From modeling I did a long time ago: there is a slight advantage to
using high velocity factor line, but it's very marginal. Just as a
dipole doesn't need to be resonant to do a good job radiating (and
receiving), so the elements in the coaxial collinear don't need to be
resonant. The phasing among the elements is dictated by the coax
between the feedpoints. Each gap between two elements is a feedpoint;
across it is impressed the line voltage. Since each line segment is a
half wave long and the conductors are reversed at each junction, the
voltage across each feedpoint is the same and in phase, less a small
amount for line loss. The element currents depend on mutual coupling
among the elements, but my simulations for VF=0.66 to VF=1.00
indicated that the current phases were always very nearly the same.

Generally, you'll want all the elements to look the same from the
outside. The top element should be the same length as the rest. It's
common to short the coax an electrical quarter wave up from the
highest gap between elements; that reflects back an open circuit to
the bottom of the top element, so really you could just as well make
the top element a tube the same OD as the rest of the elements,
connected to the inner conductor of the next lower section. The
feedpoint impedance at the bottom of the antenna is just the parallel
combination of all the feedpoints, which are generally each fairly
high (since each one is feeding a full-wave doublet, essentially), but
with ten or so sections, the net is modest, generally around 100 ohms.

Whatever the feedpoint impedance is, you need to match to it properly--
to whatever degree of matching is "proper" in your book. I generally
use a simple "L" network: a variable C across the feedpoint, and an
inductor to the feed line center conductor. It matches the impedance
and can tune out some reactance. Then you need to decouple the
antenna from the feedline, and from other metal in the area where it's
mounted. I generally use self-resonant coils in the small feedline,
one immediately below the antenna and one another quarter wave lower.
You could also try sleeves or radials...

Summary: the coax provides proper feedpoint phasing (even if the
elements are shorter than 1/2 wave because of the VF of the line
used); a matching network lets you match to 50 ohms (or other
impedance if you want); decoupling keeps "antenna" current off the
feedline.

Cheers,
Tom

Thanks Tom for the detailed explanation. My current sketch of my antenna
design uses a quarter wave sleeve on the lower end of the antenna to stub
the current off the feedline ground. I am hoping to see the antenna having a
(somewhat) characteristic impedance of 50 ohms since the transmission
elements although made out of copper pipe and copper rod are designed to be
50 ohm and the antenna is single end fed (unlike a dipole). I will make some
provisions for a small tuning structure. If I do have to tune, the nice
thing is that it will be a receive only antenna and I can get away with
small RF components.

Tom, since you seem to know quite a bit about collinear coaxial antenna
design, do you know if I should be using an even or odd amount of half wave
elements? I planned on four, do you see a problem with this.

Thanks again,
Thomas