The aerodynamic characteristics of airframes are expressed as aerodynamic transfer functions, giving the relationships between input and output for each of the three separate planes of motion, roll, pitch, and yaw. By assuming no cross-coupling between planes and linear aerodynamics, and by making certain other assumptions, which apply particularly to conventional airframes with fixed wings and rear controls, relatively simple approximate algebraic transfer functions giving the relationships between the control surface deflection (the input) and any airframe motion (the output), are obtained.

The open loop aerodynamic transfer functions thus obtained are used as part of the auto-pilot block diagram, in which the performance of other components, such as actuators, instruments and electrical networks, are also expressed in transfer function form. The aerodynamic transfer functions are useful in auto-pilot evolution and synthesis in that they aid selection of the airframe motions to be measured, modified, and fed back to close the auto-pilot loop.

For mathematical assessment of closed loop performance and stability, open loop transient and frequency responses are used, and curves of airframe responses are plotted in linear, logarithmic and polar form by standard methods from the aerodynamic transfer functions. Some methods of using these curves, which follow the general lines adopted in servo-mechanism and electronic amplifier design, are explained briefly.

Analogue computers are frequently used when the computations to be made are so complicated as to need the use of a computing machine. The aerodynamic transfer functions then form one block of the simulator set-up, and on larger computers the more exact form, including any non-linearities and cross-coupling effects, can be used.