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A badger flange is a pair of small wedges or tapers added to the standard narrow badger gate. Despite being a small piece of apparatus, it can make a noticeable difference by significantly improving the rate and reliability of badger flow during peak herding times.
The reason that badger flanges work can be found in the study of (modern) badger dynamics, where the old "ideal gas of badgers" model is as redundant as the spherical cows talked of in popular jokes. A badger herd is not an ideal gas -- it's a complex multi-particle system, mushrooms or no mushrooms.
Badger flow through gates
When you have a stream of badgers flowing though a gate, there are two likely problems. The first is decompression. If a number of faster or particularly nimble badgers pass through the gate in sequence, a gap can form, leading to herd fragmentation or "depressurisation". Obviously, the effective temperature of the post-gate part of the herd drops at the same time -- which is the part the ideal gas model got correct. If the herd fragments, time will be lost re-herding them. Even if it doesn't, the subsequent mixing of the cooled low pressure badgers and the ongoing stream of warm, high pressure ones continuing through the gate causes turbulence that is equally troublesome. The addition of badgerflanges moderates the speed of faster badgers, and constrains the more nimble ones, allowing faster throughputs with reduced decompression problems.
The second problem is the opposite, that of "flow choking". The standard modern mass produced gate is rectilinear, and this is actually the main cause of choke problems. Given that most badgers necessarily approach the gate at a slight angle, inter-badger interactions are imperfectly aligned. While two-badger interactions are usually fairly mild, and result in a low momentum offset (which averages to zero), at the relatively high pressures at a gate in peak flow, three-badger interactions are common. These result in significant net-momentum offsets, and badger misalignment; thus enhancing the gate surface effects and throttling badger flow -- hence the phrase "flow choking". This is a relatively modern problem (unlike decompression), since old style gates often had misaligned uprights and uneven ground surfaces which decreased systematic surface effects -- and, of course, flow rates were also much lower than in a modern industrial badger herding facility.
The Vortex Choke
Also, but rarely seen in practice, is the so-called vortex choke. This is when multiple three-badger interactions build up not only some population of misaligned badgers, but one that has a twist (or angular momentum). This can cause catastrophic cessation of badger flow, and subsequent delays in processing. The likelihood of this is enhanced by mismatched proportions of left and right handed badgers. At Fell's Badgeronics (where my father once worked), simulations with genetically designed right-handed mice in scale model gates can be used to reproduce vortex chokes at will. Earlier work using polar bears (all of which are naturally left handed) were nothing short of disastrous.
Never yet seen in real life, but in only computer simulation, is the most disastrous possible herding phenomenon -- a vortex choke followed by explosive decompression. The team at Fell's tried to model this utilising their mice herds, but unfortunately mice are too compressible and the vortex chokes tend to collapse smoothly. You may have heard the talk of using miniature armadillos, however this is only meant as a joke. But how does the high density badger lattice formed in a vortex choke lead to explosive decompression? Normally a vortex choke in badgers spontaneously melts with a quick return to near-peak badger flow.
The reason is badger tunnelling. A badger that manages to tunnel to the other side of the gate leaves a gap in the lattice (known as a "hole", in analogy to semiconductor physics). The high pressure in the choke then causes rapid collapse of the lattice around this defect, strong multi-badger scattering causes a bounce-back, which blasts the layer of badgers at the gate entrance into the field beyond (known colloquially as a "badger-nova"). This layer expands and cools rapidly, then is struck by the second-phase high pressure flow causing herd fragmentation, turbulence, and even injury. You might now claim that tunnelling couldn't possibly cause a problem in a modern facility with synthetic surfaces, and you'd be right. True tunnelling is confined to old-style or organic-compliant situations using earth floors or hedgerow fencing. But it has left its mark on the terminology, even if these days "tunnelling" is in fact caused by badgers jumping obstacles, a problem exacerbated by improved diets (and occasional drug taking).
The badger flange moderates high speed badgers, stopping decompression; and it diminishes misalignment from three-badger scattering, controlling choke. A modern high-speed badger herding facility would be lost without this simple device.