Barry, can't find any ref to 1D1.64D on the web unfortunately, don't know where Pentz got this from. However the thesis might give some idea where his design, and your 'accident'** fits in the scheme of cyclones, and after a skim of the 100 odd pages and a concentrated read of the summaries, I went back to Pentz's little CV in the introduction - it just doesn't seem likely he made it all up as some detractors appear to have implied.
I was interested to see how Bill Pentz (BP) compares with thesis 1D3D for your small vac cyclone. BP chooses a 15A Hoover whole house vac motor*. Current hoover bumf rates this @1600W/102cu ft min or ~ 2830 l/min. With a 1.5x3=4.5 sq" inlet, cyclone design inlet velocity is 3,200ft/min. It's 1D1.64D with D=6. From his drawing the ramp appears to turn the vortex once in 3", the height of the rectangular inlet. That's about 5 turns in all if this is maintained. The outlet is 3" dia. and 6"long.
Funnily enough the design inlet speed for the 1D3D cyclone is also 3200, so the inlet would have the same x setional area as BP's, and the reccomended airflow for D= 150mm is 93 cu.ft/min. with a 3" dia outlet also 6" long, and a vortex of just over 6 turns (thesis tables). Goodish match so far? The puzzle is how you get to shorten the cone - perhaps this is a funtion of the ramp. Maybe we should try an email to BP sometime.
BP's full size cylone appears to fit the 1D3D model if you choose 900 cu ft/in*** at 3,200 ft./sec, which gives D~18" and inlet area of 40 sq". Indeed BP talks about a 1D3D design (cyclone plan,paragraph headed cyclone design) pointing out the problem of a motor+4D+wastebin giving overall height too great for normal room. His revised design shorter, and with less flow resistance.
* Equating to UK vacs, a 1000W Numatic or small Festool does 2400l/min, Alto1500W 3600l/minand my 2 motor Numatic 4800l/min. Where does the vac you tried fit in? Also did you have a smooth transition from vac hose to cyclone so flow into the 1.5x3" inlet was laminar, and not turbulent? Also the Dyson has a twin concentric cyclone, the outer (just a little bin) removes the bigger stuff so the fine dust removing inner doesn't block up.
** Not a rudery-I mean the happy but accidental meeting of flowerpot and drum.
*** Folk grumble BP is confusing. I suppose he does rabbit on (If I were he, I'd be paranoid about dust too) However when he goes on to talk about 1900 cu.ft/min motor/impeller, he is talking about just that. Flow will drop to ~800/900 cu.ft/min when this is attached to the cyclone, filters, and pipework, so this is the figure the BP cyclone is designed for.