Archive for the ‘Aerodynamics’ Category

Continuum

Monday, July 9th, 2012
a diagram to illustrate the concept of a continuum

Continuums are Cool!

It is always good to know where you are. This knowledge provides context which can help you make good decisions. It can also help you predict how your environment might affect you physically. This is true in life, in general, but it is also true in science. As an aerospace engineer I am interested in the science of aerodynamics, where environmental context is critically important.

Environment is so important in aerodynamics because aerospace vehicles behave differently depending on where they are. Clearly an airplane and an earth-orbiting satellite operate in different regimes. One way to distinguish flight regimes is determine whether there exists a continuum.

According to wiktionary a continuum is defined as “a continuous series, or whole, no part of which is noticeably different from its adjacent parts, although the ends or extremes of it are very different from each other.”

In practical terms earth’s atmosphere is a continuum. The air is composed of many molecular particles that interact with one another. At sea level these particles are very close and densely packed. High in the atmosphere though, the particles are much less densely packed and are farther apart from one another.

The average distance between particles is called the mean free path. Gravity affects these particles and tends to pull them down to the surface, so they collect densely at sea level and the mean free path is short. With increasing altitude the mean free path increases, for a variety of reasons. Mean free path is one of two important paramters need to the define a continuum.

To discuss the second parameter I need to establish the idea of a simple airplane. The simplest airplane I can think of is a flying disk, so, imagine a frisbee. The diameter of the frisbee is the same as its chord length.For a traditional wing the chord length is the front-to-back distance from its leading edge to its trailing edge. Chord length is the second parameter needed to define continuum.

For the purposes of aerodynamics there is a continuum when the mean free path of the surrounding atmosphere is shorter than the chord length of a object under consideration, in this case, our frisbee.

Once the mean free path exceeds the chord length then there is no continuum anymore. In effect the regime is no longer atmospheric, but rather, space. The physical changes from sea level to the boundary of space are gradual; beyond that boundary the change transitioning to space is abrupt, and calls for a different type of design for any vehicle.

I find this concept compelling for its similarity to other things in life. The ageing process – a continuum. The way we learn – a continuum. Our position in life changes more often like a continuum rather than abruptly. There are many others.

Not all things in life, but many, we experience as a continuum.

I am often amazed at how the things I learned in becoming an engineer have relevance outside of their strict application in science.