text: The following analysis is taken largely from the work of Burton and Bush, and offers some mathematical insight into the role that flexibility plays in improving load-bearing characteristics of floating objects.
  Consider two plates of infinite width, thickness , and length  that are connected by a torsional spring with spring constant per unit width . Furthermore, let  be the angle between a plate and the horizontal, and  the from where the meniscus meets the plate to the horizontal. The distance from the undisturbed water line to the plate's outer edge is . The density of water is , the density of air is considered negligible, and the plate density, , shall be varied. All systems naturally assume a configuration that minimizes total energy. Thus, the goal of this analysis is to identify the configurations (i.e., values of  and ) that result in a stable equilibrium for a given value of .
  For a total system energy of , it is natural to distinguish sub-components:
   <br />
  :: Work done on the system
  :: System potential energy
  In defining , there are several associated components:
    <br />
  : is the work done on the interface by hydrostatic pressure
  : is the work done on the plates by hydrostatic pressure
  : is the work done on the plates by gravitational force
  : is the work done on the plates by surface tension forces
  Similarly, the system potential energy, , is taken to be composed of two terms:
   <br />
  : is the surface energy of the water/air interface
  : is the energy stored in the torsional spring and is equal to  
  There are two ways in which the system energy can change by an incremental amount. The first is a translation of the center of mass of the plates by some distance . The second is an incremental change,  in the hinge angle. Such a change will induce a new moment.
  As mentioned, the system will seek the orientation that minimizes  in order to find point of stable equilibrium. Writing out these terms more explicitly:
   <br />
  Here,  is the equation air/water interface,  is the incremental displacement of the interface, and  is the surface tension of water.
  For a given value of , stable equilibrium configurations are identified as being those values of  and  that satisfy
   <br />
  <br />
  Taken in a different light, these conditions can be seen as identifying  and  that result in zero net force and zero net torque for a given .