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• John R. Harry, PhD, CSCS

# Momentum in the Weight Room: Optimizing Load Selection and Quantitative Variation

Updated: Sep 6

Hey, folks. This post is a follow-up to our lab's publication accepted in the Journal of Strength & Conditioning Research, which sought to encourage the use of system momentum rather than velocity alone when determining the appropriate intensity for training, using the jump squat as an exemplar exercise. Here, I want to present the way you can use momentum to prescribe training intensities and quantitative variation to training, because accommodation and diminishing returns are the devil (as Bobby Boucher's mamma would say).

First, I need to provide some background information for those of you who've not read the article, are unfamiliar Newton's 2nd law of motion, or both, to help solidify the rationale and explain why velocity-based training is just a piece of the momentum puzzle. If you are already up to speed (see what I did there?) with Newton's 2nd law, you can skip to this section of the post.

Newton's law of acceleration is as follows:

a = ΣF/m

where a is an object's acceleration (i.e., how much it speeds up or slows down), ΣF is the sum of all external forces applied to the object, and m is the object's mass

This equation is most commonly referred to in its rearranged form that isolates the sum of forces, leaving the object's mass multiplied by its acceleration on the other side of the equation:

ΣF = ma

Based on the relationship among an object's position, velocity, and acceleration, we can re-write the above equation such that acceleration is replaced by the equation used to obtain it, which is the change of the object's velocity (Δv) divided by the change of time during which velocity changes (Δt):

ΣF = mΔv/Δt

In my undergraduate biomechanics course at Texas Tech University, I tell my students that the above equation holds a "secret" piece of information that you have to stay focused for, similar to an end-credits scene in a Marvel movie. That "secret" is momentum. It's a "secret" because you have to extract it from the equation, as momentum is the product of an object's mass and its velocity (mΔv). By isolating momentum to one side of the equation, we can create the granddaddy of all equations for motion slower than the speed of light: the impulse-momentum relationship, which states that the sum of external forces applied to an object multiplied by the time those forces are applied is equal to the objects change of momentum (i.e., the quantity of motion):

ΣFΔt = mΔv

Velocity-based training grew in popularity because there is plenty of literature demonstrating effectiveness, but the foundation for velocity-based training's effectiveness relates to the fact that velocity is inherent to Newton's 2nd law of motion. One potentially misunderstood part of the puzzle is what should be used as the inputted mass, the athlete or the athlete + load (i.e., the system). This figure below, from what I refer to as the real holy text for resistance training, does an excellent job demonstrating the importance of mass (and the way velocity is obtained from monitoring technology). Notice how the values of peak and mean velocity differ when obtained from only the external load (bar) versus the system (force plate)? Essentially, a practitioner's choice for how mass is included heavily impacts the result. The main issue with the velocity-only approach is that many practitioners hold velocity ranges in the highest regard and rarely deviate from them. One of the smartest people around, who happens to also be a pioneer of velocity-based training, Dr. Bryan Mann, came up with suggested ranges for many weight room exercises. These ranges, shown in the figure below, categorize certain combinations of training intensity (%1RM) and barbell velocity. Unfortunately, many lose sight of the fact that the ranges are suggested and not all-inclusive. Without going into too much detail for how training intensity should be selected using a velocity-based approach, training prescriptions are typically made such that a load is to be moved at a certain velocity based on the targeted stimulus (e.g., speed-strength, see block D in the figure). Data presented in the aforementioned real holy text for resistance training suggests a simple monitoring of the velocity achieved at a given load should be compared to a ± 3 % threshold relative to previous training sessions' velocity results, which indicates whether a load should be adjusted. You can also use velocity loss thresholds for this purpose, where a target velocity is considered and the training load should increase until the velocity achieved exceeds that loss threshold. These are both fine methods. The problem I have is three-fold. First, many athletes participate in sports where velocity is not the end-all-be-all, but rather an influential component. Collision sports, such as rugby and American Football are prime examples, where momentum created can be a more important attribute than velocity. Second, there are exercises known to be "ballistic", such as the jump squat, that don't reside in the velocity ranges presented above, despite being commonly considered a "speed-strength_ style exercise, which begs the question "how fast should an athlete train?". Finally, the manipulation of training load using the ± 3 % threshold or velocity loss threshold might be effective, but is most likely sub-optimal. Here's why.

Let's revisit the granddaddy equation, ΣFΔt = mΔv. The point of training with external loads is to create motion (velocity) while under greater physical demands than the normal environment (increased external mass). The trainee achieves this by applying a lot of force in a certain amount of time (or some combination of force application and time). It becomes very easy to focus on chasing certain velocities in the weight room that are close to the velocities in competition, but that can lead to lesser motion created during training or a less-than-stellar stimulus for the athlete when the motion created is well below their functional capacity. Consider the following example:

An 90 kg (~200 lbs) athlete is training with the clean pull exercise, and the global objective is to have that exercise's stimulus contribute to enhanced vertical jump ability. The athlete has a current maximum vertical jump of 0.6 m (~24 inches), which equates to a take-off velocity of 3.5 m/s. So, one my prescribe a training intensity in the clean pull where the athlete lifts the greatest load possible without the velocity decreasing by 10% (i.e., velocity loss), which would be ~3.15 m/s. So let's say the athlete's heaviest clean pull at no less than 3.15 m/s is 60 kg. This means the athlete created a system momentum (body + load) equal to ~472 kgm/s during the clean pull training. As, their jump momentum is equal to ~315 kgm/s (their body mass * their jump velocity), this load and velocity criteria is providing an adequate stimulus when compared to the target exercise.

But, let's forget about specific loads or velocities, and instead consider the momentum achieved versus the athletes maximum momentum created during the training exercise. Here, our goal shifts from locating a specific load that can be moved with a set velocity to identifying when the athlete can create the most momentum possible with the training exercise, ensuring that the momentum value is also greater than the target exercise,. So, if the athlete's heaviest clean pull with appropriate technique is 180 kg and they could perform that at 1.8 m/s, when accounting for their body mass, their system momentum would be equal to 486 kgm/s, which is greater than the previous prescription according to velocity loss. This means focusing on the velocity number during the training exercise can be limiting the athlete due to requiring them to create less motion than their ability allows.

It's important to note that all the loads and velocities performed while working up to that 180 kg should be considered. If those resulted in less momentum than the 180 kg at 1.8 m/s, then 486 kgm/s would be the target stimulus. If a lighter load was performed with a velocity that resulted in more than 486 kgm/s, then that momentum value would be the target stimulus. Data from the jump squat exercise, shown in the figure and table below, demonstrates how easy it is to locate this ideal stimulus when graphing the momentum achieved across a load spectrum. It also shows how variable the maximum momentum created can be across a group of athletes. To me, this is the way to locate the optimal training stimulus for an exercise.  Providing Quantitative Variation to the Training Load

Presuming I've convinced you to at least play around with momentum in place of velocity-only when determining the ideal training load for an athlete with a given exercise, we'll pivot to how to vary the load quantitatively. This simply means how the loads and velocities can be adjusted to avoid accommodation or negative training adaptations. Luckily, the component parts of momentum make this process very easy, and current velocity-based training users should be familiar with the process.

Let's again consider the example above, where the athlete was able to perform the clean pull for a maximum momentum of 486 kgm/s, achieved though a 180 kg load (plus their 90 kg mass) moved at 1.8 m/s. The objective for this athlete when performing the clean pull throughout a training cycle or block should be to maintain the 486 kgm/s of momentum during each session, similar to how the same 1RM percentages or velocity ranges would be used until a new test session takes place to demonstrate change or modify training. So, all that needs to happen is an increase or decrease of the load in conjunction with a decrease or increase of velocity such that the 486 kgm/s momentum value is constant throughout training.

For example, on one training day, the clean pull could be prescribed such that the athlete must perform the exercise with 120 kg and a velocity ~2.3 m/s ([90 kg mass + 120 kg load]*2.3 m/s = 486 kgm/s). For the next training session, presuming the practitioner prefers a daily undulating method, the clean pull could be prescribed so the athlete lifts 150 kg at ~2 m/s. The way in which the loads and velocities are manipulated should not matter much so long as the momentum value is constant. While the day-to-day change described in this paragraph is for a daily undulating approach, the concept can be applied to any training approach (linear, weekly undulation, etc.). Remember, the goal is to create motion under greater-than-normal demands without holding the athlete back.

Before I sign off, the strength and conditioning community NEEDS longitudinal data demonstration the momentum-based approach is superior. Still, I'll bet the house that it is, because you know, Newton hasn't really been wrong yet. Just sayin'.