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)

  1. 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.
  2. 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.
  3. Heights. Virtual reflection heights of approximately 340 km (F, day), 280 km (F, night), and 110 km (Es) were used.
  4. 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.
  5. Geometry. The take-off angle was the elevation that reached one hop of D/n at 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:

ii) Factor in Greyline effects — Solar elevation at the QSO time for both endpoints:

Reading the results

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

Boxplot: take-off angle distribution by band (wavelength order)
Bands were sorted by wavelength. The boxplot summarized the distribution of inferred take-off angles for QSOs actually worked; medians near the low-angle regime were consistent with DX-friendly radiation patterns on the higher HF bands.

Distance vs take-off angle (per band)

80 m: colour = hop count; ■ Es, ● F day, × F night; opacity = hop-fit confidence. The grey band marked the Es/F overlap region. Typical points favoured higher take-off angles than the higher HF bands, consistent with shorter per-hop ground ranges. The accompanying histograms and “k·μ” markers supported the chosen hop spacing while revealing seasonal and diurnal variability.
80 m hop-count histogram 80 m distance histogram 80 m F-fit confidence histogram
80 m distance histogram with k·μ markers 80 m distance mod μ (day) 80 m distance mod μ (night)
40 m: colour = hop count; ■ Es, ● F day, × F night; opacity = hop-fit confidence. The grey band marked the Es/F overlap region. Typical points favoured higher take-off angles than the higher HF bands, consistent with shorter per-hop ground ranges. The accompanying histograms and “k·μ” markers supported the chosen hop spacing while revealing seasonal and diurnal variability.
40 m hop-count histogram 40 m distance histogram 40 m F-fit confidence histogram
40 m distance histogram with k·μ markers 40 m distance mod μ (day) 40 m distance mod μ (night)
20 m: long-range QSOs concentrated at low angles across several hops, typical of multi-hop F propagation. The distance histogram showed clear teeth at multiples of μ, and the “distance mod μ” plots tightened around zero at those hops.
20 m hop-count histogram 20 m distance histogram 20 m F-fit confidence histogram
20 m distance histogram with k·μ markers 20 m distance mod μ (day) 20 m distance mod μ (night)
17 m: distributions were similar to 20 m, with low-angle clusters at longer distances and a clean comb structure in the histogram. Day/night μ values generally differed modestly, reflecting the reduced F-peak height at night.
17 m hop-count histogram 17 m distance histogram 17 m F-fit confidence histogram
17 m distance histogram with k·μ markers 17 m distance mod μ (day) 17 m distance mod μ (night)
15 m: hop bands were often the most distinct; the smoothed histogram’s peaks and troughs supported a stable μ estimate. Low-angle points dominated the longest paths, consistent with efficient F-layer multi-hop at higher HF.
15 m hop-count histogram 15 m distance histogram 15 m F-fit confidence histogram
15 m distance histogram with k·μ markers 15 m distance mod μ (day) 15 m distance mod μ (night)
12 m: seasonal changes in ionization influenced the balance between Es and F; when F supported longer paths, the low-angle region again carried most of the distance.
12 m hop-count histogram 12 m distance histogram 12 m F-fit confidence histogram
12 m distance histogram with k·μ markers 12 m distance mod μ (day) 12 m distance mod μ (night)
10 m: during high solar activity, long F-mode paths appeared at very low angles; at other times, Es dominated the shorter ranges. The diagnostics visualized this regime switching via μ stability and confidence.
10 m hop-count histogram 10 m distance histogram 10 m F-fit confidence histogram
10 m distance histogram with k·μ markers 10 m distance mod μ (day) 10 m distance mod μ (night)
6 m: hop counts for Es were shown for interest using a nominal Es hop length; most long-range events were Es (and sometimes TEP). The histograms often showed strong peaks around single- and double-hop Es ranges.
6 m hop-count histogram 6 m distance histogram 6 m F-fit confidence histogram
6 m distance histogram with k·μ markers 6 m distance mod μ (day) 6 m distance mod μ (night)
160 m: colour = hop count; ■ Es, ● F day, × F night; opacity = hop-fit confidence. The grey band marked the Es/F overlap region. Typical points favoured higher take-off angles than the higher HF bands, consistent with shorter per-hop ground ranges. The accompanying histograms and “k·μ” markers supported the chosen hop spacing while revealing seasonal and diurnal variability.
160 m hop-count histogram 160 m distance histogram 160 m F-fit confidence histogram
160 m distance histogram with k·μ markers 160 m distance mod μ (day) 160 m distance mod μ (night)

Where the ionosphere numbers came from

The ionosphere was measured continuously by ground ionosondes and satellites. Useful sources included:

These references underpinned the typical heights and the day/night behaviour used in the simple geometric model presented above.

Modelled with Python · Plotly