ESDU 78038 gives the equations for the instantaneous or point performance of an aircraft using the International Standardisation Organisation's Standards as a framework for the definitions and sign conventions of the quantities involved. The equations are given in vector form and as the six equations for a body-axis system. Relationships are deduced for excess power, energy and energy height. The various axis systems that can be used are introduced and the reasons for choosing any particular one explained. Appendices explain Newton's laws of motion and their application to a body of changing mass, and formulae are included for transformation of forces and angular velocities between Earth and body axes and between air-path and body axes.