1. Introduction

Alpine skiing is an extreme sport that combines speed and skill and is known for its high-risk and challenging nature. With the rapid development of alpine skiing, the refinement of technical movements and equipment design has been increasing [1]. However, the ability to control one's body, technical tactics, and equipment performance are all crucial for this sport, so studying the mechanics of skiing in depth has both theoretical and practical implications. As an essential branch of natural science, mechanics is a fundamental discipline that studies the relationship between object motion and force. Its importance in sports science is clear; in today's competitive sports, using mechanical concepts is essential for everything from improving sporting products to perfecting technical motions [2]. Leverage describes how ski bending affects the turning effect, dynamics examines the forces involved in skiing, such as gravity, friction, and air resistance, and hydrodynamics shows how to modify one's position to lessen air resistance and increase skate speed and stability. This paper adopts the methods of literature review and theoretical analysis, extensively collecting and systematically summarizing domestic and international research on alpine skiing, mechanical principles, sports biomechanics, sports injury prevention, and training strategies. It is dedicated to deeply exploring the core application of mechanical principles in alpine skiing, aiming to explore how to optimize skiing techniques through the close integration of theory and practice in order to enhance athletes' competitive performance. Additionally, it seeks to explore the interaction between equipment design and mechanical characteristics, thereby strengthening athletes' control abilities and skiing efficiency.

2. Core principles of mechanics in alpine skiing

2.1. Dynamics analysis

Alpine skiing is a complex form of sport, and its kinetic properties are reflected in the force interaction between the skier and the external environment [1]. The main forces in skiing include gravity, friction and air resistance, which determine the skier's speed, acceleration and trajectory. Gravity is the main driving force in skiing. When a skier begins to slide from the top of a slope, gravity causes them to slide down the slope [3]. The component of gravity increases and the skier accelerates more quickly on steeper slopes. Studies have shown that gravity's contribution to speed dominates on higher gradient courses, which is why athletes need to have a high degree of control over their glide speed for safety and race performance. Friction is the force between the skis and the snow surface, including static and kinetic friction. While excessive friction reduces speed, moderate friction offers stability when skiing. Using waxed skis and modifying skiing tactics to increase gliding efficiency can greatly lower the coefficient of friction. Air resistance significantly affects high-speed gliding, especially in professional competitions. Air resistance is proportional to the square of the skier's speed, which means that the faster the speed, the greater the effect of air resistance. Therefore, skiers need to adopt streamlined postures, such as bending the knees and leaning forward, in order to reduce the windward area, thus lowering the resistance and increasing the speed. Relevant studies have shown that a reasonably optimized posture can reduce air resistance by about 20%, significantly improving skiing performance. The law of conservation of momentum and energy also plays a vital role in skiing. One of the main reasons for sports injuries in skiing accidents is when a skier meets an object while skiing at a fast speed. The impact will be significant due to the shift in momentum. Reasonable distribution of kinetic energy and regulation of speed are key strategies in skiing.

2.2. Lever and balance principle

The principle of leverage and balance in alpine skiing is embodied in the motion effect of the ski and the athlete's body control [4]. Skis, as the core component of leverage, have a direct impact on skiing technique through their design and movement. The leverage effect of the ski is the key to the turning technique. The front and tail of the ski are the fulcrum and force point of the lever, respectively. When the athlete applies a certain amount of pressure, the middle part of the ski bends, forming a structure similar to an arch, which is a mechanical effect that enables the skier to complete the turning maneuver more smoothly [4]. The larger the arch of the ski, the smaller its turning radius, which is suitable for more flexible maneuvers.

On the other hand, stiffer skis are better suited to high-speed gliding and stability needs. An important mechanical component of skiing is the impact of the body's centre of gravity on balance. Skiers can regulate their balance and glide direction by modifying the location of their centre of gravity. To keep the equilibrium between centrifugal and gravitational forces, the athlete must then move their centre of gravity inside. A skier is more steady and better able to withstand outside forces if their centre of gravity is lower.

The principle of balance is also reflected in the athlete's ability to resist interference from external forces. At high speeds, skiers face not only gravity and friction but also the impact of irregular snow surfaces. If the center of gravity cannot be adjusted quickly, the skier may lose balance and fall. Therefore, the improvement of core strength and dynamic balance is often emphasized in ski training to improve the stability of athletes in complex environments. The combination of hydrodynamics and leverage effect is also reflected in the design of skis. Manufacturers optimize the hardness distribution and curvature design of skis so that they can meet the demand of leverage effect and reduce air resistance to provide better technical support for athletes.

2.3. Application of fluid mechanics in high-speed skiing

Fluid mechanics is the study of the air and liquid flow laws of the discipline, and its application in alpine skiing is mainly reflected in the analysis and optimization of air resistance [5]. Reducing air resistance is essential to increasing skiing speed and stability since air resistance makes up the great majority of the total resistance that skiers must overcome when skiing at high speeds. The magnitude of air resistance is proportional to the square of the skier's speed and is also affected by the skier's windward area and postural form. By adopting a streamlined posture (e.g., bending the knees, leaning forward, and keeping the arms close together), skiers can significantly reduce the windward area during gliding, thereby reducing air resistance. Professional skiers can reduce air resistance by about 20-30% by optimizing their posture and increase their gliding speed by about 10%.

The design of ski clothing and equipment also fully applies the principles of hydrodynamics. Modern ski clothing uses special materials and seamless design to reduce turbulence in air flow over the surface, thus effectively reducing drag. Some top brands, such as Spyder and Descente, even add micro-structures to the surface of their ski suits to resemble the design principles of sharkskin, further optimizing aerodynamic performance [6]. The shape and finish of the ski also play an important role, as skis with smooth surfaces reduce the interaction between air and snow, reducing drag and improving stability. These optimizations are especially critical in high-speed races, such as the World Cup slalom, where athletes can reach a maximum speed of over 100 km/h, and where the optimization of aerodynamic performance is directly related to performance. The wide application of hydrodynamics in ski posture optimization and equipment design provides important support for skiers in high-speed gliding. By adjusting the posture and adopting aerodynamically designed equipment, skiers can utilize gravity and kinetic energy more efficiently to achieve faster and more stable gliding performance.

3. Application of Mechanical Principles in Alpine Skiing Technology

3.1. Technical optimization

The optimization of alpine skiing technology is closely related to the principle of mechanics, and the analysis of mechanics can effectively improve the efficiency of the skier's movement and technical performance. In the process of skiing, turning technology and speed control are two core skills, and their optimization depends on a deep understanding of dynamics and balance principles. Movement decomposition and mechanical analysis are important methods for technical optimization. By breaking down the technical movement into several parts (e.g., starting, accelerating, turning, and decelerating), skiers can more easily examine the mechanical properties of each step. Turning techniques require athletes to balance centrifugal and gravitational forces in a curved path and control the trajectory by adjusting the body's centre of gravity and the skis' angle. Through camera analysis techniques and biomechanical modelling, the forces on each movement can be quantified, providing a scientific basis for optimizing the movement [7].

Mechanical optimization is also indispensable for speed control and safety improvement. By reasonably distributing the relationship between friction and gravity, athletes can achieve precise speed control in complex terrain. For example, skiers can increase friction on steep slopes by increasing the contact area between the snowboard and the snow surface, thereby slowing down and improving stability. Dynamic Balance Training and Core Strength Improvement help athletes maintain balance and cope with external disturbances during skiing. These exercises enhance the accuracy of technical movements and the stability of athletic performance by simulating the mechanical effects of the skiing environment. Technical optimization based on mechanical analysis can not only improve the accuracy of skiing technique, but also significantly improve the safety and sports performance of skiing.

3.2. Improvement of equipment design

Improvement of ski equipment design is a direct application of mechanics principles in skiing, and its core objective is to improve the speed, stability and safety of athletes by optimizing the mechanical properties of skis and wearing equipment. Ski improvement is the focus of equipment design. The curvature, hardness and material of the ski directly determine its performance. Ski arc design determines its turning radius; the larger the arc, the smaller the turning radius, suitable for more flexible technical action; hardness affects the ski's elastic deformation, and the more complex the ski is ideal for high-speed skiing stability needs. High-performance skis are designed with composite materials (such as carbon fibre and titanium alloys) to increase strength and reduce weight, thus improving skiing efficiency.

The optimization of aerodynamic equipment should be noticed, as modern skiwear uses seamless designs and low resistance materials to reduce air resistance significantly. Some brands even introduce tiny scale-like structures on the surface of the ski suit to simulate the sharkskin effect, reducing surface turbulence and smoothing air flow. In addition, the streamlined design of helmets and goggles also plays a key role in reducing wind resistance. Improvements in ski boots and bindings have further enhanced the mechanical coupling between skis and athletes, allowing athletes to transfer power more efficiently and gain precise ski control. For example, modern ski boots are designed with adjustable stiffness, giving athletes the flexibility to tailor their equipment's performance to the race's demands. Equipment design improvements have optimized the performance of ski equipment through the application of mechanics, significantly enhancing athletes' performance and safety.

3.3. Training method improvement

Efficient training methods is the key to improving the technical level of skiing athletes, and mechanics analysis provides a reliable basis for the development of scientific training programs. Through the combination of movement mechanics analysis, video feedback and specialized training, athletes can more accurately grasp the technical essentials and improve their performance. The combination of mechanics analysis and special training is the basis for the improvement of training methods. Coaches use sports biomechanics software or camera systems to analyze the dynamic mechanics of athletes' movements in skiing [8]. For example, the use of inverse kinetic models can quantify the forces on the skier in different phases of the movement so as to design a targeted training program. Studies have shown that training based on mechanics optimization can improve the stability and efficiency of athletes' movements. Video analysis and movement correction are commonly used tools in modern training. By recording an athlete's skiing movements with a high-speed camera, the coach can compare the actual movements with the mechanics model and identify deviations in the technical movements [8]. For example, if a skier's centre of gravity is positioned too high during a turn, it can easily lead to a loss of balance. Through video feedback, coaches can help athletes adjust their movements in time and strengthen the stability of technical movements through core strength and dynamic balance training.

4. Case Analysis---Movement Optimization Case

Take Austrian skier Marcel Hirscher as an example, his outstanding performance in giant slalom technique provides a model for alpine skiing movement optimization. Hirscher is known for his fast and precise turning ability in competitions, and the optimization of his technical movements results from applying mechanical principles. Center of gravity adjustment and stability optimization are the keys to Hirscher's technical success. He has mastered the precision of his centre of gravity control through continuous training, which allows him to maintain a very low centre of gravity during the turn, thus enhancing his dynamic balance. Studies have shown that Hirscher's centre of gravity height is significantly lower than that of most of his opponents, an adjustment that significantly reduces the effects of centrifugal force and improves turn stability.

The optimization of the snow pressure angle and friction of the skis is also an important factor in the improvement of his technique. In turn, Hirshhorn adjusts the snow pressure angle of the skis to maximize the contact area between the skis and the snow surface, which improves the efficiency of the turn and reduces the loss of speed. According to the data, Hirscher's turning time is usually more than 10% shorter than that of other competitors, which is a significant advantage in high-level competitions. Consistency of movement and optimization of power transfer makes his skiing more efficient. By strengthening his core, Hirscher is able to evenly distribute his body power to his skis during the turn, avoiding excessive weight or imbalance. At the same time, his movements were extremely coherent, with a smooth transition from turning to straight-line skiing, reducing energy loss during the movement.

5. Conclusion

Based on the comprehensive analysis of alpine skiing techniques and mechanical principles, this study concludes that the application of mechanics in alpine skiing plays a crucial role in optimizing skiing techniques, improving equipment design, and enhancing training methods. Through dynamics analysis, lever and balance principles, and the integration of theory and practice, athletes can significantly improve their competitive performance. The study found that mechanics-based training methods, such as movement mechanics analysis, video feedback, and specialized training, provide a reliable basis for the development of scientific training programs, enabling athletes to more accurately grasp the technical essentials and enhance their stability and efficiency. Case analysis of Marcel Hirscher further validates the effectiveness of mechanics-based optimization in alpine skiing, demonstrating significant improvements in turning stability, speed, and power transfer. However, the study did not fully account for all potential control variables that could influence skiing performance, such as weather conditions, snow quality, and personal factors such as age, experience, and physical fitness. These variables could potentially interact with mechanical principles in complex ways, affecting the outcome of the study. Future study should incorporate a more rigorous control for additional variables that could influence skiing performance, such as weather conditions, snow quality, and personal factors. This could involve conducting experiments in controlled environments or using statistical methods to isolate the effects of these variables.