The Mathematics of Torque

How heavy are Clubbells, really? How hard is it to swing a heavier Clubbell®?  How much work is it to swing it faster?  How quickly can I expect to progress in weight?  What is the increase in perceived effort as I move through the different weight divisions? This article will provide answers to these questions that make both logical and intuitive sense.

First we consider a relatively well known aspect of circular motion, the applied moment to moment force causing an object to rotate, called torque.   This is just one part of the total work involved in swinging a Clubbell®, but it is easy to understand and nicely illustrates the answers to our questions.  Also, the concepts we need will give us a deeper appreciation for the nuances of work involved in swinging any weight.

There are a couple of ways we might proceed.  We could use Newton 's Laws of Motion, applying vector analysis to the various forces involved, a method more suitable to the mathematically masochistic.  Or we could look at the work-energy relationship involved in swinging, using a few easily understood and intuitive concepts to draw some useful conclusions.                     

Let's avoid complex formulas and take a simpler approach...examining circular motion from an energy expenditure point of view (work), and how this might apply to the various Clubbell® weights.

To answer our questions and aid our understanding, we need a few concepts:

  • Force is the product of an object's mass and its acceleration. 
  • Work (perceived effort) is force acting through a distance over time.
  • Energy is the capacity to do work.
  • Power is the rate at which work is accomplished.
  • Torque is force causing rotational motion (Clubbell® weight times radius of swing)

Here, energy can be thought of as potential (inactive) and work as kinetic (active).  Then power generation becomes the rate at which we can conduct or channel our energy (convert potential to kinetic) as we swing the club.

From physics, we also know that for an object of constant mass and a circle of constant radius, the net force required to move the object in a circle is directly proportional to the square of the object's speed.   If the speed is doubled, the force is quadrupled.  In other words, to swing a Clubbell® twice as fast takes four times the work.

So the energy (expended as work) required to generate power involves torque applied over a distance (arc or full circle) for a given time (duration of swing * total reps).  Things affecting power generation are the mass of the Clubbell®, the acceleration (both keeping it going and stopping it on a dime), the distance the club moves through space (shorter or longer club, arc or full circle), the duration of the motion, and finally the speed.

We can think of (some of) the work required to swing a Clubbell® as torque applied along the arc of the swing at a given rate (speed) for a given duration (reps).  This is rather simplistic and ignores many other forces, such as centripetal force (grip strength) required just to hang on to the Clubbell®.  But the concepts are pretty intuitive.  We all know how the number and speed of reps influences our perceived effort, and our bodies know that there is a lot more going on than just torque when we work out.

Looking at the following chart (here's the multiplication), we can see how the amount of work (torque) goes up quickly as the size of the Clubbell® increases:

Weight Length Torque
5 lbs 20 inches 100
10 lbs 25 inches 250
15 lbs 25 inches 375
20 lbs 25 inches 500
25 lbs 27 inches 675
45 lbs 27 inches 1215

The difference in weight between the smallest and largest Clubbell® is only forty pounds.  But the amount of work necessary to use it is more than ten times as much.  (Units are irrelevant here for torque, since we're just looking at relative percentages).   And this isn't counting grip strength!  In addition, the explosive start and the rapid stopping on a dime compress the time component, increasing the acceleration/deceleration, so the work component jumps up (force equals mass times acceleration).

If someone did somehow manage to double the speed and also jump in size from 5 to 45, it would take an energy expenditure that goes from 100 to 4860, an increase of 48 times.  Applying this same reasoning, we can figure out the relationships between any two Clubbell®s.  For example, just a five pound jump from the 5 to the 10 pound Clubbell® increases the workload by one hundred and fifty percent, assuming no increase in rotational speed.

It is important to remember that torque is just one aspect of the work involved in Clubbell® training.  The movements are multi-planar and non-uniform, and when combination routines are considered, it would take a super-computer to figure out all the forces involved and the energy expended.

It is clearly important to accurately assess one's strength and capacity for work before jumping to the next size Clubbell®.  Circular Strength Training places real demands on the body that increase rapidly with just small increases in weight.  Adding weight multiplies work.

Michael Gannon, CST Alpha

The Clubbell certification was extremely informative. As a trainers, we have many approaches to fitness, but being able to implement something as dynamic and beneficial as clubbells just makes the training we can offer that much stronger. The clubbell certification instructed by Coach Jones was great. It emphasized proper technique providing various progressions and modifications to suite a vast range of fitness levels. I am able to use what I learned from coach Jones with any and all of my clients. This certification is a good tool for all trainers to have, or even for those who just want to get a better understanding of club bells in general.  -Tess Kovit

I really like your web site. I forwarded it to a lot of friends who still can't figure out what I'm doing now that I quit the gym. -Robert Cremers

Since learning and getting certified on the clubbell certification months ago, I have had an opportunity to try some of the techniques Ive learned. As a professional MMA fighter, it has definitely improved some of my training routines. I find I have more grip strength, which is needed in my sport. I have also noticed an increase in core strength as well as mobility in my shoulders. Also a useful tool in MMA.

Aside from my own training, I have also started using the clubbell for my more advanced personal training clients. This has been a great way for me to mix up their workouts and make them a little more interesting and fun.

I would like continue learning more clubbell movements and techniques. In a short period of time I was able to expand my training and overall fitness using a tool that has so many dynamic aspects to it. -Joey Bareng

The clubbell certification was great!  I learned a lot of new exercises & combinations that I can use with my clients.  It was very hands on, so i didn't get confused at all and the instructions were very clear as to what we would be learning.  I especially liked the progressions of the movements & exercises because I could use them with my clients who are all at different levels. -Joanne Luat

I found the Clubbell workshop very informative and helpful.  Even though I had a previous certification in the Clubbell system, I learned a lot of new information from Coach Jones.  Some of the teaching progressions and techniques had changed.  I appreciate J Janero's effort to provide continuing education to the staff by bringing in top fitness professionals like Coach Jones.  This keeps all of us current on the latest techniques and developments so that we in turn can provide the best service to the clients.  I would recommend the RMAX Clubbell Certification to all trainers. -Steve Maxwell