Hi Jerry
I have taken an antenna range to over 60 conferences. And done quite a bit or work with Helix antennas at my lab. Of the 100 or so Helix's I have tested, only about 10% were circularly polarized.
That's right, only about 1 in 10. I have proven many many times, HAMS CANNOT BUILD CP HELIX ANTENNAS!
It is amazing how a Helix Antenna can have an Axial Ratio of over 20 dB. That's about the same axial ratio as you get from many Yagi's. The few helix's that worked were usually built by a professional in the field.
Unless you have actually tested your Helix on a range, the chances are about 9 out of 10 is it not CP
(Yes, it is a valid statement that all antennas are ellipticaly polarized, CP and Linear are just special cases.).
As an example, the wave comes down the helix, hits the tip, them reflects as a standing wave on the helix structure with an opposite CP sense.
You can put a helix antenna on an antenna range, then start trimming the tip with some wire cutters a few millimeters at a time. The Axial ratio will be constantly changing. You can, with some experimenting, find the CP point, but statistics are against you without any testing.
And the Kraus Formulas are about 3 dB Optmistic.
Winding the helix on a plastic pipe creates all sorts of problems. In free space the radio wave travels along the wire at about 95% the speed of light. When you wrap the wire on a plastic tube, the velocity factor is now about 60%.
The effective length and turns ratio is completely different from the calculations. And darn near impossible to even simulate What is the dielectric constant of that plastic you got at the hardware store? And If you did look up the Er, that value was measured at 1kHz, not 1269 MHz! So unless you actually measured the Er at 1269 MHz, your CST, HFSS, OPENEMS, etc simulation is not valid.
Sam, G4DDK was the first to measure the effects of using just one dielectric boom with the helix winds attached directly to the boom. i.e. one boom and the helix turns attached to the boom at their 12 O'clock position.
The dielectric effects of the boom tilts the beam in the direction of the boom.and really reduces the gain of long helix antenna.
The NASA way, central boom and spokes to support the helix is by far the best way to go.
73 Kent WA5VJB