# math modeling of honeycomb construction



## carolina2002

Hi I am a graduate student researching a mathematical model for honey comb construction. I am wondering if any of you TBH bee keepers have access to ellipsoidal hives similar to the one in this image. If so it would be really helpful if I could get some images and measurements from your hives. Thanks in advance for any help!


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## AvatarDad

carolina2002 said:


> Hi I am a graduate student researching a mathematical model for honey comb construction. I am wondering if any of you TBH bee keepers have access to ellipsoidal hives similar to the one in this image. If so it would be really helpful if I could get some images and measurements from your hives. Thanks in advance for any help!
> View attachment 27742


Hiya Carolina!

New beekeeper, but an old engineer. 

Some Top bar beekeepers use drums or barrels, which will give a semi-circular cross-section. That's the closest I've seen. I personally only do the trapezoidal shape.

You are familiar with "caternary" I assume? The bees hang (festoon) this way while building comb, so I bet the shape is close to that (this is a guess, since I'm not inclined these days to plow through the literature). Maybe that's the hypothesis you are testing...

You should be able to take any incomplete frame, and measure their natural inclination from that; their natural shape should not be constrained until they near the walls of the container. So, either of the so-called Kenya or Tanzanian TBHs (or even the barrel shape mentioned above) might do as long as you are measuring frames which are not full yet. 

Finally, befriending a beekeeper who does cutouts might also be a good path for you. If bees are building inside a huge wall, their combs should adopt a natural profile as long as they don't run into horizontal blockages in the wall. The same goes for bees building in hollow trees.

You might have to wait until Spring for some good action: most bees around here are now preparing for the winter, and are not building comb so much.

Good luck with that project. I've been wishing lately I had picked a bee-related field for my own graduate work. I wonder if Tom Seeley would give me a job?

Mike


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## Hops Brewster

open air hives as in your picture are rather uncommon for the A. melifera. For African bees it is more common. European bees will normally colonize above ground cavities in trees and buildings, below ground cavities less common. Africanized bees are also more prone to below-grade cavities than European. 

As Avatar put forth, those natural ellipsoid comb formations would most easily be found in hollow trees, walls and junk equipment, such as you might find in a junkyard or farmyard. The majority of beekeepers use rectangular frames in boxes, not conducive to ellipses. some beekeepers use frames without a wax or plastic foundation and in these you will see ellipses as the comb is built, but the comb will eventually take the rectangular form as the frame fills in. Those who use horizontal hives commonly see these ellipses to the extent of the cavity size.

The shape of the broodnest, with its surrounding food stores, also forms an ellipse.


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## Michael Bush

Combs are built to fit the cavity:
Trapazoid top bar hive comb:
http://www.bushfarms.com/images/BeeCamp2016/TopBarSpotTheQueen.jpg
Rectangular top bar hive comb:
http://www.bushfarms.com/images/TTBHComb.JPG

If you want a lot of detail on comb building I would start with Volume II of Huber's New Observations On Bees. 
https://www.amazon.com/Hubers-Obser...kmr0&keywords=hubers+new+observations+on+bees

If you want more then here are the modern books on the topic:
https://www.amazon.com/gp/product/3642543278/ref=oh_aui_search_detailpage?ie=UTF8&psc=1
https://www.amazon.com/gp/product/3642714609/ref=oh_aui_search_detailpage?ie=UTF8&psc=1


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## JeronimoJC

You should also search for beekeeper using Perone hives. There aren't many, but those hives are exactly what you are looking for.


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## ruthiesbees

I would think you would want to be looking at comb built by swarms. If a topbar hive beekeeper is actively manipulating their comb for more drawn comb, the elliptical shape goes away fairly quickly as empty bars are added between drawn comb. But here is a photo I have, if it helps you any.


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## carolina2002

ruthiesbees said:


> I would think you would want to be looking at comb built by swarms. If a topbar hive beekeeper is actively manipulating their comb for more drawn comb, the elliptical shape goes away fairly quickly as empty bars are added between drawn comb. But here is a photo I have, if it helps you any.
> 
> View attachment 27746


Ruth,
Thank you very much. Those types of images are what I am looking for. Do you know approximately how old that hive is? Could you gather measurements along the widest axis for length, width, and depth for several of the combs and let me know which combs the measurements came from and could you give me measurements for the overall hive? Also could you take a few more images with some type of reference for scale such as a coin? And lastly do you have an approximation on the number of bees you have working on that hive?

Thanks so much in advance for any help!


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## carolina2002

Mr. Bush,

Do you have any images of your hives similar to the one Ruth Meredith posted?

Thanks!


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## ruthiesbees

carolina2002 said:


> Ruth,
> Thank you very much. Those types of images are what I am looking for. Do you know approximately how old that hive is? Could you gather measurements along the widest axis for length, width, and depth for several of the combs and let me know which combs the measurements came from and could you give me measurements for the overall hive? Also could you take a few more images with some type of reference for scale such as a coin? And lastly do you have an approximation on the number of bees you have working on that hive?
> 
> Thanks so much in advance for any help!


I tend to "shuffle" my combs like a deck of cards for different purposes. The darker comb is obviously older, but only by a few months. The bees did not drawn them out in this order or arrangement. I will let the bees draw two straight combs and then I insert an empty bar to let them draw the third. I think for this actual picture, I was getting ready to "store" them for the winter in the back side of the hive, so it was just a conglomeration of comb and probably drawn by different hives. I have multiple topbar hives and nucs. The hives are 45" long The nucs about 10" long to fit 5-6 combs.

Knowing that my comb wasn't drawn by one single beehive, in that arrangement, did you still want measurements?


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## bibbster

I have some top bars with this type of comb on them in various stages. I'm not that far from you, so you are welcome to come by and take all the measurements and pictures that you may need if you'd like.


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## Michael Bush

I don't take that many pictures... but maybe I do somewhere. I will try to look. What exactly are you looking for? I have pictures with measurements on natural spacing in a brood nest if that is helpful.


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## carolina2002

Yes Ruth if you are willing and able I could definitely use the measurements from your combs. I have uploaded a diagram that helps to describe what I need. For each comb I would like 1.) the estimated age of the comb, 2.) the length of the comb along the longest axis ( I have labeled it with green) 3.) the width of the comb along the widest axis ( I have labeled it with red) 4.) the depth of the comb (I have labeled it with blue) and lastly 5.) an estimate of the number of bees it took to build that particular comb. And if you can get a coin in the picture for scaling purposes that would be even better.
I really appreciate your help on this project. (Maybe it will get published.)


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## carolina2002

Mr. Bush,
I am inserting an image that I believe explains what I am looking for.
View attachment 27793


I am looking for combs that have an elliptical shape similar to the one in the diagram. From my understanding, if bees have unlimited room to build their hives, they will naturally form combs with these elliptical shapes and several of these elliptical shapes together will form an ellipsoidal hive. I am wanting to model this mathematically.

For each comb I would like 1.) the estimated age of the comb, 2.) the length of the comb along the longest axis ( I have labeled it with green) 3.) the width of the comb along the widest axis ( I have labeled it with red) 4.) the depth of the comb (I have labeled it with blue) and lastly 5.) an estimate of the number of bees it took to build that particular comb. And if you can get a coin in the picture for scaling purposes that would be even better.
I really appreciate your help on this project.


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## carolina2002

That would be wonderful. Are you available this coming Wednesday? Or next Saturday or Sunday?


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## ruthiesbees

I will see what I can come up with tomorrow (Labor Day) when I am in a hive. This one hasn't built it out to the trapezoid shape yet, and the colony is pretty docile (until I steal their queen tomorrow and make them into a 5 section queen castle.) I should be able to turn the bars on their heads for a new photo and take some measurements as well.


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## JeronimoJC

This beekeeper took some comb dimensions from a Perone hive. You may be able to contact him/her thru this blog. https://solarbeez.com/category/perone-hive/

Also, you can scale dimensions from the pics using the Perone hive standard dimensions.


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## ruthiesbees

carolina2002 said:


> View attachment 27793
> 
> 
> Yes Ruth if you are willing and able I could definitely use the measurements from your combs. I have uploaded a diagram that helps to describe what I need. For each comb I would like 1.) the estimated age of the comb, 2.) the length of the comb along the longest axis ( I have labeled it with green) 3.) the width of the comb along the widest axis ( I have labeled it with red) 4.) the depth of the comb (I have labeled it with blue) and lastly 5.) an estimate of the number of bees it took to build that particular comb. And if you can get a coin in the picture for scaling purposes that would be even better.
> I really appreciate your help on this project. (Maybe it will get published.)


Excel file is ready. Will try posting here or in a private Beesource message if I can't attach here. Also the photos can be found on the bees' Facebook page. https://www.facebook.com/media/set/?set=a.1451086314917894.1073741865.687315994628267&type=1&l=07298d5054


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## ruthiesbees

This is the comb that the following data is for.

This hive was made up from a 2015 fall born queen that was pulled from her larger hive in spring 2016. She was placed in a nuc with 4 drawn bars. 
On May 28, 2016, the 4 bar nuc was stepped up to a 10 bar nuc. One or two drawn bars might have been given to them at that time, bringing the 
total number of pre-drawn bars to 6. 4 empty bars were given to the nuc between May 28 and Aug 10. On Aug 10, the hive had outgrown the 10 bar nuc 
and needed to be bumped into a regular size 45" long hive to prevent a swarm. No additional drawn bars were give, but by Sept 5, they had drawn 4 more bars 
of various lengths and widths. 


Bar # (left to right in this photo)	Width	Length	Depth	Depth of wooden bar	What was on it	
1	15.5"	9"	1.5"	1 3/8"	honey	
2	8"	5"	.75"	1 3/8"	drone brood/honey	
3	14"	8"	1.5"	1 3/8"	honey	
4	13.5"	8"	1.5"	1 3/8"	capped worker brood	
5	15"	8"	2"	1 3/8"	open worker brood	
6	15"	8"	1.75"	1 5/8"	eggs	
7	13"	7"	1.5"	1 3/8"	honey/worker brood	
8	7.5"	7"	.75"	1 3/8"	capped worker brood/ honey	
9	15"	8.5"	2"	1 5/8"	eggs/honey	
10	15.5"	8.5"	2.5"	1 5/8"	egg/honey	
11	6.5"	7.5"	1.25"	1 3/8"	capped worker brood/ honey	
12	15.5"	8.5"	2.5"	1 5/8"	open worker brood (queen found here)	
13	14"	6"	1.5"	1 3/8"	capped worker brood	
14	15"	7.5"	2"	1 3/8"	honey	

Any questions can be directed to Ruth Meredith at [email protected].


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## madhu

I stumbled on this and was surprised no one mentioned the Hobosphere, which is "elipsoidal" exactly as Carolina , you were seeking.

Hobosphere Bienenkugel - Google Search

I do second the Perone Hive for this type of study also. It makes sense. and practical , easy to build.


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