QSO Take-off Angles — M7SQI
Plots were generated from the station log.
What the viewer shows
Each point represents a QSO. From great-circle distance, a probable take-off angle (TX elevation) was inferred using a simplified ionospheric hop model with virtual reflection heights. Colours encode the inferred hop count; shapes indicate propagation/time: ■ Es, ● F (day), × F (night). Point opacity reflects hop-fit confidence. A light grey vertical band marks the Es–F overlap region, where classification is less certain.
If this interactive plot page is a little too much for your browser, a static PNG version can be found here.
How the angles were calculated (ham-science summary)
- Per-band Es/F split. Short-range distance histograms were smoothed and a threshold was selected; values were then clamped to a sensible range. On 6 m a higher threshold was adopted, because paths there were typically Es.
- F single-hop spacing (μ). The distance histograms exhibited a comb at multiples of an underlying hop length. A seed μ was estimated from that periodicity, refined by minimizing the spread of distance mod μ, and finally tuned by a short grid search per band and for day/night.
- Heights. Virtual reflection heights of approximately 340 km (F, day), 280 km (F, night), and 110 km (Es) were used.
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Hop count.
For F-mode,
n ≈ round(D/μ)was used with guards against sub-hop artefacts and unrealistic values, assuming ground-touch per hop. For 6 m, multi-hop Es counts were optionally reported using a nominal Es hop length. -
Geometry.
The take-off angle was the elevation that reached one hop of
D/nat the chosen virtual height on a spherical-Earth approximation. In code form:e = atan2(2h′, D/n)(in degrees). No path-loss modelling was applied—this was geometry only.
This approach is geometry-rigorous but ionosphere-approximate. It infers plausible launch-angle regimes and probable hop structures
for the QSOs actually observed; it does not reconstruct exact propagation paths. The model assumes approximately repeated,
ground-touch F-mode hops and great-circle geometry. Unequal hops, ionospheric tilts, ducts, chordal paths, off-great-circle propagation,
and full ray-tracing were not modelled. TOA is computed with atan2 and clamped to ≥0°;
unusually shallow solutions are treated as candidate low-angle anomalies, not confirmed propagation modes.
NOTE: Work still in progress —
i) Very low inferred TOA values are flagged as possible chordal/ducted candidates:
- Possible chordal/ducted candidate: 4–6°
- Probable chordal/ducted candidate: <4°
- These flags indicate unusually shallow inferred geometry only; they do not prove chordal or ducted propagation.
ii) Factor in Greyline effects — Solar elevation at the QSO time for both endpoints:
- Use any SPA lib (e.g.,
astral,pysolar,ephem). - Get
sun_alt_txandsun_alt_rxin degrees and tag:- Dual greyline (strict): |alt| ≤ 6° at both ends
- Single-end greyline (strict): exactly one end |alt| ≤ 6°
- Near-greyline (loose): repeat with 12°
- (Optional) Sample points along the great-circle; if >50% have |alt| ≤ 6°, tag as a path “terminator-skimmer”.
Reading the results
- Typical DX angles. On 20/17/15 m, long paths commonly clustered in the low-angle regime (roughly single-digit to low-teens degrees).
- Why 40 m looked “shorter-hop”. Higher average launch angles (plus daytime D-layer absorption) tended to shorten per-hop ground ranges compared with 20/17/15 m.
- 6 m was Es-dominated. At mid-latitudes, F2 at 50 MHz was rare; multi-hop Es and, seasonally, TEP were more typical drivers of long 6 m paths.
- Antenna Analysis I ran some antenna modelling analysis to try and validate the data here. The Results can be seen on this page
Limits & uncertainty
Single virtual heights, equal hop lengths, and great-circle propagation were assumed; off-great-circle tilts, ducts and full ray-tracing were not modelled. Median take-off angles were expected to carry a small systematic uncertainty (a few degrees), which was acceptable for band-to-band comparisons. Known outliers and implausible distances were capped or excluded to avoid misleading tails.
Related: Terrain and Ground Effects (Boscastle QTH)
For context on how the measured take-off angles relate to the real antenna environment, I’ve published a companion analysis: Boscastle DX Terrain Analysis.
That page examines how local ground conductivity, soil salinity, and the west-facing slope of the site modify the theoretical radiation pattern. Using both modelled and measured data, it shows that the 40 m end-fed (≈ 2 m AGL, ~89 m ASL) radiates far flatter than a textbook low wire—largely due to Brewster-angle reinforcement over moist, semi-saline soil and the downhill terrain toward the Atlantic. The result is a real-world take-off minimum near 8 degrees, consistent with the dominant mode seen in the empirical TOA dataset. In short, the coastal geometry acts as a natural low-angle amplifier: physics, geography, and sea air all conspiring to make a modest longwire perform like something rather taller.Angle distribution by band
Distance vs take-off angle (per band)
Where the ionosphere numbers came from
The ionosphere was measured continuously by ground ionosondes and satellites. Useful sources included:
- GIRO / DIDBase: global ionosonde network with ionogram-derived parameters (foE, foF1, foF2, hmF2, etc.). DIDBase and the GAMBIT nowcast.
- NOAA NCEI Mirrion: near real-time plots of foF2, hmF2, and foEs, plus the World Data Service archive. Mirrion real-time · NCEI ionosphere portal.
- Reference models: the International Reference Ionosphere (IRI) provided monthly climatology of electron density and F-region parameters. IRI · NASA CCMC IRI.
- Spaceborne profiles: COSMIC-2 radio-occultation delivered global electron-density profiles used for validation and nowcasting. COSMIC-2 data.
- Regional examples: UK RAL/Chilton and Belgium RMI/Dourbes maintained long time series of ionosonde measurements. Chilton / UKSSDC · RMI Dourbes.
These references underpinned the typical heights and the day/night behaviour used in the simple geometric model presented above.