Welcome to Top Bar Tuesdays! This is the second post in a six-part series on top bar hive design. I was surprised to see how many variations there were for the basic shape of a top bar hive, and how little many authors discussed the different options, so I thought a few posts highlighting what I see as pros and cons of common approaches might be useful.

This post looks at the body of the hive, in particular the end of the hive. When I search the Internet for top bar hive plans, I find instructions for building top bar hives from barrels, wooden boards, and even sunflower stalks. I’ve become interested, some would say obsessed, with what is the “best” design. After some research, more thought and a little too much math, I decided that some designs may be better than others, but the multitude of approaches appear to work just fine for both the bees and an aspiring beekeeper like myself.

### Langstroth Frames

One key difference I see that is rarely mentioned is the available area for honeycomb. This made me wonder what type of TBH has an area similar to the standard Langstroth frames. Langstroth frames are so widely used that perhaps the size of these frames is relevant to or somehow preferred by the bees. So I sketched out the standard Langstroth frame shown here, based on a build-it-yourself diagram I found on beesource.com.

By the way, I must apologize for all the math in this post. You can avoid this by skipping to the wrap up at the end, or indulge me as I share my recent calculations. What can I say? Math is fun. I also apologize for working in inches, as for some reason the U.S. is still using such archaic units of measurement. Crazy, I know, but I am a product of my culture so I use inches.

Back to the frame: there are generally three types of Langstroth frames: deep, medium, and shallow. As shown in the graphic, these frames have a top of 19 inches across, an internal width of 17 inches, and different depths (d). The deep frame, with a depth of 9 1/8 inches, is often used as the main hive body. The wood in many designs is 3/8 or 0.375 inches wide, except on top where it is 3/4 or 0.75 inches. So the interior comb height is the frame depth minus 0.75 + 0.375 or 1.125 inches (whew!). So the honeycomb area in these frames is 17 inches wide with a depth depending on the type of frame. The following lines calculate the comb depth and areas for each type:

Deep Comb Depth = 9.125 – 1.125 = 8.0 inches

Medium Comb Depth = 6.25 – 1.125 = 5.125 inches

Shallow Comb Depth = 5.375 – 1.25 = 4.25 inches

Langstroth Deep Comb Area = 17 x 8.0 = 136 square inches

Langstroth Medium Comb Area = 17 x 5.125 = 87.125 sq. in.

Langstroth Shallow Comb Area = 17 x 4.25 = 72.25 sq. in.

So, roughly speaking, if you want to match the comb capacity of a deep Langstroth frame, then a top bar hive should have an inner comb area of around 130 square inches.

### Barrel Hive Frames

For the barrel hive design I mentioned previously, you may notice that half the barrel is used as the body of the hive. The area of a circle is pi (π) times the radius squared (πr^{2}), so we can determine what size barrel matches the Langstroth frames.

I’ll skip the details, but the result is that a barrel should have a radius of 9.3 inches to yield a deep comb area; and a radius of 7.4 inches to yield a medium comb area. This may mean that a barrel bigger than 19 or 20 inches in diameter is a bit large, as in addition to yielding heavier frames the comb size is larger than the comb produced by the deep Langstroth frames. Or perhaps the bees simply don’t use the whole area if the barrel is so big. I’m not sure. Interesting to ponder, especially since many plans for a top bar hive from a barrel recommend a 55-gallon food-grade plastic drum, which are typically around 23 inches in diameter (radius of 11.5).

55-gallon Barrel TBH Comb Area: ½π(11.5)^{2} = 207.74 square inches

### Wooden TBH Frames

Let’s turn our attention to top bar hives based on wooden boards, since this is how TBH’s are often presented and sold (see for example Dadant or Aunt Bea’s). The end of such a hive is illustrated in the diagram. There are three boards: the base (b) and two sides (s1 and s2). In order to have a symmetrical design, not to mention a level hive, we really need s1 and s2 to be the same length. The sides are attached at the same angle (A) to the base board. The overall height of the hive (h) and the width of the top (t) are also shown.

After looking at a number of sites, there seem to be two common designs that appear again and again. I call these the one-to-one design and the two-to-one design, based on the ratio of the sides to the base. The following diagram illustrates a somewhat idealistic view of each approach. In the first, the boards are all the same width, while in the second the sides are twice the width of the base. Note that the total width of the three boards in both hives is 30 inches (10+10+10 in the first; 12+6+12 in the second).

Both designs have their advantages. The one-to-one design mirrors the shape and angle of the bee’s honeycomb, which is appealing to some folks, not to mention it provides a greater comb area, as we’ll see in a moment. It does have a longer top bar, which gives the bees more opportunity to curve the comb, which they apparently may do on a longer bar. Some proponents claim that bees are less likely to attach comb to the sides in this design, though other folks dispute this claim.

The two-to-one design is a bit more compact, and the shorter top bar is preferred by some as it may encourage straighter comb. The more compact area may also retain heat better in cooler climates.

The shape created by both these designs is called a trapezoid, in fact the TBH is an isosceles trapezoid because the opposite angles are the same. I’ll again spare you the details, but using a little trigonometry we can determine that the top of the one-to-one design is 20 inches, and the top of the two-to-one design is 14.2 inches. If you look up the formula for the area of an isosceles trapezoid, you can use this to produce the following results:

One-to-One TBH Comb Area = 129.9 sq. in.

Two-to-One TBH Comb Area = 113.94 sq. in.

### Total Comb Area

As you may have guessed, I can get caught up in the math, so find it quite interesting to compare the areas of the different designs. What is more interesting (to me, anyway…) is how these slight changes in area affect the total available comb area across the length of the hive. That is, if we take the typical 10-frame Langstroth hive with deep frames, we get the following:

Langstroth Deep 10-Frame Comb Area = 10 x 136 = 1,360 square inches

If you do the math, the 55-gallon barrel hive reaches this area in a mere 7 frames. For the one-to-one TBH you need 11 frames; in the two-to-one TBH you need 12 frames. With a smaller comb area on each frame, a longer hive is needed to achieve the same amount of comb. This could be important if a beekeeper is looking to maximize productivity, though I should mention that most authors agree Langstroth hives are generally more productive than top bar hives.

### Wrap Up

So what does all this mean? That is a fine question, and I’m not quite sure of the answer yet. In this post we compared the individual area for honeycomb on each frame in different hive configurations. This is summarized as follows:

Langstroth Deep Comb Area = 136 square inches

Langstroth Medium Comb Area = 87.125 sq in

Langstroth Shallow Comb Area = 72.25 sq in

55-gallon Barrel TBH Comb Area = 207.74 sq in

One-to-One Wooden TBH Comb Area = 129.9 sq in

Two-to-One Wooden TBH Comb Area = 113.94 sq in

With these numbers, we found that in order to match the total comb area of a 10-frame Langstroth deep hive, we would need 7 frames in the barrel hive, 11 frames in the one-to-one wooden hive, and 12 frames in the two-to-one wooden hive.

I wonder if the different frame areas impact a hive’s ability to survive the winter, or the overall mood of a colony. This might be an advantage of the Langstroth stacking approach, as you end up with a larger overall nest area with two stacked Langstroth boxes of any size, whereas in top bar hives you can only make the box longer. I suspect that if you made a top bar hive the depth of a shallow or even a medium Langstroth frame the bees would find it too small, and would abandon the hive.

In the next post of this series we’ll look at the impact of this discussion on some real-world designs for top bar hives.

*This series is based on the children’s poem Here is the Beehive, which begins as follows*

*Here is the Beehive (Part 1)
*

*But where are all the bees? (this post)*

(more to come!)

(more to come!)

*The title of this post makes me think of the plight of bees in our time. There is a great Ted Talk by Marla Spivak on this topic which is worth watching.*

Something doesn’t seem right to me. You state a deep frame being 17 X 8 provides 136 square inches of brood space, however every frame is two sided – doesn’t each deep frame provide 272 square inches of brood space contrary to your Total Comb Area paragraph? Other areas your math is right, 2720 per 10 frame box and 5440 per double deep 10 frame hive body? But comparing a frame single side (136 sq inch) to other frame designs when no frame is single sided just seems confusing unless I missed somewhere that you stated you were considering one side of each frame.

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Hey Donald. Yes, I think you are correct. I seem to only consider one side of the frame throughout the discussion without actually saying this. You do indeed have to account for both sides of the comb, and this applies to both the Langstroth and the top bar frames.

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