We have established that carving is superior to skidding and that to carve our turn radius must be a circle. To expand on that look at the figure to the left. In the figure g is acceleration due to gravity, alpha is angle of the slope, v is velocity, beta is the angle the snowboard makes from perpendicular on the slope and Rt is the radius of the turn. We can use the new information from this along with the equation from our previous page in order look at what angle the snowboarder makes with the snow.
tan(theta)=gcos(alpha)/(gsin(alpha)cos(beta)+v^2/Rt)
Theta will give us the angle the snowboarder makes with the ground. If theta gets to large or small the snowboarder will fall down.