Now the death spiral is a really interesting thing to look at when talking about the physics of figure skating. Before I even start talking about the physics here is a video showing you what exactly the death spiral is.

                                                           

So now lets look into the physics of what is happening during that move. Below this is a figure that depicts all of the important quantities that we will need in addressing this physics problem.

                                                                             

In this picture:

  • mA is the mass of the female skater 

  • mB is the mass of the male skater 

  • M is the mass of the system, which is equal to the combined mass of the male and female skater (M = mA + mB). Note that the red dot represents the location of the center of mass of the system. 

  • LA is the distance from the center of mass of the female skater to the center of mass of the system M 

  • LB is the distance from the center of mass of the male skater to the center of mass of the system M 

  • P is the pivot point (center of rotation) of the system. This is where the front tip of the male skater's blade is planted into the ice 

  • R is the radius of the circle traced by the center of mass of the system M, about point P 

  • w is the rotation rate, in radians/s

Also please note that LB < LA , this is because the male skater is heavier than the female skater so the center of mass is closer to him.

If we want to find out how much force the male skater is exerting on the ice to maintain his position, we can use Newton's 2nd law, and look at the pair as if they were a rigid body because they are moving as a single unit. Let's now consider the diagram below where

  • ac is the centripetal acceleration of the center of mass M due to the rotation rate w. This acceleration points towards the center of the circle (of radius R) 
  • FP is the force exerted by the ice on the male skater's blade at point P. This force acts in the direction of the centripetal acceleration ac
                                                                                                  

Now lets use Newton's 2nd equation: F=Ma to find the force that the male skater is exerting on the ice.
Centripetal Acceleration:
ac = w2 R                                                           w= rotation rate

So therefore,
Fp = Mac 

and
Fp = (mA + mB)w2 R

With that equation you will have all know variables in your cases and you will be able to find out exactly how much force the male skater is required to exert on the ice to stay in place during the move.