Originally Posted by
Savs
Hanley, I think you know a lot of physics, but damn you for calling me out. Rip, this is gonna be long. I'm sorry.
I think there are two questions. (1) Why does a belt allow a lifter to lift more weight? (2) Does training with a belt increase the strength of the trunk musculature faster than training without one?
I don't know the answers, and won't attempt to answer (2); however, perhaps I can constructively add to the discussion by first discussing the zeroth question: How does the belt work? I don't understand the mechanism behind the "it gives you something to push against" argument, even though that explanation may be true. The "hoop stress" approach makes more sense to me.
The executive summary for the "hoop stress" explanation, as I understand it: The tensile stress in the trunk musculature (and the belt, if worn) produces the abdominal pressure which opposes an anterior movement of the spine. An anterior movement of the spine tries to increase the surface area of the abdominal cavity by increasing the radius, R, of the roughly-cylindrical cavity. Contraction of the trunk musculature tries to keep the surface area, and thus R, fixed.
I'll use the following simplifications. The anterior spine is supported by pressure inside two cavities which are separated by a diaphragm. The abdominal cavity is filled with an incompressible fluid, while the thoracic cavity is partially filled with gas. I'll ignore leaks from these cavities (by assuming we clamp down on sphincters (anal, urethral, and upper esophageal), and the pressure transferred out through the blood is opposed by material surrounding the blood vessels). Furthermore, I'll model the abdominal cavity as a cylinder of radius R and height h, treating the diaphragm as a flat surface, not domed.
Using those simplifications, I'll focus on the abdominal cavity. First, an aside. For incompressible fluids, one change change the surface area but can not change the volume. For example, one can squeeze a water-filled balloon and change its shape, but not its volume (volume can change with a gas-filled balloon). The shape with smallest surface area per volume is a sphere. Water droplets try to form spheres because Nature likes to minimize energy, in this case minimize the surface energy produced by the surface tension at the water-air boundary. The minimum energy corresponds to the minimum surface area.
Similar to the water droplet's surface tension, if we consider the trunk musculature a membrane, contraction of the muscles produces a tensile membrane stress. This stress produces an inward force similar to the hoop stress produced by the belt. The inward force acts to minimize the surface area, and for our cylinder that means reducing R at the expense of increasing h (whose increase will be opposed by the diaphragm). At maximum contractile strength, the cavity will assume a shape with some minimized surface area (although not the minimal surface area). This will also produce a maximized pressure, since pressure is inversely related to radius.
Within the cavity we have incompressible fluid which transfers the surface-tension force of the trunk musculature to the anterior lumbar spine. Let's now assume the forces on all sides of the lumbar spine are balanced. If some external force acts to push the lumbar spine toward the abdomen (that force per unit area is greater than the abdominal pressure), that movement of the spine will change the shape of the abdominal cavity. Opposing that attempt to change the shape, and thus the surface area, is the surface-tension force of the trunk musculature. Movement of the spine tries to increase R, while the contraction of the trunk muscles try to keep R fixed.
In order to hold R fixed, the muscles must contract harder. If the muscles can not produce enough force per unit area, the hoop stress of the belt provides additional inward force. Both oppose an increase of the radius. The belt opposes an increase in its circumference (thus an increase in radius), while the contracted musculature - each fiber opposing an increase in length - oppose an increase to the surface area (also an increase in radius).
This post hasn't been succinct. I'm very sorry, I tried to hastily cut as much as possible. One last point for Hanley (or any other math nerds). John, you got me thinking why does increasing R matter? If you're interested, what I found was with the cavity modeled as a cylinder, an increase in surface area means a positive increase in R (as long as 2R > h). For a tall, narrow cylinder, an increase in surface area is accomplished by a decrease in R. Write down the area of the cylinder and take differentials of both sides. For fixed volume you should find:
dA = 2π dR (2R - h). As long as the term in the parenthesis is positive, positive dR means positive dA.