Downwash modelling for three-lifting-surface aircraft configuration design

This paper introduces a semi-empirical model to predict the downwash gradient at the horizontal tail of a three-lifting-surface aircraft. The superposition principle applied to well established formulations valid for two lifting surfaces is not a reasonable approach to calculate the downwash of a canard-wing-tail layout, and this article demonstrates that such a basic technique leads to incorrect results. Therefore, an ad hoc prediction model is proposed that considers the combined nonlinear effects of canard and main wing inductions on tail downwash, being based on a full factorial design sweep of CFD simulations obtained by varying the main geometrical parameters of the three lifting surfaces. A suitable analytical formula for the downwash gradient is established through a process of data analysis and factor extraction. The presented model extends the validity of the available models for traditional two-lifting-surface designs by means of a correction factor. The engineering estimation method introduced here exhibits an acceptable accuracy, as well as relatively small prediction errors, and it is suitable for conceptual and preliminary studies of three-surface layouts. The value of this methodology is confirmed by the validation with the results of numerical and experimental investigations on a case study aircraft.