https://www.astronomy.me.uk/wp-content/uploads/2026/05/SETI_Horn_Flare_Angle_Calculations-1.docx
Using the usual amateur SETI “Horn of Plenty” dimensions:
- Horn length L = 1.22 m (4 ft)
- Aperture width A = 0.91 m (3 ft)
- WR-650 throat width a = 0.165 m
the flare half-angle is:
alpha = arctan((A – a)/(2L))
Substituting:
alpha = arctan((0.91 – 0.165)/(2 x 1.22))
alpha = arctan(0.3053)
alpha ~= 16.97 degrees
So:
- Half flare angle ~= 17.0 deg
- Full included flare angle ~= 33.9 deg
With a 1 m extension added to the horn:
- New length L2 = 2.22 m
Then:
alpha2 = arctan((0.91 – 0.165)/(2 x 2.22))
alpha2 = arctan(0.1678)
alpha2 ~= 9.53 degrees
So with the extension:
- Half flare angle ~= 9.5 deg
- Full included flare angle ~= 19.1 deg
Practical maximum acceptable deviation
For a 1420 MHz hydrogen-line horn intended for amateur SETI/radio astronomy work, a practical engineering tolerance is roughly:
- about +/-10 to 15 percent in flare angle
before noticeable degradation in:
- impedance match
- sidelobes
- standing-wave ripple
- gain smoothness
Therefore:
Original horn:
- Nominal half-angle: 17.0 deg
- Practical acceptable range: about 15 deg to 19 deg
Equivalent included angle:
- about 30 deg to 38 deg
Extended horn:
- Nominal half-angle: 9.5 deg
- Practical acceptable range: about 8.5 deg to 10.5 deg
Equivalent included angle:
- about 17 deg to 21 deg
The longer horn is more sensitive to construction errors because the flare is shallower, so panel alignment matters more.