Thoughts On The Force-Velocity Curve And Implications For Training

The amount of force your muscles are capable of producing varies with both the type and velocity of contraction because of differences in cross-bridge mechanics and the rate at which cross-bridges can be formed. This is known as the force-velocity curve.

When you lift a weight your muscles contract concentrically, heads on the myosin filaments attach to actin filaments, bend and pull them, then release and reattach. When you hold or lower a weight your muscles contract eccentrically, the myosin heads work more like breaks, trying to hold on, then bending back, detaching and reattaching. These braking attachments are stronger, which is why you can hold or lower a much heavier weight than you can lift. A few years ago Dr. Michael Reedy of the Duke University Cell Biology department explained it to me as follows,

In a nutshell – more crossbridges attach and hang on tightly – due to to either or both causes of recruitment:

1) backbending distortion of one-headed crossbridges allows the second head of each myosin to attach, and they backwalk a few steps, smoothing the plateau of force that develops in phase 2 of ramp-stretch. (I love this idea, inspired from the Linari paper, but good evidence for it is not available yet.)

2) all weak-binding M*ADP*Pi heads of myosins that collide with backsliding actin hang on tightly to resist lengthening– and the more generous interface geometry for braking attachments by M*ADP*Pi allows more myosins to attach and evolve into brakes than are able to attach and evolve into purely isometric or shortening motors.

Much of my structural research over the next couple of years will focus on getting evidence for or against 1) and 2). We get snapshots of muscle structure by x-ray diffraction, and by 3D EM tomography of thin sections from fibers quick-frozen during mechanical actions and responses of interest.

When your muscles contract concentrically, the faster the contraction velocity the lower the force your muscles can produce because the limits of the rate of cross-bridge attachment and detatchment result in fewer attachments being formed. The graph below, adapted from Skeletal Muscle Structure, Function, & Plasticity: The Physiological Basis of Rehabilitation by Richard Lieber (page 62), shows how muscle force rapidly decreases with increases in concentric contraction velocity, and how much more force your muscles can produce contracting isometrically and eccentrically.

The Force-Velocity Curve

This is part of the reason you can’t lift a heavy weight as fast as you can lift a lighter weight, and why you lift more slowly as you fatigue. This is also why it is more effective to increase the resistance and the tension on your muscles by increasing weight than by increasing velocity. Although more force is required to accelerate a weight more rapidly to increase velocity, since the faster you lift the less force you can produce you will have to use a lighter weight. By moving more slowly you can use a heavier weight, especially if you increase the relative time spent performing the much stronger eccentric portion of the repetition.

Keep in mind while the force-velocity curve, load and tension are important they are only a few of many factors which must be considered and balanced against each other. The slower you lift the more weight you can use for a given time under load, but you do so at the expense of mechanical work which appears to contribute to microtrauma. Also, although you can only lower as much weight as you lift (unless you have a person or machine assist you during the positive) the duration of the positive and its length relative to the negative also affect the load you can use since concentric contractions are more fatiguing.

For example, whether you perform five positive emphasized reps using a ten second lifting and three second lowering cadence or five negative emphasized reps using a three second lifting and ten second lowering cadence, your reps and time under load will be the same, but the negative emphasized will be easier with the same weight (this is also a good example of how mechanical definitions of work and power and even average resistance over time are poor ways of measuring what’s happening during exercise; same mechanical work, same power, same resistance, same time under load, different levels of difficulty).

Shouldn’t we be trying to make exercise harder though? Absolutely, but there are many ways to do this, and one is by manipulating your speed of movement and the relative duration of the positive and negative to increase the load you can use and the tension on the target muscles for a given time under load which increases your average intensity. Negative emphasized reps are only easier than normal or positive emphasized reps if you use the same weight. If you use a heavier weight, however, you can increase the tension without reducing your time under load, metabolic stress, or mechanical work.

Continuing with the previous example, whether you perform the positive emphasized or negative emphasized protocol if you use a weight that would allow you to achieve momentary muscular failure after the same number of reps and time under load your intensity of effort — how hard you are working relative to your momentary ability — would be one hundred percent. However, since you can use a heavier weight for negative emphasized reps the intensity of effort at the start of the exercise would be higher as would your average intensity of effort.

As a general rule, also taking into consideration safety and efficient loading, you should move at least slowly enough during exercise to be able to reverse direction smoothly, without bouncing or jerking the weight, to be able to maintain correct body positioning and/or alignment over the full range of the exercise, and to be able to focus on contracting the target muscles. If you’re not sure how slowly you need to move to do this at first, it is better to move too slowly than too quickly. However, beyond some point, moving more slowly during the positive relative to the negative can decrease the load you are capable of using. If you perform the positive too fast have to reduce the load due to the force-velocity curve. If you perform the positive too slow relative to the negative, you will have to reduce the load due to a faster rate of fatigue. Somewhere in between there is an optimum range of positive and negative cadences that provide the best balance of being able to produce a higher level of force during the positive and having a high enough ratio of negative to positive duration to allow for heavier loads and more tension without the total rep being so long the mechanical work is significantly reduced. I don’t know what this cadence might be, but I am currently experimenting with negative emphasized protocols and will be proposing a study designed to answer this question to a few people I know in research.

It is important to keep in mind I’m only speculating about the greater mechanical work increasing microtrauma, that tension also increases microtrauma, and that either way, microtrauma is only one of many factors which stimulate improvements in strength and size. While all else being equal it is plausible, I am not aware of any good evidence that more mechanical work per time, which requires a faster contraction velocity and lower load, produces more microtrauma than less mechanical work per time, with a slower contraction velocity and heavier load. The results of Ellington Darden PhD’s recent experiments with a single extremely slow negative emphasized rep, of Mike Mentzer’s and John Little’s static holds, and of Ken Hutchins’ SuperSlow and timed static contraction show little or no mechanical work is required to stimulate impressive increases in strength and size if the tension is high enough.

It is also important to keep in mind that load is not as important as tension (and it is possible to significantly increase load while reducing tension on the target muscles by limiting exercise to the portion of the range of motion where the lever against them is small), and all of this assumes you are using strict form and either training on machines with properly designed cams or performing free weight and body weight exercises in a manner resulting in relatively congruent strength and resistance curves. How you perform each repetition is far more important than how many repetitions you perform or how much weight you lift.

While it is unknown whether there is an ideal speed of movement during exercise or an ideal ratio of positive to negative speed, the force-velocity curve makes it clear that repetitions should be performed slowly, rather than quickly. From the second edition of Skeletal Muscle Structure, Function, and Plasticity: The Physiological Basis of Rehabilitation by Richard Lieber page 60:

Muscles are strengthened based on the force placed across them during exercise. The force-velocity relationship of muscle indicates that high velocity movements correspond to low muscle force, and that low velocity movements correspond to high muscle force. Since strengthening requires high force-producing exercises, the velocities must, necessarily be relatively low. High velocity movements may have other beneficial effects (e.g. improve muscle activation by the nervous system), but not at the muscle tissue level. The take home message – keep velocity low for strengthening.

…page 83

It has been experimentally determined from biochemical studies that the cross-bridge connections between actin and myosin attach at a certain rate and detach at a certain rate. These rates are referred to as rate constants. At any point, the force generated by a muscle depends on the total number of cross-bridges attached. Obviously, this number represents the net balance between the number of cross-bridges attached versus detached. Because it takes a finite amount of time for cross-bridges to attach (based on the rate constant of attachment), as filaments slide past one another faster and faster (i.e., as the muscle shortens with increasing velocity), force decreases because of the lower number of cross-bridges attached. Conversely, as the relative filament velocity decreases (i.e., as muscle velocity decreases), more cross-bridges have time to attach and to generate force, and thus force increases.

…and from the fourth edition of Exercise Physiology: Human Bioenergetics and Its Applications by George Brooks on page 390 it says,

As compared to lifting light loads, isotonic responses to given stimuli when lifting heavy loads results in a greater latent period, slower movement, and less movement. The effect of strength training is to make the load appear lighter. The force-velocity relationship is hyperbolic in nature. Greater loads produce slower speeds but greater tension.

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  • Angst Jul 17, 2014 @ 9:49

    Holy shit…. I shoulda done better in school.
    Drew, do you offer tutoring services? lol

    • Drew Baye Jul 17, 2014 @ 12:59

      Hey Angst,

      I don’t tutor, but if you’ve got any specific questions about this I’d be glad to answer them.

  • Ravi Sinanan Jul 17, 2014 @ 10:04

    Good stuff Drew. Good to see people challenge conventional “wisdom”, with solid research.

  • Jim Jul 17, 2014 @ 12:23

    Michael Reedy taught me Microanatomy in Medical School. Good man. Go Duke.

  • MarkLloyd Jul 17, 2014 @ 14:06

    It’s funny to me that faith in fast lifting is mostly a remnant of Bob Hoffman’s Olympic weightlifting background, yet Hoffman himself got good results experimenting with slow reps.

    • Drew Baye Jul 19, 2014 @ 16:43

      Hey Mark,

      Hoffman recommended using a variety of protocols, including isometrics, very slow reps, and reps at an unrestricted speed of movement. He wrote a book called Functional Isometric Contraction – Advanced Course in 1962 which focused primarily on isometrics but also a ten second lifting and ten second lowering protocol he called “muscle contraction with measured movement”.

      • Dave S Jul 19, 2014 @ 19:29

        Drew,

        Was that the same protocol that Hoffman also said to wait ten seconds between reps?

        I had a copy of an article about that but I lost it. There may have been seven different exercises He listed.

        • Drew Baye Jul 19, 2014 @ 21:17

          Hey Dave,

          If I recall correctly, the MC-MM protocol was a ten second positive and ten second negative followed by a ten second rest-pause.

          • Dave S Jul 19, 2014 @ 22:21

            Yes thats the one. I had the article and the routine that was listed. I lost it,and I cant find it again with a google search.

            I know some of the exercises were Squat,Deadlift, two hand overhead press,two arm curl,I think upright row. I was just curious about it,and wanted to see if I could find it again.

            Thanks for getting back to me

            • Drew Baye Jul 28, 2014 @ 12:39

              Hey Dave,

              In the chapter Muscle Contraction With Measured Movement in Functional Isometric Contraction: System of Static Contraction Hoffman recommends what he calls his “simple six”:

              1. Arm Curl
              2. Upright Row
              3. Shoulder Press
              4. Bent-over Row
              5. Deadlift
              6. Squat

              I would change this to:

              1. Squat
              2. Chin-up
              3. Dip or Chest Press
              4. Bent-over Row
              5. Shoulder Press
              6. Stiff-leg Deadlift

  • Joe Jul 17, 2014 @ 14:42

    Hey Drew,

    Do you have any ideas why that study referenced got the results it did? Any obvious flaws or fallacies you see in the study? As someone who has tried “explosive” methods, I’m pretty certain it’s not a very effective means of improving strength or size or performance.

    • Drew Baye Jul 19, 2014 @ 13:02

      Hey Joe,

      I removed the paragraph commenting on the study until I am able to read the full text and go over it in more detail. This conflicts with other research, and I suspect the reasons for the differences in the groups were due to differences in effort resulting from the speed and load selection. It is dangerous and irresponsible to recommend lifting as fast as possible during exercise, so I will definitely be addressing this in another article.

  • Maverick Jul 18, 2014 @ 7:55

    Thanks for explaining this concept in such a clear and concise way, Drew. I’ve had mNt a debate with fellow trainers over this topic and the way you have presented this information here has enhanced my knowledge of the relationship between muscle force and velocity and it’s effect on development and my ability to articulate it.
    The quality and quantity of your articles have both increased lately! Pleas keep it up! Young trainers like me (and our clients) out there are getting better for it!

    • Drew Baye Jul 19, 2014 @ 12:49

      Hey Maverick,

      Thanks, and please let me know if you have any questions not already covered in the article.

  • John O'Rourke Jul 20, 2014 @ 9:53

    Superb article Drew. I have tried to point out to a few people that you are stronger when you move slowly but I don’t think they believed me. I have always suspected that a reasonably slow movement allowed greater cross bridging as well as being safer. Still a lot of unanswered questions but it certainly keeps it interesting.

  • Craig Jul 21, 2014 @ 19:25

    Just to clarify: You can lift more weight when you move slowly because the muscle can produce greater tension. But moving more slowly with a given amount of weight won’t, by itself, do much to increase muscle tension?

    • Drew Baye Jul 22, 2014 @ 12:40

      Craig,

      Your muscles can produce more force at slower concentric contraction velocities due to greater cross-bridging, so the slower you go the heavier the weight you can use, however moving more slowly with a weight won’t increase the tension. What moving more slowly does is minimize variation in resistance force due to acceleration, keeping the tension more consistent (relative to other factors) over the full range of the exercise. To accelerate a weight more quickly requires you to contract with more force, but doing so imparts energy to the weight that reduces the force you have to contract with to continue positive movement after acceleration, so the end result is still the same average tension. The only way to avoid this is to accelerate constantly, increasing the risk of injury at the end point of some exercises.

      Moving more slowly allows for both a heavier load and more consistent tension over the full range of motion.

      • Ryan Hall Aug 1, 2014 @ 1:18

        Drew,

        I think I posted this in 2009:

        I am quoting from Lieber. Given a sufficiently heavy load, muscle (my words), “force drops off rapidly as velocity increases. For example, in a muscle that is shortening at only 1% of its maximum contraction velocity (extremely slow), tension drops by 5% relative to maximum isometric tension. Similarly, as contraction velocity increases to only 10% maximum (easily attainable physiologically), muscle force drops by 35%! Note that even when muscle force is only 50% maximum, muscle velocity is only 17% Vmax. The take-home lesson is that as a muscle is allowed to shorten (faster – my words), force drops precipitously.”

        “It has been determined that the cross-bridges between actin and myosin attach at a certain rate and detach at a certain rate… At any point in time, the cross-bridges generated by a muscle depends on the number of cross-bridges attached. Because it takes a certain amount of time for the cross-bridges to attach (based on the rate of constant attachment), as filaments slide past one another faster and faster (i.e., as the muscle shortens with increasing velocity), force decreases due to the lower number of cross-bridges attached. Conversely, as the relative filament velocity decreases (i.e., muscle velocity decreases), more cross-bridges have time to attach and generate more force, and thus force increases.”

        As you know, I always recommend the Lieber textbook on muscle physiology to anyone interested in the subject.

        🙂

        • Drew Baye Aug 3, 2014 @ 13:20

          Hey Ryan,

          Thanks for the additional explanation. Hopefully this helps settle some arguments about rep speed and force production.

          • Ryan Hall Aug 3, 2014 @ 14:39

            Drew,

            Understanding the muscle force velocity curve, this blows away the idea of a constant 20% difference between concentric, isometric, and eccentric strength.

            Ryan

  • Donnie Hunt Jul 22, 2014 @ 11:29

    I love these kind of articles. Admittedly some of this stuff is still over my head but still interesting stuff 🙂

  • Dave Aug 3, 2014 @ 14:06

    Thanks Drew,

    I was wondering what Hoffman recommended. I just could not remember.

  • Greg Aug 14, 2014 @ 18:33

    Drew,

    First of all, I’d just like to put out there that your work has been completely life altering. I used to be a high volume weightlifter and long slow distance runner. I’ve put an end to that and since this february my workouts have consisted exclusively of 5-7 single set compound and isolation exercises until failure once a week. I’ve noticed gains in strength via the records I keep, that roughly correlate with higher recovery times between workouts.

    That said, my current gains aren’t where I expected them to be and I’m not at a level I’ve documented myself in the past that seemed to take me a shorter time to acheive. I decided to dive into the literature a little more and was suprised to see results countering utilization of single sets in favor of multiple sets. Below are a couple of citations to the those studies…

    Wolfe, Brian. “Quantitative Analysis of Single vs. Multiple Set Programs in Resistance Training.” Journal of Strength & Conditioning Research (2004). Web.

    James, Kreiger. “Single vs. Multiple Sets of Resistance Exercise for Muscle Hypertrophy: A Meta-Analysis.” Journal of Strength & Conditioning Research (2010). Web. .

    I’m finding a lot of meta analysis literature, which I realize can have its problems with objectivity and accuracy, but then I also found this study whose results seem to counter both the single set and slow repitition speed position. They found an 11% improvement in strength with increased repitition speed with single set exercises and a 23% improvement using multiple sets compared to single set subjects….

    MUNN, J., R. D. HERBERT, M. J. HANCOCK, and S. C. GANDEVIA. Resistance Training for Strength: Effect of Number of Sets
    and Contraction Speed. Med. Sci. Sports Exerc., Vol. 37, No. 9, pp. 1622–1626, 2005.

    Their physiological speculation for why increased repitition speeds might produce more of an adaptation was, “Training with fast speeds leads to higher discharge rates of single motor units and more frequent occurrence of brief interspike intervals (doublet discharges). These phenomena might underlie the greater training response.”

    What are your thoughts Drew?

    • Drew Baye Aug 15, 2014 @ 9:01

      Hey Greg,

      I have written about both single versus multiple sets and the problems with studies on rep speed in Thoughts On Relative Volume Of Single And Multi-Set Workouts and Evidence-Based Resistance Training Recommendations: Part 3 and Ralph Carpinelli has thoroughly debunked Krieger’s metaanalysis in Critical Review Of A Meta-Analysis For The Effect Of Single And Multiple Sets Of Resistance Training On Strength Gains.

      While some people or muscle groups with a high percentage of slow twitch fibers may benefit from additional volume most people will not get better results from performing any more exercise than necessary to work all the major muscle groups and may get worse results, assuming they perform their sets properly, with a high degree of effort and for an adequate duration.

      Rate coding, the increase in discharge rates, will also increase as you approach momentary muscle failure regardless of repetition speed, so there is no need to go fast to accomplish this.

      • Greg Aug 16, 2014 @ 20:13

        Very Interesting. Thanks Drew.

        I’m still confused about why a heavier load necessitates a greater stimulus… For instance, I quantified my sets in units of foot-pounds to standardize the differences in mass and reps between workouts. Now the weird part is I find in some workouts my total work output is higher with lighter weights. (i.e. A higher ft-lb figure).

        If I’m keeping a consistently slow 5/5~ second cadence and I’m confident I’m going to MMF or at least approaching it, aren’t I receiving a greater stimulus with a lighter load instead of the heavier one, because I’m capable performing more work and thus more microtrauma with the former?

        • Drew Baye Aug 21, 2014 @ 14:33

          Hey Greg,

          There is a trade off. Too little weight and you have insufficient tension on the muscles, too much weight and you have insufficient duration for significant metabolic stress, which is also an important factor in stimulating muscular strength and size increases. Fortunately, a broad range of repetitions or time appears to be effective for most people as long as the intensity of effort is high, although some people tend to do better with slightly lower or higher reps.

          That being said, although intensity of effort appears to be the most important factor, when all else is equal (mechanical work, set duration, etc.) a heavier load does appear to be more effective, possibly because it results in a higher average intensity of effort over the duration of the exercise. This is something I cover in Advanced HIT Methods.

  • JJ Aug 21, 2014 @ 22:35

    Hey drew have a question for you. Are cybex machines good? Do they have a good functioning cam? My wife and I are going to join the local YMCA and cybex is what they have.

    • Drew Baye Aug 23, 2014 @ 11:38

      Hey JJ,

      Some Cybex machines are very good, some are very poorly designed, and most are somewhere in between. They’re much better than a lot of other stuff out there, though.

      • JLMA Sep 27, 2014 @ 0:21

        JJ, Drew,

        I recently joined the local LA Fitness and they have two brands of weight machines, Hammer Strength and Life Fitness.

        Most of the machines I tend to use “don’t fit or feel right”. During the exercises, it feels unstable (even if in the beginning position it feels fine) and I fear that my lower back is put in a unstable position.

        I am considering going back to closed-kinetic-chain exercises working out at home, but I am concerned I will miss how much easier increasing tension progressively is with machines…

        Just my thoughts.

        • Drew Baye Sep 28, 2014 @ 12:02

          JLMA,

          Life Fitness machines aren’t horrible, but they’re not very good either. The Hammer Strength machines are much better, although not as efficient due to the need to plate load, unless they have the selectorized Hammer Strength MTS machines.

          If you don’t like their equipment and can’t find another gym with equipment you like, working out at home with free weights and/or bodyweight can be just as effective, and much less of a pain in the ass since you don’t have to wait for equipment or deal with traffic or a crowded, noisy training environment.

  • Goran Jun 27, 2015 @ 6:47

    Hi Baye,

    thank you for this article.

    Please I have a question, about the x-axis (velocity) of the force-velocity curve.

    in some sources the scaling used for velocity-axis is (+ve) and in others is (-ve), are both possible and why?

    Regards.

    • Drew Baye Jun 27, 2015 @ 12:42

      Goran,

      It’s not clear if by -ve and +ve you mean eccentric (negative) contraction velocity and concentric (positive) contraction velocity, or if you mean drawing the graph with a positive change/increase or negative change/decrease in velocity from left to right.

      In the graph pictured, adapted from Skeletal Muscle Structure, Function, and Plasticity: The Physiological Basis of Rehabilitation by Richard Lieber, from left to right the velocity first decreases from 100% eccentric contraction velocity to 0%, or isometric contraction, then increases from 0% to 100% concentric contraction velocity. This is the best and most useful way to present this information.

  • David klein Mar 24, 2016 @ 12:08

    Absolutely f@cking superb! Why isn’t this on body building.com!? I think I can guess why. Brilliant, keep it up, I aspire to attain such a vast knowledge bank as you posses.

    • Drew Baye Mar 25, 2016 @ 12:54

      Thanks David, and I’m glad to see more people promoting sensible training in Europe!