Theory and Practice of Aircraft Performance

APPENDIX CFundamental Equations

Some elementary yet important equations are listed herein. Readers must be able to derive them and appreciate the physics of each term for intelligent application to aircraft design and performance envelope. The equations are not derived herein – readers may refer to any aerodynamic textbook for their derivation.

C.1 Kinetics

Newton’s Law:

Therefore energy (i.e. rate of work) for the unit mass flow rate m is as follows:

Steady‐state conservation equations are as follows:

(C1)

(C2)

With viscous terms, it becomes the Navier–Stokes equation. However, friction forces offered by the aircraft body can be accounted for in the inviscid flow equation as a separate term:

(C3)

From the thermodynamic relationships for a perfect gas between two stations, this gives

(C4)

C.2 Thermodynamics

Using perfect gas laws, entropy change through shock ...