Compressibility and incompressibility

Early chapters emphasised that air is compressible; it was also emphasised, though perhaps not emphatically enough, that though it is compressible it does, in fact, behave at ordinary speeds almost as though it were incompress­ible. Of course such an assumption is not true, air is really compressible or, what is sometimes more important, expandable at all speeds and the density does change, i. e. increases or decreases, as the wings and bodies of aeroplanes move through air at quite ordinary speeds, but the point is that the error in making the assumption is so small as to be negligible, while the simplification that the assumption gives to the whole subject is by no means negligible.

As we approach the speed of sound the error in making this assumption of incompressibility can no longer be justified, the air is definitely compressed, or expanded. We are now dealing with a compressible and expandable fluid.

It should be clear from this that the change is gradual, not sudden; it is all a question of deciding when the error becomes appreciable, and a rough idea of the error involved may be obtained from Table 11.1, which represent the error in assuming the ordinary laws of aerodynamics when estimating the drag of a body moving through air at the speeds mentioned.

It will be sufficiently clear from this that we must begin to change our ideas at speeds considerably lower than 340 m/s.