Flat-Copper-Strip Flat-Spiral-Primary Inductance Calc's?

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Kurt Schraner" <k.schraner-at-datacomm.ch> 

Hi,

anybody has handy a good method or formula for inductance calculation 
of  flat-strip flat-spiral primaries? I made one for my little UBTT 
(Uni-Bern Tesla Twin), which primary can be seen here:

http://home.tiscalinet.ch/m.schraner/FlatPrim_1555.jpg
(view is from underside, when installed!)

When using the usual wheeler formula for spiral-prim's as an approximation 
[ L(uH) = (R * n) / (8R+11W ) ], the calculated values are about 17% higher 
than measured, for this coil, see:

http://home.tiscalinet.ch/m.schraner/Lstrip.gif

...while for another ~similar coil, made from PVC-insulated wire:

http://home.tiscalinet.ch/m.schraner/UBTT_1Prim_kl.jpg
(view is from underside, when installed!)

...the weeler formula, as expected, is working well, with an average error 
of about 2%:

http://home.tiscalinet.ch/m.schraner/Lwire.gif

In case sombody wants doing his own calculations, here...

The input data of the Copper-strip flat-spiral primary:
		metric        english	
inn.dia.Di =    18.00 cm      7.09  inch
out.dia.Da =    34.00 cm      13.4  inch
spacing	S =    0.545 cm      0.215 inch <-- _between_ turns!
Cu strip d =    0.055 cm      0.022 inch
Cu strip width =  2.0 cm      0.787 inch
# turns	n =     14.2          14.2	


The input data of the PVC-wire flat-spiral primary:				metric        english			
inn.dia.Di =    17.50 cm      6.89  inch
out.dia.Da =    33.3  cm      13.13 inch  Da=34.4  cm (measured.)		
spacing	S =    0.180 cm      0.071 inch  S =0.236 cm (measured.)
wire dia d =    0.275 cm      0.108 inch		
# turns	n =    17.8            17.8			

The inductance measurements were done at 1000Hz, with a digital LCR-meter 
of the "automatic bridge type" (ESCORT ELC131D, Taiwan).

Perhaps I'm asking about an old hat: then it would be nice to have a link 
for a solution (I think some of the problems have already been discussed, 
regarding the very low inductance primaries for OLTC's?). On the other 
hand, my question is directed to 2 "goals":

1.) Better physical understanding of why a copper-strip, wound to a coil, 
has a smaller inductance, than a wire or tube wound to a coil.

2.) Correction of the appropriate formulae in my design spreadsheet:
     http://home.datacomm.ch/k.schraner/TCplan.zip
     (Version 1.03 of May 2004)       ...also on Terry's site.

Best regards

Kurt