## Articles

### Summation of Forces About The Knee Equals Zero: Knee Loading In A Properly Performed Low-Bar Squat

##### by Tom Bailey | January 12, 2022

Before I found the Starting Strength program, I was a runner and basketball player, with the resulting sore knees consistently limiting what I intended to do. I expected the same knee soreness or worse when I began to low-bar squat in middle age as part of my Novice Linear Progression. I was surprised that my knees felt great as my squats progressed through my NLP. Later I read Starting Strength: Basic Barbell Training 3rd edition, which details how the knee is loaded during a properly performed low-bar squat (the author is compelled to use the phrase “properly performed low-bar squat” to specify the squat form indicated in Starting Strength and instructed by Starting Strength Coaches, in order to differentiate it from high-bar squats, partial squats, front squats, and up-on-the-toes versions frequently found in the Exercise Science literature), and why the forces acting on the knee are balanced. In my college engineering classes, we would describe this state as “The summation of forces about the knee equals zero,” or expressed mathematically, Fknee = 0.

The sum of forces acting upon the knee, or the cumulative magnitude and direction of those forces is the subject of this article. It is important to understand that Fknee = 0 does not mean there are no forces acting upon the knee in a squat. Rather, the magnitude and direction of the forces cancel each other out such that the net effect is negligible. In the study of Statics or Kinetics we refer to this state as the forces being balanced [1, 2]. Starting Strength trainees know that in a properly performed low-bar squat, it is primarily the hip extensors – adductors, glutes, and hamstrings – as well as the knee extensors (quads) which generate the force transferred to the bar. This becomes obvious when a low-bar squat is performed correctly, as the trainee will use “hip drive” to move the weight, not merely knee extension.

Instead of using the knees as either the brakes or the prime movers, the trainee learns to use the stretch of the adductors, glutes, and external groin muscles to initiate hip drive from the bottom position, while the hamstrings support the back angle during the upward drive of the hips. The knees are simply along for the ride, provided the feet are shoulder width apart, toes pointing out at 30 degrees, and the knees are shoved out as the femurs stay in line with the feet. If we feel anything in the knees, it usually indicates a partial squat, the Center of Mass forward of mid-foot, or knees not shoved out into sufficient abduction. In other words, if we feel it in our knees we are not properly performing a low-bar squat. Everyone knows that, right?

The author under the bar at proper depth. At this position, the forces acting upon the knee are balanced assuming the knees are in proper position, the center of mass is over the mid-foot, and proper depth is reached.

It never bothered me until now that few people understood that properly performed low-bar squats were safe for the knees. Here’s why: my son recently had to undergo knee surgery for cartilage damage sustained from playing competitive volleyball. We live in a large city in the Northeast, considered to be the home of some of the best hospitals and medical professionals in the world. We were fortunate to have a highly regarded orthopedic surgeon perform the operation at a nationally known hospital. In fact, this surgeon is so highly regarded he has a building (or is it a wing?) named after him at the hospital.

At my son’s appointment two months after surgery, I asked the doctor a question that I knew I shouldn’t have asked, but as usual I couldn’t help myself. “Doctor, when the cartilage is fully healed, what’s your take on squats?” My wife gave me that look, because she knew what I meant. I won’t bore you with the details, but the good doctor’s reply was something about “a conference overseas reviewed it” and how high school athletes should not squat but instead use the leg press machine. Showing some discretion, I wisely decided against mumbling a famous Mark Rippetoe line under my breath: “You don’t get to do the squat wrong and then call it unsafe.”

In his book Strong Enough? Thoughts from Thirty Years of Barbell Training, Rip addresses this issue precisely: “This is not to say doctors, PTs, and nurses haven’t been exposed to knee anatomy. They have, but they have not been exposed to correct squatting, and thus they have no idea about how the movement is related to knee anatomy.” It’s one thing to read that and nod my head in agreement, and it is quite another to be sitting in that doctor’s office, in the building named after him, looking at all the board certifications and diplomas on the wall while listening to him tell my family that squats are unsafe.

Why would a well-respected orthopedic surgeon not know that properly performed low-bar squats are safe for the knees? After all, there must be volumes of peer-reviewed and well-cited published papers that conclusively demonstrate that properly performed low-bar squats do not harm the knee. (I have two medical doctors in my family. They are unbelievably intelligent, so I thought it odd that this doctor would hold that opinion.) All I had to do was find a few of these published studies to demonstrate that properly performed low-bar squats are safe, and ask the surgeon to read them. Problem solved.

I got this. Hold my beer.

I imagined the large number of respected studies which accurately measure the tensile and compressive loading and shear forces on the knee during a low-bar squat. Obviously the Exercise Science community has this covered, right? Not so much, as I was to find out, because I would have to: a) remove “properly performed” and “low-bar” from my search criteria, and b) not be concerned with how a squat is defined. As proof, allow me to present the first three ExSci studies I found when I searched for “knee loading during a squat.” After I saw these I realized that if the doctor had the same studies, of course he would draw the wrong conclusions.

The first study seemed to be very applicable: Forces and Moments on the Knee During Kneeling and Squatting [3]. Great title, but my hopes were dashed when I saw how the squat position is defined.

Notice how the squat is performed, which appears to be a partial squat while up on the toes.

A diagram from the paper Forces and Moments on the Knee During Kneeling and Squatting indicating how a squat was performed in the study.

A partial squat while up on the toes? I thought this was a typo until I saw another diagram later in the study with the exact same form, now with with external force diagrams. The key takeaway here is that performing partial squats while up on the toes passes for a “squat” in the literature. I can only assume that if the doctor saw this article he now believes that is the squat position to be used.

A Free Body Diagram (FDB) used in the same study. Note the center of mass well forward of mid-foot and the heels well off the ground.

Further, consider how a partial squat position on the balls of the feet can skew any calculations. Note the angle of the so called z-axis while the tibia is is pushed forward and how that changes the resulting moment on the knees as the the weight is directly on the balls of the feet. We should question how the conclusions would be different if the feet were flat and the Center of Mass was over the mid-foot. For many reasons, I passed on deriving any meaningful conclusions from this paper.

The second study had a title which also caught my attention. I was excited to read Knee Joint Loading in Healthy Adults During Functional Exercises: Implications for Rehabilitation Guidelines [4]. However, buried deep in the paper was this description of how a squat was performed:

Squat: squat down from upright standing to 90° of self-perceived knee flexion and rise. Participants started in upright standing, with arms fixed at the waist and both feet on a separate force plate. The squat was analyzed from the first 1.5% decrease in vertical ground reaction force until stabilizing in a zone around 1.5% of the ground reaction force.

See the problem here? The scariest words in strength training are involved: “self-perceived.”

Self-perceived depth – that’s a good one! Imagine an untrained sedentary person with likely poor strength and balance attempting to accurately self-evaluate a multi-joint movement without an objective criterion for depth. Why not ask the untrained sedentary study participants for their “self-perceived” RPE, and then plot RPE vs self-perceived depth? I also disregarded this paper’s conclusions, specifically due to the lack of an objective criterion for squat depth.

I stopped searching the literature after I found this third study, Analysis of the Load on the Knee Joint and Vertebral Column with Changes in Squatting Depth and Weight Load [5]. The abstract is below:

A search of relevant scientific publications was conducted between March 2011 and January 2013 using PubMed. Over 164 articles were included in the review. There are no realistic estimations of knee-joint forces for knee-flexion angles beyond 50° in the deep squat. Based on biomechanical calculations and measurements of cadaver knee joints, the highest retropatellar compressive forces and stresses can be seen at 90°. Provided that technique is learned accurately under expert supervision and with progressive training loads, the deep squat presents an effective training exercise for protection against injuries and strengthening of the lower extremity. Contrary to commonly voiced concern, deep squats do not contribute increased risk of injury to passive tissues.

Note the two key takeaways in the abstract: 1.) over 160 related scientific publications were reviewed, and 2.) not a single one of them addressed knee flexion close to that of a properly performed low-bar squat. I give the authors of this third study credit for reaching an appropriate conclusion about the safety of squats. (But what the hell is this about cadavers?)

After reviewing these three studies, how can I blame a doctor for not having good information about the forces acting upon the knee in properly performed low-bar squats? Based on what I have read from Exercise Science academics (it’s “Science”, right?), I feel less inclined to blame a doctor for not having good information. So where can someone discouraged by the so called ExSci literature possibly find a succinct description and diagram of forces acting upon the knee, preferably from an actual practitioner and coach of a properly performed low-bar squat?

Let’s return to Starting Strength 3rd edition. The “Learning to Squat” chapter details how the hamstrings exert a posterior tension on the tibia, and the quads exert an opposing anterior force on the tibial plateau. As far as the anterior and posterior cruciate ligaments (ACL and PCL) are concerned, they simply stabilize the tibia and femur at the bottom position, but are essentially unloaded due to the agonist/antagonist action of the quads and hamstrings across the knee. From a free body diagram perspective, forces acting upon the knee are equal in magnitude and opposite in direction. When the toes are pointed out around 30 degrees and femurs track the feet, there is no rotational force internal or external to the knee regardless of load.

Rippetoe concludes with an important conditional statement: “With sufficient depth and correct knee position, anterior and posterior forces on the knee are balanced.” But note the important qualifiers: sufficient depth (hip crease slightly below the top of the patella), and correct knee position (knees parallel to the feet), and the implicit assumption that the bar is over mid-foot. It’s almost as if someone is saying that you don’t get to do a squat wrong and then call it unsafe.

Ultimately, each of us has to answer a question posed by Rip in Strong Enough?: “Are you willing to let medical professionals make excuses for your lack of willingness to do the hardest, most productive exercise in the weight room, an exercise that has been proven safe by decades of use by millions of people? I don’t think you are. Prove me right.”

#### References

1. Engineer-in-Training Reference Manual, 7th Edition, 1990, Michael R. Lindeburg, P.E., Professional Publications, Ch. 32 Determinate Statics and Ch. 44 Kinetics.
2. Mechanical Engineering Reference Manual for the Professional Engineer Examination, 11th Edition, 2001, Michael R. Lindeburg, PE, Professional Publications, Ch. 43, Determinate Statics, Conditions of Equilibrium
3. Forces and Moments on the Knee During Kneeling and Squatting Jonisha P. Pollard, William L. Porter, and Mark S. Redfern
4. Knee Joint Loading in Healthy Adults During Functional Exercises: Implications for Rehabilitation Guidelines, Sam Van Rossom, PhD, Colin R. Smith, PhD, Darryl G. Thelen, PhD, Benedict’s VanWanseele PhD, Dieter Van Assche, PT, PhD, Ilse Jonkers, PhD.
5. Analysis of the Load on the Knee Joint and Vertebral Column with Changes in Squatting Depth and Weight Load, Hagen Hartmann, Krause Wirth, and Markus Klusemann.

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