Hi Oz!
WELCOME ABOARD the (crazy) ads-b bandwagon.
(1) Antenna dimensions: As Dave (trigger) has rightly summerized, any length of wire acts as antenna & picks radio signals, but for each frequency/wavelength, there is an optimum length which gives best result.
(2) The Beauty of ¼ wavelength: The ¼ wavelength whip with a groundplane has the beauty of having an impedance close to 75 ohms, and hence is naturally matched to 75 & 50 ohm systems of coax cable & receiver. The whip is connected to core wire of coax cable, and the groundplane is connected to shield of coax. The groundplane is can be in numrous forms, some are listed below:
(a) Three or four Horizontal radials, ¼ wavelength. The impedance of antenna in this configuration is 30 ohms, a close match to 50 ohm system used by hams.
(b) A metallic disc, ¼ wavelength RADIUS. The impedance of antenna in this configuration is 30 ohms, a close match to 50 ohm system used by hams.
(c) Spider - Three, four, six or eight radials, ¼ wavelength, bent down 45 degrees below horizontal. The impedance of antenna in this configuration is 70 ohms, a close match to 75 ohm system of satellite/tv coax & dvb-t usb receiver. It is also not far from 50 ohm system and gives a reasonable match to it.
(d) Cantenna - Cylendrical/sleeved groundplane made of an inverted food or drink can, vertical cylinderical wall cut to ¼ wavelength. The impedance of antenna in this configuration is 65 ohms, a close match to 75 ohm system of satellite/tv coax & dvb-t usb receiver. It is also not far from 50 ohm system and gives a reasonable match to it.
(3) The correct length of ¼ wave whip : The 1090 Mhz wave in air is 275 mm. Hence ¼ wavelength is 68.75 mm which is rounded to 69 mm. When RF curren travels in a wire, the length of wave is slightly less (1% to 5%), and depends on dia of wire use. The figure of 65.4 mm originates from ARRL book used by hams, and mainly pertains to lower freqencies of 440 mhz & below (uhf, vhf, hf).
I have tried to trim the BARE 69 mm whip, 2 mm a time, and at 67 mm it showed slight improvement, but at 65 mm it showed slight degradation. I tried this with INSULATED 69mm whip & got best results at 66mm.
As Dave has rightfully mentioned, make a whip 70 mm, start trimming a mm a time till you say oops, it is bad, then go back to length which gave you the best results.
(4) The ½ wavelength vs ¼ wavelength: The ½ wavelength has higher Gain (dB) than ¼ wavelength, but it also has much higher impedance (several hundred ohms). This makes the ½ wavelength whip a poor performing antenna on 75 & 50 ohm systems, unless some form of impedance matching device is used (or an amplifier is inserted between antenna & coax cable to compensate for reduced signal transfer from antenna to system due to impedance mismatch).