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Secrets of Speed and Quickness Training
A collection of articles
by Dr. Larry Van Such - Vol. 17 - Part 2





Part 1 - Resistance Band Training For Athletes
Part 2 - Resistance Band Training vs Weights - Do The Math
Part 3 - Resistance Band Training with Isometrics
Part 4 - Becoming An All-Star Athlete


The Math Shows Why Isometrics with Resistance Band Training Differs From Isometrics With Weights

Part 2 of 4

Have you ever wondered why certain exercises are easy at the start, tough in the middle and perhaps easy again toward the end?

Let’s take the biceps curl using dumbbells as an example. At the start of this exercise, let’s say you are standing up on both feet and a 25 lbs. weight is down by your side. See Figure A.

As you proceed with the biceps curl, you start to flex your forearms upward. During the first few degrees of elbow flexion, the weight is easy to move. For example, a 25 lbs. dumbbell flexed to just 30º in front of you feels only like 12.5 (lbs.– feet)** at the elbow. See Figure B.

At 45º of elbow flexion, the 25 lbs. weight feels about 17 (lbs.– feet)** at the elbow. See Figure C. It’s not until you start getting near 90º of elbow flexion where the full weight of the 25 lbs. dumbbell, held in your hand, is experienced at your elbow joint and biceps muscle. See Figure D.

If you go above 90º, the exercise starts to get easier again. See Figure E.

Some of you who are reading this may also find that you can catch your breath with this exercise at the top end of this motion, where the weight seems to collapse a little back toward your shoulders.


Figure A. 0º elbow flexion.

Figure B. 30º elbow flexion.

Figure C. 45º elbow flexion




Figure D. 90º elbow flexion.

Figure E. 120º elbow flexion.

Everyone experiences this situation; it doesn’t matter who you are. This is because the mechanics involved in the biceps curl are basically the same for everybody. More specifically, the amount of force generated at the elbow joint, as you may have guessed, changes in proportion to the angle of this joint as it traverses its full range of motion during a curl.

**Introducing the MOMENT of FORCE.

Measured not just in lbs., but in lbs-feet

You may have noticed that in determining the force applied at the elbow joint was not just written in lbs., but in lbs.–feet. This unit of measurement is the called the Moment of Force and it is defined more specifically as follows:

A moment of force is any force that can provide the effect of turning about an axis if it does not act parallel to the axis or have a line of action which passes through the axis.

Understanding the concept of how the moment of force is calculated is not necessarily easy, but it is not that hard either. There is a little basic geometry involved and that’s about it.

Once you see how the moment of force is calculated one or two times, you should be able to calculate it for any angle in our biceps curl example by simply interchanging one number; and you will then be able to see why the biceps curl exercise is easier in some places than others.

Do the math!

In Figure 1 below, the athlete is holding a 25 lb. dumbbell down by his side in the starting position. His elbow is not flexed but rather extended to 180º and his forearm is perpendicular to the ground. The forearm represents the moment arm, LA, and is estimated, for our purposes, at 1 foot in length.

In this position, the weight has a line of action which passes through the axis, which is the elbow joint. So, our expectation, based upon the definition of the moment of force above, is that there should be 0 lbs of force applied to the elbow joint in this positon.

We also know this instinctively when we perform it in the gym since this is also a resting position for this exercise; in other words, no force on the biceps muscle in this position means no extra effort is required to move the weight at the elbow joint. Let’s see how this calculates out:


Figure 1. Elbow fully extended to 180º.

Calculation of moment of force at the elbow joint using the following equation:

Melbow = FP x L A

In Figure 1 above we have:

F1 = 25 lbs., A1 = 90º, LA = Moment Arm (forearm length) = 1 ft.

First, we have to convert the 25 lbs. weight acting straight down to one that is perpendicular to the moment arm (forearm).

FP = Fperpendicular = F1 x Cosine A1 (90º)

Fperpendicular = 25 lbs. x 0 = 0 lbs.

Now we can calculate the moment of force at the elbow joint using the equation:

Melbow = FP x LA

Melbow = 0 lbs. x 1 foot = 0 lbs-feet.

The moment of force is calculated to be 0 lbs. feet, i.e. no moment force on the elbow. This is what we expected and is why this exercise is easiest in the beginning; the elbow joint has no rotational force applied to it, i.e., the force will not cause the elbow joint to rotate clockwise or counterclockwise in this position

Now let’s see what happens when we decide to move the weight by flexing the elbow to say, 30º. See Figure 2 below.

Here, the elbow is flexed to 30º. This is angle A0 in the figure near the elbow. The force F1 is still 25 lbs. and is acting straight down, however, it needs to first be converted to a force acting perpendicular to the moment arm, LA. Again, LA is the length of the forearm and is estimated to be 1 foot long. The perpendicular force is labeled FP in the figure. The angle A1, is 60º and is the angle needed to bring this force perpendicular to the moment arm, not 30º. Therefore, the moment of force is calcuated below:


Figure 2. Elbow fully extended to 30º.

Calculation of moment of force at the elbow joint using the following equation:

Melbow = FP x L A

In Figure 2 above we have:

F1 = 25 lbs., A1 = 60º, LA = Moment Arm (forearm length) = 1 ft.

First, we have to convert the 25 lbs. weight acting straight down to one that is perpendicular to the moment arm (forearm).

FP = Fperpendicular = F1 x Cosine A1 (60º)

Fperpendicular = 25 lbs. x 0.5 = 12.5 lbs.

Now we can calculate the moment of force at the elbow joint using the equation:

Melbow = FP x LA

Melbow = 12.5 lbs. x 1 foot = 12.5 lbs-feet.

As expected, the amount of force at the elbow joint starts to increase with flexion of the elbow joint by the biceps muscle. This number should increase all the way up to 90º of elbow flexion, then it should begin to decrease again after that.

This is because the only variable in this equation is the angle in which the elbow joint is flexed and that variable is tied into the perpendicular force equation, which is needed to ultimately determine the moment of force, by calculating it’s cosine equivalent. The maximum value of any cosine computation is 1, and that occurs only at 90º. Every other number produces a cosine computation of less than 1.

This is what is experienced in the gym with this exercise, so let’s go ahead and see if our calcuations prove this. Let’s see what happens at 45º of elbow flexion. See Figure 3 below.

Here, the elbow is flexed to 45º. This is angle A0 in Figure 3 near the elbow. The force F1 is still 25 lbs., however, it needs to first be converted to a force acting perpendicular to the moment arm, LA. The angle A1, is also 45º and is the angle needed to bring this force perpendicular to the moment arm. Therefore, the moment of force is calcuated below:


Figure 3. Elbow is flexed to 45º.

Calculation of moment of force at the elbow joint using the following equation:

Melbow = FP x L A

In Figure 3 above we have:

F1 = 25 lbs., A1 = 45º, LA = Moment Arm (forearm length) = 1 ft.

First, we have to convert the 25 lbs. weight acting straight down to one that is perpendicular to the moment arm (forearm).

FP = Fperpendicular = F1 x Cosine A1 (45º)

Fperpendicular = 25 lbs. x 0.707 = 17.67 lbs.

Now we can calculate the moment of force at the elbow joint using the equation:

Melbow = FP x LA

Melbow =17.67 lbs. x 1 foot = 17.67 lbs-feet.

Again, as expected as well as experienced in the gym, the amount of force at the elbow joint starts to increase with flexion of the elbow joint by the biceps muscle.

Now let’s see what happens at 90º. This is angle A0 in Figure 4 below. The force F1 is still 25 lbs., however, in this case, it does not need to be converted to a force acting perpendicular to the moment arm, LA because it already is. This is angle A1, and is the ‘angle’ between F1 and FP, which is 0º. Therefore, the moment of force is calcuated below:


Figure 4. Elbow is flexed to 90º.

Calculation of moment of force at the elbow joint using the following equation:

Melbow = FP x L A

In Figure 4 above we have:

F1 = 25 lbs., A1 = 0º, LA = Moment Arm (forearm length) = 1 ft.

First, even though the force (F1) is already perpendicular to the moment arm, we should calculate it anyway.

FP = Fperpendicular = F1 x Cosine A1 (0º)

Fperpendicular = 25 lbs. x 1 = 25 lbs.

Now we can calculate the moment of force at the elbow joint using the equation:

Melbow = FP x LA

Melbow = 25 lbs. x 1 foot = 25 lbs-feet.

Again, as expected as well as experienced in the gym, the amount of force at the elbow joint increase with more flexion of the elbow joint by the biceps muscle.

But does the moment of force continue to increase with elbow flexion beyond 90º? Experience in the gym tells us it should decrease, but let’s take a look anyway.

This time the angle of the elbow joint is 120º. This is angle A0 in Figure 5. The force F1 is still 25 lbs., however, it needs to first be converted to a force acting perpendicular to the moment arm, LA. The angle A1, is determined through geometry as 30º and is the angle needed to bring this force perpendicular to the forearm. Therefore, the moment of force is calcuated below:


Figure 5. Elbow is flexed to 120º.

Calculation of moment of force at the elbow joint using the following equation:

Melbow = FP x L A

In Figure 5 above we have:

F1 = 25 lbs., A1 = 30º, LA = Moment Arm (forearm length) = 1 ft.

First, we have to convert the 25 lbs. weight acting straight down to one that is perpendicular to the moment arm (forearm length).

FP = Fperpendicular = F1 x Cosine A1 (30º)

Fperpendicular = 25 lbs. x 0.866 = 21.65 lbs.

Now we can calculate the moment of force at the elbow joint using the equation:

Melbow = FP x LA

Melbow = 21.65 lbs. x 1 foot = 21.65 lbs-feet.

Again, as expected, the biceps curl becomes easier once we get past 90 degrees of elbow flexion.

Again, the only variable in this equation is the angle of the elbow joint:

Melbow = F1 x’s Cosine A1 x LA

F1 = 25 lbs. (Constant)

LA = 1 foot. (Constant)

A1 (Varies from 0º to about 140º for natural elbow flexion)

The static weight of the dumbbell never changes both in its amount of force as well as it’s direction of force. It is always 25 lbs. acting straight downward and therefore, the entire force delivered to the biceps muscle through the elbow joint is a function of the angle of the joint only.

What happens when resitance bands are used?

When resistance bands are used this way instead of weights, there are two more dynamic variables that get added to the equation which makes calculating the amount of force delivered to your muscles a little more difficult. It also makes the final forced delivered to them more unpredictable.

The first additional variable has to do with the change in the value of the force that is applied with different degrees of motion of a particular joint, such as the elbow in our example here.

Whereas a weight will always deliver the same force, 25 lbs in this example, the force of a stretched band increases as the band is stretched further and decreases as the band is stretched less.

The second additonal variable is the direction of force delivered by the stretched band. Unlike the static weight which always acts straight down, the direction, or vector of the force supplied by the band is always directed back toward where the other end is attached. It rarely acts perpendicularly straight down.

What happens when the band is held steady as in an isometric contraction?

Both of these variables continuously change, even with isometric holds during an exercise. This is because a muscle undergoing a significant amount of force while trying to hold the resistance in a fixed position will still move, ever so slightly as motor units are recruited to support the demand of the force.

These small changes, sometimes only a millimeter or two in the beginning, start to increase as a muscle weakens and begins to tire. The more they increase, the more dynamic the change is in the amount of force and direction of force delivered back in to the muscle forcing it to immediately compensate even to the slightest of changes.

Therefore, the variable resistance of the bands along with the varying angles of its force, when applied to muscles using an isometric training strategy and for the proper length of time, is the key to training your muscles for a more dynamic and athletic response. It is an extremely superior form of speed training when done properly. We call it pure speed training.

It will take some explaining to do and will be done in part 3. If you understood this much so far, or at least can relate to the idea that changes in angles affect the amount of forces on the joints, it shouldn’t be a problem for you.

“We’ll bring you up to speed!”®

Part 1 - Resistance Band Training For Athletes
Part 2 - Resistance Band Training vs Weights - Do The Math
Part 3 - Resistance Band Training with Isometrics
Part 4 - Becoming An All-Star Athlete

Always glad to help!
Dr. Larry Van Such




Speed Training For All Sports
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