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Bret’s Intro: I’m very excited about the publication of our recent article. The three of us (Andrew Vigotsky, Chris Beardsley, and yours truly) have devoted a large percentage of our studies over the past few years to biomechanics, and although it’s not always sexy, it’s very important for fully understanding various concepts in strength & conditioning. 

Many of us strength coaches devoured the works of Mel Siff, Vladimir Zatsiorsky, and Yuri Verkhoshansky in hopes of gaining insight to better equip us as practitioners. While much of their work was esoteric and over the heads of the majority of strength coaches, every once in a while we gleaned some useful information. I believe that the information in our article, although esoteric, is indeed useful, especially pertaining to powerlifting and athletics. What is fascinating is that increased muscle moment arms are definitely beneficial for strength and high force activities, but for power and high speed activities, they can actually be counterproductive (we explained this in the full article). 

This publication would not have been possible had it not been for Andrew Vigotsky’s superior drive, passion, curiosity, and mathematics background. I can think up concepts but I lack the mathematical skills to model and validate them. Huge props to Andrew for his diligence and talent!

Cliff Notes: As a muscle grows larger, it can produce more torque (rotational force) through greater linear force created by the muscle, but also through greater leverage about the joint center, and the leverage improves by approximately the square root of the increase in the muscle’s cross-sectional area. 

Biomechanically, how does hypertrophy increase strength?
By Andrew Vigotsky

Two years ago, while helping construct the Biomechanics of the Squat and Deadlift manual for Bret’s 2×4: Maximum Strength product, Bret explained to me that increasing a muscle’s size will increase its moment arm. He and Chris Beardsley illustrated this relationship in their Hip Extension Torque manual, but although it made intuitive sense, there were no published studies modeling this relationship. While concepts are neat and useful, it is important in science to construct models to explain mathematical relationships and validate the concepts.

We recently decided to develop this model and submit it to PeerJ for publishing. The model was accepted and published today. It’s open-access so you can download the full paper HERE. The model describes the relationship between a muscle’s size (anatomical cross-sectional area) and its leverage (moment arm length).

* Click HERE to Download the Full PDF *

First, I think it’s important that the readers understand what, exactly, a moment arm is, and why it matters for strength. As you know, the body is made of bones that rotate about joints. Muscles and external forces “fight” one another to rotate the joint. The forces that have a tendency to rotate a joint are classically called torques, or moments. Torques or moments equal the force applied to the bone times the moment arm, or perpendicular distance of that force to the axis of rotation (see below). With regards to a muscle, the larger the moment it can produce, the stronger you are.


When muscles increase in size, the amount of force they can produce also increases – this is well known and accepted. Obviously a larger muscle will be able to produce more force than a much smaller muscle. However, the other component to generating a moment, a muscle’s moment arm length, has not been well studied. It has been shown that they are correlated (Akagi et al. 2012; Sugisaki et al. 2010), and one study even showed that, with a 33.6% increase in triceps brachii anatomical cross-sectional area, the triceps brachii moment arm increases by 5.5% (Sugisaki et al. 2014).


In order to gain a better understanding of this relationship, my colleagues – Bret Contreras and Chris Beardsley – and I developed a model of the biceps brachii and brachialis, wherein the original size of the muscles were atrophied to one-half their original size and hypertrophied to two times their original size. We were able to calculate the new moment arm lengths, and how the new moment arm affected each muscle’s tendency to flex the elbow (joint moment contribution, or torque that each muscle produces). Our main findings can be found in Table 1, below.


This is a relatively unexplored area of biomechanics and hypertrophy that may be important to consider. Not only does the muscle produce more force, but also, depending on the muscle and joint angle, its mechanical advantage will change. We have included an infographic below that summarizes our study and findings.



Akagi R, Iwanuma S, Hashizume S, Kanehisa H, Yanai T, and Kawakami Y. 2012. In vivo measurements of moment arm lengths of three elbow flexors at rest and during isometric contractions. Journal of Applied Biomechanics 28:63-69.

Sugisaki N, Wakahara T, Miyamoto N, Murata K, Kanehisa H, Kawakami Y, and Fukunaga T. 2010. Influence of muscle anatomical cross-sectional area on the moment arm length of the triceps brachii muscle at the elbow joint. Journal of Biomechanics. 10.1016/j.jbiomech.2010.06.013

Sugisaki N, Wakahara T, Murata K, Miyamoto N, Kawakami Y, Kanehisa H, and Fukunaga T. 2014. Influence of Muscle Hypertrophy on the Moment Arm of the Triceps Brachii Muscle. Journal of Applied Biomechanics. 10.1123/jab.2014-0126


  • Very interesting Bret, nice contribution ahead, by changing lever it’s suppose that the joint gain more stability or less?

  • Tom Jukes says:

    It seems strange that this even needs to be said. Of course a bigger muscle is a strong muscle!

  • Patrick Connolly says:

    I wondered this as soon as we started studying moment arms in physics way back in the day, can’t wait to grab the time needed to read this study!

    I wonder, could this be a contributing mechanism for warming up helping you to lift greater weights? I’ve always assumed it was all neural, but I wonder if a light pump couldn’t help you lift more due to greater leverage – at least as far into the set as it takes for occlusion to take it’s toll on ATP production.

    Great articles non-stop.

    • Bret says:

      Great comment Patrick! This is definitely a possibility and one that I thought of while we were working on this project. And you’re exactly right in speculating that it could help on one hand and hinder on the other hand due to greater fatigue, so there’s probably a fine-balance. It could help explain a portion of a PAP effect, but studies would be required to elucidate this.

  • Sean says:

    Could you revise or do another diagram that shows the muscle at work like in the biceps diagram but with arrows and text explaining the moment arm, lever arm, muscle relationship? It would be extremely helpful to us novices ( and many scientists likely) to understand this in a tangible way.
    Thanks for all the hard work you guys do, always appreciate your insights!

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