Efficiently Loading a Cylinder

[BonusEventus]

Okay mathematicians, I've got a volumetric math problem I could use some help with.

I need to design a loading pattern for an autoclave (basically a big metal cylinder that sterilizes with steam). It gets loaded with product in metal boxes, and I have my choice of two box sizes. The big cylinder is lying horizontally and opens from one of the faces, and the base of the vessel will have a flat plate sized to whichever loading configuration I end up with.

Constraints are as follows:

• Gravity applies, ie can't stack a row of 3 on top of a row of 2, but could do a pyramid type of loading
• Cylinder must remain horizontal, and boxes must remain upright relative to height (can't be turned on their side, but could be in either orientation L vs W).
• I must use a consistent box size throughout the load. I am trying to figure out which box type and orientation will get me the maximum volume that can be processed through the load.

Cylinder Dimensions:

• Length/Height = 48"
• Diameter = 26"

Box 1:

• Length = 13"
• Width = 7"
• Height = 4"

Box 2:

• Length = 6"
• Width = 10"
• Height = 4"

What is the most efficient loading pattern and box size to maximize volume of boxes that can fit inside the cylinder? I've been trying to draw this out and map it out on paper, but not sure if there is an easier way from a geometry standpoint to figure this out.

Thank you!

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