# Modeling, Simulation, and Cruise Characteristics of Wingtip-Jointed Composite Aircraft
## 4 Lift Drag Ratio Analysis of Composite System Cruise Process  
During cruising, the fuel consumption rate of the engine is related to \(T_{R}\) (the thrust required) by the engine and \(W\) (the weight of the aircraft system) [23].  
\[T_{R}=\frac{W}{K}. \tag{20}\]  
The specific mathematical relationship shown in Equation (20) proves that a larger value of \(K\) leads to a smaller value of \(T_{R}\) and provides better cruising performance. Therefore, the aircraft system will fly longer and further with the same volume of fuel.  
In order to analyze the distribution law of the lift-drag ratio with the relative roll angle, the full-trim strategy that meets the requirements of compound flight cruise was adopted.  
Figure 9: Wingtip-jointed aircraft system simulation results with different trim strategies.  
Polynomial approximation is a commonly used tool to approximate functions. In the interval of seeking the minimum point of a function, we can use the value of the objective function at several points to construct a polynomial as the approximate expression of the objective function, then use the minimum point of the polynomial as an approximation for the original objective function. Iterative calculation is repeated until a satisfactory result is obtained; this method is called interpolation. Not only are the function values on the nodes equal, but the corresponding derivative values are also required to be equal; even the higher-order derivatives are equal. The interpolation polynomial satisfying this requirement is called a Hermite interpolation polynomial [24].  
The initial conditions of the calculation example were set to a height of 5000 m and a Mach number of 0.282. The angle of attack varied from \(-4^{\circ}\) to \(10^{\circ}\) with sampling interval of \(1^{\circ}\). The \(\varphi_{12}\) sampling data include \(\pm 40^{\circ}\), \(\pm 20^{\circ}\), \(\pm 10^{\circ}\), and \(0^{\circ}\), such that 105 sample data were obtained, according to the CFD modeling and composite flight dynamics model; these are shown as the discrete points in Figure 10.  
Figure 10 also shows the lift-to-drag ratio curves for different relative roll angles obtained using the PCHIP method, where \(\alpha_{Kmax}\) represents the corresponding attack angle for maximum \(K\) value. The curves prove \(\alpha_{Kmax}(40^{\circ})>\alpha_{Kmax}(-40^{\circ})>\alpha_{Kmax}(20^{\circ})> \alpha_{Kmax}(0^{\circ})>\alpha_{Kmax}(-20^{\circ})=\alpha_{Kmax}(10^{\circ})> \alpha_{Kmax}(-10^{\circ})\). The data curves also demonstrate that the optimal relative roll angle for the maximum value of lift-to-drag ratio among all the different sampling relative roll angles was \(0^{\circ}\), and the maximum \(K\) value was 29.31 with an angle of attack of \(2.27^{\circ}\). Compared with other relative roll angles, the lift-to-drag ratio of \(\varphi_{12}=0^{\circ}\) was always the largest; in the range of \(-2^{\circ}\) to \(5^{\circ}\), \(K(40^{\circ})<K(-40^{\circ})<K(20^{\circ})\)\(<K(10^{\circ})<K(-10^{\circ})<K(0^{\circ})\), while the distribution rules in other ranges are complicated to summarize.