We are now ready to introduce magnetic fields, which are generated by electrical currents and which apply forces on moving charges and current-carrying wires. Historically, magnetic effects in lodestones, an iron ore that can be magnetized, have been known for a long time. The first magnetic compasses date back to about 1000 BCE, and the ancient Chinese are believed to have used such devices for navigation as early as 1100 CE. The properties of magnetic fields can be derived from a number of observations of magnetic effects that have been recorded over many years. One of the earliest such observations, by Hans Christian Oersted in 1820, was that a current-carrying wire exerts a torque on a permanent magnet (such as a compass). Current-carrying wires can also exert forces on each other, as first observed by Biot and Savart and more fully characterized by Ampère. Finally, beams of charged particles, such as electrons in a cathode ray tube (see TechNote 3.4), are deflected when in the presence of current-carrying wires. Each of these phenomena can be described quantitatively in terms of a magnetic field produced by current distributions, as we will discuss throughout this chapter.

The design task facing us is to shape the wing to realize aerodynamic characteristics well suited to the mission. Doing this requires a prediction method of either L1, L2, or L3 genus that maps the given geometry to its pressure field and ultimately to its performance. An early multidisciplinary design and optimization activity is the cycle 1 parametric design of the clean wing, A parametric design study evaluates the aircraft baseline configuration and it has the ability to arbitrarily vary those parameters that influence its shape and hence its performance. It determines the sensitivity of the vehicle effectiveness against some of the established requirements. The parametric effects of, for example, varying the wing planform are assessed, leading toward optimization of the layout by some measure of effectiveness. L0 and L1 tools are enhanced with surrogate models to speed up the aerodynamic evaluations. The vortex lattice method is presented as a mainstay tool in the clean-wing design process and is illustrated using a number of examples. The discussion of the design task continues for high-speed flight missions, indicating where the fidelity must be increased to L2 and L3 tools.