Proceedings of the ASME 2016 International Mechanical Engineering Congress & Exposition IMECE 2016 November 11-17, 2016, Phoenix, USA IMECE2016-66664 ON WIND-DRIVEN LAND VEHICLES G. Reina,∗ M. M. Foglia Department of Engineering for Innovation Department of Mechanical, Mathematics University of Salento and Management Engineering Lecce, Italy 73100 Politecnico of Bari Email: [email protected] Bari, Italy 70125 Email: [email protected] ABSTRACT aA Slip angle of the front wheel This paper deals with the study of a land-yacht, that is a aPR Slip angle of the rear right wheel ground vehicle propelled by wind energy. There is a large in- aPL Slip angle of the rear left wheel terest in exploring alternative source of energy for propulsion b Slip angle of the vehicle and wind energy could be a feasible solution being totally green, vG Vehicle velocity available and free. The idea envisaged by a land-yacht is that u Longitudinal component of vG of using one or several flexible or rigid vertical wing-sails to v Lateral component of vG produce a thrust-force, which can eventually generate a higher y Yaw angle travel velocity than its prevailing wind. A model of a three-wheel Fx;A Longitudinal force of the front wheel land-yacht is presented capturing the main dynamic and aerody- Fx;PR Longitudinal force of the rear right wheel namic aspects of the system behaviour. Simulations are included Fx;PL Longitudinal force of the left wheel showing how environment conditions, i.e. wind intensity and di- Fy;A Lateral force of the front wheel rection, influence the vehicle response and performance. In view Fy;PR Lateral force of the rear right wheel of a robotic embodiment of the vehicle, a controller of the sail F Lateral force of the rear left wheel trim angle and front wheel steer angle is also discussed for au- y;PL F Vertical force of the front wheel tonomous navigation. z;A Fz;PR Vertical force of the rear right wheel Fz;PL Vertical force of the rear left wheel NOMENCLATURE X, Y, Z Components of the wind thrust in the vehicle reference frame Id Instantaneous center of rotation of the vehicle G Center of mass Rm Motion resistance R Curvature radius hG Center of mass height a Front pitch p, q, r Coordinates of the CoE in the vehicle reference frame b Rear pitch in Attack angle l Vehicle pitch t Vehicle width d Steer angle INTRODUCTION Land sailing refers to the motion across ground of a wheeled vehicle propelled by wind through the use of a sail. The term ∗Address all correspondence to this author. 1 Copyright c 2016 by ASME comes from analogy with (water) sailing. The first historical ex- wheels can be obtained, respectively, as: ample of wind-powered vehicles can be traced back to China in 552 AD [1]. However, the precursor to the modern land-yacht was invented in 1600 by the Flemish scientist Simon Stevin in v + y˙ a aA = − d (1) Flanders for recreation purposes [2]. In 1900, Louis Bleriot´ con- u tributed to develop land sailing as a popular sport and in 1967, the first “big” land-yacht race was organized by a French Foreign Legion officer along a 2700 km path across the Sahara Desert [3]. Another variation of the land-yacht is the Whike, [4], which com- v − y˙ b bines land sailing with cycling and it can, therefore, be used in aPR = (2) u + y˙ t absence of wind, for example in urban environments. 2 A large body of research has been devoted to improve the performance of vehicles featuring one or several flexible or rigid vertical wing-sails [5], [6], [7], [8]. The wing-sails have the shape of an airfoil, and installed on wheels/boat to be used in v − y˙ b aPL = t (3) land/water. In principle, the airfoil can constantly produce a lift- u − y˙ 2 force that can generate a higher vehicle velocity than its prevail- ing wind. For example, a speed of 203.1 km/h was recorded for a land-yacht in 2009 when wind speeds were fluctuating between The forces acting on the system are shown in the free-body di- 48 and 80 km/h [9]. agrams of Fig. 2. Due to the interaction with the wind, a stress The use of wind-propelled vehicles has also been proposed for distribution is generated across the sail. It is assumed that the re- planetary exploration by NASA [10], [11]. JPL as well devel- sultant force is applied directly to a single point of the foil, which oped wind-driven inflatable spherical robots for polar expedi- is referred to as the aerodynamic Center of Effort CoE (see [13], tion [12]. and labeled as S in Fig. 2) and at which the total moment pro- duced from all forces over the foil can be represented by a single This paper presents a model that describes the response of a force producing the same moment. In reality, the actual position land-yacht given the command input, i.e. steer angle and sail trim of this CoE is a function of a set of parameters, including the way angle, and wind conditions. Emphasis is given to the study of the in which the sail is trimmed, but we will ignore this effect and as- interaction between wind and sail that generates the forces that sume that the position of S remains constant. The resultant force propel the vehicle. One of the challenges towards autonomous or wind thrust has three components, i.e., (X, Y, Z). The wind driving is to set a proper angle of attack against the relative trust component X allows the land-yacht to overcome the motion wind in order to steer the land-yacht to a planned destination. resistances and accelerate. Currently, the angle of wing-sail is manually adjusted by land By applying Newton law to the land-yacht under the assumptions sailors. Therefore, to develop autonomous wind-driven vehicles, of rigid bodies, small angles, negligible rolling resistance of the it is necessary to evolve their steering mechanisms from manual wheels (i.e., FxA = FxPR = FxPL = 0), it gets to automatic. A dual-input “expert” system is proposed to ad- dress this issue. x : −F d + X + R = M(u˙ − y˙ v) Results obtained from extensive simulations are included to ver- yA m y : F +Y + F + F = M(v˙+ y˙ u) ify the model and investigate the vehicle performance in open- yA yPL yPR z : Fz + FzPL + fzPR + Z − Mg = 0 loop (locked commands) and closed-loop operations. t (4) Mx(G) : (FyPL + FyA + FyPR)hG + (FzPL − FzPR) 2 + Zq −Yr = 0 My(G) : FyAdhG − FzAa + (FzPL + FzPR)b + Xr − Zp = 0 Mz(G) : FyAa − (FyPL + FyPR)b +Y p − Xq = Iy¨ VEHICLE MODEL where the i−th tire lateral force Fyi can be considered as propor- tional to the sideslip angle ai for small ai In this section, the kinematic and dynamic model of a land- yacht is presented. In Fig. 1, it is shown the kinematic scheme of the vehicle. Let Xv;Yv;Zv, be the vehicle-body frame (V-frame) Fyi = −Ca ai i = A;PR;PL (5) whose origin is assumed to coincide with the center of mass, G. With reference to the parameters introduced in the Nomencla- ture, and under the assumption of planar motion and small an- Ca being the lateral stiffness of the tire. gles, the slip angles of the front wheel and rear left and rear right Equation (4) can be expressed as a function of the highest deriva- 2 Copyright c 2016 by ASME FIGURE 1. KINEMATIC MODEL FOR A THREE-WHEEL VEHI- (a) CLE tive FyAd X Rm u˙ = − M + M + M + y˙ v FyA Y fyPL fyPR v˙ = M + M + M + M − y˙ u F a y¨ = yA − (F ) b + Y p − Xq I yPL+FyPR I I I (6) FzA = Mg − FzPL − FzPR − Z 2Yr Zq hG FzPL = t − 2 t − 2(FyPL + FyA + FyPR) t + FzPR Zp Xr FyAdhG FzAa FzPR = b − b − b + b − FzPL The motion of the land-yacht is governed by the first three dif- ferential equations of Eq. (6) that depend on the state variables (u, v, y˙ ). The remaining equations are algebraic equations where (b) the unknowns are the wheel vertical loads (i.e., FzA;FsPR, FzPL). VEHICLE AERODYNAMICS With reference to Fig. 3, the true (absolute) wind speed, w, can be expressed in the inertial frame as w = wcosgt xi + wsingt yi (7) where gt is the true wind angle. We are interested in the ap- parent (relative) wind, wr, i.e., the vector difference of the true wind expressed in the vehicle reference frame and the yacht ve- locity, since the wind thrust is directly related to wr. In addition, wr should be referred to the CoE of the sail having coordinates (c) [p;q;r]T FIGURE 2. FORCES ACTING ON THE VEHICLE: (a) (Xv-Yv T T wr = w − V − [0;0;y˙ ] × [p;q;r] (8) PLANE), (b) (Yv-Zv PLANE), AND (c) (Xv-Zv PLANE) 3 Copyright c 2016 by ASME wrx in = p − arccos( ) i f wr · h < 0 jwrjjxj (10) wrx in = −[p − arccos( )] i f wr · h > 0 jwrjjxjp The attack angle is definite positive if counter-clockwise. In turn, the knowledge of in allows the lift and drag coefficients CL(in) and CD(in) to be defined. Experimental data referring to the sym- metric NACA0012 profile used in this research can be found for example in [14] and they are reported in Fig.