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## DYNAMIC FLUID RESISTANCE CONVERSION ANALYSIS

The Waveweight’s unique key benefits using water as a dynamic mass distribution can be further explained using traditional solid-body equations involving the concepts of moment of inertia and torque. In order to give meaningful analysis without involving high level fluid dynamics or needlessly overcomplicating the model, the following assumptions are made:

1) All water in the Waveweight tubing acts as a solid mass. 2) There is no water within the Waveweight crossbars. 3) The Waveweight water tube caps are massless - all mass exists within tube walls and crossbars.

In this analysis, we will be comparing the Waveweight and a solid plate weight when doing the “bus driver” exercise. The “bus driver” exercise consists of holding a weight out at arm’s length then slowly rotating the weight by ninety degrees then rotating back to the starting position. This motion is repeated both clockwise and counter-clockwise until the desired number of reps is achieved. The Waveweight’s unique shape and distribution of mass causes it to act like a much heavier plate weight when used in rotational exercises (such as the “bus driver”).

## MOMENT OF INERTIA

Moment of inertia is the resistance of the object to rotational forces, or a measurement of how difficult it is to start or stop something from spinning. For example, large, heavy tires take much more energy to start spinning than slimmer, lighter tires.

Using the equations for moment of inertia for a solid cylinder, moment of inertia for a hollow cylinder, and the Parallel Axis Theorem, the moment of inertia for an empty 11 pound Waveweight is 22.78 lb·ft2.

Using the equation for moment of inertia for a solid disk, the moment of inertia of an average 45-pound, 17.5 inch diameter plate weight is 11.96 lb·ft2.

The Waveweight is almost twice as difficult to rotate in the “bus driver” when held by the innermost grips compared to a 45-pound plate weight, even though it weighs one quarter as much.

Using the equation for a solid disk and rearranging to solve for mass (), an empty 11 pound Waveweight is equivalent to a 85.70 pounds plate weight.

Adding water to the Waveweight further increases the difficulty of rotation. Adding one pound of water to each tube of the Waveweight is equivalent to adding an average of 4.19 pounds of plate weight needed to provide the same resistance.

## TORQUE

Torque is defined as a twisting force that tends to cause rotation (i.e. turning a car steering wheel or twisting a screw driver).

Increasing the moment of inertia also causes the torque required to rotate the object to increase as well. Using the “bus driver” exercise, the average time for a single ninety-degree rotation of a 22-pound plate weight is around 0.425 seconds.

Using the equation for rotational acceleration, a 22-pound plate weight requires 6.34 ft·lbs of torque to perform the “bus driver” exercise. Using an empty 11 pound Waveweight for the same exercise requires 26.7 ft·lbs of torque – over four times as much torque the plate weight.

Adding water to the Waveweight greatly increases the difficulty of rotation. To compare the Waveweight and the plate weight when performing the ‘bus driver’ exercise, we begin with the Waveweight with 2 pounds of water in each tube in a modified vertical position so the water remains at the bottom of the tubing.

At the very start of the rotation, the torque required is to rotate an empty Waveweight is 26.7 ft·lbs. During the first half of rotation, the torque required to maintain constant rotational acceleration must increase in order to counteract the opposing torque of gravity pulling the water back down up to a maximum of 31.8 ft·lbs. Conversely, in order to come to a complete stop at horizontal, the torque required decreases dramatically to 21.6 ft·lbs then slowly tapers out to 19.6 ft·lbs. This decrease is due to gravity helping to slow the rotation of the Waveweight during the second half of the rotation.

This example demonstrates the dynamic exercise that the Waveweight provides. The continually changing torque requirements stress the body in more varied ways than can be accomplished using standard weights.

It has been demonstrated that the Waveweight inherently provides a dynamic exercise experience. The addition of fluid dynamic analysis would only further prove the ever-changing physical output that the Waveweight is designed to produce. By harnessing the dynamic nature of water to give its user a workout that is more vigorous, real-to-life, and applicable to everyday scenarios than traditional solid weights, the Waveweight is as versatile and creative as its user.