#### CaptainBrock

##### Newly Enlightened

- Joined
- Nov 14, 2012

- Messages
- 44

Packing efficiency is defined as the percentage of total volume of the containing tube occupied by the cells. One might expect three cells in a triangular arrangement to have a greater packing efficiency than four cells in a square pattern because hexagonal packing in a large field is known to be more efficient than square packing.

Let's see what happens when the cells are packed into a cylindrical tube. In the following analysis, only the two-dimensional cross-sectional area is considered, and cells are represented by unit circles with a radius of one.

Diagram of three cells packed in a cylindrical tube:

Computation of packing efficiency for three cells in a tube:

Diagram of four cells packed in a cylindrical tube:

Computation of packing efficiency for four cells in a tube:

The result was surprising to me. The four cells occupy the space within an enclosed tube more completely than three cells do! The four cells use 68.6% of the internal space, while the three cells use only 64.6%

The minimum diameter of a tube enclosing four 18650 cells will be 2.4142*18.6 mm = 44.90 mm.

The minimum diameter of a tube enclosing three 18650 cells will be 2.1547*18.6 mm = 40.08 mm.

These numbers are theoretical minimums and do not include wall thickness of the container tube or internal cell holder structure. I measured the outer body diameter of a four-cell NiteCore TM-15 at 50.0 mm, and the body diameter of a three-cell Thrunite TN31 is given as 49.1 mm.

Conclusion: A three-cell configuration wastes more internal space than a four-cell configuration, and resulting diameter of a four-cell flashlight will be only very slightly greater than that of a three-cell flashlight.

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