First take a look at the HOVERMAN Type 1 [Type 2 added Reflector Rods], which was CONSTRAINED to have EQUAL-LENGTHS throughout...NO EXCEPTIONS...unfortunately (esp. back in the 1960's when UHF TV Band went all the way up to Ch82), the Frequency Response rolled-off, starting on about Ch40 [So it's actually a fairly good match for TODAY's Ch52 Max]:
Hoverman Type1 (NO Reflector) [UHF Raw Gain = 8.0 to 11.0 to 8.0 dBi, SWR Under 3.6 (Poor, since presumed AWG12)]
Now, take a look at the Autofil's SBGH [One of the first Single Bay Grey-Hoverman's], which was CONSTRAINED to have EQUAL-LENGTHS throughout...EXCEPT the Top/Bottom Horizontal Spurs were shorter and the Top/Bottom Center Gaps were SAME as the Feedpoint Gap (at Middle). At bottom of this post you will see 300ohms "Foldable" SBGH implementation. Gain & SWR Curves are as follows....higher Max Gain, but at expense of Lower Channels: [Clearly SBGH was derived from the Original Hoverman Type 1....hence the name]
SBGH - NO Reflector by Autofils [UHF Raw Gain = 6 to 11.5 dBi, SWR Under 3.2 (Fair) Presumed AWG9]
And NOW, take a look at nikiml's OPTIMIZED SBGH, where the Lengths and Gap Sizes are NOT CONSTRAINED, bearing in mind that different choices of Optimization Parameters can trade off Gain vs SWR, as well as WHERE the Max Gain occurs....the fol. represents nikiml's choice of tradeoffs:
nikiml's Antenna pages - GH0 UHF antenna [UHF Raw Gain = 7.8 to 11.9 to 9.8 dBi, SWR Under 2.2 (Excellent), Presumed 1/4=-in Copper Tubing]
Note that in the above Diagram, I tried to match the Semi-Circular Arcs to what I call the "ZZ-8" [each of two Zig-Zag Elements has 8 straight sections, with arbitrary lengths and orientations], which does NOT constrain the orientation of the outer two Elements....where the particular arrangement shown above was actually for one of my QUASI-OMNI designs....hence the difference. In the ARC version I could make Inner and Outer Semi-Circular ARC's different sizes....but I wouldn't try to make each Quarter-Circle a different Variable Size. I suspect that an OPTIMIZED "ARC-4" Antenna would have LOWER Gain than SBGH due these differences....so perhaps I should ALSO try letting the OUTER Quarter-Circles vary in their angular arrangement, so it could point OUTWARDS....so stay tuned for some 4nec2 Model Results in a week....or two....for Apples-to-Apples comparison I also need to rerun the above SBGH files, with ALL of them presuming the SAME 1/4-in O.D. Element Size.
As far as physical construction goes, I would recommend interconnecting Semi-Circular Arcs with Vertical Screws, hammering and drilling PAIRS of Holes into the ends of the Copper Tubing (i.e. 1/4-in for Refrigerator Ice Maker) so they are flat and can form a tight fit....thereby avoiding the breaking problem if you simply tried to make a 180-deg bend at each interconnection. TWO Holes are needed to provide mechanical rigidity, similar to fol. 1/2-in Copper Tubing, except rotated to use VERTICAL Screws:
http://imageevent.com/holl_ands/loops/vhfloop