For some reason , I always find myself involuntarily pondering the mechanics of skiing. From a mechanical perspective, why edge the skis? Why lean inward?cAt which point in a turn is the speed fastest? Where is the leg under the most pressure? Where is the lean angle the greatest? Can all these questions be answered through mechanics?
200Wan Ci’s tutorials mention that skiing is all about turning, and that the turns should be smooth and rounded. Here, we assume carving out a standard half-circle turn (I don’t know if such turns exist in real skiing), as shown1in theCfigure, whereAa turn starts atCand ends atA, assuming the point after the neutral stance where the body begins to lean inward into the turn,Cis the point before starting to extend out of the turn. Is the force situation at these two points the same? The answer should be no. For example, if we ride a bicycle in a circle on a flat stage, without a doubt, the whole bike must lean inward. Assuming constant speed and radius, the lean angle at any point on the circle should be consistent—there’s no reason for it to be otherwise. But if one end of the stage is raised to form a slope, and we still ride on this inclined stage at the same radius and speed, would the bike’s posture at different points on the circle still be the same? Intuition says no. Is intuition correct? Can we find concrete mechanical evidence that it’s indeed different?
The laws of gravity and circular motion tell us: First, for the same object moving in a circle with the same radius and speed, the required centripetal force is the same. Second, the direction of the centripetal force is parallel to the plane of the circle and points toward the center. Third, during skiing, assuming no active leg push to exert work, the only external force applied is gravity. In a skiingCturn, the centripetal force is provided by a component of gravity—no other forces are involved (the force from the snow on the legs is a reaction force from another supporting component of gravity, used to balance that supporting force, not to act as centripetal force). Fourth, the direction of gravity is always perpendicular to sea level. Fifth, the gravity acting on an inclined object can be resolved into components (or said to be decomposable into forces in different directions), where the direction of the centripetal component’s projection is determined by the body’s projected inclination relative to sea level, not by the slope or terrain of the position. These six points hold true whether on a slope or a flat surface. So, what’s the difference between a flat surface and a slope? The answer is: the angle is different—that is, the angle between gravity and its centripetal component(in the2 figureG1). On a horizontal surface, the angle between gravity and the centripetal component is the same at any point on the circle:90degrees. But on a slope,Athe centripetal componentG1(pointing downhill) forms an acute angle with gravity atC, while the centripetal componentG1(pointing uphill) forms an obtuse angle with gravity at(. TheG1at both points are equal because the speed and radius of the circular motion are the same). According to the principles of force analysis, theAsupporting componentG2atCmust be smaller than the supporting componentG2atLOW CYou will feel the greatest pressure on your legs here. Not only that,Cthe angle between the supporting force component at this point and the snow surface (not the horizontal plane) must be smaller thanAthe supporting angle at this point. This is why atLOW Cthis point, the edge angle (or inward lean) is the greatest (the inward lean angle+and the supporting angle=90in degrees).
This also explains why edging is necessary: to create an inward lean angle, which in turn creates a centripetal force component. As the body leans inward and the legs lean inward (without counter-arching), the inward-leaning legs cause the boots and board to lean inward, and the inward-leaning board means edging. At the same time, the forward supporting force generated by digging the edge into the snow is strong enough—far greater than the sliding friction of skidding—to counteract the powerful downward supporting force component of gravity. And why the large edging angle? Because the faster you go, the greater the needed centripetal force, and since gravity remains constant, the only way to increase the centripetal force is to increase the inward lean angle.
The above describes two special points where the direction of body lean (i.e., the direction of the centripetal force) aligns with the radius line (the line connecting the boot and the center of the circle). The force dynamics are relatively simple here. However,Cat other points along the turn besides these two, the forces involved are more complex. For example, at point1, according to skiing requirements, the body must remain perpendicular to the snow surface along the fall line (which looks like leaning forward when viewed from the horizontal plane), while simultaneously leaning inward toward the center of the circle along the radius of the turn arc (i.e., leaning sideways). At this point, the overall lean posture is different from the simple uphill or downhill leans at pointsBin FigureA andC. Instead, it combines both a downhill lean and a lean toward the center of the circle—merging the two. Relative to the horizontal plane, it’s a lean diagonally forward. In this case, the projection of the skier’s gravity on the snow surface will deviate from the line connecting the boot and the center of the circle (the radius line). As a result, the centripetal component of the skier's gravity will no longer point directly toward the center along the radius line but will instead point slightly downhill from the center. This off-center component won’t provide sufficient centripetal acceleration (to change the direction of motion), so the turning arc will become smaller (straighter, less round). To maintain the arc, the skier must manually adjust their overall lean posture. Adjusting the side lean angle won’t help—only adjusting the forward lean angle will. That means reducing the forward lean. In terms of action, this is reflected by shifting the body’s weight backward. When the forward lean angle is adjusted to a certain degree, the projection point of gravity will return to the radius line, and the direction of the centripetal component of gravity will also realign with the center.