To achieve a stable and controlled arc on snow, our physico-biomechanical system must reach a state of Rotational Equilibrium. This is defined by the balance between internal muscular forces and external physical loads. Let’s remember that forces displace us, but torques (or moments) make us rotate or lean.
The Dynamic Balance Equation
The total torque acting on our center of mass during a carved turn can be expressed as muscular torque, centrifugal torque, gravity torque and snow reaction torque.
For a Stable Carved Turn (Constant Edge Angle), the sum of all torques must be zero (0): Muscular Torque + Centrifugal Torque = Gravity Torque + Snow Torque. This means that if the sum of the forces keeping us stable is less than the sum of the forces pushing us toward the ground or trying to flatten the ski, we lose our balance and either fall or skid.
Put simply, if the sum were not zero, our edge angles would change. If gravity wins, we hit the ground (inward fall). If centrifugal/snow torques win, our skis straighten up and we lose the turn’s arc.
Component Breakdown
- Muscular Torque (Internal Torque): the torque generated by the adductor and rotational chain (isometric/eccentric). This is the “holding force” that maintains the kinetic chain’s integrity, i.e., the effort from our legs (especially adductors and core) to maintain the structure. If velocity is insufficient, our muscles must “hold” the body to prevent it from collapsing.
- Centrifugal Torque (Outward Torque): generated by velocity and turn radius (Fc . height). This is the primary stabilizer and our best ally at high speeds. It is the force that pushes us toward the outside of the turn. The faster we go, the more “support” we feel from this force to keep from falling to the ground.
- Gravity Torque (Inward Torque): the Gravitational Fall Torque that pulls us toward the snow due to inclination. Since we are inclined toward the center of the curve, gravity pulls us toward the snow. If there were no other force, we would fall sideways immediately.
- Snow Torque (Reaction Torque): the resistance the snow exerts against the base of the ski, attempting to “flatten” the edge angle.
Operational Scenarios
- The High-Speed Scenario: at high velocities, the centrifugal torque is large enough to nearly cancel out the gravity torque. In this case, the muscular torque acts primarily as a precision stabilizer, requiring less “brute force” to maintain the arc.
- The Low-Speed / High-Inclination Scenario: if velocity drops, the centrifugal torque decreases significantly. To prevent an “inside bale,” we must drastically increase the muscular torque (adductor tension). This explains why carving at low speeds is physically more exhausting for the hips.
- The Collapse Scenario: if muscular torque + centrifugal torque is less than gravity torque + snow torque, the Critical Maintenance Torque is lost, the edge flattens, and we either skid or fall inward.
To prevent gravity from “beating” the centrifugal force and causing us to fall inward (meaning, to keep the equation from being “less than”), we have two main paths on the mountain:
- Increase Velocity: since centrifugal force depends directly on the square of the velocity, going faster generates a much stronger outward torque that “holds” us up against the snow.
- Tighten the Turn Radius: if we are moving slowly, we can compensate by reducing the turn radius (making a tighter turn). This increases the centrifugal force and allows us to maintain our lean without falling.
If we cannot do either of those, our only option is to apply pure muscular force (our adductors), which is why technical skiing at low speeds is so exhausting.
Conclusion
A perfect carved turn is a physical balancing act. At low speeds, since centrifugal torque is weak, muscular torque must be massive—this is why slow carving is so much more exhausting for the legs. Our goal should be to modulate velocity and radius to maximize centrifugal support, thereby optimizing the muscular torque required to hold a specific edge angle. This synergy is the essence of high-performance biomechanics in postmodern skiing.
