Great response, except, change all those X= to R= and the J= to X=... At least that is how most antenna analyzers, as well as many books on the subject, would show that data...
It depends. I've shown above somewhere (pages ago in this thread, will have to fish it out) that if their is no capacity hat on this antenna, instead you use a 1/4 wavelength vertical and tune to resonance the impedance changes at resonance. Remember, a capacity hat is a load, just like a loading coil. In the case of this antenna and using a different cap hat, I would be prepared to not only change the length of the elements of the cap hat, but the length of the upper vertical element that leads to it as well. With this you can maintain resonance (X), and still have a means of control over impedance (R) as well.
Specifically with this antenna, Oscar said he used no capacity hat on his home made Astroplane. I also remember him saying something about a suggested ring size? I don't know if he made any other adjustments to his antenna design, or even if what I think I am remembering is in response to his lack of a cap hat in his design. It is a change I would likely make if I removed said cap hat from this antenna design...
When it comes to engineering capacity hats, I have some formulas for various shapes of capacity hat in the various versions of the ARRL Antenna Books from over the years. It is possible to calculate how large of a cap hat you need based on the design that you intend to use. If it were me, I would model it and use that as a starting point. HomerBB, on the other hand, would likely build it and make it so it was adjustable in both length of element before the cap hat, and length of the elements on the cap hat, and tune till he got what he wanted. I can't say any one of these methods will yield better results than another, however it is listed in the order from more of an engineering way of doing things to more of a hobby way of doing things.
The DB