA R / S / G scales, solar-wind shocks, southward Bz and measured sporadic E appear as events in the advice.

07

Alerts

Time-stamped alerts for storm onset, strong flares, southward Bz, approaching lightning and satellite passes — each with a plain explanation of what it does to your bands.

08

History

HAMIOS keeps 90 days of solar and band data in charts, so you can see what a storm did to your bands or how the solar flux has been trending.

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Models & Formulas

The models HAMIOS uses, exactly as they are in the source code (HAMIOS 5.8). They are deliberately simple and fast; the accuracy comes from calibrating them on live measurements.

In short

This part is for the technically curious: the actual formulas behind HAMIOS. You do not need them to use the program — each one comes with a line in plain words.

☉Sun position

In plain words: Where the Sun is, to within a hair — so HAMIOS knows exactly where it is day and where it is night.

Solar declination, equation of time and the subsolar point follow the NOAA solar calculator (after Meeus), accurate to about 0.01°. Day and night use a Sun elevation of −0.83° (refraction plus the Sun's radius). The same function drives the map, the gray line and the propagation model.

T = Julian centuries since J2000.0 L₀ = 280.46646° + 36000.76983° · T M = 357.52911° + 35999.05029° · T λ = L₀ + C − 0.00569° − 0.00478° · sin Ω (C = equation of centre) δ = asin( sin ε · sin λ ) (ε = obliquity of the ecliptic) λ_sun = −15° · (UT − 12 h + EoT) (subsolar longitude) cos z = sin φ · sin δ + cos φ · cos δ · cos(λ − λ_sun) day: z < 90.83°
foF2Critical frequency of the F2 layer

In plain words: How strong the mirror is: stronger with more sunspots and more sunlight; weaker at night, near the poles and during storms.

foF2 follows from the sunspot number (SSN) and the Sun's zenith angle one hour earlier — the ionosphere lags the Sun. Between a night value and a noon value the shape follows (cos z / cos z_noon)^0.6. It is reduced at high latitudes and during storms (Kp above 3).

f_noon = 4.0 + 0.045 · SSN f_night = 2.2 + 0.016 · SSN [MHz] s = min( 1.1, ( cos z(t − 1 h) / cos z_noon )^0.6 ) foF2 = ( f_night + (f_noon − f_night) · s ) · ( 1 − 0.25 · max(0, (|φ| − 40°) / 40°) ) foF2 ×= 1 − 0.035 · max(0, Kp − 3) M(3000) = 2.9 + 0.3 · min(1, s) MUF(3000) = foF2 · M(3000)
calCalibration on the nearest ionosonde

In plain words: If a measuring station is nearby, HAMIOS trusts its measurement more than its own estimate — fully for now, less and less for later hours.

The nearest ionosonde within 2000 km, with a measurement younger than 90 minutes and a reliable ionogram (confidence ≥ 50), sets two correction factors. They count fully now and fade with a half-life of 8 hours for forecasts further ahead.

c_f = foF2_measured / foF2_model c_M = MUFD_measured / MUF_model (both 0.5 … 1.8) w = 0.5 ^ (Δt / 8 h) foF2 = foF2_model · ( 1 + (c_f − 1) · w ) MUF = MUF_model · ( 1 + (c_M − 1) · w )
LUFLowest usable frequency

In plain words: How much of the signal is soaked up on the way: most around noon, hardly any at night. More power or FT8 lets you go a little lower.

The LUF grows with the Sun's elevation (D-layer absorption) and the solar flux, rises at high latitudes during storms and is lowered by your station's margin (mode, power, antenna). Where NOAA D-RAP measures absorption, the LUF is at least the highest affected frequency it reports.

LUF = 1.6 + 5.5 · (cos z)^0.75 · ( 1 + 0.004 · (SFI − 70) ) [MHz] LUF ×= 1 + 0.12 · max(0, Kp − 3) · max(0, (|φ| − 45°) / 20°) LUF ×= √( 20 / (20 + S) ) S = station margin in dB (absorption ∝ 1/f²) LUF = max( LUF, HAF_D-RAP )
PChance per band

In plain words: Turns the MUF and LUF into a simple percentage per band.

The MUF is a median: at the MUF a band is open on about half of the days, at 0.85 × MUF on about nine out of ten. Two logistic curves, one at each end of the window, give the chance per band.

P(f) = 1 / (1 + e^((f / MUF − 1) / 0.07)) × 1 / (1 + e^((LUF − f) / (0.15 · LUF))) P(MUF) = 0.50 P(0.85 · MUF) ≈ 0.90
pathPaths and the skip zone

In plain words: Long paths are checked at every bounce point, and the weakest point decides. Short paths get a lower maximum — that is the skip zone.

Paths up to 4000 km are evaluated at their midpoint, longer paths at ¼ and ¾ of the way (one control point per hop of about 3000 km); the weakest point decides. Short hops get a lower MUF because the signal meets the layer more steeply — that is what creates the skip zone on the propagation map.

MUF(d) = min( MUF(3000), foF2 · √(1 + (d / 600 km)²) ) for d < 3000 km distance: haversine · control points: spherical interpolation along the great circle
KpAurora

In plain words: Where the northern and southern lights are — measured by NOAA, or estimated from Kp when that measurement is missing.

Normally the map shows NOAA OVATION's measured aurora probability. Without it, HAMIOS falls back to a Kp-driven oval around the IGRF-2025 geomagnetic poles:

geomagnetic pole (north): φ_p = 80.65° N, λ_p = 72.65° W θ = 23° + 2.5° · Kp (colatitude of the oval's edge) φ = asin( sin φ_p · cos θ + cos φ_p · sin θ · cos ψ ) λ = λ_p + atan2( sin θ · sin ψ, cos φ_p · cos θ − sin φ_p · sin θ · cos ψ ) ψ = 0 … 2π
TLESatellite orbits

In plain words: Where each satellite is — accurate to about 10 km, without extra software.

Satellite positions use Kepler's equation with the secular J2 perturbations (precession of the ascending node and of the argument of perigee) and the TLE's decay term — within about 10 km of the full SGP4 model over a day, without external libraries.

a = ( μ / n² )^(1/3) μ = 398 600.4418 km³/s², n from the TLE k = 1.5 · J₂ · (R_E / p)² · n p = a · (1 − e²) J₂ = 1.08263 · 10⁻³ dΩ/dt = −k · cos i dω/dt = k · (2 − 2.5 · sin² i) M = M₀ + n · Δt + (ṅ / 2) · Δt² E = M + e · sin E (iterated)

Known limits. The base model has no winter anomaly and no equatorial anomaly, and it treats the ionosphere over a path as smooth. Near an ionosonde the calibration corrects most of that; far from any ionosonde the model is on its own — which is exactly why HAMIOS lets real WSPR, DX-cluster and PSKReporter spots overrule it.