**Macroscopic**Shuttle imagery of re-entry phase.

When observing a gas, it is typical to specify a frame of reference or

length scale. A

*larger* length scale corresponds to a

macroscopic or global point of view of the gas. This region (referred to as a volume) must be sufficient in size to contain a large sampling of gas particles. The resulting statistical analysis of this sample size produces the

**"average"** behavior (i.e. velocity, temperature or pressure) of all the gas particles within the region. By way of contrast, a

*smaller* length scale corresponds to a

microscopic or particle point of view.From this global vantage point, the gas characteristics measured are either in terms of the gas particles themselves (velocity, pressure, or temperature) or their surroundings (volume). By way of example, Robert Boyle studied

pneumatic chemistry for a small portion of his career. One of his experiments related the macroscopic properties of pressure and volume of a gas. His experiment used a J-tube

manometer which looks like a

test tube in the shape of the letter J. Boyle trapped an

inert gas in the closed end of the test tube with a column of

mercury, thereby locking the number of particles and temperature. He observed that when the pressure was increased on the gas, by adding more mercury to the column, the trapped gas volume decreased. Mathematicians describe this situation as an

inverse relationship. Furthermore, when Boyle multiplied the pressure and volume of each observation, the

product (math) was always the same, a constant. This relationship held true for every gas that Boyle observed leading to the law, (PV=k), named to honor his work in this field of study.There are many math tools to choose from when analyzing gas properties. As gases are subjected to extreme conditions, the math tools become a bit more complex, from the

Euler equations (inviscid flow) to the

Navier-Stokes equations^{[8]} that fully account for viscous effects. These equations are tailored to meet the unique conditions of the gas system in question. Boyle's lab equipment allowed the use of

algebra to obtain his analytical results. His results were possible because he was studying gases in relatively low pressure situations where they behaved in an "ideal" manner. These ideal relationships enable safety calculations for a variety of flight conditions on the materials in use. The high technology equipment in use today was designed to help us safely explore the more exotic operating environments where the gases no longer behave in an "ideal" manner. This advanced math, to include

statistics and

multivariable calculus, makes possible the solution to such complex dynamic situations as space vehicle reentry. One such example might be the analysis of the image depicting space shuttle reentry to ensure the material properties under this loading condition are not exceeded. It is safe to say that in this flight regime, the gas is no longer behaving ideally.