The Importance Of Non-Linearities In Aircraft Preliminary Design

Usually in preliminary design phase many assumption and simplifications are made to have a fast and preliminary sizing of aircraft component. However, neglecting some effects can lead to wrong design with the need sometimes to come back to initial conceptual or preliminary design phase after some more advanced analysis made with higher fidelity methods (i.e. CFD Navier- Stokes numerical aerodynamic calculations). The aim of this work is to highlight the importance of several non-linear effects that usually are not considered in preliminary sizing, but are extremely essential to have a reliable design which can satisfy design requirements even with a certain safety margin. The paper will present some analysis of non-linear effect influence on aircraft longitudinal and directional stability and control which can significantly affects the sizing of horizontal and vertical tail leading to wrong prediction and possible not-compliance with design requirements. The example and calculations were performed through ADAS software, already presented at CEAS 2011 conference. As a relevant example, following figures show the importance to consider non-linear effects for the correct design of a vertical tailplane. The example refers to a regional turboprop aircraft similar to ATR72. As well known the vertical tail design should be designed basically for minimum control speed requirements and for possible achievable equilibrium in side-slip at low speed (approach) and high angles of sideslip with maximum rudder deflection. The maximum achievable sideslip angle should be higher than 12-15 deg. Figure 1 show the initial design performed with only consideration on minimum control speed. The thrust of one engine has been considered and the equilibrium has been imposed to design a suitable vertical tailplane. The assumption refers to a classical vertical tail with rudder chord ratio of 0.35, with vertical tail aspect ratio of 1.55 and with a rudder extension of 80% of the vertical tail available span. The horizontal tail effect has been carefully considered. The first design was characterized by a vertical tail area of 12 m2 to satisfy Vmc requirements (=1.1 Vs1). The same figure 1 show that this Sv lead to a ratio between directional stability derivative and control stability derivative equal to about 0.43. In Figure 2 it can be clearly seen that this vertical tail area leads to a directional control derivative much higher than the stability derivative. In fact the directional stability of the aircraft seems to low, even the control requirements for OEI conditions are met. Figure 2 show the importance to consider non-linear effects due to non-linear instability of fuselage and non-linear behaviour of rudder efficiency and vertical tail lift versus beta to check the possibility to equilibrate the aircraft directionally at high angles of sideslip (through comparison of the two yawing moments). If the VT area is increased to 17 m2, the ratio of two derivatives become close to 1 and the aircraft is characterized by good stability, However, as can be observed from Figure 3, the second vertical tail leads to a maximum achievable sideslip angle (estimated taking into account all non-linear effects) lower than 15 deg.