## Sunday, October 28, 2012

### Physics in Figure Skating: The Death Spiral

Figure skating is obviously an interesting application of physics, and the success of many of the "moves" that skaters do depends on whether or not they are able to exert the force that is physically required for what they are aiming to accomplish. Specifically, I chose to look at the physics behind the "death spiral," which is a common "move" that is is seeming difficult in figure skating. The death spiral is when a male skater pulls a female skater in a circle while she is almost completely perpendicular to the ice. See a video of it here: http://www.youtube.com/watch?v=bOsWG3BeslE

I chose to qualitatively look at the center of mass between the two skaters, simplifying their relationship to being one rigid body. Since CM=(m1x1+m2x2)/(m1+m2), I intuitively observe that the center of mass lies closer to the male skater. This makes sense because as a male skater who weighs more, his mass will be larger and therefore the resulting calculation for center of mass will lie closer to him.

Next I considered looking at the speed the pair would probably be skating in. Based on the video, I presumed that the pair did about one revolution in two seconds. To find the angular velocity, I know that w=2piT, so plugging in 0.5 for T estimates that the skaters' angular velocity was about 3.1 radians per second. Next, to find their approximate linear velocity I assumed their radius of rotation (from the center of mass to where the male plants his foot) was about 0.5 meters. Accordingly, I know that v=rw, so plugging in 0.5 in for r and 3.1 in for w, I found their linear velocity to be about 1.6 meters per second.

Next, I chose to look at what forces are involved between this pair as they rotate. They have a centripetal acceleration that comes from the force that the male exerts on the female in planting his blade into the ice. This force is the centripetal force that keeps the pair rotating. Based upon Newton's second law, I know that F=ma. Furthermore, I know that radial acceleration is equal to w^2r. Plugging this in, I can get an equation to estimate the force, F=(m1+m2)w^2r. Supposing that the female weighed about 50 kg and the male about 79 kg, I estimate the force to be about 620 N.

In my interpretation, I thought it was important to consider whether this amount of force seems reasonable. The male must exert 620 N of force in order to successfully complete the "death spiral." In looking at the force that the male can exert with his body weight, I found that he could exert about 770 N (F=ma=79*9.8). Therefore, the 620 N that the male must exert is a reasonable estimate, and more importantly possible. This is obviously good news for the female skater, who must trust that the male skater can keep his skate stabilized while the force is exerted as she spins, otherwise the stunt could result in an accident. Lastly, another consideration in the calculation of this force is that the force of tension in the hands of the skaters must equal 620 N--the skaters grips must withstand the large force.

Based upon my investigations above, it is apparent that the death spiral is a pretty difficult stunt in the world of figure skating. This is probably why its completion receives high scores in the judging rounds of major competitions.

Figures that may help visualize:
Source: http://www.real-world-physics-problems.com/physics-of-figure-skating.html