More On The Force-Velocity Curve And Repetition Speed

It seems a lot of people are still confused about the force-velocity curve, the basic physics of lifting and lowering a weight, and their implications for training, so I’m going to provide a few more examples in hopes of getting these points across.

When the net sum of all forces acting on an object are zero its velocity (its speed and direction) is constant and the object is said to be in a state of equilibrium. This is true regardless of the speed of the object, including if it’s speed is zero.

To hold a barbell motionless, at a constant velocity of zero, the upwards force you apply to the bar must equal the downwards force of gravity on the bar. To lift or lower a barbell at a constant velocity the upwards force you apply to the bar must equal the downwards force of gravity on the bar. However, unless you are performing a purely isometric exercise, your velocity will not be constant. Your speed must change as you lift or lower the weight, starting and ending at zero and increasing in between, and your direction must change between lifting and lowering.

A change the velocity of an object, either of speed, direction, or both, is acceleration. For an object to accelerate, either increasing or decreasing it’s speed, changing it’s direction, or both, the force coming from one direction must be greater than the net forces opposing it. To start lifting a barbell or to bring it to a stop when lowering it you must apply more force than the force of gravity on it to accelerate it. To bring a barbell to a stop when lifting it or to start lowering it you must apply less force than the force of gravity to allow gravity to accelerate it. Once acceleration stops and you are moving at a constant velocity the barbell is once again in equilibrium, and the net forces acting upon it will be zero. If not, it will continue to accelerate.

The rate of acceleration, whether a change in speed, direction, or both, depends on the force applied. The greater the the force the greater the change in speed or direction. When lifting a barbell the more force you apply the faster it will accelerate from the start and the less force you apply the faster gravity accelerates it to a stop. When lowering a bar the opposite occurs. The less force you apply the faster the barbell accelerates downward and the more force you apply the faster you will slow it to a stop.

When an object is accelerating it’s momentum changes, as does its kinetic energy. When people talk about using momentum to lift a weight what they’re really talking about is kinetic energy. When you lift a barbell, as you accelerate it upwards from the start you impart kinetic energy to it. The greater the acceleration, the greater the kinetic energy you give the barbell. The barbell’s kinetic energy then reduces the amount of force you have to apply to continue lifting it after accelerating, by an amount proportional to the force applied during acceleration, so that the average force applied balances out. Because of this, the average force  you have to apply when lifting a barbell is the same regardless of whether you accelerate rapidly or slowly. The only difference is in how much the force varies.

To lift a barbell very quickly you must apply a force significantly greater than the force of gravity during positive acceleration. The barbell’s kinetic energy will then reduce the force you must apply to an equal amount less than the force of gravity. Relative to the force of gravity on the barbell the force you apply will be very high at first, then very low over some portion of the range of motion when lifting at fast speeds.

To lift a barbell very slowly you must apply a force only slightly greater than the force of gravity during positive acceleration. The barbell’s kinetic energy will only reduce the force you must apply after acceleration by an equally slight amount. Relative to the the force of gravity on the barbell the force you apply will be only slightly higher at first, and only slightly lower over some portion of the range of motion when lifting at slow speeds.

The graphs below, from a force-gauge experiment performed by Brian Johnston in 2005, demonstrate the difference in the variation in force between an “explosive” repetition (with a positive duration of less than one second and a slower negative) and a repetition performed at a slower speed (a five second positive and five second negative duration).

Force gauge measurement of explosive repetition performance

Where the positive movement begins the force increases rapidly, then drops off rapidly for the remainder of the movement. The relatively flat portions of the graph represent the slower negative movement.

Force gauge measurement of slow repetition performance

The repetition performed at a 5/5 cadence resulted in very little variation in force. The negative (first half of the graph) required slightly lower force than the positive due to friction in the machine used (friction works against you when lifting, increasing the force you must apply, and with you when lowering, decreasing the force you must apply).

Although it takes more force to accelerate a weight rapidly, the force your muscles are capable of producing decreases as concentric contraction speed increases. On page 83 of the second edition of Skeletal Muscle Structure, Function, and Plasticity: The Physiological Basis of Rehabilitation Richard Lieber explains,

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.

This is why you can not lift a heavier barbell as fast as you can lift a lighter one; the faster you want to lift a weight the more force is required, but the faster your muscles contract concentrically the less force they are capable of producing. As lifting speed increases the amount of weight you are able to use decreases. Or, to look at it another way, the heavier the weight used the slower you will be able to lift it.

Proponents of fast repetition speeds claim the increased force during acceleration compensates for this, however this increase only occurs briefly during positive acceleration when lifting, and is followed by a proportional reduction in force. The average force is still the same as it would be if you were holding the weight motionless or lifting it slowly, it just varies more, and since the faster the repetition speed the less weight you can lift, the lower this average force will be.

In addition to this, the acceleration at the beginning of the lifting movement occurs when the muscles under load are at a greater length, which also negatively effects their ability to produce force. This is also the position where the muscle is most susceptible to injury, which is a good enough reason to avoid fast repetitions.

Why then, if your muscles are capable of producing less force at faster concentric contraction velocities can you lift more weight for ten repetitions at a fast speed than ten repetitions at a slower speed? Simple. Because the slower your speed of movement the longer the time under load when the same number of repetitions is performed. You can lift a lot heavier weight for fifteen to twenty seconds than you can for over a minute.

However, if you perform an exercise for an equal amount of time rather than an equal number of repetitions you can lift a heavier weight moving more slowly. For example, while you can lift more weight performing ten repetitions at a 1/1 cadence than you can performing ten repetitions at a 10/10 cadence, you can lift more weight performing repetitions at 10/10 for sixty seconds than you can performing repetitions at 1/1 for sixty seconds.

Although the mechanical work performed would be greatly reduced, this is not a problem, as it is possible to stimulate significant improvements in muscular strength and size and most if not all other general factors of functional ability with isometric exercise protocols which involve zero mechanical work. Tension and duration are more important than mechanical work, and slower reps allow for more tension over an equal duration or for the same tension over a longer duration.

Another important consideration regarding tension is the effect of lifting speed on the ratio of positive to negative strength. The amount of force a muscle can produce contracting eccentrically is greater than what it can produce contracting concentrically even at very slow contraction speeds, so even when lifting slowly the relative intensity of effort will be lower during the negative. The faster the repetition speed, the lighter the weight that can be lifted, and the lower the relative intensity of effort required to lower it.

Eccentric to Concentric Strength Ratio Curve

While tension and duration are important and influence results, intensity of effort is by far the most important factor in stimulating muscular strength and size increases. This primarily means continuing an exercise to momentary muscular failure, the point of maximum intensity of effort, but the average intensity of effort over the duration of the exercise is also a factor, and because slower lifting speeds reduce the difference between positive and negative strength and the reduction in relative intensity of effort during the negative they increase the average intensity of effort.

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 repetitions should be performed slowly, rather than quickly if your goal is to improve muscular strength and size. Quoting Richard Lieber, again, from page 60 of Skeletal Muscle Structure, Function, and Plasticity: The Physiological Basis of Rehabilitation,

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.

A few final words on the subject from Nautilus inventor Arthur Jones…

Perhaps the most important consideration: a proper style of performance requires a relatively slow speed of movement. Too slow provides all of the benefits and produces none of the potential problems, while too fast avoids some benefits and does produce problems, generally problems resulting from high levels of impact force.

and…

The next time somebody suggests that you move suddenly during any form of either exercise or testing, smile and walk away, because you are talking to a fool.

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  • George Sheehan Nov 24, 2014 @ 14:24

    Hello Drew…yes, the evidence of slower reps is obvious; thanks for bringing this out. A number of orthopedists are of the opinion that using quick lifts in the gym, set up athletes for injuries on the playing field. Doing power cleans etc. do not make the athlete any more prepared for his performance in the sport. The late/great Arthur Jones was right.

    • Drew Baye Nov 28, 2014 @ 1:28

      Hey George,

      Arthur was right, and the orthopedists are right. There is no reason for any athlete other than Olympic lifters to perform the Olympic lifts. You can improve an athlete’s strength and power more effectively and more safely with conventional barbell exercises performed at a controlled speed.

  • Steven Turner Nov 25, 2014 @ 16:44

    Hi Drew,

    I don’t think the so-called “explosive” training experts will ever admit that moving the weight slower means greater muscle force. But as you state that science says that there is greater overlap of actin/myosin when moving the weight slower than “explosive” speed. Whatever “explosive” means, talk about an unscientific term.

    Crossfit use the olympic lifts and terms explosive for there training but than they go and do huge amount of reps. When they get to the end of the rep range with fatigue they are actually starting to move the weight slowly as they struggle to lift the weight with bad form. Actually when your using high reps it is more muscle endurance workout not an “explosive” lifting workout.

    With most of these explosive lifts in the first few reps there are huge spikes in the force velocity curve but as fatigue sets in the spikes would be a lot less, as shown in the diagram

    • Drew Baye Nov 28, 2014 @ 1:26

      Hey Steven,

      No, they won’t, but realize that a lot of this also depends on your frame of reference. If you match reps or mechanical work, the faster reps will involve greater peak and average forces because you can lift more weight for a shorter amount of time. However, if you match time, the slower reps allow for greater average force because you can produce more force thus lift a heavier weight at slower contraction velocities. Or by slowing down you can lift the same amount of weight for a longer time. Since tension and time under load appear to be more important than mechanical work I think it makes more sense to compare them this way (the effectiveness of isometric protocols like static holds and timed static contraction proves no mechanical work is required to increase muscular strength and size).

      Also, since the force of concentric contraction is reduced by increased lifting speed and also by the longer length of the muscle at the start of acceleration (length-force curve) this may appear contradictory to some. If the muscle is capable of producing less force as concentric contraction velocity increases it would seem the risk of injury goes down as rep speed increases, but this assumes the force is only coming from the target muscles. Usually, however, when people attempt to lift a weight in a fast or “explosive” manner, they involve all sorts of extraneous movement and other muscle groups, which may result in a higher amount of force being transmitted to the load through the target muscles. The hip and back extension people use when performing fast barbell curls is an example of this. The force produced during extension by the larger, stronger hip and back muscles is transmitted to the bar through the shoulders and biceps. Your biceps may not be capable of producing enough force to injure themselves, but your back and hip extensors can produce enough force to injure your biceps.

      And while some will point out that not everybody who uses fast, sloppy form suffers pulled or torn muscles or other traumatic injuries, over time the cumulative wear and damage will increase their susceptibility to injury in the gym or during other physical activities.

  • Jack Nov 26, 2014 @ 0:54

    Hi Drew,

    Great stuff and great blog. Many of your readers enjoy the information you provide. I know that you base your DECISIONS with scientific research and ALL the information you absorb by discussing them with others. One of my reasons for reading your blog is I know that if you saw/read something that contradicts with what you “preach”, you will modify the information accordingly.

    • Drew Baye Nov 28, 2014 @ 1:07

      Hey Jack,

      Of course. You’ve got to follow the evidence wherever it leads. It may not lead where you want or expect, but it’s better to follow a truth you don’t like than a falsehood you do.

  • Jamieson Bardy Nov 26, 2014 @ 8:21

    Hi Drew,
    Fantastic article, as always.
    Hopefully by presenting such a clear and concise arguement this will put this issue to bed for once and for all. Although I guess those of the ‘bro science’ fraternity will no doubt insist fast reps produce greater force and better results blah blah blah!

    Btw, a massive ‘thank you’ for the rep speed advice, switching from 2/8 to 4/8 and aiming for TUL of 50-80 seconds has worked instantly.

    Best,
    Jamie.

    • Drew Baye Nov 28, 2014 @ 1:04

      Hey Jamieson,

      Thanks and you’re welcome. There are still a lot of things about this I need to explain in future posts, but this covers most of the questions I got from people about this.

  • Jim Null Nov 26, 2014 @ 15:00

    Drew,

    I’ve enjoyed all your posts on this topic. My question is in regards to the 4/10 lifting speed Wayne Westcott experimented with. If in fact it were proven to be more effective than a 5/5 lifing speed, what mechanism would be responsible for the difference in effectiveness?

    Jim

    • Drew Baye Nov 28, 2014 @ 1:00

      Hey Jim,

      Wayne Westcott and I talked about this and thought the advantage was due to the longer, more metabolically-efficient negative allowing for a heavier load and more tension. I don’t know if this is the case though, which is why I would like to see a study performed comparing normal, positive-emphasized, and negative-emphasized reps matched for both average work and TUL. I would like to see a comparison of 6/6, 4/8, and 8/4 cadences and a repetition range of four to six (approximately 48 to 72 seconds, the same as the old Nautilus guideline of performing eight to twelve repetitions at a 2/4 cadence). I have spoken with James Steele about this, and there is a possibility of doing a study on this eventually.

      • Jim Null Nov 28, 2014 @ 12:30

        Drew,

        I would really like to see what further study on this topic could tell us. If a slower eccentric proves to be advantageous, I may have to apologize to all the clients who I have berated for “sandbagging” on the negative phase of the rep!

        Humorously,
        Jim

        • Drew Baye Nov 29, 2014 @ 13:24

          Hey Jim,

          I have gradually moved to a 4/8 cadence with my own workouts and clients and it has been working very well. It would still be nice to see it compared to normal and positive-emphasized reps matched for time and work in a proper study, however.

  • KPS Nov 27, 2014 @ 5:13

    Good finishing touch to “Force-Velocity Curve And Repetition Speed”. So it is primarily TUL with highest possible intensity that matters. I changed my routine from regular 1/1 to approx. 3/7, the best I could do now. However, I find breathing difficult and get breathless even while consciously breathing. The normal 1/1 was easy with exhale/Inhale for lifting/lowering. How to tackle this.

    • Drew Baye Nov 29, 2014 @ 13:22

      Hey KPS,

      High intensity of effort and an appropriate TUL for the individual are necessary for optimal results. A broad range of reps or time can be effective, but some people get better results with less or more reps/time, and this can even vary somewhat between muscle groups.

      Breathe with your mouth open, as relaxed and naturally as possible. Don’t try to match your breathing to the movement, exhaling while lifting and inhaling while lowering, as is often recommended. Don’t hold your breath at any point during the exercise.

  • Lifter Nov 27, 2014 @ 11:37

    Great article Drew and Happy Thanksgiving.

    What’s your take on rate of force development (ROFD) in regard to slow repetitions compared to fast? Are you sold on the research indicating that as long as you’re moving as quickly as possible once an appropriate amount of fatigue has accumulated that you can increase ROFD to the same degree as explosive repetitions, and do so more safely because of the slow speed that will result?

    Thanks!

    • Drew Baye Nov 27, 2014 @ 13:40

      Hey Lifter,

      Yes, the intended rather than actual speed is what is important for stimulating improvements in rate of force development. It is not necessary to move fast, it is only necessary to attempt to do so once you have fatigued the target muscles enough that the fastest you are capable of moving is slow.

  • des Nov 28, 2014 @ 12:38

    very informative article. thanks.

  • Bradley Nov 29, 2014 @ 11:34

    Hi Drew,
    Great article, nice to see some graphs!!!!!!! I was looking for graphs showing exactly this so am a happy bunny!
    Would i be right in thinking the area under the graph be the force-impulse? And would this impulse be the same in both graphs or higher in the 5/5?

    • Drew Baye Nov 29, 2014 @ 13:38

      Hey Bradley,

      No, because the force-impulse is the product of the average force and the duration is is exerted, and this graph only compares contraction force at different eccentric and concentric contraction velocities, not what can be maintained for a given time.

      For sets performed to momentary muscular failure with an equal time under load, however, the force-impulse would be higher with slower repetitions because of the greater force production at slower concentric contraction velocities allowing the use of a heavier weight.

  • Bradley Nov 29, 2014 @ 11:45

    I can see why a lot of people think that faster lifting stimulates more fast twitch fivbres and therefore targets the ‘glycogen pools’ a lot faster than the slower repetitions, as the force in the exlosive lift essentially doubles from 30lbs to 60lbs, where as the 5/5 repetitions barely reaches 35 lbs.
    I think though that as long as the force is at a reasonable amount ( most studies point to around 70% of 1 RM but this changes based on the speed that one moves, so could be any percentage really. The thing is the better the quality of the repetition the closer to our % of 1 RM we get. its actually a stupid way of explaining intensity of effort.

    • Drew Baye Nov 29, 2014 @ 13:56

      Hey Bradley,

      The slower the positive speed of the repetition the more force you can produce and the more weight you can lift, all else being equal, but if you also move in a manner which maintains a higher average lever against the target muscles you will require less weight to create the same amount of tension. Also, if you are performing sets lasting at least thirty to forty seconds you will not be able to use as much weight as sets lasting half as long. The greater risk of injury with faster reps is not due to the peak forces alone, but the combination of greater peak force and higher load.

      Slowing down makes it possible to use a heavier weight for the same time, or lift the same weight for a longer time, but if you use a lot longer time under load the weight you need less weight. Since going to momentary muscular failure and achieving maximum intensity of effort is more important for stimulating increases in strength and size than absolute load this is not a problem, though. Going slower allows you to train with maximum intensity of effort and minimum risk of injury.

  • Charlie Nov 29, 2014 @ 14:21

    I’m thinking about deadlift…
    Recently use Smith rack with 360 lb from kneecaps to upright. I did 10 reps in 30 seconds. How shall I progress? Turn the tables and do 9 reps in 30, a little slower, maybe intentionally work up to just a static hold just above the knees. I’ll save the weight progression for hip thrust and save my lumbars.

    • Drew Baye Dec 4, 2014 @ 1:01

      Hey Charlie,

      If you’re doing more than four or five reps in thirty seconds, even over that short range of motion, you’re going way too fast. Slow way down, take about four seconds to lift and another four seconds to lower the weight, making an effort to reverse direction at the start as slowly as possible.

  • Bradley Nov 30, 2014 @ 15:10

    Yes very true. I do like to train with lighter weights these days, just feels so much more difficult.

  • Leo Dec 19, 2014 @ 15:16

    Drew,
    When you undertake your SS bodyweight experiment, how will you make it progressive?

    • Drew Baye Dec 22, 2014 @ 14:05

      Hey Leo,

      The progression system I’ve developed for bodyweight training is explained in detail with illustrated examples for each exercise in Project Kratos.

  • Jerry Pinter Dec 30, 2014 @ 23:02

    Hi Drew,

    Your article is very interesting to me since I have experimented over the years with rep speed. I have been an advocate of HIT since I started training back in 1980, trying various versions of it including several years of Super-Slow and most recently HIT as prescribed by Darden and Jones.

    A couple years ago I collected quite a bit of data on rep speed and time under load (TUL) using my own workouts. I was surprised to find that the faster I did my reps, the faster I reached failure (shorter TUL). I found this same trend for all 22 exercises I measured. For example, on a Cybex calf machine with 505 lbs, I reached failure in 120 seconds using super-slow 10/10 cadence (6 reps). With the same weight next workout (505 lbs) using fast reps (1/1 cadence) I reached failure after 25 reps in only 48 seconds. Similar results were seen for all body parts, exercises, machines and free weights alike. Fast reps were performed from 2 to 5 seconds depending on exercise. Slow reps were always 10/10 cadence. Fast reps always produced shorter TUL with the same weight as slow reps.

    Here is how I interpret these results (and I know this will produce critical response from readers): In both sets of calf raises discussed above, I was reaching failure (could no longer budge the weight) with the same weight (505 lbs) and thus the same level of “inroading”. However, I will argue that the fast rep set was more intense because the level of inroading was achieved after only 48 seconds, whereas with 10/10 reps it took 120 seconds to reach the same level of inroad. Thus my argument is that if you are targeting a specific TUL for your sets (say 40 seconds) and level of inroad (say 70% 1RM) you should perform fast reps in good form.

    I welcome feedback and comments on this. Thanks and I enjoy your website!

    Jerry

    • Drew Baye Dec 31, 2014 @ 12:38

      Hey Jerry,

      Hey Jerry,

      I performed a similar experiment years ago and found the same thing, faster cadences resulted in shorter time to momentary muscular failure on all exercises in everyone tested, despite the slower cadence always being tested second. However, there is another way to look at this. With the same load, a faster cadence will result in a shorter TUL, but with a slower cadence you can use a heavier weight for the same TUL and the additional tension is beneficial.

      Also, since there appears to be little difference in long term results with different protocols in determining repetition speed safety should always be the primary consideration, and if you are performing your repetitions fast they will not be in good form (by my standards – most people’s idea of “good” form is actually quite bad). The turnarounds, especially the lower one, should be performed smoothly enough that the variation in force caused by acceleration is within a few percent, and most people have difficulty doing this well at cadences faster than 4/4 over typical exercise ranges of motion.

      Quite frankly, however

  • shane Aug 13, 2017 @ 16:07

    drew,
    i have always explained it to people like this: your body doesn’t necessary recognize the amount of sets or repetitions it is exposed to but what it does recognize is the amount of time a muscle is made to contract for and more importantly the amount of time it is made to contract maximally for. and slower contractions are more beneficial because muscles are capable of producing more force at slower speeds of movement. this is the simplest way i have found to explain it to people before going more technical.

    shane