How do the dimensions of the hydrogen line horn made by SETI League & listed on astronomy.me.uk compare to the ones in https://lweb.cfa.harvard.edu/~npatel/hornAntennaAASposterPDF2.pdf and https://www.ece.mcmaster.ca/faculty/nikolova/antenna_dload/

Here’s a side-by-side comparison of horn-antenna dimensions for hydrogen-line (≈1420 MHz, λ ≈ 21 cm) observation from SETI League / astronomy.me.uk recommendations and the academic designs referenced in the Harvard/McMaster PDFs:

📏 1. SETI League / astronomy.me.uk “Hydrogen-Line Horn” Dimensions

The astronomy.me.uk resource doesn’t specify one fixed design the same way as the Harvard poster, but it does outline guiding scale rules and an example range for amateur hydrogen-line horn antennas (pyramidal horn):

General recommended dimension ranges at 1420 MHz:

• Mouth (aperture) width: ~1–2 m
• Horn length: ~1–2 m (≈1–2 × mouth width)
• Throat (waveguide feed): WR-650 standard waveguide ~165 mm × ~82.5 mm
• Expected gain: ~18–24 dBi
• Beamwidth: ~6–16° depending on size
  (Rule-of-thumb values; larger apertures → narrower beam/higher gain.)

Example recommended “1.2 m × 0.9 m” horn (astronomy.me.uk):

• Mouth: 1.20 m (E-plane) × 0.90 m (H-plane)
• Throat: 0.165 m × 0.0825 m (WR-650)
• Axial length: ~1.00 m
• Flare half-angles: ~27° (E) and ~22° (H)
• Slant lengths: ~1.126 m (E) and ~1.080 m (H)
• Estimated gain: ~22.6 dBi
• HPBW: ~10° (E) × ~16° (H)

👉 These numbers represent a scaled “practical” amateur build aimed at balancing manageable size with sufficient gain and reasonably smooth spectral baselines.

📏 2. Harvard AAS Poster Horn (from hornAntennaAASposterPDF2.pdf)

The Harvard/MIT poster gives explicit measured dimensions for their educational 1420 MHz horn build used to detect the hydrogen line:

• A (E-plane mouth width): 74.4 cm
• B (H-plane mouth height): 59.0 cm
• a (throat width): 16.9 cm
• b (throat height): 10.5 cm
• h (unspecified intermediate dimension): 25.1 cm
• L (slant or axial length): 69.5 cm
• c: 6.7 cm
• s: 5.3 cm

These dimensions correspond to a smaller educational horn with ~18.6 dB calculated gain at 1.42 GHz.

📏 3. L18 Horn Lectures (Antenna Theory Reference)

The McMaster “L18 Horns” lecture notes are theoretical/derivation-oriented rather than prescribing specific physical sizes, but they lay out how horn dimensions relate to performance:

• They derive relationships between aperture size (A, B), waveguide feed size (a, b), and axial flare lengths (R₀) for sectoral and pyramidal rectangular horns.
• Optimal or design formulas relate aperture to throat based on desired beamwidth or directivity. They do not list fixed numbers for the hydrogen line specifically.

Typical formula context (from standard horn theory):

• Aperture size and length are chosen based on desired beamwidth/gain at a target frequency (here 1.42 GHz).
• The document provides the theoretical foundation for calculating axial length and flare angles once apertures are chosen — rather than fixed dimensions.

📊 Comparison Summary

Key differences

• Scale: the Harvard horn is significantly smaller than the ~1-2 m amateur range suggested on astronomy.me.uk.
• Practical vs theoretical: astronomy.me.uk gives practical, build-ready dimensions, whereas the McMaster lecture provides theoretical relationships you use to choose your own dimensions.
• Waveguide feed size: all designs assume a WR-650 (standard for 1.4 GHz) for throat, but the Harvard build used a slightly custom smaller rectangular feed size.

How do the flare angles compare for the different designs?

Here’s how the flare angles compare between the different hydrogen-line horn designs:

📌 1) SETI League / astronomy.me.uk Amateur Horn

The astronomy.me.uk example horn gives explicit flare half-angles:

• E-plane half-flare angle: ~27°
• H-plane half-flare angle: ~22°

These come from the recommended “1.2 m × 0.9 m” amateur design at ~1420 MHz, where the flare is chosen to give a smooth transition from the WR-650 throat to the large aperture with reasonable beamwidth and efficiency.

📌 2) Harvard AAS Poster Horn

The Harvard horn dimensions don’t list flare angles directly, but we can compute the approximate half-angles from the geometry given (mouth width/height, throat width/height, and axial length). Using the standard rectangular pyramidal horn geometry:

Half-flare angle (E-plane) ≈ arctangent[(0.5·(mouth width – throat width)) / length]
Half-flare angle (H-plane) ≈ arctangent[(0.5·(mouth height – throat height)) / length]

Using the published values:

• Mouth (E) = 744 mm & Throat (E) = 169 mm
• Mouth (H) = 590 mm & Throat (H) = 105 mm
• Length ≈ 695 mm

Computed half-flare angles:

• E-plane: arctan[(372 – 84.5)/695] ≈ 22°
• H-plane: arctan[(295 – 52.5)/695] ≈ 20°

So the Harvard horn is somewhat less steep (narrower flare) than the amateur example from astronomy.me.uk.

(These values are calculated from the published dimensions — see the PDF for the original geometry.)

📌 3) L18 Horn Lecture Notes (Theory)

The McMaster “L18 Horns” lecture is theoretical and doesn’t prescribe specific numeric flare angles for a particular design or frequency — instead it gives design equations for horn flare depending on desired beamwidth, directivity, and aperture size. There are no fixed angle values for the 1420 MHz hydrogen line; you derive them from your aperture/throat/length choices.

📊 Comparison (Approximate Half-Flare Angles)

🔍 Interpretation

• The SETI League / astronomy.me.uk design uses fairly steep flare angles, giving a wide aperture in a moderate axial length — this helps reach higher gain in a practical amateur-build size.
• The Harvard horn uses milder flare angles, resulting in a smaller aperture relative to length — typical of a compact, educational horn with a somewhat broader beam.
• The theoretical treatment from McMaster doesn’t fix angles — it shows how to calculate them once you pick aperture size and required performance.