*2.5. Calculation of the Vertical Tail Plane Geometry*

The calculation of the vertical tail size is performed via a MATLAB® script that loops the whole process described in Section 2.4. The needed aircraft parameters are obtained from the aircraft designs calculated in MICADO. For atmospheric parameters, the ICAO standard atmosphere [26] at sea level is used. Depending on the wiring configuration selected (on-wing or cross wiring), the yawing moments resulting from the thrust of the remaining engines and the drag from the inoperative propellers are determined. Then, starting from a simplified original geometry of the VTP, the initial values for the coefficients and derivatives are calculated. In order to be able to utilize the aforementioned diagrams from Roskam Part VI [25], they were evaluated at discrete points and implemented as tables, splines or polynomial equations and interpolated between the given values. Using Roskam's statement that the maximum rudder deflection must not be more than 25◦, Equation (4) gives the maximum value for *Cn<sup>δ</sup><sup>r</sup>* and via Equation (5) the maximum *Cy<sup>δ</sup><sup>r</sup>* . The resulting new surface of the vertical tail plane can be derived from Equation (6).

With the assumption that the shape of the vertical tail as well as the outer profile depth and longitudinal position of the horizontal stabilizer do not change, the new vertical tail geometry and the new position of the aerodynamic centre can be calculated. These serve as an updated starting point for the calculation of the corrected coefficients and the iteration begins again. This is performed until the difference between the newly calculated surface area and the previous one is beneath the convergence limit, set to 0.1% for this study.

To carry out this investigation, some simplifications are made. First, the geometric shape of the vertical tail plane is simplified to correlate with Roskam's assumptions. The original Beechcraft 1900D, as well as the partial turboelectric aircraft described in Section 2.2, feature a vertical tail with a rather complex geometry. With the equations from Roskam it is very difficult to accurately model this shape, as they only give the surface area, the span and the sweep angle. Therefore, the vertical tail is changed to a simple trapezoid whilst maintaining the surface area and the average sweep angle of the original

tail to minimize the effects of this simplification. The position of the horizontal tail and the profile depth of the top of the vertical tail are kept constant to minimize the influence on the longitudinal stability of the aircraft. The simplified and original geometry can be seen in Figure 4.

**Figure 4.** Original and simplified (red) geometry of the vertical tail.

The fuselage, on the other hand, is kept the same and held constant for all calculations. Only the size and position of the wing and the vertical and horizontal tail are allowed to change. The power-split between the different engines is also fixed, each propulsor contributes equally to the total thrust of the aircraft. Possible reductions in the power setting of the electric motors in case of engine loss are not taken into account in this study.
