Newton and Resistance Bands

April 19, 2011

On Saturday, I witnessed a young man really getting his sweat on in the gym. He was laying on his stomach on a bench, with a band looped under the frame of the bench and up over the back of his head. This band was providing the resistance for what was, at best, a clear misunderstanding of the term “chin-ups”; he was lifting his head in a nodding motion, with the apparent goal of strengthening his neck. He looked extremely silly, but he was partaking in an emerging trend in the weight room – accommodating resistance.

What is logic of these chains and bands? Read on.

First a quick primer on moments – the effect of a load to a lever arm some distance from a joint.

The moment is calculated as the cross product of the force times the lever arm. In a simple 2-D analysis this equates simply to force times distance.

Let’s look at the bench press. When you bench press, your pectorals exert a force on the humerus at the insertion point, creating a moment to counteract the moment induced by the load of the bar. To push the weight upward, the moment from the muscle force must be greater than the moment exerted by the weight of the bar.

The moment (about the shoulder) created by the load is the horizontal distance from the shoulder to the elbow multiplied by the weight of the bar.

The arm angle (denoted by theta) is the angle your upper arm (length r) makes compared to the ground. As your arms straighten in lifting the bar, that horizontal distance decreases, decreasing the moment required to lift the weight, therefore decreasing the muscle force.

This is where chains and bands come in. With a chain, the higher the bar goes, the more chain it lifts of the ground, increasing the weight. With bands, stretching the band further increases the load according to Hooke’s Law:

“k” is the spring constant of the band, and “y” is the distance the band is stretched from its rest, or “unstretched” length.

Whether you use chains or bands, the force of the load (and therefore the load moment), increases linearly with distance as the load is raised.

Let’s take a look at the muscle force required as a function of the bar height (click to enlarge):

You can see that the force profile is a lot different when accommodating resistance is employed. It’s important to note that in order for the maximum muscle force to be the same, the weight of the bar must be decreased. You can see that with AR, the muscle force is lower at first and hits the maximum later in the range. When force is plotted vs. distance, the area under the curve is the work performed, or the energy used by the muscle. In this case, the work required is much higher with AR. With the numbers I used, 216% higher.

So why isn’t everyone using bands? Because the bench press is not intended to be performed at constant acceleration.

One of the common arguments against AR revolves around Newton’s second law:

To move the weight from rest at the bottom of the lift, you must accelerate it. Weight lifting coaches will tell you that you should lift with a constant muscle force, increasing the acceleration of the load through the movement. Let’s look at what happens when you lift the bar with constant muscle force (click to enlarge):

You can see that in the classic, or “natural” method, the acceleration of the bar increases throughout the movement when constant muscle force is applied. Here, the work performed is the same for both cases (same constant muscle force over the same distance), the acceleration (and velocity) of the bar just stays lower with the use of AR.

So is AR useful?

Here’s the catch: no one is capable of applying perfectly constant muscle force throughout the bench press. If you did, the bar would fly out of your hands. Of course, decelerating the bar near the top of the range shouldn’t take up much of the length of the movement, because the acceleration of gravity is helping you. However, large weights have large momentum, and if you get it moving fast (as you will with constant muscle force and no AR), it takes more force or time to slow it down.

I think it comes down to how skilled you are. If your bench press is more constant speed than constant force, AR will force you to perform more work on each set. Conversely, if you do a good job of applying constant muscle force, AR won’t do anything but slow your bar down.

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