3.1 The concept design

The main flight parameters of the smart morphing long-endurance UAV are presented in Table 2, while the flight profile is shown in Fig. 5.

Table 2 Flight parameters of the smart morphing long-endurance UAV

Figure 5. The smart morphing long-endurance UAV flight profile.

3.2 Configuration layout design

A single 115-hp Rotax 914F/UL turbo-charged four-cylinder engine powers the UAV, and a large-aspect-ratio wing is adopted to reduce the induced drag with an inverted V-shaped tail to avoid the influence of the flow of the wing. The Three-Dimensional (3D) configuration layout of the smart morphing long-endurance UAV is shown in Fig. 6.

Figure 6. The configuration layout of the smart morphing long-endurance UAV.

3.3 Morphing design

The morphing bends the trailing edge of the wing to change the wing camber while leaving the thickness distribution unchanged. The distribution of the morphing wing is shown in Fig. 7. Along the span length, it is divided into the wing–body connection section, the transition section and the camber-variable section. The camber-variable section accounts for 80% of the wing span. The morphing is uniform along the span.

Figure 7. The morphing wing distribution.

The morphing structure is designed with reference to HongDa Lis article^{(Reference Li15)}. The details of the morphing wing are shown in Fig. 8. The transition section uses a flexible skin. One end is the rigid wing rib, while the other end is the morphing structure. The morphing structure includes the rigid structure, the driving skin (which is mainly made of shape memory alloy), the flexible baseplate that is fixed to the rigid structure and can be deformed by the driving skin, and the artificial muscles, which are used to hold the flexible baseplate in place. Thus, by controlling the driving skin, the morphing structure can change the trailing edge on demand.

Figure 8. The morphing wing design.

The maximum thickness of the initial aerofoil is 13%, distributed at 32.5% of the aerofoil chord. The relative camber is 4.93% at 30% of the aerofoil chord. The lift-to-drag ratio of this aerofoil at the cruise Reynolds number is shown in Fig. 9. The maximum L/D of this aerofoil occurs at 6.5 where its lift coefficient is equal to 1.327. The lift coefficient required for cruise is about 1.32, so this aerofoil is selected as the original aerofoil because of its maximum L/D at the cruise lift coefficient.

Figure 9. The L/D of the original aerofoil.

The unit chord aerofoil was parametrised using the CST parametrisation method, based on the expression^{(Reference Guan and Li11)}

(1) \begin{equation}Z(x)=x^{N1}(1-x) ^{N2}\sum_{i=0}^nA_iS(x)_i+0.5x\bigtriangleup thTE. \end{equation}

where $\sum_{i=0}^nA_iS(x)_i$ is the shape function, Z(x) is the Z coordinate of the mean camber line, N1 and N2 determine the shape of the aerofoil (for this aerofoil, $N1=0.5$ and $N2=1$) and A$_i$ are the control parameters. The sixth-order Bernstein function is adopted as the shape function, that is, $n=6$, thus A0–A6 are introduced as seven control parameters to control the upper and lower wing surfaces. Among these, the change of the sixth control parameter A6 on the leading edge of the aerofoil is small and can be ignored. It can be used as a control parameter for the shape of the trailing edge. By changing the value of the sixth parameter A6 of the mean camber line expression while maintaining the same thickness distribution, bending the trailing edge to change the camber without changing the thickness can be simulated. The sixth parameter A6 corresponding to the initial aerofoil mean camber line is 0.0745. To ensure the rationality of the aerofoil change, A6’s change range is set as [–0.1, 0.4], and the corresponding aerofoil change range is shown in Fig. 10.

Figure 10. The aerofoil change range.

4.1 Balance equation, aerodynamic model and engine model

4.1.1 Balance equation

The balance equations in the climb stage are as follows:

(2) \begin{equation}T\sin\alpha+L=W\cos\gamma+ma_x,\end{equation}

(3) \begin{equation}T\cos\alpha-D=W\sin\gamma+ma_x.\end{equation}

The balance equations in the cruise stage are as follows:

(4) \begin{equation}T\sin\alpha+L=W,\end{equation}

(5) \begin{equation}T\cos\alpha-D=ma_x.\end{equation}

4.1.2 Aerodynamic model

According to the ‘Aerodynamics Manual’, the lifting coefficient of a high-aspect-ratio aircraft can be calculated using Equation (7), assuming that the contribution of the fuselage to the lift is negligible. In this article, the wing has no twist. Thus, the whole UAV lift calculation model is established as Equation (8). The coefficients $C_{yswing}^\alpha$ and $C_{yhtail}^{\alpha}$ can be calculated from the aerofoil correlation coefficient using Equations (9) and (10), assuming an elliptical lift distribution. Meanwhile, the downwash angle can be calculated using Equation (11)⁽¹⁶⁾.

(6) \begin{equation}L=O.5\rho V^2S_WC_y,\end{equation}

(7) \begin{equation}C_y=C_{yswing}^\alpha(\alpha-\alpha_0)+C_{yhtail}^\alpha(1-\varepsilon)\alpha\frac{s_{ht}}{S_W},\end{equation}

(8) \begin{equation}C_y=C_{yswing}^\alpha(\alpha-\alpha_0)+0.183C_{yhtail}^\alpha(1-\varepsilon)\alpha,\end{equation}

(9) \begin{equation}C_{yswing}^\alpha=\frac{C_{foil}^\alpha}{1+1.5\frac{C_{foil}^\alpha}{\pi A}},\end{equation}

(10) \begin{equation}C_{yhtail}^\alpha=\frac{C_{fhtail}^\alpha}{1+1.5\frac{C_{fhtail}^\alpha}{\pi A}},\end{equation}

(11) \begin{equation}\varepsilon=0.159\frac{C_{yswing}^a}{C_{foil}^\alpha}.\end{equation}

The drag coefficient of a high-aspect-ratio aircraft is calculated using Equation (13). $C_{D0}$ is divided into the wing drag coefficient at zero lift $C_{D0wing}$ and the fuselage drag coefficient at zero lift $C_{D0fuselage}$ as shown in Equation (14). $C_{D0wing}$ is calculated using Equation (15). $C_{Di}$ can be calculated using Equation (16), and $K_1$ and $K_2$ are empirical coefficients. The whole UAV $C_{D0}$ and $C_{Di}$ can be calculated using Equations (17) and (18)⁽¹⁶⁾.

(12) \begin{equation}D=O.5\rho V^2S_WC_D,\end{equation}

(13) \begin{equation}C_D=C_{D0}+C_{Di},\end{equation}

(14) \begin{equation}C_{D0}=C_{D0wing}+C_{D0fuselage}\frac{s_{fuselage}}{S_W},\end{equation}

(15) \begin{equation}C_{D0wing}=2(1+1.44c+2c^2)\, (1-0.09 {\rm M}^2),\end{equation}

(16) \begin{equation}C_{Di}=K_1C_{yswing}^2+K_2C_{yhtail}^2,\end{equation}

(17) \begin{equation}C_{D0}=0.0100633+0.0092(1-0.09{\rm M}^2),\end{equation}

(18) \begin{equation}C_{Di}=0.936\frac{C_{yswing}^2}{47.91}+0.183\frac{C_{yhtail}^2}{20.7}.\end{equation}

The aerofoil’s aerodynamic coefficient data were generated using Xfoil for various cambers and flight Mach and Reynolds numbers. The invariable setting used in Xfoil is an ‘Ncrit’ value of 9, due to its very good correlation with experiment according to research on the eN method of transition prediction by Smith and Gambeoni^{(Reference Van Ingen17)}. The Reynolds and Mach number settings change with the flight conditions.

4.1.3 Engine model

The variation of the output power of the ROTAX 914F/UL engine with RPM is shown in Fig. 11^{(Reference Qin, Li and Wang12)}. The relationship between the RPM and fuel consumption is shown in Fig. 12^{(Reference Qin, Li and Wang12)}, where A indicates the engine take-off state and B the engine continuous throttle performance. The change in the output power of the engine with altitude is shown in Fig. 13^{(Reference Qin, Li and Wang12)}. The relationship between the fuel consumption rate s (L/h) and the output power P is obtained as follows:

(19) \begin{equation}s=10.566+0.26P{\rm (A),}\end{equation}

(20) \begin{equation}s=5.199+0.29P{\rm (B).}\end{equation}

Figure 11. Change of engine output power with RPM.

Figure 12. Change of fuel consumption with RPM.

Figure 13. Change of engine output power with altitude.

4.2 Decision-making method

In the decision-making process, the particle swarm optimisation algorithm is adopted, the weight factor is 0.8 and both learning factors are set to 1.5. The decision-making process is shown in Fig. 14. First, the original particle swarm is obtained, then the location of each particle is adjusted one by one according to the force balance constraint. Second, the fitness of each particle is calculated using the model established in this article, to determine the best fitness of the original particle swarm and the best fitness of each particle. The location of each particle is then changed according to the location of the particle with the best particle swarm fitness and the past location corresponding to the best-ever fitness of that particle. Then, the above steps are repeated until the prescribed number of iterations is reached. Throughout this process, the smart flight operation can be simulated by adjusting the UAV shape, the angle-of-attack $\alpha$ and the flight speed V according to the flight environment.

Figure 14. Morphing decision method.

4.3 Decision objectives

The purpose of the climb stage is to climb to the cruise altitude rapidly. Therefore, the morphing decision-making goal in the climb stage is to maximise the rate of climb, expressed as follows: Max(V$_y$).

During the cruise stage, the ‘instantaneous endurance’ and the endurance E are calculated as follows; the morphing decision-making goal in the cruise stage is to maximise the endurance E:

(21) \begin{equation}\frac{dE}{dW}=-\frac{1}{CT}=-\frac{n_p}{C_{Power}VT},\end{equation}

(22) \begin{equation}E=\int_{W_i}^{W_f}-\frac{1}{CT}dw.\end{equation}

5.1 Flight process simulation

In the climb stage, the true airspeed corresponding to the maximum climb rate changes with altitude. For the smart morphing long-endurance UAV designed herein, the climb stage starts at 0km with a flight speed of 127.8km/h and the climb altitude is 7km. During the whole climb stage, the engine is working at its maximum output power condition.

In the cruise stage, the smart morphing long-endurance UAV cruises at the same altitude of 7km but with a variable angle-of-attack, speed and shape parameter A6, to achieve the goal of maximum endurance (14).

The initial weight of the long-endurance UAV is 1020kg, and the available fuel for the two stages is 220kg.

5.2 Smart morphing simulation

In the climb stage, the main variable parameter is the flight altitude. Therefore, the smart morphing simulation is carried out for every kilometre of altitude. The smart morphing objective is to maximise the climb rate, while the decision factors are the aerofoil shape control parameter A6 and the flight angle-of-attack $\alpha$. The changes of the aerofoil parameter A6 and the angle-of-attack $\alpha$ during climb are shown in Fig. 15. The corresponding change in the flight speed V is shown in Fig. 16. Figure 15 shows that, with increasing flight altitude, the optimal angle-of-attack $\alpha$ and the aerofoil shape control parameter A6 change with altitude regularly and obviously. With increasing altitude, the optimal climb mode exhibits a continuously reduced angle-of-attack and increased shape control parameter A6.

Figure 15. Changes of the aerofoil shape parameter A6 and the angle-of-attack $\alpha$ with altitude in the climb stage.

Figure 16. Corresponding change of flight speed with altitude in the climb stage.

The main parameter varying during the cruise stage is weight, and the smart morphing decision-making simulation is carried out for every 20kg of fuel consumed. The smart morphing objective is to minimise the fuel consumption per unit time, s. The decision factors are the aerofoil shape control parameter A6, the angle-of-attack $\alpha$ and the flight speed V. The variation of the aerofoil shape parameter A6 and the angle-of-attack $\alpha$ with the UAV weight is shown in Fig. 17. The corresponding change of flight speed is shown in Fig. 18. It can be seen that, during the cruise stage, with the consumption of fuel, the optimal cruise mode is to reduce the aerofoil shape parameter A6, angle-of-attack $\alpha$ and flight speed V continuously. Compared with the climb stage, the variation of the aerofoil shape control parameter A6 and the angle-of-attack $\alpha$ during the cruise stage is smaller because the weight change has less impact than the altitude. Also, the value of A6 needed for improving endurance is also larger than during the climb stage. This occurs because reducing the drag can improve the endurance, so the larger A6 is, the less camber the aerofoil has, which means that $C_{Di}$ can be reduced.

Figure 17. Changes of A6 and $\alpha$ with weight in the cruise stage.

Figure 18. Change of V with weight in the cruise stage.

5.3 Smart morphing effect on endurance improvement

The climb rate V$_y $ of the smart morphing long-endurance UAV is compared with the climb rate V$_{y0}$ of the long-endurance UAV without smart morphing technology in Fig. 19, revealing an increase in the average climb rate by about 0.16%. The fuel consumption rate of the engine in the climb stage is 20.625kg/h. The total fuel consumption in the climb stage is calculated as follows, where V$_y $ is calculated at every 1km of altitude:

(23) \begin{equation}\bigtriangleup W=\sum_{i=1}^7\bigtriangleup W_i=\sum_{i=1}^7\frac{20.625}{V_y}.\end{equation}

Figure 19. Change of the smart morphing long-endurance UAV climb rate with altitude compared with the long-endurance UAV without smart morphing.

The calculation shows that, in the climb stage, the fuel consumption of the smart morphing UAV is 11.47kg, representing a reduction by 0.02kg compared with the long-endurance UAV without smart morphing. The saved fuel can be used in the cruise stage to extend navigation. This shows that, in the climb stage, the use of smart morphing has a small effect on the climb rate. At the same time, as the climb altitude is only 7km, the fuel saved by the smart morphing throughout the whole climb stage is not obvious.

During the cruise stage, the fuel consumption per unit time (kg/h) of the UAV with and without smart morphing varies with the UAV weight as shown in Fig. 20. It can be seen that the average fuel consumption per unit time (kg/h) is reduced by 1.3% when adopting smart morphing. The endurance is calculated as follows, where E is calculated for every 20kg of fuel consumed:

(24) \begin{equation}E=\sum_{w_i=1004}^{W_f=749}\frac{20}{dW}.\end{equation}

Figure 20. Change of the smart morphing long-endurance UAV fuel consumption rate (kg/h) with weight in the cruise stage compared with the long-endurance UAV without smart morphing.

The calculation results show that, with the 208kg available fuel, the endurance of the UAV without the smart morphing is 18.1h, while the endurance after adopting smart morphing is 18.85h. The endurance of the long-endurance UAV in the cruise stage increases by 3.7% in total when using the smart morphing method.