The Bee World – April, 1929 – Pages 52 – 55
E. B. WEDMORE.
In BEE WORLD for December, 1928, the Rev. Yates Allen questions the well-worn instruction that foundaton should be so placed in a frame or section that the sides of the hexagons are vertical. The reasons generally given in the guide books are twofold; firstly, that the bees prefer to build combs this way, and secondly, that a comb so built is stronger than one having angles at the sides and horizontal faces at the top and bottom of the cells. The first reason is built upon incomplete observation and the second on insufficient consideration.
I propose to show that the bees’ preference is in no way related to mechanical strength or any effect of gravity, but mainly on the life of the support on which they commence to build the individual comb. Furthermore I shall show that comb has the same strength whether subjected to stress parallel to the sides of the cells or normal to them, and that it is no matter which way the foundation be mounted.
For brevity I shall describe comb built with vertical walls as “vertical way” and comb built with the tops and bottoms of cells horizontal as “horizontal way.”
If anyone will read Huber, or examine for themselves, they will find that when the bees commence to build they accumulate wax until a wall like lump is built up on the support and then form the beginnings of cells by working on the wax from both sides. The hollows thus formed are worked until the walls are thin and stand out at right angles to the base. It would not be right to say that the bees could not make the walls stand out at some other angle or that they cannot build in any other way. The normal result, however, of extending similar hollows until they meet, the procedure so beautifully described and illustrated by Huber, is to produce walls at right angles to the base, and on examining a natural comb, built on any surface lying at any angle one finds that the bees commence by building out walls at right angles to the surface.
Now in most cases the bees commence building on a horizontal surface, as for example the underside of a branch or the underside of the top of a hole in a tree, or from a wax runner in the top of a frame. In these cases the first walls formed are vertical and this substantially secures the setting of the whole comb. It will be observed, however, that when a comb is started from the side wall of a box hive or from the face of a dummy, the first walls built are again normal to the surface and therefore horizontal, and this again determines the setting for the rest.
It will be observed that a rotation of only 30 degrees converts a hexagon with vertical walls into one with horizontal walls, and occasionally a natural comb gets distorted this much so that one started vertical way is finished horizontal way or vice versa. Furthermore, one started from a surface sloping only 30 degrees from the horizontal will be built horizontal way. When a swarm of bees starts to build in an old-fashioned skep, if the swarm does not depend from the centre the comb is frequently started along a face sloping about 30 degrees and comes out horizontal way, more or less.
On such combs and on combs built from the wall the greater weight of bees on the longer free edge frequently causes a sag which rotates the hexagons, so that a comb started horizontal way is more than usually liable to distortion and to be completed vertical way. Thus there is more than one reason why one generally finds naturally built combs built vertical way.
Now as to the mechanics of the subject there is a sort of idea that the vertical walls in vertical way are better able to withstand the weight of comb below than are the zig-zag verticals found in horizontal way. The two constructions are shown in Figures 1 and 2.
In Fig. 1 the weight of depending comb is supported by a row of vertical walls A, A, which share the load, and it is transmitted from each wall to the next by the walls B, B, of which there are two transmitting load from each A, in one row to the A walls in the row below. In Fig. 2 the weight is carried by the zig-zag verticals C, C, C, which in tending to straighten put considerable tension on the horizontal walls D, D. If the same vertical load in ounces be applied to support A, as to a support C, C, C, any mechanical engineer will advise that the strain on the individual walls C, C, will be greater than on A, A, in the ratio 2: radix 3. It will be found, however, on examining the number of walls per inch run of comb width that there are more verticals C, C, than A, A, again in the ratio 2: radix 3. In supporting a given weight of comb per inch run of width then, the stress per vertical will be reduced in Fig. 2 in just the same ratio as the stress per individual wall is greater. Thus the vertical walls have to resist the same individual forces in Fig. 2 as in Fig. 1.
The matter may be stated more simply another way. The forces are in every case transmitted from wall to wall at their meeting places, and at each meeting place or angle we have three walls meeting at equal angles and from symmetry the forces in the three walls must be equal. This will be found supported by any textbook on mechanics with a qualification which I shall deal with later. Meanwhile we conclude that the forces in the more or less horizontal walls B, B, in Fig. 1, and D, D, in Fig. 2 are equal to those in the verticals. This conclusion is supported by the fact that the bees make all these walls of the same thickness save that in deep combs, putting a great weight on the upper rows of cells, the walls will sometimes be found thickened at the top, and especially the points of attachment between the walls and the support. (The mid rib carries only about one quarter of the total weight).
Our conclusion leads, however, to another fascinating problem which I have never seen stated, although the solution of it accounts completely for certain characteristics of combs with which we are all familiar, so familiar in fact that we have taken them for granted.
The problem is what becomes of the horizontal stresses, for from the above description it is clear that the horizontal walls D, D, and those nearly horizontal B, B, are subjected to stresses as great as those of the vertical walls to which they are attached. What then happens to the stresses in the outermost horizontal walls when they do not reach to a rigid support to which they can be secured? We cannot get rid of the difficulty by finishing up with no outside horizontal walls as on the left hand side of Fig. 2, for the corners E, E, E, need pulling to the left to prevent the zig-zag vertical on that side from straightening under tension, just as much as if there were horizontal walls attached to F, E, E. The answer is to be found partly in the mid rib forming a continuous and common bottom to the cells in both sides, but not wholly, for clearly this mid rib cannot by itself offer support near the mouths of the cells, and the cells are not so rigid as to need more. Consider for example a comb of honey carrying on the cell walls say 10 ounces of honey or brood and bees per inch of width below a certain level (here, as above, width is measured along the face), then this stress is divided between 5 vertical walls at front and 5 ditto at back of comb in the inch width, giving therefore a stress of one ounce per wall per cell, back and front. This fixes the horizontal forces at this level, also at one ounce per wall, enough to crush the thin cell walls unless further support were given.
Now examine a comb, partly built, with free edges and see what a beautiful structure the bees provide to resist this force. As is well known the comb tapers to an edge on both sides and the edges of the cells on both sides are thickened up so that there is a relatively stiff open structure in both surfaces which both protects the mouths of the cells and assists in resisting the horizontal stresses. Fig. 3 shows a horizontal section of a small partially built natural comb in which M is the mid rib and F, F, the stiffened faces constructed as shown in Fig. 4 in which the thickening is slightly exaggerated. The tapering at the two sides serves to direct the forces back on to the mid rib. The form of the whole structure is beautifully calculated to serve its purpose.
As is well known, when the bees continue the structure shown, they proceed first to accumulate more wax on the mouths of the cells, and then they work in the thickened portion so as to draw out the walls further, proceeding uniformly over the whole exposed face so as to obtain the tapered edge and the smooth convex face. Any other face would not be so stiff.
In saying above that the forces on these walls, meeting at a corner and making equal angles, were equal, I made a reservation. The statement made would be necessarily true if the walls were hinged together at the corner, but, in fact, there is some rigidity at the corner and especially at the base of the cell where the mid rib is. Now, further examination will show that the forces cannot be exactly equal in an actual comb because the stress due to the weight of the comb is a maximum on the top row of cells and nothing on the bottom edge. If there are 40 rows of cells the weight will diminish by about one-fortieth between each row and the next. This slight graduation of the forces is undoubtedly taken up by the slight stiffness of the structure as a whole. This is assisted also by the thickening of the corners of the cells, which thickening again serves another useful purpose which we may see by examining Fig. 5, which shows in full lines three walls meeting at angles of 120 degrees. Any mechanic will tell you that if these three walls be subjected to tension in the direction of the arrows, even though the forces be balanced about the centre, there will be a tendency to crack at the sharp corners where there will be a concentration of force. This, however, can be got over by the engineer’s device of rounding out the corners, a device used by the bees also, as indicated by the dotted lines.
We have seen how the stresses on the walls decrease as the bottom of the comb is approached. It is interesting to examine a finished comb. If in a walled chamber, it will be found built out to the walls and attached to them most of the way down. This serves three purposes. The horizontal stresses are well provided for. The cells at the edges are used to the full and some of the forces depending weight can be transmitted to the side walls. Below a certain level the edges are free and a bee space is left so that the bees have ready access from side to side and do not have to provide the stiff bracing to the side walls which would be partly wasteful. Yet they like to use the cells built around the bottom for breeding purposes for which they require to be full depth. Now if no provision were made these outside cells would be weak, exposing a maximum of thin and unsupported walls and angles. For this reason the bees make a start all round with the neat row of cells but make them very shallow and turn their mouths outward. The structure is worth examining. It provides a nice stiff mechanical edge and at the same time those numerous shallow pockets which, when swarming time comes, are so easily converted into queen cells.
I have noted on worker comb newly made in a skep and consisting only of white wax cells, walls at sides and bottom, equal in thickness and less than four thousandths of an inch thick. On now white drone comb I have noted side walls about six thousandths thick and base walls about nine thousandths thick.
Finally let me put this poser to the observant beekeeper. Fig. 6 shows alternative arrangements of the cell bottom, both obtained vertical way. Now the observer may consider that he, and perhaps the bees, would prefer arrangement A to arrangement B. Let him then try and arrange the foundation in a frame to give arrangement A throughout. He cannot do this.