Interesting but complicated!  I think I'll stick to my own design of a half cylinder, the diameter of which is 17", the same as National kit to enable a degree of interchangeability, and to allow the bees to draw comb in their preferred catenary shape.  I build them from recycled pallet planks so they are virtually free.  The entrance is at the sunny end as the bees tend to have their brood near the entrance and stores at the rear, making harvest and inspection easy.

I recently applied Pi and discovered that the comb size is almost exactly that of a National brood comb.

One of the advantages of the top bar hive is that the bees themselves decide on cell size rather than the 'one size fits all' imposed on them by foundation.  Some years ago I measured worker comb cell size top right, centre and bottom left both sides and found (as I recall, not having the figures to hand) that size ranged between 4.8mm and 5.6mm with an average of 5.2.  What I found interesting was that, when plotted on a graph and the wiggles smoothed out, there was a distinct U shape from front to rear of the hive.

I am gradually phasing out the use of foundation based combs in my standard hives by cutting out the dark, bred-in parts of old combs, leaving a shallow 'footprint' around the perimeter for guidance.  The brood pattern of the subsequent combs has to be seen to be believed!  It isn't measurable scientifically but my impression is that the hives where this has been done seem to do better than those still on the old system.  Standing in front of the hive and watching, you can see a range of sizes of worker.  Maybe this helps the team to be more flexible.

Chris

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