Result for
ITU method
Signal strength vs distance
Below the dashed line a listener no longer gets reliable reception. Hover over the plot to read values.
Result for
ITU method
Below the dashed line a listener no longer gets reliable reception. Hover over the plot to read values.
Scroll or pinch to zoom, drag to pan. Heights are exaggerated and wave tilt is drawn ×3 so you can see them.
Click the map to add a receiver.
Search a place or pick an action above, then click the map. Click a pin to select it; right-click or double-click removes it. Drag to pan, scroll or pinch to zoom. Your scenario is saved automatically on this device.
A relay picks up the main transmitter off-air with a directional antenna (ITU-R P.1812 over the real feed path) and rebroadcasts on its own frequency. It is fed when its input is at least 10 dB above the minimum usable field of the main service. Receivers use whichever station gives the best margin.
Each site is served by the best station (transmitter or relay, or the best tower in the Mobile tab). Select a row to see its path and terrain.
See the mountains, buildings and signal level along the selected path in the Terrain profile tab.
Plan 2G–5G cell sites: tower heights, sectors and the link budget, then each test point's serving cell and the coverage map.
Methods: ITU-R P.529 (Hata), M.2412 (UMa), P.1812 beyond range, P.2108 clutter, P.2109 building entry, P.838 rain, P.1812/P.1546 location variability.
OpenCelliD is an open database of real cell sites (2G GSM, 3G UMTS, 4G LTE, 5G NR) with their operator and measured range. Create a free account at opencellid.org, then either import the Sri Lanka file (MCC 413, CSV or .csv.gz) or use your API key to load the cells around your location.
No real cell data loaded yet
OpenCelliD positions are estimated from crowd-sourced measurements, so they can be off by tens to hundreds of metres. Antenna height, direction and power aren't in the data, so imported cells are modelled as 30 m omni sites at typical power. For your own sites, set these in the Transmitters table.
New towers you add on the map use this height. Each tower's own height, sectors, azimuth and tilt are in the Towers table below the map.
Every number in this app comes from the equations below. Pick a model to see the calculation step by step, which checks pass, and where the model stops being valid. Lecturers can use this to discuss accuracy and limitations.
Method
“!” marks a check that fails or a known simplification. Values update as you move the distance slider or change the model in the Lab.
Each test compares the app's code with an independent reference value: published tables, ITU definitions, hand calculations, or limits that the physics must satisfy.
Paste drive-test or field-strength measurements, or values read from an ITU-R curve (e.g. P.368, P.1546). One row per point: distance_km, value. The selected model above is compared, and the points are drawn on the Lab chart.
Equations, validity range, ITU reference and known limitations of each model.
Short explanations of each effect you can test. Open a card, then try the matching experiment in the Lab.
A ground (surface) wave is a vertically polarized wave that is guided along the boundary between air and earth. Currents induced in the ground drag the lower part of the wavefront, so it follows the earth's curvature well beyond the optical horizon. That is why MW (medium-wave) AM broadcasting gives stable daytime coverage over hundreds of kilometres.
Horizontal polarization is short-circuited by the conducting ground, so groundwave systems use vertical masts.
Losses depend on ground conductivity σ and relative permittivity εr. The lab computes ITU-R P.368 the way the ITU's GRWAVE program does: the exact Sommerfeld–Norton solution for a flat earth, then the Fock/Wait residue series for the curved earth (see the Models tab for every step).
Small p means little loss (sea water, low frequency). Large p means rapid attenuation (dry ground, high frequency).
p grows with frequency through both λ and x. At 200 kHz over sea the attenuation factor stays near 1 for hundreds of kilometres. At 10 MHz over dry land, groundwave is gone within a few tens of kilometres. This is why LF and MF carry broadcasting and navigation, and HF relies on the sky wave.
Ground losses tilt the wavefront forward. The power flow then has a downward component that feeds the losses in the earth. The tilt angle is roughly tan ψ ≈ 1/√|εr − j x|. Wave tilt is larger over poor ground. The scene exaggerates it three times so you can see it.
The flat-earth formula is good up to about 80/∛fMHz km. Beyond that, diffraction around the curved earth adds loss, roughly 0.04·∛f dB per km at standard refraction. Refraction in the lower atmosphere bends waves slightly. It is modelled with an effective earth radius factor k. Larger k (super-refraction in warm, humid inversions) reduces the curvature loss. k = 1 increases it.
A wave returns when f ≤ fo·sec φ (secant law). Steep rays at high frequency escape, which creates the skip zone.
By day, the D layer absorbs the MW sky wave, so only the ground wave is heard. At night the D layer vanishes and the sky wave returns strongly hundreds of kilometres away. Where ground and sky waves arrive with similar strength (within about 6 dB), their changing phase causes deep fading and distortion. The lab shades that zone on the plot.
For a land–sea path, the field is the average of forward and reverse calculations, in dB:
Over sea after a coastline, the field can actually rise for a while. This is the "recovery effect".
The lab is a teaching model, not a planning tool. Use ITU-R P.368 (groundwave curves), P.527 (ground constants), P.1147 (MF sky wave), P.533 (HF) and P.372 (radio noise) for real work. The sky wave here is a median value. Real signals fade by 5–10 dB within minutes.
| Ground (surface) wave | Vertically polarized wave guided along the earth's surface. Main MW/LF daytime service. |
| Sky wave | Wave reflected (refracted) back to earth by the ionosphere. |
| Conductivity σ | How easily the ground carries current, in S/m. Sea ≈ 5, average land ≈ 0.003, rock ≈ 0.0001. |
| Permittivity εr | How strongly the ground stores electric field energy. Matters most at higher frequencies. |
| Numerical distance p | Norton's measure of how "electrically far" a point is over lossy ground. Larger p means more loss. |
| dBµV/m | Field strength in decibels above 1 µV/m. 60 dBµV/m = 1 mV/m. Every 20 dB is ×10. |
| Critical frequency fo | Highest frequency a layer reflects at vertical incidence (foE, foF2). |
| Skip zone | Region with no ground wave and no returning sky wave. |
| Fading zone | Region where ground and sky waves are similar in strength and interfere. |
| Millington's method | Standard way to combine different ground types along one path. |
| Great-circle path | Shortest route between two points on the earth's surface. |
Multiple choice, true/false, select-all and numeric questions. Numeric answers are marked against the app's own ITU calculations. Practice mode shows feedback straight away; exam mode marks everything when you submit.