Understanding Force Curves

What is a force curve (FC)?  A FC is a graphical representation of the relationship between the external expression of instantaneous maximal force production and muscle length (muscle length is sometimes represented by joint configuration).

When we discuss force production, we must start by classifying force as either internal or external with relationship to the muscular system.  An example of internal forces would be those that are created by the muscles acting on the bones.  Conversely, an external force would be the force of a 10lb dumbbell acting against the biceps during a curl or gravity acting against the body as a whole.

Internal force production is strongly influenced by muscles length and the concurrent joint configuration.  We know that a muscles ability to produce force is the greatest when it is slightly longer than resting length.  It is at this length that the maximum number of contractile mechanisms are available to perform work. 

This gives the muscle its greatest potential to pull.  Furthermore, at this length the parallel elastic components of the musculo-tendon units are still within optimal performance boundaries.  This creates a harmonious combination that results in amplified performance.

Typically, when we test for internal force production, we do it by measuring its external expression.  If you have ever performed a quad/ham ratio test, you have performed a test that compares the external expression of the internal force capabilities of the quadriceps and the hamstrings. (Note: there are other muscles at work during these tests, but these are the prime movers, so they are usually the only ones discussed.)

The interesting part is that the ratio between internal force production and external expression does not stay constant.  This is apparent the first time you discover your sticking point.  This is primarily due to the complex system of levers that comprise the body.

Basic levers are made up of two opposing forces and an axis or fulcrum.  For instance, during a biceps curl, the forearm creates a lever that involves the elbow joint.  The center of rotation in the elbow joint is what is known as the axis, or pivot point of the lever mechanism.  The biceps are going to create an effort force, or a force that is going to move the arm concentrically.  The dumbbell is going to create a load force, or a force that is going to move the arm eccentrically.

Since gravity only works in a purely vertical plane, you must be able to visualize the force that the dumbbell is producing as a vector (line) perpendicular to the ground.  As you visualize this vector, try to visualize another that runs vertically through the axis (elbow) and a third that runs vertically through the biceps attachments on the radius and ulna (forearm).

You should now see three lines running parallel.  The axis and muscle insertion lines should be close together, and the dumbbell line will be a good distance away. The important element here is the distance between these lines.

This distance that is representative of the horizontal distance the dumbbell is from the muscle attachment is known as the resistance arm.  The horizontal distance of the muscle attachment from the axis is known as the effort arm.  If you place the effort arm (length) over the resistance arm (length), you get a ratio called the mechanical advantage.

Seeing as we know that the dumbbell is not changing its weight as we curl it, why does it feel heavier during that certain range of motion (our sticking point)?  Typically, it is at this time that the dumbbell is the furthest away (horizontally) from the elbow joint.  It is at this time that the length ratio between the resistance arm and the effort arm is the greatest. Since the ratio is high, the mechanical advantage is low.

This is one reason why people with longer arms and legs are normally not as strong as people with shorter limbs.  They have to deal with a bigger ratio and thus, a lower mechanical advantage.

Now that you understand that the further (horizontally) a weight is from its joint axis the heavier it is going to feel, it should make since that during a typically range of motion, the distance the weight is going to be from the axis is going to change.  This change is going to dramatically influence the mechanical advantage.  Concurrently, the amount of internal force required to move that dumbbell through a full range of motion is going to change with that mechanical advantage.

This is how the term force curve (or strength curve) got its name.  If you were to plot the mechanical advantage at several joint angles throughout a range of motion, it would form a curve.  This curve would consequently represent your different strength capabilities at those points.

Once we look at the interaction of these force curves during multi-joint activities, we start to see a composite force curve. Since the interaction of each lever is completely distinctive, this curve tends to be dissimilar to the individual curves (see figure 1).

Figure 1.  Composite Force Curve: From Science and

Practice of Strength Training.  Zatsiorsky, 1995

In this curve you will notice a rapid drop off.  It is at this point the force production ceases and momentum takes over.   It is important to note that the first half of the graph is representative of the force application characteristics we previously discussed.  The second half should be ignored due to the scope of this article.

Force Curves and Weight Training

Now that you understand force curves, lets discuss some methods of weight training that we typically use and their true relationship to the force curve. 

Free weights have been the training method of choice for many years now.  Since training with free weights has so many functional advantages, it has made training with machines obsolete.  When you look at the force curve of a free weight you will notices, that one it is not really a curve, and two it is completely flat (figure 2a).  Since time and displacement have not effect on the load of a free weight (a ten-pound db is always going to be a ten-pound db), the load over displacement graph is flat.

We can change the feel of this graph by changing the velocity for which we move the dumbbell.  Moving a weight faster is going to require more work, so the muscle activity will elevate.  The only problem with this is that it typically creates a greater deceleration phase, which means that the end range of motion is not getting adequate loading.

Many years ago, Nautilus decided to fight back and offer the world of strength training something that free weights could not.  They developed and elliptical cam (figure 2d) that would change the external load expression throughout the range of motion.  Nautilus defined what the typical strength curve would look like, and designed the pulley to match this curve.  This was quite innovative, but still fell short by performance standards. 

Not only were people losing the degrees of freedom associated with free weights, they were training on equipment that was not designed for their strength characteristics.  Not many people fit the typical profile used to design the pulleys.  Since so many people are different, the average tends to lye between what truly exists.  This made the flair of the elliptical cam fall by the way side and the free weights once again prevailed.    

Louie Simmons, owner of Westside barbell, and completive powerlifter, had been searching for an answer to this problem for some time.  Through his research and practical application, Louie began to tread into unfamiliar territory by adding heavy chains to the bar during free weight training. He noticed that his lifters were starting to experience huge gains in their strength. 

As time went by, and the popularity of chain training grew, the need to push the barrier a little farther once again presented itself.  Lou had heard from a colleague we had mentioned a new product known as Jumpstretch Bands.  Lou decided to try adding these bands to the training system, and once again, noticed huge gains in performance.

Finally, the ability to apply accommodative resistance to three-dimensional training was here.  We could have the benefits (tenfold) of the principles behind the elliptical pulley, yet maintain the obvious benefits of training with free weights.

Copyright Progressive Sporting Systems Inc., 2004-2006

Progressive Sporting Systems Inc., 4610 South Lost Street, Terre Haute, IN 47802