As a high school math teacher, I have heard the phrase “I am not a math person” more times than I would like to count. The truth is, being human qualifies us all as being “math people”—it is just a choice of whether or not we embrace it. At the core of mathematics lies the ability to reason. We all can recognize patterns and form a conclusion (inductive reasoning) or apply previously learned facts to a situation to form a conclusion (deductive reasoning). We can try to run from mathematics or pretend it doesn’t exist, but the reality is that it is omnipresent.
“But Rob, that’s not the kind of math I’m talking about!” Yes, I get it. Formulas, numbers, and wild symbols can be extremely intimidating and cause a person to go into shutdown mode. So, what are you to do when faced with this complexity? Like anything else, find a master teacher who can take complicated ideas and reduce them to digestible pieces.
Dr. Dan Cleather is a person who falls into this category. I was first introduced to his work when his Little Black Book of Training Wisdom was for sale on Amazon for one dollar. I figured I had nothing to lose with the purchase, and it will always remain near the top of my “best bang for the buck” list when it comes to books. I immediately took to his writing style: eliminate fluff, do not talk over the reader, emphasize clarity above all else. So, I was extremely excited when Force: The Biomechanics of Training came out earlier this year.
Force is a 152-page book divided into 26 short chapters. I viewed each chapter as a mini-lesson. While the book could easily be read in a single two- to four-hour sitting, I found value in taking my time. Beginning the book coincided with the installation of a sauna in my basement—over the course of 20 days, I read a chapter or two upon entering the sauna (10 minutes of reading) and then sat and thought about what I’d read (10 more minutes). After exiting the sauna and showering, I wrote down my thoughts. This process allowed the content to “stick” much more than a normal read.
In this review, I will cover seven topics:
- Maximizing impulse
- Force vector theory
- Debunking the force-velocity curve
- Force absorption?
I chose these because they either had the most impact on me or I believe they are essential for you to get a feel for the content presented. While I found having a math background helpful in reading, it is 100% NOT a prerequisite! Dr. Cleather does a great job of explaining everything the reader needs to know, and he provides the mathematical explanation behind it in footnotes for those who are interested in “nerding out.”
Not surprisingly, Cleather opens with a discussion of force and how it is the cause of change in velocity. One of the issues we find in human movement is that force isn’t applied consistently. This example of a countermovement jump gives an overlay of the force-time curve during the process of the jump. The inconsistent force applied during the movement makes it challenging to calculate the total force applied.
This is where calculus comes in to save the day—and the good news is we do not need to understand the nitty-gritty part of the calculus, just the concept! Figure 1 shows a hypothetical force-time curve during a countermovement jump. The total force applied is the area underneath the curve, called the impulse.
Cleather points out that impulse (total force) and change in velocity are directly proportional to one another. In other words, if impulse increases, so does the change in velocity. Cleather emphasizes that an issue he sees in training circles is a lack of focus on impulse. He states, “In many cases, we can explain differences in explosive physical performances in terms of impulse generation.” Instead, he sees coaches more interested in peak power or peak force—more on both of these later.Cleather emphasizes that an issue he sees in training circles is a lack of focus on impulse…he sees coaches more interested in peak power or peak force, says @HFJumps. Click To Tweet
3. Maximizing Impulse
If impulse is such a big deal, how can we go about improving the amount applied during a movement? Again, if the area underneath a force-time curve represents an impulse, Dr. Cleather identifies three ways in which the area can be increased:
- Increase the amount of time the force is applied.
• This creates a greater “width” for the area.
- Increase the peak force applied over the same time interval.
• This creates a greater “height” for the area.
- Increase the rate of force development over the same time interval.
• This increases the slope of the curve, which allows for a greater area underneath. In other words, the athlete reaches higher force faster.
This section probably caused the most significant amount of reflection for me, and it will never be finished. As a track coach who truly enjoys the process of developing more efficient and explosive sprinters, optimizing impulse is something that is always on my mind.
In general, as running speed increases, ground contact time decreases. To make up for the loss of time on the ground, the force applied has to increase so the runner can move faster. A simple way to think of this is if the base of a rectangle decreases (less ground contact time), then the height (force) must increase by more than the base decreases to create a greater impulse (area of the rectangle).
In order to optimize impulse, a coach must consider two parameters: force and time. However, it is not just about optimizing impulse; it is doing so within the limits of the task at hand. If we are discussing sprinting at maximum velocity, there is a spectrum of ground contact times that are deemed acceptable based on the level of the athlete. In general:
- Shorter ground contact times are great. The athlete has an opportunity to get to the finish line faster. However, there could be an athlete who is unable to showcase their gift of exerting force in the shorter time interval. This could lead to slower times!
- More force is great if it can be applied in the same or shorter time interval. If the athlete spends too much time on the ground to achieve higher forces, the impulse does go up. However, the race clock is still ticking, and the greater impulse may not make up for the excessive time on the ground (or the possible extended time in flight thereafter).
Before discussing power, we first need to define work. Remember, the area under a force-time curve is the impulse. If we change the x-axis to represent position (creating a different-looking curve), the area under the force-position curve would be the work; or, as Cleather states, “total force with respect to distance moved.”
This relates to power because power is the rate of doing work. In other words, power equals work divided by time. As stated earlier, power is often a metric that coaches focus on. Cleather feels this is misguided:
“For many explosive sports skills, the change in velocity during the movement is one of the most important performance variables. This is why impulse is so important for us—impulse accrued is directly proportional to the velocity change. Unfortunately, there isn’t the same type of direct link between power and change in velocity, and so it is less useful for qualifying explosive sports performance.”
If the “direct link” does not click here, think of it this way: Impulse is the area under a force-time curve. To calculate power, work must first be accrued, and then it needs to be divided by time. Cleather goes on to say,
“There is, however, an indirect link between power and change in velocity. This means that power will still tend to be well correlated with explosive performances like vertical jumping or weightlifting. These correlations lead coaches to believe that power is the most important variable and are sometimes used to justify their interest in it.”
I will say that this section on power was one that I had to revisit multiple times. Categorizing items as “over an interval” versus “instantaneous” was helpful for me. Regardless, it has caused me to rethink tests to capture power as a metric.This section on power was one that I had to revisit multiple times…It has caused me to rethink tests to capture power as a metric, says @HFJumps. Click To Tweet
5. Force-Vector Theory
This was one of my favorite sections, partly because of Cleather’s humor when pointing out that the name is silly (force is a vector), but mostly due to the elegance he used to break down a body-fixed coordinate system versus a world-fixed coordinate system and the implications when they are misused.
Cleather begins with a straightforward example: If an athlete were to run into a jump off a single leg and try to jump as high as possible, the ground reaction force would be directed vertically (think directed through the body and out of the head). The body-fixed and world-fixed coordinate systems would be the same in this example. If an athlete were to perform a block start, the ground reaction force would have a horizontal component in relation to the world-fixed coordinate system (maybe forming a 50-degree angle with the horizontal). However, the ground reaction force would still be directed through the body and out of the head in reference to the body-fixed coordinate system.
Cleather then provides an example where this concept shows an issue with a claim. The barbell hip thrust is a popular exercise, and some advocate for its use due to a “horizontal component” to the movement like the one found when an athlete accelerates. However, the reality is that the ground reaction force in the exercise is directed vertically to the world-fixed coordinated system and NOT through the athlete’s body and out of their head as it is in acceleration. This does not mean that the exercise is pointless; it just means that the “horizontal component” argument should not be used.
6. Debunking the Force-Velocity Curve
The force-velocity curve has always bothered me. As a track coach, I have a bias about the importance of sprinting, which would be placed at the far right of the curve, signifying high velocity but low force. This never sat well with me, as I know sprinters have a vertical ground reaction force of 3+ times their body weight…on a single leg. In many cases, the force of a sprint during a single contact would be similar to that found within a rep of a 90% of 1RM back squat. The 90% of 1RM back squat falls on the far left of the curve, signifying high force but low velocity.
If there is a similar force, does it make sense to place the activities on different parts of the spectrum?Cleather does a wonderful job of explaining this issue… and clarifies what the curve should be called: the load-velocity curve. If force is replaced with load, the relationship works. Click To Tweet
Cleather does a wonderful job explaining this issue with specific examples and clarifies what the curve should be called: the load-velocity curve. If force is replaced with load, the relationship works.
The velocity is low if the load is high (heavy back squats). The velocity will be high if the load is low (bodyweight). Language matters, and I am 100% on board with this change. Load and force are two different entities. Cleather states, “We don’t necessarily require a large load to express high forces, and in sport we are often most interested in increasing the force that an athlete can apply against a fixed load—their own body weight.”
7. Force Absorption?
A common phrase utilized in strength and conditioning is “absorbing force.” I have certainly used it in the past; however, I stopped once I read a thread from Dr. Cleather on social media. Again, language matters, and we need to be sure we strive to deliver messages as clearly and accurately as possible. Precise language eliminates ambiguity.
It is why I do not allow students to call the denominator “the bottom” in my math class. There are cases where “the bottom” would not be specific enough. It is why I do not let my children say they did “stuff” at school. Anyone who has seen the “Yada Yada” episode of Seinfeld knows the danger of allowing ambiguity.
Many readers will probably say that hairs are being split here, but I will side with Dr. Cleather on this one. The thread linked above does a wonderful job of explaining the reasoning, but in the book, Cleather provides the foundation as to why a force cannot be absorbed: “This is a direct consequence of Newton’s 3rd Law. If an object exerts a force upon us, we in turn exert the same force back on it. We do this by producing, not absorbing, forces.” The eccentric portion of a movement is where the “force absorption” is believed to exist. The correct terminology is “ability to express force eccentrically.”
Cleather does state that elastic energy can be stored and reused, but he identifies that it does come with specific criteria:
- The shift in movement must be rapid. Think short ground contact times such as in sprinting and particular jumping. A movement is often said to be a “true plyometric” if the contact time is below 250 milliseconds.
- Stiffer tendons are more efficient in storing elastic energy. “However, in order to stretch a stiffer tendon, the athlete will need to be stronger.”
A perk of teaching AP Calculus is that it overlaps nicely with concepts that most of my students are dealing with in AP Physics. A few days ago, they asked me if I thought I could teach physics. My response was, “At the moment, no—physics is hard.” What I meant by that is that while I understand a good portion of the mathematics behind the physics, I would need to spend more time with the concepts to teach them effectively.
Dr. Cleather has done a fantastic job of taking complex material and making it digestible for all, and this review only scratches the surface. Outstanding chapters on hot strength and conditioning topics such as velocity-based training, dynamic correspondence, dynamic systems theory, and force-velocity profiling will undoubtedly challenge readers’ thoughts.Physics may not be everyone’s favorite, but a baseline understanding by anyone in athletics would help eliminate some of the “interesting” claims, methods, and beliefs displayed on social media. Click To Tweet
Physics (and math) may not be everyone’s favorite content. Still, a baseline understanding by anyone involved in athletics would help eliminate some of the “interesting” claims, methods, and beliefs regularly displayed on social media. Invest a few hours in Dr. Cleather’s book and an understanding of force will always be with you.
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