Here are construction plans of a Turnstile antenna that I use for space communication on the 2 meter amateur radio band. Specifically for 145.80 mHz.
A Turnstile antenna with a reflector underneath it makes a good antenna for space communications because it produces a circularly polarized signal pattern and also has a broad, high angle pattern. Due to these characteristics, there is no need to rotate the antenna.
My design goals were that it had to be cheap (of course!) and made from easily available materials. In looking at other turnstile antenna designs, one thing that has always bothered me is that they use coax (un-balanced feedline) and directly feed the antenna (balanced load). According to the antenna books, this situation tends to cause the coax to radiate, and upset the overall radiation pattern of the antenna.
What I decided to do is to use "folded dipoles" instead of traditional ones. Then feed the turnstile antenna with a 1/2 wavelength 4:1 coaxial balun. This type of balun also takes care of the "balance-to-unbalance" problem usually encountered as well.
The drawing below shows how to make a turnstile antenna. Please note, this is not to scale.
Construction of a turnstile reflector antenna consists of two 1/2 wavelength horizontal dipoles that are oriented 90 degrees from each other (like a big X). Then feed one dipole 90 degrees out of phase of the second one. One problem with Turnstile Reflector antennas is that the structure to hold up the relector part can be cumbersome. Fortunately (some might disagree) I decided to build my turnstile antenna in my attic. This solves another problem in that I also don't have to concern myself with is weatherizing the antenna.
For the folded dipoles I used 300 ohm TV twinlead. What I had on hand was low loss "foam" type. This particular twinlead has a velocity factor of 0.78. You will also notice in the above drawing that the lengths ot the dipole aren't what you would expect for 2 meters. This is the length I ended up when I was finished adjusting for minimum SWR. Apparently the velocity factor of the twinlead figures into the resonance of the folded dipole. As they say, "Your mileage may vary" on this length. I would also like to point out that in the drawing above the feedpoint of the folded dipoles is actually in the center of the folded dipole. I made the drawing this way for clairity.
In order to get the radiation pattern in the upward direction for space communications the turnstile antenna needs a reflector underneath it. For a broad pattern the antenna books recommend 3/8 wavelength (30 inches) between the reflector and the turnstile. The material I chose for the reflector is ordinary window screen you can pick up at a hardware store. Make sure it is metal screen as there is a non-metal type of window screen they sell as well. I purchased enough to lay out an 8 foot square on the rafters of my attic. The hardware store couldn't give me one big piece for all of this, so I overlapped pieces of screen by about a foot on the seam. From the center of the reflector, I measured up 30 inches (3/8 wavelength). This is where the center, or the crossing point of the folded dipoles are located.