Hi Again Todd,
<<< Recently an Australian DXer constructed a 135 mm diameter MW FSL using forty one Jaycar LF1010 (9 x 100 mm) ferrite rods. These rods are more affordable than anything else available on Australian eBay . >>>
It would be very helpful if that Australian DXer could post a design photo showing the number of coil turns, type of Litz wire, type of variable cap, type of frame, etc. Then I could simply use math to decide how to make larger and smaller sizes of that same type of FSL, using the Jaycar 9 x 100mm ferrite rods.
Using the longer 9 x 180mm ferrite rods will give more inductance for a given coil size, slightly reducing the number of Litz wire turns required to tune the same frequencies as the 9 x 100mm ferrite rod design coil.
<<< Also, how are the number of Litz wire turns calculated to provide 520 to 1750 KHz coverage for a given number of rods? >>>
Since I've never used the Jaycar rods I can't give you an exact formula, but the number of rods is related to the coil diameter, and if 41 rods results in a 135mm coil diameter for the Jaycar rods, you do have enough information to design a new FSL, but ONLY if you use the exact same components as the Australian DXer used (ferrite rods, wire type, variable cap type, etc.). This assumes that he was able to get 530-1701 kHz coverage with his design. You can use the math formula that I described in an earlier post, and it should get you within one coil turn of being exactly the right length. Like Steve said, you shouldn't use expensive Litz wire for rough testing; only use expensive Litz if you are sure of the number of coil turns necessary for full MW band coverage with the Jaycar variable cap (if that's what you plan to use). Any components different from what the OZ DXer used will throw off the math calculation formula for coil turns.
<<< Any thoughts on the theory behind why certain variable capacitors offer higher Q? >>>
Like Steve said, the phenolic insulator type of variable cap is not the highest Q type available, but for my own FSL designs (which require rugged construction to survive rough travel, and weather extremes) they make good sense. The discovery of superior performance with the "384P" variable cap (from Mike's Electronic Parts, with Oren Elliot Products being the OEM) was completely by accident. Apparently they have made some type of substitution which provides significantly higher "Q", and better gain performance. How and why this happened is a mystery, but the difference in DXing performance is pretty astonishing. All of my recently constructed FSL's use this variable cap, as well as the models given to Craig and Chris prior to the recent Kauai DXpedition.