Transformation from Stability Axis to Body Axis

The origin of the body and stability axes is the same and the only rotation is the inclination a of that of the XZ plane of the stability axis with the body axis. By putting C = f = 0 and U = a in the elements of matrix T in Equation A.28, one obtains the matrix TSB to transform from stability axis to body axis

Transformation from Stability Axis to Wind Axis

This transformation is given by the following matrix

Transformation from Body Axis to Wind Axis

The origin of wind and body axes is the same and the two axes system are related through the flow angles a and b – Substituting C = b, U = a, and f = 0 in the elements of matrix T in Equation A.28, one obtains the matrix TWB to transform from body axis to wind axis-

(A.37)

Thus, using the transformation matrix T defined in Equation A.28 and knowing angles C, U, f, one can obtain a transformation from one axis to another.

A6 aerodynamic derivatives—preliminary determination

The preliminary estimates of the derivatives are generally obtained by using methods like data compendium/handbook methods (DATCOM) and computational fluid dynamics (CFD). These methods are valid for low AOA and subsonic/supersonic Mach number regions. At high AOA, the effects of flow separation, boundary layer flow, vortex flow, and shock intensity and location at transonic Mach number complicate the accurate determination of these derivatives. For these conditions, the data from the WT experiments and flights of similar aircraft are used in conjunction with the handbook methods (DATCOM). Subsequently or concurrently, the derivatives are determined from suitable WT experiments. Further refinements can be made using advanced CFD codes. The estimates thus obtained are employed for studies related to the selection of the baseline configurations for aircraft and missiles. These estimates are generally known as predicted values (or initial refer­ence values) of the aerodynamic derivatives or simply the ‘‘predictions.’’ After conducting several WT tests, the preliminary estimates are refined and the vehicle configurations are optimized for obtaining the desired performance and controllabil­ity and used for studies on load estimation. Subsequently, the prototype vehicle is built and preliminary flight tests are conducted. One of the purposes of these flight tests is to estimate the aerodynamic derivatives from the flight data generated by conducting certain specific maneuvers on the vehicle (usually aircraft and rotor – crafts). These aspects are discussed in Chapters 7 and 9. Mathematical models

(specifically the aerodynamic derivatives or stability and control derivatives, which occur in the equations of motion) of aircraft dynamics are generally available from WT experiments and analytical methods before flight tests. Due to extensive WT testing and progress in aerodynamics and system technologies, reasonably accurate mathematical representations (models) are available. As a result of this, satisfactory characteristics, validated through extensive flight simulation, could be designed into the aircraft prior to flight. This has given more weightage to the model verification exercise to be performed along with pilot’s assessment. The vehicle’s dynamical characteristics are described by equations of motion and parameters that have physical meaning. These parameters are to be estimated from flight test data. These estimated parameters are compared with those obtained from WT experiments and analytical methods (e. g., CFD/DATCOM—all put together as prediction methods). Flight-determined stability and control derivatives (FDD) are also used in handling quality criteria (see Chapter 10) to assess the overall pilot-aircraft interactions and performance. Hence, Taylor series (expansion) of aerodynamic coefficients is generally found very useful in representing the stability and control derivatives.