The Art of Phugoid

In this chapter, we will explore some aspects of mathematical model of glider flight. This model is called Lanchester's phugoid theory^3.1, developed by Frederick Lanchester [Lan] at beginning of the twentieth century. While this model has its drawbacks, it still is used today to explain oscillations and stalls in airplane flight.

Since this model, like many models, is a set of differential equations, we will need some results which are typically covered in a course on differential equations. We will cover the relevant material briefly here, but readers needing a more in-depth treatment are encouraged to look in a text on ordinary differential equations, such as [BDH], [HW], or [EP]. Of these, the approach in [BDH] is perhaps closest to the one presented here.

Footnotes

... theory^3.1

Folklore has it that this name was chosen by Lanchester because he wanted a classically-based name for his new theory of oscillations occuring during flight. Since the Greek root phug ( $\phi$$\nu$$\gamma$$\eta$, pronounced ``fyoog'') as well as the Latin root fug- both correspond to the English word ``flight'', he decided on the name ``phugoid''. Unfortunately, in both Greek and Latin, this means ``flight'' as in ``run away'' instead of what birds and airplanes do-- the same root gives rise to the words ``fugitive'' and ``centrifuge''. The Latin for flight in appropriate sense is volatus; the Greek word is potê ( $\pi$o$\tau$$\eta$).