Z
z_LoveLearn
Guest
Dimensional packing problem:
Pack identically-sized smaller cylinders inside the smallest-possible larger cylinder.
That question may be reduced to -
Pack identically-sized smaller circles inside the smallest-possible larger circle
Ratio Solutions:
Two 1.000-diameter inner circles require 2.000-diameter outer circle
Three 1.000-diameter inner circles require 2.154-diameter outer circle
Four 1.000-diameter inner circles require 2.414-diameter outer circle
The four inner circle solution may be solved as 1 + Square Root of 2 = (1 + 1.414) = 2.414
AA Cell Diameter x Height Dimension range stated in millimeters (mm)
AA Cells may be from 13.5 to 14.5 mm diameter x 50.5 mm long
AA Rechargeable: 14.1 ± 0.6 mm. diameter
Representative In-Range Three AA-Cell Packing Solutions:
14.0 mm x 2.154 = 30.16 mm = 1.19 inch
14.5 mm x 2.154 = 31.23 mm = 1.23 inch
14.7 mm x 2.154 = 31.66 mm = 1.24 inch
Representative In-Range Four AA-Cell Packing Solutions:
14.0 mm x 2.414 = 33.80 mm = 1.33 inch
14.5 mm x 2.414 = 35.00 mm = 1.38 inch
14.7 mm x 2.414 = 35.49 mm = 1.40 inch
D-Cell Diameter x Height dimension range limits
D Cells may be from 33.1 to 34.2 mm diameter x 61.5 mm long
33.1 to 34.2 mm = 1.30 to 1.346 inch
Some earlier-reported AA-Cell diameter measurements:
Sanyo-GE ???? NiCd 0.546 (within 4-pack size limits)
Nexcell ??? mAh NiMH 0.548 (within 4-pack size limits)
Nomem 1500 mAh NiMH 0.550 (within 4-pack size limits)
Nomem 1800 mAh NiMH 0.554 (within 4-pack size limits)
Nomem 1600 mAh NiMH 0.554 (within 4-pack size limits)
Creative 1800 mAh NiMH 0.555 (within 4-pack size limits)
Nomem 2300 mAh NiMH 0.557 zero clearance, wont work
Powerex 2200 mAh NiMH 0.560 Too large
I have developed a solution by which AA-Cell size limits may be
tweaked to enable creating well-functioning D-Cell replacement
packs from four AA cells which would not appear possible from
the above analysis. I'll illustrate and describe it in my next post
to this thread. Clearly, some currently-available AA-Cells can
be used to form four-cell packs which can fit within space normally
allocated to accept all D-Cell diameters.
It would be helpful to generate a more contemporary list of popular
rechargeable AA cell diameters.
John
Pack identically-sized smaller cylinders inside the smallest-possible larger cylinder.
That question may be reduced to -
Pack identically-sized smaller circles inside the smallest-possible larger circle
Ratio Solutions:
Two 1.000-diameter inner circles require 2.000-diameter outer circle
Three 1.000-diameter inner circles require 2.154-diameter outer circle
Four 1.000-diameter inner circles require 2.414-diameter outer circle
The four inner circle solution may be solved as 1 + Square Root of 2 = (1 + 1.414) = 2.414
AA Cell Diameter x Height Dimension range stated in millimeters (mm)
AA Cells may be from 13.5 to 14.5 mm diameter x 50.5 mm long
AA Rechargeable: 14.1 ± 0.6 mm. diameter
Representative In-Range Three AA-Cell Packing Solutions:
14.0 mm x 2.154 = 30.16 mm = 1.19 inch
14.5 mm x 2.154 = 31.23 mm = 1.23 inch
14.7 mm x 2.154 = 31.66 mm = 1.24 inch
Representative In-Range Four AA-Cell Packing Solutions:
14.0 mm x 2.414 = 33.80 mm = 1.33 inch
14.5 mm x 2.414 = 35.00 mm = 1.38 inch
14.7 mm x 2.414 = 35.49 mm = 1.40 inch
D-Cell Diameter x Height dimension range limits
D Cells may be from 33.1 to 34.2 mm diameter x 61.5 mm long
33.1 to 34.2 mm = 1.30 to 1.346 inch
Some earlier-reported AA-Cell diameter measurements:
Sanyo-GE ???? NiCd 0.546 (within 4-pack size limits)
Nexcell ??? mAh NiMH 0.548 (within 4-pack size limits)
Nomem 1500 mAh NiMH 0.550 (within 4-pack size limits)
Nomem 1800 mAh NiMH 0.554 (within 4-pack size limits)
Nomem 1600 mAh NiMH 0.554 (within 4-pack size limits)
Creative 1800 mAh NiMH 0.555 (within 4-pack size limits)
Nomem 2300 mAh NiMH 0.557 zero clearance, wont work
Powerex 2200 mAh NiMH 0.560 Too large
I have developed a solution by which AA-Cell size limits may be
tweaked to enable creating well-functioning D-Cell replacement
packs from four AA cells which would not appear possible from
the above analysis. I'll illustrate and describe it in my next post
to this thread. Clearly, some currently-available AA-Cells can
be used to form four-cell packs which can fit within space normally
allocated to accept all D-Cell diameters.
It would be helpful to generate a more contemporary list of popular
rechargeable AA cell diameters.
John
