How does number of turns and spacing effect spiral antenna?

Hi,

I have a question. How does increasing the number of turns and increasing spacing between the turns effect spiral antenna's following parameters:

1. Gain
2. VSWR
3. Return Loss
4. Directivity
5. Any other parameters you know

Thank you!

The number of turns affect the antenna directivity, the spacing affect the gain, and the diameter affect the polarization and input impedance.
The input impedance generally is given by: Z(ohms)=140*[(Π*D) / λ] where D is the diameter.

Look this one http://www.tuc.nrao.edu/~demerson/helixgain/helix.htm
and this one http://www.alzacomm.com/downloads/Helix_Letter.pdf

Can you please how do they affect them? I mean increasing no of turns enhances or degrades antenna directivity?

Please give a reference for these if you have one. Thank you