Granular Resistance Force Theory


To date we have not found  a resistance exercise or physical therapy device for upper body muscles and joints associated with surfing, swimming, and related physical therapy that provides sport-specific and practically identical ROM and/or resistance that is instantaneously and simultaneously adjustable while operating the apparatus. The S4 Trainer, however, does provide these ROM and resistance features thanks to a novel approach to its design based on Granular Resistance Force Theory (GRFT).

GRFT has been developed and studied through analysis of how granular media act as both as a solid and a viscous liquid. As such, the resistance provided by granular media is dependent on a complex set of factors when objects move through the media. The physics underlying GRFT support a new approach to resistance exercise that is altogether different than filling bags or other containers with granular media such as sand or rice for purposes of weightlifting.

This new approach is fundamental to the design of the apparatus herein disclosed whereby a user will not lift granular media to experience resistance but rather will exercise desired muscles and joints when moving hands and arms through granular media.

As a result, the embodiment of the apparatus disclosed herein is distinct from all previous resistance exercise apparatuses in two significant ways:

  • resistance exercise is provided through ROMs heretofore not accommodated by any exercise device, specifically ROMs as experienced while paddling a surfboard, upper-body swimming strokes, and physical therapy programs designed to rehabilitate upper body muscles and joints associated with those and other sports;
  • resistance exercise is provided that, due to the nature of the resistance/force characteristics of granular media, can be instantaneously controlled by the user simultaneously while engaged in the exercise.

These fundamental factors establish the novelty of the apparatus through the application of GRFT as investigated by a selection of studies summarized below.

How a solid acts like a liquid with respect to resistance acting on a object moving through granular media was the subject of Slow Drag in a Granular Medium, Albert et al., (Dept. of Physics, University of Notre Dame, 1998). This study quantifies how the drag originates not only in the grains in front of the moving object but in the successive layers of grains as well. The resistance between the grains and the moving object fluctuates as strain builds and is released by reorganization of the grains. The resistance properties include grain size, surface texture, grain shape, and packing density of the medium. The study’s results support the applicability of GRFT to understanding the resistance of granular media in response to the insertion of objects into, and subsequent lateral movement through, the media.

Stick-slip Fluctuation in Granular Drag, Albert, et al., (Physics departments of the University of Notre Dame, Eotvos University in Hungary, Seoul University in Korea, and Pennsylvania University, 2001) explored the fluctuations experienced in the resistance to an object moving through a granular medium. The study concluded that the resistance has a quadratic dependence on the depth of object insertion due to 1) long-range force chains that are propagated through the medium when a moving object applies force against the resistance of the medium as it moves through the medium, 2) the bulk properties of the granular medium, and 3) the characteristics of the medium’s container such as shape, size, and orientation.

Granular Drag on a Discrete Object: Shape Effects on Jamming Albert et al., (University of Notre Dame and the Department of Physics and Materials Research Institute, Pennsylvania State University, 2001) investigates the non-linearity of resistance based on the depth of an inserted object. Although fluid drag has been studied extensively, drag resistance within a granular medium is quite different and therefore opens up a new field of research. The study focuses on the moment when the granular medium ceases to act as a solid and begins to flow like a liquid. This study also cites the finite size and shape of the granular medium container as a factor in the resistance dynamic.

The Effectiveness of Resistance Force Theory in Granular Locomotion, Zhang and Goldman, (School of Physics, Georgia Institute of Technology, 2014) investigates the loading of frictional contacts between grains in a granular medium. The study focused on terrestrial materials, specifically sand, and how a sandfish lizard and shovel-nosed snake “swim” through sand. The study used poppy seeds and tiny glass spheres to investigate how the resistance of these granular media allowed for the forward propulsion of the lizard and snake by virtue of the dynamics explained by GRFT.

Depth Dependent Resistance of Granular Media to Vertical Penetration, Brzinski et al., (Dept. of Physics and Astronomy, University of Pennsylvania, 2013), focused on 1) the depth of penetration of an object, 2) resistance force as being independent of the rate of motion of the object, the force chains extending from the inserted object deep into the medium, and 3) the draining angle of the medium when the solid grains begin to flow like a liquid. This last area of study referenced a “background sea of grains”, a term that lends credence to the correlation between the study and the use of granular media as a source of resistance exercise for surfers and swimmers given their use of the ocean and bodies of water for recreation and competition. The loaded forces involved between the intruder (the surfer or swimmer’s hand) and the surrounding “sea” are oppositional. These oppositional forces cause the surfer or swimmer to move forward across or through the water. (When using the apparatus herein disclosed, that forward motion is translated into increased muscular effort since 1) the user’s body remains stationary while engaged in the exercise and 2) granular media are significantly more viscous than water.)

These studies provide a general understanding of GRFT based on quantitative measurements of granular media resistance. Their sound scientific analysis provides a rationale for the use of granular media as a source of resistance for exercise purposes. The logic of GRFT underpins the novel application of granular media to the development of the apparatus herein disclosed.


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