# Design, Modeling, and Simulation of a Wing Sail Land Yacht
## 1 Introduction
[16] describe a land yacht developed with a NACA0012 airfoil. The airfoil has a wingspan of 1 m and a lateral area of 0.5 m\({}^{2}\). The chassis has a triangular shape with a front wheel and two rear wheels and has a mass of 8 kg. 6. [PERSON] et al. [17] describe a land yacht with a wing sail and a chassis. The NACA0015 airfoil has a wingspan of 0.8 m, a lateral area of 0.24 m\({}^{2}\), and a rotation range of 0\({}^{\circ}\) to 270\({}^{\circ}\). The chassis has four steel wheels and plastic frame. 7. [PERSON] et al. [18] detail a land yacht model which has a NACA0012 airfoil with a wingspan of 3 m and a lateral area of 2 m\({}^{2}\). The triangular chassis has three wheels and weighs 100 kg. The main characteristics of the above reviewed land yachts are compared in Table 1. All these prototypes share the type of sail--symmetrical wing sails--and perception sensors--Global Navigation Satellite Systems (GNSS) receivers, inertial and wind direction, and velocity units. Apart from the proposals of Reference [13; 17; 18], the remaining platforms adopt a four-wheeled chassis with a higher rear wheel baseline. This design option provides, according to Reference [11; 15; 16], greater stability and maneuverability. Land yachts are not only governed by the principles of sailing [4], but sail design is an essential part of their development [19]. The research and development performed on rigid-wing sails has a much bigger scope than just land yachts. This type of sails is, as previously stated, commonly used in marine vessels, such as sailboats. Like the autonomous land yachts, several autonomous rigid-wing sailboats have been developed by the scientific community. Some examples of these vessels are: (i) the Atlantis autonomous catamaran [20] which uses a NACA0015 airfoil as the wing sail with a wingspan of 5.37 m and a lateral area of 7.8 m\({}^{2}\). Furthermore, the wing sail is free rotating, meaning it is not controlled directly and aligns with the wind direction (as it is a symmetrical airfoil). Instead, the wing sail is controlled by a wing flap that induces torque on the wing sail, making it shift slightly to an angle of attack; (ii) the Autonomous Robot for Ocean Observation sailboat [21] which uses a rigid-wing sail with a wingspan of 1.30 m and a lateral area of 0.23 m\({}^{2}\); (iii) the ASPire [22], which uses a free-rotating wing sail with a NACA632-618 profile. The wing sail wingspan is of 2.8 m, and the lateral area is of 2.1 m\({}^{2}\). Considering the modeling and/or simulation of platforms propelled by wing sails, there is scant research on land yachts:  
1. [PERSON] et al. [23] derive a mathematical model for a four-wheel land yacht powered by a wing sail. They model the structure, steering gear, servomotors and force of wing sail and, then, simulate the motion of land yacht according to the mathematical model. The mathematical model analyzes both the linear and steering motions. The simulation and actual experimental results confirm the feasibility and reliability of the proposed land-yacht modeling. 2. [PERSON] et al. [17] present the design, simulation and development of a wind-driven land yacht propelled by a wing sail. The authors conduct a theoretical analysis and use ANSYS Fluent simulation software to determine the lift and drag coefficients corresponding to each combination of attack and heading angles, and the best attack angle corresponding to each different heading angle. The simulation and experimental upwind results were concordant. The modeling and/or simulation of sailboat platforms equipped with wing sails is more abundant. The following list holds a set of representative works:  
1. [PERSON] and [PERSON] [24] design, simulate and develop a wind (rigid wing sail) and solar-powered autonomous surface vehicle (ASV). Before building the ASV, the control simulation was performed with a velocity prediction program (VPP). Initial field trials showed that the experimental and simulated boat speeds and wind speed/directions were consistent. 2. [PERSON] et al.