The helical antenna is one of the best directional antennas of circular polarization. It is highly tolerant, can vary slightly the diameter or pitch of the helix with virtually no impact on performance (although consistency is important), and the length or number of turns will determine the gain of the antenna.
I decided to build a model of 6.5 turns, with a gain of approximately 11dB, and a beamwidth of 60 degrees, making it easy to aim towards the plane, and is a good compromise between gain and antenna size.
As for the method for matching the impedance of the antenna, I opted for the Hecker transformer, because it gives consistent results, without requiring individual tuning with a SWR or a network analyzer.
SIZE AND WEIGHT
Length: 390 mm
Diameter: 220 mm
Weight: 477 gr
Length: 213 mm
Diameter: 115 mm
Weight: 176 gr
LABORATORY TESTS HELICAL 1.2GHz
A huge band width (as expected of a Helical) from 900MHz to 1700MHz
And a gain of 11.51dB, with a beam width of about 60 °:
LABORATORY TESTS HELICAL 2.4GHz
Bandwidth from 1759 to 2617MHz:
Gain 12.04dB, with a beam width of about 60 °: