To add to the discussion the July/Aug 2007 Amsat Journal has an article covering some gain comparisonmeasurements I made between four 13 turn (2.88 wavelengths) 13cm antennas with different square solid aluminum reflectors. The sizes were 0.56 wavelengths, 0.84 wavelengths, 1.0 wavelength and 1.4 wavelengths. There was no difference between the 0.84, 1.0 and 1.4 wavelengths but the antenna with the0.56 wavelength reflector had 1.5 db less gain.
However for my 70cm helix antennas I followed the Satellite Handbook minimum size of 0.6 wavelengthsor slightly over 16 inches. I used 1/2 inch hardware cloth mesh to keep the weight and windloading down. These antennas have performed well however it appears that they would be a bit better with a somewhat larger reflector.
A brief description and picture of the 70 cm reflector is in the November/December 2005 Amsat Journal article on The Development of a Quarter Wave Match for helical antennas.
Clare VE3NPC
Hi All: I am rebuilding a 440 MHZ Helix that I built several years ago . It worked very well, but I would like to reduce the size of the reflector to a more manageable size than I had before. The only reference to reflector size I can find is, "minimum 20" ". I may be looking in the wrong places. I would appreciate it, if someone would steer me in the right direction. Thanks, Pete, K1HZU