R.W.P. King studied wire dipoles for years and supposedly produced over 100 PhD students doing the same. The details are really really hard to get right and abs

R.W.P. King studied wire dipoles for years and supposedly produced over 100 PhD students doing the same. The details are really really hard to get right and absolutely require empirical work. There are two core problems. One is that while Maxwell’s equations do model practically all EM phenomena, and therefore should make everything amenable to simulation, it requires detailed knowledge of material properties everywhere. Dealing with pure vacuum (or crisp, clean air over short distances) is therefore totally easy because it is all homogeneous and well-measured. But antennas convert electrical activity to traveling waves in space, so they are necessarily made up of different matter than the thing you want to transmit or receive into. Now you need to know the material properties of the antenna structure in a way that is incredibly hard to know. So we just approximate it as a series of uniform copper cylinders and say that one of them is connected perfectly to a cable using an infinitesimally thin gap. Yagi-Uda antennas depend upon complex interactions among the wires to achieve surprising levels of gain, and these details actually matter strongly. But they are practically unmodelable. So we simulate something and work hard to reconcile both the simulation (requires a lot of theoretical knowledge) and the actual antenna. The other problem is also hard. In Maxwell’s equations, you can book it down to a single equation describing how energy is converted to a traveling wave. That energy conversion involves a Dirac delta function (our shorthand for “itty bitty thing the rest of the system doesn’t otherwise interact with “). The delta function goes to infinity at some point. A real energy source is just some weighted collection of these deltas. In other words, I have a bunch of singularities. At some nominal distance from each singularity, the math is well-behaved. Close-up, however, things fall apart. Numerical precision is exhausted quickly, field strengths go off the rails, phase velocities exceed the speed of light (Hertz has some fun wtf moments at the end of one of his notebooks grappling with this), and other fun effects. Software hates this. So theoreticians come up with ways to model these singularities at a close, but non-zero distance for a bunch of special cases. Software must decide among the cases with hints from the human operator and match up with the desired geometry. It’s super hard to get right in all cases. My advisor and others at OSU spent decades coming up more special cases to enable rapid design of dish antennas, and certain shapes of wire antennas, and even to accelerate stealth F-117 design. Compared to all of this craziness, even a theoretical person like me will still spend a lot of time in the lab because it is just faster and strictly more accurate. Antenna design is often characterized as black magic. It really isn’t. We just don’t know literally everything about the world and it sometimes matters for these devices. The mystery is not inward towards the mind, but outward towards the universe at small and large scales.