The research on wing sail of a land-yacht robot

Abstract

A wind-driven land-yacht robot which will be applied in polar expedition is presented in this article. As the main power of robot is provided by wing sail, improving the efficiency of wing sail is the key for its motion. Wing sail is composed of airfoil, so airfoil theory is researched first, and then several airfoils and their aerodynamic performance are compared, and a high-efficiency airfoil is selected. After that, overturning torque and start wind speed of robot are analyzed to determine the size of the wing sail. At last, the wing sail is manufactured and checked, and it is tested by start wind speed experiments, running speed experiments, steering motion, and obstacle avoidance experiments. The minimum start wind speed is 6 m/s. When wind speed is 10.3 m/s and angle of attack is 90°, running velocity of robot is 1.285 m/s. A land-yacht robot can run steering motion well and avoid obstacle to the target. The result shows that wing sail satisfies the motion requirement of land-yacht robot.

Introduction

Antarctic expedition plays an important part in scientific research, energy, climate, environment, and so on. But the extremely hostile environment of Antarctic is cruel for scientists, and it greatly restricts scientific exploration. Compared to vast Antarctica, people activities are limited in a very small scope. To overcome the difficulties, robot has become an important tool. The development and deployment of autonomous robots for a number of applications have been successfully completed. For example, the quadruped walking robot Dante-1, the mobile robot Nomad, the Robot Antartico di Superficie (RAS), the cool robot, and the Prism (Polar Radar for Ice Sheet Measurements) are taken and applied in Antarctic expedition.^1–5 However, most of these robots are powered by batteries or fuel.^6–8 Electrical or combustion engine deployed in autonomous robots must suffer severe limitations on endurance. The purpose of long-term expedition for autonomous robots is still in initial stage. So, new energy is needed to replace the traditional way.

As we know, there is abundant wind resource in Antarctica, and it is widely distributed with high average wind speed (the maximum wind speed is 160 km/h). Wind energy has been continuously considered as a green, available, and economical alternative source of energy. For centuries, the transformed wind energy to drag force has been used for transportation in watercrafts. Wind energy contribution ranges from the development of agriculture to the improvement of human transportation; from ancient windmills to recent electricity energy. Thus, it is proven as an attractive prospect for investigation, and it is applied in planetary exploration, ocean exploration, polar expedition, and so on in recent years by many researchers. American NASA JPL developed direct wind-driven inflatable spherical robot used in polar expedition; American NASA Langley researched on the Tumbleweed Rover for planetary exploration, including TumbleCup, Dandelion, and BoxKite. ⁹ A Windsurfing & Sled robot is introduced in Antarctic exploration. ¹⁰

In comparison with wind-driven robots, we know that the form of sailing is better than spherical robot in autonomous movement, attitude controllability, and efficiency. Sail commonly includes rigid wing and cloth sail, and it is widely used in sailing, land yacht, and unmanned autonomous surface craft. Traditional sails are mostly soft cloth sails. After the scholar PF Rynne from Florida Atlantic University, ¹¹ M Neal from Aberystwyth University, ¹² M Khayyat from Sharif University of Technology, ¹³ and AW Blakeley from University of Auckland ¹⁴ researched and compared soft cloth sails and rigid wing sails, and the results showed that the latter was better in aerodynamic performance and the soft cloth sails easily rolled over when it encountered strong wind. Although a rigid sail was applied in Windsurfing & Sled robot, ¹⁰ it was similar to soft cloth sails in the structure, and the efficiency is not very high on a whole.

As sail provides the main power for wind-driven robot, improving the efficiency of sail is a key point. Based on this, the sail was designed in the form of airfoil, which resembles an airplane. The wing-sail robot, which was researched in Concordia University, ¹⁵ Canada, used NACA0012 symmetrical airfoil to drive forward. Height of the wing sail was 1000 mm and chord length was 500 mm. A proportion of 1:4 robot prototype was manufactured. When wind speed reaches 20.1 m/s, it can obtain the maximum initial acceleration of 3.9 ms⁻². In recent years, NALSA ¹⁶ held activity across the dry lakebed and desert terrain. The vehicle was driven by lightweight and efficient sail. The Ecotricity Greenbird ¹⁷ combines the advantages of airplane wing and F1 racing car. There is no engineer and it is not consume any fuel which is driven by wind. In 2009, it refreshed the wind-driven sailing car speed record and reached 202.9 km/h in Neptune’s dry lake, California. Dodd Mars Sailor was researched in Virginia Air and Space Center. ⁹ It was designed according to some historical land sailor. The aim is intended to exploration of Mars. The wing-sail design used a small aspect ratio. Rigid and compact arrangement of the wing sail made the sailor easy to drive. A variety of wing sails was applied in unmanned surface vessels for oceanographers and climate scientists. ¹²

The previous structures used three wheels. It is easy to overturn, no enough stability when it moves, and not easy to control the direction. The Dodd Mars Sailor used four wheels, but it did not consider steering structure. For these reasons, a wing sail will be used in four wheels wind-driven land-yacht robot. Considering the stability performance and speed requirements of the robot in the Antarctic environment, NACA0012 wing sail and sails of surface vessels may not adapt to land-yacht robot. So, a wing sail is designed and presented for the land-yacht robot in this article.

Mechanism of land-yacht robot

Land-yacht robot is mainly composed of steering gear, wing sail, vehicle frame, a dual-front-wheel steering mechanism, wind sensor, four wheels, and control unit as shown in Figure 1. The hull is an aluminum frame structure that would efficiently eliminate the hull’s interference to air motions, that is, there is no thrust force deriving from the hull. The studding sail is fixed to the output shaft of the servo motor and guided by pillow-block bearings so that it can rotate from 0° to 360° to the hull by controlling the servo motor. In addition, the land yacht has four wheels: two of them are part of the dual-front-wheel steering mechanism which connects with the steering engine to achieve turning movement, while the other two are connected by a long axle to prevent the land yacht from capsizing and to ensure its stability.

Figure 1.

Schematic diagram of land yacht.

Airfoil design and aerodynamic characteristics

The common airfoil family includes NACA, DU, FFA-W, and RIS series. Comparing aerodynamic characteristics thin airfoil and thick airfoil, thin airfoil can produce more lift force, but its pressure is distributed in smaller range in the leading edge; thick airfoil’s pressure distributes uniformly, but lift force is less than thin airfoil. Considering the manufacture and strength of the wing sail used in Antarctic environment, airfoil thickness remains constant or changes little, so the airfoil of moderate thickness is more suitable. For these reasons, four-digit NACA series airfoil is selected as basic airfoil. The optimum airfoil is selected and designed according to thickness, force, angle of attack, wind speed, and so on.

Four-digit NACA series airfoil can be expressed by the upper and lower surface coordinates. ¹⁸ It shown as follows

$$\begin{array}{c}\multicolumn{1}{c}{y_t=\pm 5t(0.2969\sqrt{x}-0.1260x-0.3516x^2}\\ \multicolumn{1}{c}{+0.2843x^3-0.1015x^4)}\end{array}$$

(1)

Equation of airfoil camber

$$y_c=\frac{m}{p^2}(2\mathrm{px}-x^2)0\le x\le p$$

(2)

$$y_c=\frac{m}{{(1-p)}^2}[(1-2p)+2\mathrm{px}-x^2]p\le x\le c$$

(3)

where x is the coordinate in length, from 0 to c; y_t is the airfoil thickness; y_c is the airfoil camber; t is the maximum thickness; m is the maximum camber; and p is the position of maximum camber. According to equations (1)–(3), airfoil is uniquely determined by the variables m, p, and t, and these are chosen as design variables.

According to the working condition of robot, harsh environment of Antarctic, and the changing wind speed and direction, if wind speed is too large, robot is easily overturned. At this moment, security strategy should be taken and the angle of attack of the wing sail should be made zero, so that the force of the wing sail is minimized to avoid danger. For this reason, symmetrical airfoil is taken into account. As this, m = 0 and p = 0.

According to the characteristics of thick and thin airfoils, moderate thickness airfoil is chosen; so, we select t ₁ = 0.18, t ₂ = 0.16, and t ₃ = 0.14. These airfoils are NACA0018, NACA0016, and NACA0014.

We compare the aerodynamic performance of these three kinds of airfoils in Computational Fluid Dynamics (CFD). The Gambit is used to generate mesh grid. In meshing step, the leading edge of computational mesh is enlarged to 10 times of the airfoil’s chord length and the trailing edge of computational mesh is enlarged to 20 times. The first layer of mesh height is 0.005 m, and the total grids are 195,600. The boundary conditions are velocity inlet and pressure outlet. Airfoil surface boundary is no-slip. Pressure–velocity coupling uses SIMPLE algorithm, pressure discrete uses standard format, and momentum discrete and turbulent viscosity correction use second-order upwind (Figure 2).

Figure 2.

Computational mesh of airfoil.

Computation results and analysis

In order to analyze the influence of changing angle of attack on airfoil aerodynamic performance, lift coefficient C_l and drag coefficient C_d are computed in this article under the angle of attack 0°–25°; then, the curves expressed change tendency. In the same condition, we also compare the computation and experimental values. The results are shown in Figure 3.

Figure 3.

Calculated and test values of different thickness.

From Figure 3, in these airfoils, when the angle of attack α < 11, the computation lift coefficient and drag coefficient of airfoil are close to test values. It shows that computation in CFD is accurate and credible. When the angle of attack α > 11, the calculated lift coefficient is larger than test values and drag coefficient is smaller than test values. The maximum error of lift and drag coefficient is shown in Table 1.

Table 1.

Maximum error of lift and drag coefficients.

Thickness		Angle of attack	Test	Calculation	Error
t = 0.18	CL	16	0.846	0.9394	0.093
	CD	16	0.304	0.221	0.083
t = 0.16	CL	15	0.779	0.881	0.102
	CD	14	0.281	0.1804	0.1
t = 0.14	CL	14	0.722	0.839	0.117
	CD	16	0.351	0.216	0.135

Lift–drag ratio curve

Lift–drag ratios of three airfoils are shown in Figure 4. Lift–drag ratio reflects aerodynamic performance of airfoil, the larger the better. The maximum value of t = 0.18 is 8.05 when the angle of attack α is 7. The maximum value of t = 0.16 is 7.58 when the angle of attack α is 8, and the airfoil t = 0.14 is 7.02 when the angle of attack α is 7. Lift–drag ratio reaches to the maximum quickly and then drops very fast as the angle of attack increases. The reasons are airfoil stalling and drag coefficient increasing rapidly. Both of them make a significant reduction.

Figure 4.

Lift–drag ratios of different thickness.

Considering the robot working environment, change in wind speed is great. For this reason, airfoil aerodynamic performance is compared in different Reynolds. The maximum deviation in different Reynolds is shown in Table 2. The maximum deviation of lift coefficient is 0.081, 0.092, and 0.108 in the same angle of attack. The maximum deviation of drag coefficient is 0.041, 0.052, and 0.058. The lift coefficient and drag coefficient change tendency of t = 0.18 in different Reynolds is shown in Figure 5. When the angle of attack is small, lift and drag coefficients are almost the same. When the angle of attack is greater than 10°, the difference is significantly slow. The other two were similar. It showed that there was little effect on lift and drag coefficients when Reynolds changes. The data of airfoil t = 0.18 are the minimum.

Table 2.

Maximum deviation in different Reynolds.

Airfoil	Lift coefficient	Maximum deviation at the same angle of attack	Drag coefficient	Maximum deviation at the same angle of attack
t = 0.18	CL	0.081	CD	0.041
t = 0.16		0.092		0.052
t = 0.14		0.108		0.058

Figure 5.

Lift and drag coefficient change tendency of t = 0.18 in different Reynolds.

The above analysis shows that airfoil t = 0.18 possesses higher lift–drag ratio, lift coefficient, and lower roughness sensitivity. So, the airfoil is chosen to constitute wing sail. In contrast to NACA airfoil family, the NACA0018 satisfies the wing-sail requirement.

Mechanical analysis of wing sail

When wind acts on the robot, the force and speed analyses of the wing sail are shown in Figure 6.

Figure 6.

Force and speed analyses of wing sail.

where $\theta$ is the angle between the heading and the apparent wind, $\varphi$ is the angle between the true wind and the apparent wind, $\beta$ is the angle between the heading and the true wind, $\alpha$ is the angle of attack, and γ is the angle of the wing sail. The density of air is $\rho$ and the area of the wing sail is $A_s$ .

As we know from the hydrodynamics, under the influences of apparent wind speed, wing sail generates a lift force $F_L$ vertical to the apparent wind and a drag force $F_D$ along the apparent wind. $F_L$ and $F_D$ can be decomposed into thrust $F_T$ and lateral force $F_H$ . $F_T$ is parallel to the heading direction and $F_H$ is perpendicular to heading direction. So, $F_T$ pushes the robot forward and $F_H$ makes it to overturn and generates heeling moment.

When the robot is completely downwind, the wind angle is 0° and clockwise is positive. In Cartesian coordinate system, the thrust and lateral forces of the wing sail affect the robot pedestal. It is expressed as follows

$$\begin{array}{c}\multicolumn{1}{c}{F_L=\frac{1}{2}{C}_L\rho V^2{A}_s}\\ \multicolumn{1}{c}{F_D=\frac{1}{2}{C}_D\rho V^2{A}_s}\end{array}$$

(4)

$$\begin{array}{c}\multicolumn{1}{c}{F_T=F_L\sin \theta -F_D\sin \theta }\\ \multicolumn{1}{c}{F_H=F_L\cos \theta +F_D\sin \theta }\end{array}$$

(5)

$$\begin{array}{c}\multicolumn{1}{c}{C_T=C_L\sin \theta -C_D\cos \theta }\\ \multicolumn{1}{c}{C_H=C_L\cos \theta +C_D\sin \theta }\end{array}$$

(6)

Typically, the aerodynamics of the wing sail is obtained by wind tunnel experiment, and then it is expressed as the polar chart of the wing sail, as shown in Figure 6. $C_L$ and $C_D$ can be represented in the form of function

$$\begin{array}{c}\multicolumn{1}{c}{C_L=f(\alpha ,\lambda ,\nu )}\\ \multicolumn{1}{c}{C_D=g(\alpha ,\lambda ,\nu )}\end{array}$$

(7)

where $\nu$ is the camber ratio of sail, $\lambda$ is the aspect ratio of sail, and $\alpha$ is the angle of attack.

So, equation (6) change into equation (8)

$$\{\begin{array}{c}\multicolumn{1}{c}{C_T=C_L\sin \theta -C_D\cos \theta =f(\alpha ,\lambda ,\nu )\sin \theta -g(\alpha ,\lambda ,\nu )\cos \theta }\\ \multicolumn{1}{c}{C_H=C_L\sin \theta +C_D\cos \theta =f(\alpha ,\lambda ,\nu )\sin \theta +g(\alpha ,\lambda ,\nu )\cos \theta }\end{array}$$

(8)

In a certain $\theta$ value, the changing angle of attack $\alpha$ , the curve of $C_T$ , and $\alpha$ are obtained. If $C_T$ acquires maximum under some angle of attack $\alpha$ , this would be considered as the best angle of attack. It is an extreme point on the curve. It can be expressed as equation (9)

$$\frac{\partial f}{\partial \alpha }\sin \theta -\frac{\partial g}{\partial \alpha }\cos \theta =0$$

(9)

The angle of attack $\alpha$ can be calculated by the interpolation method. The best angle of attack is ${\alpha }_{\mathrm{opt}}=\alpha$ .

At the same time, the best wing-sail installation angle ${\phi }_{\mathrm{opt}}$ can be obtained, which is the angle of the wing sail

$${\phi }_{\mathrm{opt}}=90-\theta +\alpha$$

(10)

From equation (10), the angle of attack can be controlled well (Figure 7).

Figure 7.

Block diagram of wing-sail control system.

where $\rho$ is the air density

$$\rho =1.293\times \frac{273.15P_r}{(273.15+T_r)·P_s}$$

(11)

where $P_r$ is the actual atmospheric pressure, $T_r$ is the temperature, and $P_s$ is the standard atmospheric pressure, $1.01\times {10}^5\mathrm{Pa}$ .

$V$ is the apparent wind, which is the vector between true wind $V_c$ and forward velocity $V_s$ , $V^{\to }=\overrightarrow{V_c}+\overrightarrow{V_s}$ . The velocity vector triangle $\Delta \mathrm{AOB}$ in Figure 6, according to cosine theorem, can be expressed as follows

$$\{\begin{array}{c}\hfill V={(V_c^2+V_s^2+2V_c·V_s\cos \beta )}^{\frac{1}{2}}\hfill \\ \multicolumn{1}{c}{\varphi =\arcsin \left(\frac{V_s}{V}\sin \beta \right)}\end{array}$$

(12)

From equations (4)–(6), the lateral force of area $\mathrm{dA}$ is

$$d{F}_H=\frac{1}{2}\rho V^2(C_L\cos \theta +C_D\sin \theta )\mathrm{dA}$$

(13)

The wing sail is equivalent to a rectangle, whose length is $H_s$ and width is $W_s$ . So, area $\mathrm{dA}$ is

$$\mathrm{dA}=W_s·\mathrm{dh}=\frac{A_s}{H_s}\mathrm{dh}$$

(14)

where $H_s$ denotes the height of the wing sail.

Lateral torque of the wing sail is calculated as follows

$$M=\underset{h_i}{\overset{h_e}{\int }}\mathrm{dM}=\underset{h_i}{\overset{h_e}{\int }}h·d{F}_H$$

(15)

where $h_i=0.1+{\Delta }_h$ is the installation height of bottom and ${\Delta }_h$ is the distance from wing sail to shaft. So

$$\begin{array}{c}\multicolumn{1}{c}{M=\rho ·\frac{V^2{A}_s(C_L\cos \theta +C_D\sin \theta )}{4H_s}}\\ \multicolumn{1}{c}{[H_s^2-0.1^2+2{\Delta }_h(H_s-0.1)]}\end{array}$$

(16)

When the lateral wind is totally on the wing sail, the lateral torque of robot is the biggest, and it is the most dangerous. If the forward velocity of robot is 0, the apparent wind is maximum, that is, $V=V_c$ . At this moment, $\theta =90°$ and the angle of attack $\alpha =90°$ . According to Figure 6, $C_D=2.051$ . So, equation (16) is modified as

$$M_{\max }=\rho ·C_D·\frac{V_{c,\max }^2{A}_s}{H_s}[H_s^2-0.1^2+2{\Delta }_h(H_s-0.1)]$$

(17)

Robot is unstable as there is lateral torque during the motion. Stability is determined by the distance of rear wheels. The mechanical analysis of robot pedestal is shown in Figure 8. $2L_2$ is the front wheel distance and $2L_3$ is the rear wheel distance.

Figure 8.

Mechanical analysis of robot pedestal.

So, robot can withstand the overturning moment which is as follows:

When $G_A$ is shifted to the front wheel

$$\begin{array}{c}\multicolumn{1}{c}{{F″}_A=G_A}\\ \multicolumn{1}{c}{{M″}_A=G_A·L_1}\\ \multicolumn{1}{c}{M_{\mathrm{front}}={F\prime }_A·L_2}\end{array}$$

(18)

When $G_A$ is shifted to the rear wheel

$$\begin{array}{c}\multicolumn{1}{c}{{F\prime }_A=G_A}\\ \multicolumn{1}{c}{{M\prime }_A=G_A·L_1}\\ \multicolumn{1}{c}{M_{\mathrm{rear}}={F″}_A·L_3}\end{array}$$

(19)

Land-yacht robot in which the lateral overturning did not occur should be satisfied

$$min\{M_{\mathrm{rear}},M_{\mathrm{front}}\}\ge M_{max}$$

(20)

Land-yacht robot in which the front and rear overturning did not occur should be satisfied

$$min\{M{\prime }_A,{M″}_A\}\ge M_{max}$$

(21)

$$M_{c,min}=\{M_{\mathrm{rear}},M_{\mathrm{front}},{M\prime }_A,{M″}_A\}$$

(22)

$G_A$ is the total load of robot

$$\{\begin{array}{c}\hfill G_{A0}=(M_B+M_W+M_C+M_S+M_P)g\hfill \\ \multicolumn{1}{c}{G_A=G_{A0}+M_{\mathrm{BW}}g}\end{array}$$

(23)

where $M_B$ is the mass of pedestal; $M_W$ is the wing-sail mass; $M_C$ is the controller mass; $M_S$ is the total sensor mass; $M_P$ is the total power mass; and $M_{\mathrm{BW}}$ is the total counterweight mass, $0\le M_{\mathrm{BW}}\le 8\mathrm{kg}$ .

According to the moment equilibrium, the condition $M_{c,\min }\ge M_{\max }$ must be satisfied. The system parameters are listed in Table 3.

Table 3.

System parameters of maximum lateral torque.

$P_r$	$T_r$	$V_{c,\max }$	$L_2$	$L_3$	$\Delta h$	$G_{A0}$
$1.01\times {10}^5\mathrm{Pa}$	$-{30}^{°}C$	$20m/s$	$0.225m$	$0.45m$	$0.10m$	$215.82N$

Considering the working condition, if the width of the wing sail is too large, it may generate too much lateral torque and make robot overturn; if it is too small, there is no enough thrust. According to Mirzaei and Rad, ¹⁵ the ratio of length and width is 4, that is, the aspect ratio is 4, W_s /H_s  = 1:4.

Combining equations (18)–(23), we can solve H_s  = 1.03, so we select H_s  = 1 and W_s  = 0.25.

Start wind speed

From Figure 6, we know that $F_T\ge 0$ is the driving force and $F_T<0$ is the drag force. The angle of attack can be expressed as follows

$$\{\begin{array}{c}\hfill \alpha =\beta -\varphi -\gamma \hfill \\ \multicolumn{1}{c}{\theta =\beta -\varphi }\end{array}$$

(24)

Combine equations (4)–(6) and (24)

$$\{\begin{array}{c}\hfill F_T=\rho V^2{A}_s[C_L\sin (\beta -\varphi )-C_D\cos (\beta -\varphi )]\hfill \\ \multicolumn{1}{c}{F_H=\rho V^2{A}_s[C_L\cos (\beta -\varphi )+C_D\sin (\beta -\varphi )]}\end{array}$$

(25)

Robot is a four-wheel structure, so it has rolling friction when running. It can start in lower wind-driven force

$$F_f={\mu }_s·N$$

(26)

where ${\mu }_s$ is the rolling friction coefficient and $N$ is the support force

$$N=G_A=G_{A0}+M_{\mathrm{Bw}}g$$

(27)

So, robot starts when $F_T\ge F_f$ in a specific temperature $T_r$ . At this moment, the forward speed $V_s=0$ ; from equation (12), $v=V_c$ , $\varphi =0$ , and ${\alpha }_w=\beta -\gamma$ . Combining equations (4)–(6) and (25)–(27), the start wind speed satisfies the following relationship (Table 4)

$$\{\begin{array}{c}\multicolumn{1}{c}{V_{c0}\ge \sqrt{\frac{{\mu }_s(273.15+{\mathrm{T}}_{\mathrm{r}})(215.82+9.81M_{\mathrm{Bw}})}{92.50(C_L\sin \beta -C_D\cos \beta )}}}\\ \multicolumn{1}{c}{C_L\sin \beta -C_D\cos \beta >0}\end{array}$$

(28)

Table 4.

System parameters of start wind speed.

$T_r$	$C_L$	$\beta$	${\mu }_S$	$M_{\mathrm{Bw}}$
$-{30}^{°}C$	$1.05$	${90}^{°}$	$0.05$	$8\mathrm{kg}$

Solving the above equation, we obtain $V_{c0}\ge 5.96$ . So, the minimum wind speed is 6 m/s. The average wind speed in Antarctica is approximately 17.8 m/s. so, it satisfies the requirement of start wind speed.

Wing-sail manufacture

Optimization model of the wing sail is shown in Figure 9.

Figure 9.

Optimization model of wing sail.

Selection of aspect ratio

English Aberystwyth University ¹² has manufactured four sailing boats. They selected different sizes of wing sail. Aspect ratio λ is 6.94, 5.35, 3.53, and 4.04, respectively. From their research and analysis, we knew that the final aspect ratio tended to be 4. Sharif University of Technology ¹³ chose λ = 2 as the aspect ratio, as the airfoil was relatively thin. Considering that the airfoil of land yacht has moderate thickness and the application is on land, we chose small aspect ratio. After calculation and comparison, we selected λ = 4 as the aspect ratio.

Wingspan and wing-sail area

The size of the wing sail researched in Sharif University of Technology was 100 cm × 50 cm; the wing sail studied in Florida Atlantic University ¹¹ was large; four wing sails of English Aberystwyth University were 125 cm × 18 cm, 107 cm × 20 cm, 3 m × 85 cm, and 52.5 cm × 13 cm. The weight of the land yacht was about 20 kg. Considering the rolling friction coefficient, drive force, and anti-rollover resistance, the force of the wing sail was about 10 N. After the calculation in CFD and simulation of the wind speed in Antarctic, the size of the wing sail was determined. It was 100 cm ×25 cm, which satisfied the aspect ratio λ = 4.

The wing sail was manufactured by a three-dimensional (3D) printer (see Figure 10). The sizes of the 3D printer is L × W × H = 200 mm ×200 mm × 225 mm. In order to satisfy the processing requirements, the wing sail is divided into five pieces and the height of every piece is 200 mm. Then, each part is connected by glue. The connecting structure is shown in Figure 11.

Figure 10.

Working of 3D printer.

Figure 11.

Connecting structure of wing-sail section.

As the 3D printer, the thickness of the wing sail is 2 mm. For the material, it should be light with low temperature and certain strength, so the polylactic acid (PLA) is applied. The wing sail is supported by single mast. In order to reinforce the strength of the wing sail, there are 10 holes having close contact with the inner wall of the airfoil, which is symmetrical with XZ plane. It is used to mount carbon fiber tube whose diameter $D=6\mathrm{mm}$ . The carbon fiber tube strengthens the rigidity of the wing sail. Around the mast, there are also four holes which uniformly install the carbon fiber tube with the diameter $D=4\mathrm{mm}$ . Hence, in the condition to satisfy the installation requirements and aerodynamics, the mast is close to 0.4 of the airfoil’s chord length. ¹⁹ There is a connecting plate on the wing sail. It separates the wing sail from the robot and makes the mounting height of the wing sail to adjust. So, the model and main parameters of the wing sail are shown in and Figure 12 and Table 5, respectively.

Figure 12.

Wing sail of NACA0018.

Table 5.

Main parameters of wing sail.

Chord	Height (Hs )	Thickness (δ)	Area (AS )	Weight
0.25 m	1 m	2 mm	0.25 m2	2.15 kg

Stress analyses

The wing sail is symmetrical on ZX plane. When the apparent wind speed $V$ is along the normal vector $\overrightarrow{n}$ of ZX plane, the surface pressure of the wing sail is maximum and the mast becomes most dangerous. At this time, the apparent wind speed along the normal vector $\overrightarrow{n}$ is

$$v=V_c\sin \chi -V_s\cos \chi$$

(29)

The surface force of the wing sail is

$$F_{\mathrm{surface}}=\frac{1}{2}\rho v^2{A}_s$$

(30)

where $\chi$ is the angle between the true wind and the wing sail, $P_r$ is the actual atmospheric pressure, $T_r$ is the temperature, $P_s$ is the standard atmospheric pressure, and the maximum true wind is $V_{c,\max }=20\mathrm{m}/\mathrm{s}$ . When the direction of the true wind is perpendicular to the wing sail, $\chi =90°$ and $V_{\max }=V_{c,\max }=20\mathrm{m}/\mathrm{s}$ . Combining equations (29)–(30)

$$F_{\mathrm{surface},\max }=72.63\mathrm{N}$$

In order to ensure that the wing sail is perpendicular to the ground, the mast will bear the shear force from the surface of the wing sail. The stress of the mast is shown in Figure 13.

Figure 13.

Stress of mast.

The surface pressure of the wing sail is simplified to concentrate load at the center

$$F_{\mathrm{surface},max}-\sum _{i=1}^6{F}_i=0$$

(31)

If the mast has a rigid shaft, then the force of every point is equivalent to each other. That is, $F_1=F_2=\cdots =F_i(i=6)$

$$F_{\mathrm{surface},max}-6F_1=0$$

(32)

Considering the safety factor

$$F\prime =S·F_1$$

(33)

If S = 1.4, combining equations (31) and (32), the force of every point is

$$F\prime =16.946\mathrm{N}$$

When the land yacht is running, the bending moment is very important to the wing sail. If the wing sail is one-end fixed, the bending moment is shown in Figure 14.

$$M(c)=\underset{0}{\overset{L}{\int }}q·\mathrm{xdx}=\frac{1}{2}q{L}^2=\frac{1}{2}{F}_{\mathrm{surface},max}{L}^2$$

Figure 14.

Bending moment of one-end fixed.

When the wing sail is both-end fixed, the bending moment is shown in Figure 15.

Figure 15.

Bending moment of both-end fixed.

According to the bending moment formula of the both-end fixed beam, ²⁰ the deformation compatibility condition of cross-sections A and B is that the deflection angle is 0.

$$\begin{array}{c}\multicolumn{1}{c}{{\theta }_A=0}\\ \multicolumn{1}{c}{{\theta }_B=0}\end{array}$$

(34)

Using superimposed method, we can get the deflection angle of cross-sections A and B

$${\theta }_A={\theta }_{A,q}+{\theta }_{A,M_A}+{\theta }_{A,M_B}=\frac{q{L}^3}{24\mathrm{EI}}+\frac{M_{A}L}{3\mathrm{EI}}+\frac{M_{B}L}{6\mathrm{EI}}$$

(35)

$${\theta }_B={\theta }_{B,q}+{\theta }_{B,M_A}+{\theta }_{B,M_B}=\frac{q{L}^3}{24\mathrm{EI}}-\frac{M_{A}L}{6\mathrm{EI}}-\frac{M_{B}L}{3\mathrm{EI}}$$

(36)

Solving equations (34)–(36)

$$\begin{array}{c}\multicolumn{1}{c}{M_A=\frac{q{L}^2}{12}=\frac{F_{\mathrm{surface},max}{L}^2}{12}}\\ \multicolumn{1}{c}{M_B=\frac{q{L}^2}{12}=\frac{F_{\mathrm{surface},max}{L}^2}{12}}\end{array}$$

According to the force balance equation, we can obtain the support reaction forces $F_{\mathrm{Ay}}$ and $F_{\mathrm{By}}$ as

$$F_{\mathrm{By}}·L-\underset{0}{\overset{L}{\int }}\mathrm{qxdx}=0$$

(37)

$$F_{\mathrm{By}}=\frac{1}{2}\mathrm{qL}=\frac{1}{2}{F}_{\mathrm{surface},max}L$$

Similarly

$$F_{\mathrm{Ay}}=\frac{1}{2}\mathrm{qL}=\frac{1}{2}{F}_{\mathrm{surface},max}L$$

Therefore, the equation for bending moment is

$$M(c)=-\underset{0}{\overset{x}{\int }}\mathrm{qxdx}-M_A+F_{\mathrm{Ay}}·x(0\le x\le L)$$

(38)

$$M_{max}(c)=\frac{1}{24}q{L}^2=\frac{1}{24}{F}_{\mathrm{surface},max}{L}^2$$

Stress–strain analysis of the mast is shown in Figures 16 and 17, respectively. Apply load on the mast as shown in Figure 13 and add fixed constraint at the bottom. So, the mast is in the state of cantilever beam model. According to the material mechanics, in the bending moment, “+” denotes tension and “−” denotes compression.

Figure 16.

Stress distribution when one end is fixed.

Figure 17.

Deformation distribution when one end is fixed.

From Figure 16, we know that the point of shape change causes stress concentration easily. The force is maximum, which is the most dangerous section. Position “1” is in compression, ${\sigma }_{1,max}=-43.93\mathrm{MPa}$ . Position “2” is in tension, ${\sigma }_{2,\max }=3.95\mathrm{MPa}$ . Figure 17 shows that the deformation will gradually increase in the axial direction under shear force when the lever is fixed at one side. The maximum deformation of the mast is located in the farthest point away from the fixed end, ${\Delta }_{\max }=1.236\mathrm{mm}$ . Inclination of the mast is as follows

$$\eta =\arctan \left(\frac{{\Delta }_{\max }}{L}\right)=\arctan \left(\frac{1.236}{1000}\right)=0.07°$$

After the mast is mounted on the robot, if the top side of the mast is fixed by a stay cable, it becomes both-end fixed. In this condition, the stress and strain are shown in Figures 18 and 19, respectively. From Figure 18, Positions “1” and “3” are in compression, and the value is $\sigma {\prime }_{1,\max }=-14.85\mathrm{MPa}$ and $\sigma {\prime }_{3,\max }=-8.00\mathrm{MPa}$ , respectively. Positions “2” and “4” are in tension, and the value is $\sigma {\prime }_{2,\max }=\sigma {\prime }_{4,\max }=1.28\mathrm{MPa}$ . Figure 19 shows that the maximum deformation of the mast is in the middle when fixed at both ends. The value is $\Delta {\prime }_{\max }=0.1384\mathrm{mm}$ , so the inclination of the mast is as follows

$$\eta =\arctan \left(\frac{{\Delta \prime }_{\max }}{L}\right)=\arctan \left(\frac{0.1384}{1000}\right)=0.008°$$

Figure 18.

Stress distribution when both ends are fixed.

Figure 19.

Deformation distribution when both ends are fixed.

Material of the mast is aluminum 6061, and its tensile yield strength is 55.2 MPa. According to the mechanics of materials, the compressive strength of the metallic materials is much larger than the tensile yield strength. So, when one end and both ends are fixed, the tensile stress is

$$\begin{array}{c}\multicolumn{1}{c}{max\{|{\sigma }_{1,\max }|,|{\sigma \prime }_{1,\max }|,|{\sigma \prime }_{3,\max }|\}}\\ \multicolumn{1}{c}{<{\sigma }_s,|\sigma {\prime }_{3,\max }|<|\sigma {\prime }_{1,\max }|<|{\sigma }_{1,\max }|}\end{array}$$

The compressive stress is

$$\begin{array}{c}\multicolumn{1}{c}{\max \{{\sigma }_{2,\max },{\sigma \prime }_{2,\max },{\sigma \prime }_{4,\max }\}<\sigma {\prime }_s,\sigma {\prime }_{2,\max }}\\ \multicolumn{1}{c}{=\sigma {\prime }_{4,\max }<{\sigma }_{2,\max }}\end{array}$$

From above, the stress of the mast is better when it is fixed at both ends, and the inclination is $\alpha \prime <<\alpha$ when the wing sail suffers the maximum surface pressure. The smaller the mast inclination, more consistent the aerodynamic properties and theoretical values of the wing sail. Error of autonomous control system will be reduced, and it becomes steadier. Furthermore, the robot works in polar region; but due to maintenance inconvenience and hostile working conditions, the mast safety factor must be greater than that when used in normal engineering applications. To ensure the wing sail’s long-term work, the both-end fixed mast design is selected.

Experiments

Start wind speed

Experimental purpose is the start characteristics of the robot in different angle of attack and different wind speed $V_{\mathrm{cT}}$ . The angle of attack is adjusted by rotating the wing sail, which is controlled by the motor. The wind speed is adjusted by the blower (Figure 20).

Figure 20.

Experimental environment and land-yacht robot.

Experimental device includes the land-yacht robot, an anemometer and the blower, and the control and measurement system. The control and measurement system includes single-chip microcomputer STM32, controller S3C6410, RF chip nRF24L01, inertial navigation xsens MTi, and the GPS. This system is developed in Linux. The system structure is shown in Figure 21 and Figure 22.

Figure 21.

Schematic diagram of measurement and control system.

Figure 22.

Test flow diagrams.

The Global Positioning System (GPS) positions the robot and the inertial navigation records the posture. This information is sent to the single chip and the controller by the RF chip nRF24L01. The single chip records the wind speed, the angle of attack, and the start state. The controller sends the command to the motor, steering gear, senor, and other actuators.

Test methods: (1) the angle between the wind and the wing sail is 90°. The distance of the robot and the blower is changed to obtain different start wind speed and select test points. We set the wind speed $V_{\mathrm{cT}}=6\mathrm{m}/\mathrm{s}$ , $V_{\mathrm{cT}}=6.5\mathrm{m}/\mathrm{s}$ , $V_{\mathrm{cT}}=7\mathrm{m}/\mathrm{s}$ , and $V_{\mathrm{cT}}=7.5\mathrm{m}/\mathrm{s}$ . (2) The angle of attack $\alpha$ is changed to alter the force of the wing sail. We select $\alpha =90°$ , $\alpha =60°$ , and $\alpha =45°$ . The result is shown in Table 6.

Table 6.

Start wind speed in different angle of attack.

$V_{\mathrm{cT}}(m/s)$	$\alpha$
	90°	60°	45°
6	√	×	×
6.5	√	×	×
7	√	√	×
7.5	√	√	√

Result analysis

From the mechanical analysis of the wing sail, we know that $F_T=F_L\sin \theta -F_D\cos \theta$ , where $F_L=C_L(1/2)\rho V^2{A}_S$ , $F_D=C_D(1/2)\rho V^2{A}_S$ , and $V$ is the apparent wind speed. When the robot starts, $V=V_{\mathrm{cT}}$ . As the angle between the wind and the wing sail is 90°, the larger the wind speed $V_{\mathrm{cT}}$ , the greater the thrust produced. When the angle of attack $\alpha$ changes, $S$ is altered. So, $F_{T,\alpha =90°}>F_{T,\alpha =60°}>F_{T,\alpha =45°}$ when the angle of attack is small, and it needs lager start wind. When the angle of attack is 90°, the minimum wind speed is 6 m/s. It is consistent with the computation result.

Running speed experiment

Experimental target is to test the average speed of the robot in different wind speed. Device includes the land-yacht robot, an anemometer, the blower, and the control system. Control system is the same with Figure 21 and Figure 22. The test system contains a Gyroscope inertial navigation, which records the location coordinates to calculate the running distance; a timer, which records the running time. Both of them are connected to a single-chip microcomputer which sends the command of start or end. When the distance and time are obtained, the average speed can be computed. After several test in different wind speed, the result is shown in Table 7.

Table 7.

Running velocity in different wind speed.

Distance	Angle of attack	Start wind speed	Time	Running velocity
4.4 m	90°	6.5 m/s	5.78	0.761
			5.43	0.810
			5.34	0.824
Average			5.52	0.797
4.4 m	90°	8 m/s	4.88	0.902
			5.16	0.853
			4.45	0.989
Average			4.83	0.911
4.4 m	90°	10.3 m/s	4.53	1.325
			4.70	1.277
			4.79	1.253
Average			4.67	1.285

If we keep the distance and wind speed same, the angle of attack of the wing sail changes; the result is shown in Table 8.

Table 8.

Running velocity in different angle of attack.

Distance	Angle of attack	Start wind speed	Time	Running velocity
4.4 m	90°	8 m/s	4.88	0.902
			5.16	0.853
			4.45	0.989
Average			4.83	0.911
4.4 m	60°	8 m/s	7.79	0.565
			7.68	0.573
			7.23	0.609
Average			7.57	0.581
4.4 m	45°	8 m/s	9.32	0.472
			9.87	0.446
			9.76	0.451
Average			9.65	0.456

From the start wind speed test, we know that $F_{T,\alpha =90°}>F_{T,\alpha =60°}>F_{T,\alpha =45°}$ ; the larger the wind speed, the greater the thrust. Comparing the data of the running experiment, we found that the running velocity is proportional to the angle of attack and wind speed. In the same distance and angle of attack, $V_{s,10.3}>V_{s,8}>V_{s,6.5}$ . In the same distance and wind speed, $V_{s,\alpha ={90}^{\mathrm{o}}}>V_{s,\alpha ={60}^{\mathrm{o}}}>V_{s,\alpha ={45}^{\mathrm{o}}}$ . When the wind speed is 10.3 m/s and the angle of attack is 90°, the running velocity of the robot is 1.285 m/s. It can satisfy the requirement of detection and exploration. Even when the wind speed is low, it can keep running in certain velocity.

Steering motion

Robot steering motion capability can be measured by tracking trajectory curve.

Robot gesture refers to the position and orientation of global coordinate system. In Figure 23, the robot position is expressed by (x, y) and the direction angle is $\gamma$ ; so the system parameters of the robot can be represented by $(x_c,y_c,\gamma )$ .

Figure 23.

Kinematical parameters of robot.

The kinematic differential equations of the robot is shown in equation (39)

$$\{\begin{array}{c}\hfill \stackrel{·}{x}=v(t)\cos \gamma \hfill \\ \multicolumn{1}{c}{\stackrel{·}{y}=v(t)\sin \gamma }\\ \multicolumn{1}{c}{\stackrel{·}{\gamma }=\omega }\end{array}$$

(39)

$v(t)$ and $\omega$ are the moving speed and angular velocity, respectively. It can be represented by the following matrix

$$\left[\begin{array}{c}\hfill \stackrel{·}{x}\hfill \\ \multicolumn{1}{c}{\stackrel{·}{y}}\\ \multicolumn{1}{c}{\stackrel{·}{\gamma }}\end{array}\right]=\left[\begin{array}{c}\hfill \begin{array}{c}\hfill \cos \gamma \hfill \\ \multicolumn{1}{c}{\sin \gamma }\\ \multicolumn{1}{c}{0}\end{array}\begin{array}{c}\hfill 0\hfill \\ \multicolumn{1}{c}{0}\\ \multicolumn{1}{c}{1}\end{array}\hfill \end{array}\right]\left[\begin{array}{c}\hfill v(t)\hfill \\ \multicolumn{1}{c}{\omega }\end{array}\right]$$

(40)

If there is a planned trajectory curve S(t) in the global coordinate system, it is constituted by a series of target points. (x_c, y_c ) is the nearest target point from the current location (see Figure 24). The relations between the parameters are shown in equation (41)

$$\begin{array}{c}\multicolumn{1}{c}{\mathrm{dx}=x_c-x}\\ \multicolumn{1}{c}{\mathrm{dy}=y_c-y}\\ \multicolumn{1}{c}{\tan \sigma =\mathrm{dy}/\mathrm{dx}}\\ \multicolumn{1}{c}{\beta =\gamma -\sigma }\\ \multicolumn{1}{c}{D=\sqrt{d{x}^2+d{y}^2}}\end{array}$$

(41)

Figure 24.

Parameters of trajectory tracking model.

Mobile robot is a highly nonlinear time-varying system. In the complex environment, it is difficult for the traditional Proportion Integration Differentiation (PID) controller to achieve the desired effect. However, fuzzy control is a nonlinear control and it belongs to intelligent control. It is not highly dependent on the mathematical model of the controlled object in a fuzzy controller, so it is applied to design the trajectory tracking control system. The overall structure of the fuzzy trajectory tracking control system is shown in Figure 25.

Figure 25.

Fuzzy trajectory tracking control system.

In this control system, the fuzzy controller has four input and output variables. The input variables are D and β. D is the distance between the current position and the target point. β is the angle difference between the current and the desired angles. The outputs are moving speed $v(t)$ and angular velocity $\omega$ . $\beta$ is an important input parameter, and it decides the direction and the angular velocity of the robot.

In turning motion, the experimental environment is shown in Figure 26. We set the land-yacht steering deflection angle δ = 15° and the angle of attack is also 5°, 10°, 15°, and 25°. The purpose is to examine the performance of the wing sail when the land yacht turns. The result is shown in Figure 27.

Figure 26.

Steering motion of land-yacht robot.

Figure 27.

Planned trajectory and running trajectory of steering motion.

Blue line denotes the planned trajectory and red line is the running trajectory of the land yacht. During this process, the driving force which is generated by the wind decomposes into thrust and lateral force. From the experimental result, two trajectories are very close and little difference is found between each other. After the analysis, as the force is generated by the wing sail, the lateral force cannot overcome the centripetal force and the friction, so the curvature of the trajectory is little bigger than the planned trajectory. But at the beginning, both trajectories are almost coinciding. Their error satisfies our requirement. The land yacht can track the steering motion well.

Obstacle avoidance experiment

The autonomous control system of the land-yacht robot is shown in Figure 28

Figure 28.

Autonomous control system chart of land-yacht robot.

Role of the trajectory planner is to design a target trajectory of the robot according to the expedition task and send the instructions to the navigation control unit. The information of the target trajectory, trajectory feedback by the GPS and sensors, is sent to the direction controller and the steering gear by the navigation control unit. The aim is to adjust the direction of the land yacht. The wing-sail control unit makes it by keeping a certain angle of attack according to the information of the anemometer and the encoder, so that the wing sail obtains the optimal driving force.

We take the experiment in an environment of 10 m × 10 m. The obstacles are static. The land-yacht robot avoids any obstacle and gets the shortest path. First, the environment map which is generated by the trajectory planner is stored in the land yacht as a square matrix which denotes input to path planning algorithm. The experimental environment is shown in Figure 29(a). Considering the radius of the land yacht, the security zone of the obstacles, and collision avoidance, the environment can be transformed into a map of 10 × 10 grids, and red areas represent the obstacles. So, the land yacht is regarded as a particle during movement. The result is shown in Figure 29(b).

Figure 29.

(a) Experimental environment of obstacle avoidance and (b) The grids map of environment.

The path planning of the land yacht according to the environment and the real-time running gestures is shown in Figure 30.

Figure 30.

Experimental scenes.

We conducted this experiment five times. In each test, the land yacht reached the target without collision. From this, we know that the land-yacht robot can avoid obstacle well, as well as running curved motion.

Compared to Windsurfing & Sled, ¹⁰ the land-yacht robot is small in size, lightweight, and flexible. It can start up in relatively small wind speed. The wheels instead of sleigh can get a faster movement speed, more convenient steering motion, and adjust rapidly.

Conclusion

This work describes a wing sail that was chosen and manufactured, which is potentially used for polar expedition robot. First, the airfoil theory was studied and some similar airfoils were compared. Then, an efficient airfoil was used for composing a wing sail. Based on this, the wing sail was designed, checked, and manufactured. At last, starting and running experiments of the robot were taken. The result satisfied the power requirement of the environment exploration.

The research presented here shows that wing sail providing power for robot is possible. The possibilities for long-term autonomous operation have been discussed and presented as a real possibility for the near future. Further work needs to be undertaken to optimize wing shapes and sizes and to test the full potential of using multiple wing sails to improve performance and stability.