Should We Train at 30% of 1RM to Maximize Power Production?

Over the past few weeks I’ve heard the “Magic 30%” number tossed around on two different occasions in terms of the training load that maximizes power production, so I figured it was time to write an article on this topic. The theory is that we should train athletes with explosive movements at 30% of their 1RM because this is the load that shows the highest peak power outputs and therefore this load will maximize the athletes’ power production and athleticism.

This line of reasoning is faulty for several reasons, but first, let’s look at the research. I’ll state up front that the research is very complicated due to the fact that sometimes “mean power” is used, sometimes “peak power” is used, and sometimes just “power” is used. Different equations and methods are also used in determining max power. Calculations sometimes incorporate bodyweight and sometimes they do not. Different types of movements are employed, for example free weight squat jumps versus machine squat jumps. And finally, different types of subjects are used…various ages, genders, training statuses, types of athletes, levels of strength, etc., which complicates matters as well.

That said, it’s still very valuable to analyze the research. Here are some quick findings on a spectrum of different studies.

Research

Optimal loading for peak power output during the hang power clean in professional rugby players

Peak power output – 80% of 1RM for hang power clean, no significant difference from 40-90%.

Optimal loading for the development of peak power output in professional rugby players

Peak power output at 30% of 1RM for ballistic bench throw and 0% (just bodyweight) for squat jump.

Determining the Optimal Load for Maximal Power Output for the Power Clean and Snatch in Collegiate Male Football Players

Peak power at 80% for Power Clean and Snatch.

The Load That Maximizes the Average Mechanical Power Output During Explosive Bench Press Throws in Highly Trained Athletes

Peak power for Bench throws at 55%.

Optimal loading for peak power output during the hang power clean in professional rugby players.

Peak power for hang power clean at 80%, no significant differences from 40-90%.

The load that maximizes the average mechanical power output during jump squats in power-trained athletes

Peak power for jump squat at 55-59%, no significant differences from 47-63%.

Power outputs of a machine squat-jump across a spectrum of loads

Peak power at 21.6% for jump squat.

Leg power in young women: relationship to body composition, strength, and function

Peak power for leg press at 56-78%.

Human muscle power output during upper- and lower-body exercises

Peak power for Squat at 50-70%, peak power for bench press at 40-60%.

Maximal strength and power characteristics in isometric and dynamic actions of the upper and lower extremities in middle-aged and older men

Peak power at 30-45% for bench press, peak power at 60-70% for half squat.

The relationship between maximal jump-squat power and sprint acceleration in athletes.

Peak power at 30-60% for split jump squat, peak power at 50-70% for squat.

The Effect of Heavy- Vs. Light-Load Jump Squats on the Development of Strength, Power, and Speed

Low load explosive training appears better than high load explosive training for power.

COMPARISON OF OLYMPIC VS. TRADITIONAL POWER LIFTING TRAINING PROGRAMS IN FOOTBALL PLAYERS

Olympic lifting seems better than powerlifting for power.

Velocity specificity, combination training and sport specific tasks.

No difference between strength trained and power trained for netball throw velocity.

Power versus strength-power jump squat training: influence on the load-power relationship.

Combined strength and power training appears better than just power training.

Squat jump training at maximal power loads vs. heavy loads: effect on sprint ability

Power training appears no better than heavy training for sprint speed.

Inter-relationships between machine squat-jump strength, force, power and 10 m sprint times in trained sportsmen

Squat jumps at lighter and heavier loads not well correlated with acceleration.

Conclusions

It appears that each exercise has its own unique range of loading for peak power production, and often the range is pretty broad. The “Magic 30%” figure just doesn’t hold up. Furthermore, individual peak power production can vary considerably from one person to the next, so it’s unwise to generalize and assume that an individual falls in the norm when their anthropometry, physiology, anatomy, etc., could cause them to stray from the norm.

There is mixed and inconclusive evidence on which loads maximize athletic performance indicators (as well as mixed research on what load maximizes peak power for the various lifts). The best load is most likely specific to the individual and could have much to do with the individual’s “weak link.” For example, if they’re weak but pretty elastic perhaps you should try to get them strong, and if they’re strong but not explosive, perhaps you should focus on power and reactive strength.

It’s important to consider the fact that squatting and jump squatting motions aren’t biomechanically similar to sprinting so the correlation with advanced athletes may be relatively weak. Power is just one quality; there’s also speed, agility, endurance, skill, strength, etc. In sports, there are many different force-velocity relationships, so it’s wise to pay attention to different types of strength and loads. It appears that combined training and training with mixed loads is superior to uni-dimensional training and training at a single load. Some lifts lend themselves better to heavy lifting and some lifts lend themselves better to explosive lifting…perhaps it’s best to just train squats and bench press heavy, Olympic lifts relatively heavy (which means explosively), jump squats a little lighter and more explosively, and use sprints, plyos, and ballistics for the primary “rapid stimulus.” This ensures that you hit all the points on the force-velocity curve.

Finally, variety and periodization are important considerations in program design. With the many types of plyometrics, ballistics, sprint drills, towing drills, explosive lifts, and heavy lifts, there’s no reason to stick with solely one load (as a percentage of 1RM) indefinitely.

56 Comments

  • Rhys I says:

    Good work Bret, i heard Coach Boyle discuss this on the strength coach podcast and seeing as this is related to my current masters dissertation it was did cause me to hit my head against the wall a few times. Peak power and mean power varies depending on the exercise as you said. So to look at one study with one exercise and assume its the same for all exercises is just plain stupid.
    None of the Olympic Lifters i train with ever lift 30% of anything. Even the warm up sets start heavier than that! What they might do is work to a heavy single though then drop to 60-80% (depending on lift variation and experience) of that weight and perform 3-5sets of 3 reps at that weight. If you do 30% of your 1RM clean your techniques gonna suck and your probably gonna throw the bar into your chin, not to cleveer either way! Ha

    • Rhys I – great comments. I have to disagree with you though…you “lift” 0% when you have your athletes do plyos (which is likely the % that maximizes jump squat peak power), so through combined training we all (strength coaches) most likely cover all of our bases anyway as far as different types of strength and power production are concerned. Agree? Thanks for the comment!

  • Eric Moss says:

    Great post Brett! I always find your stuff informative.

    Eric

  • Ofir Levi says:

    wonderful piece by the ass master once again. This could be useful. Thanks !

  • Nick Horton says:

    Nice! Great stuff.

    You want to know the “dirty little secret” to how I get my athletes to jump higher and sprint faster? I make them add plates to the bar! It’s a rare athlete that is too strong. Most young athletes are both slow AND wimpy.

    80%, or between 70% to 90% of max, on a power clean is about what most guys are going to do their 5 reps of 5 with in a classical strength program. So, I’m not shocked that thats the range the studies are showing works best for peak power production.

    I’d like to add something:

    The reason a number of studies have shown that Oly lifters have some of the highest vertical jumps around is (in my opinion) that they do the FULL lifts, and they do them heavy as hell all the time.

    As a group, they DON’T have what you’d expect out of high jumping people – long Achilles tendons. (Yes, they likely have a higher proportion of type IIb muscle fibers, but then, so do most athletes at a high level.)

    You don’t need to do fancy-pancy jump squats if you do the clean and snatch correctly. Done right, these moves mimic a vertical jump almost exactly. Done wrong (as they nearly always are) they resemble some sort of bar-humping hip smack that has little carryover … which forces one to use things like jump squats more aggressively.

    Also, doing the FULL lifts builds in a reactive bounce out of the hole that has a great training effect that is under utilized by strength coaches, generally.

    Third, doing the Jerk – for real – also trains the legs to act reactively under massive weights in a way that mimics vertical jumping. Again, done wrong, it is little more than a sloppy push press.

    If you add in normal plyo stuff like box jumps and broad jumps, you have a very well rounded jumping routine.

    I get that with upper body stuff, you’re likely better off doing “plyo-esque” work with lighter weights – this is why explosive push ups work so well. But, as most of the studies above showed, for your lower half, stay heavy.

    I think a lot of strength coaches make their lives harder by avoiding what it takes to learn how to properly teach the Oly lifts to their athletes (it isn’t THAT hard), and are then forced into finding a whole crap-load of auxiliary exercises to fill in the gaps. That is just not an efficient way to do things.

    • Great comment Nick! Agree about the Oly lifts. They take time and most coaches don’t want to dedicate the energy and attention necessary (especially when a crafty coach can find ways around them).

  • P. J. Striet says:

    Good stuff as always

  • Mark Young says:

    Great read Bret!

    I actually read a study online recently suggesting that the backward overhead medicine ball test correlates well with the type of sport you play.

    Jump athletes (volleyball) do better at explosive tests like this that measure power than non-jump (wrestling) athletes. Non jump athletes scored higher in strength measures such as 1RM bench and leg press.

    It made me think about how much of an emphasis we should place on power in certain types of athletes. I know it is “cool” to do Oly lifts, but necessary?

    As with many things, I think it comes down to context. Train power for those who need it, but don’t waste too much time training it in those who don’t.

    Would you agree?

    • Nick Horton says:

      You’re right, of course, that training for your sport is a priority. But, there are not a lot of athletes who don’t need more power.

      While there are some sports where there is no jumping at all, that is rare. And even in those where there isn’t jumping, there is usually an explosive horizontal movement like sprinting or slamming into someone as in football.

      Outside of the distance/endurance sports, most athletes would do better if they were better able to explode when the time comes. If that is a vertical explosion, then the Oly lifts are your best bet. If it’s a horizontal one, then you might be better off with hip thrusts and kettle bell swings.

      In my opinion, especially with younger athletes (sub 22 years old, or recreational athletes) it is best to train them to be explosive in all planes of motion. This means doing Oly lifts AND swings, squats, deads, AND hip thrusts (Bret’s sold me on them, particularly for athletes like sprinters, football players, etc).

      OH, and Oly lifting is “cool” for the same reason a high protein diet is cool for athletes – it works. 🙂

      I know that for coaches without much experience with the Oly lifts (most), they seem like too much of an investment – no doubt, they are a pain in the ass at first. But, the payoff is greater than the investment of time it takes to learn how to properly teach them to athletes.

      I still contend that coaches are doing their athletes a disservice if they don’t *at least* teach proper mechanics on the power clean and power snatch. They aren’t the end-all, be-all, of strength training. But, they are a fundamental component, and they save massively in terms of training economy.

      I’ve never seen a football player who didn’t benefit from a proper use of power cleans. And football is certainly not a “jumping” sport.

      • PolyisTCOandbanned says:

        “OH, and Oly lifting is “cool” for the same reason a high protein diet is cool for athletes – it works. ”

        Sometimes this stuff sounds more like religion than science. There are a lot of people touting high protein with very little strong statistics (or phsyiology) to prove the need. But it “seems like it should be important” and “is how we’ve always done it”. If athletes really need all this protein, what about manual laborers? Should the FDA revise the RDA? And why haven’t they? if it is such a NO BRAINER?

        Another thing Every time someone does a study*, they end up showing no statistical difference in strength gains for lifters on machines or on free weights. This happens whether the study is done by a Nautilus advocate or someone who wanted to prove the benefits of free weights. But we still persist in hearing how free weights will make you huger. Instead of this argument, which the muscle fibers do not seem to buy, a better argument would be that the free weight movements are more fun, can be higher loaded, are more athletic, feel manlier, time efficiency, whole body benefit, etc. But I really don’t think the quad muscle fibers care if you are doing a manly Rippetoe squat or if you are on the evil, evil, Smith machine…

        *I don’t mean literally every single study, but I pulled a couple good literature surveys and they found this general result across many previous studies (and one with retesting).

      • Great thoughts Nick. Pretty much sums up my thoughts. It’s all about combined training and hitting different loads, vectors, velocities, strength-types, etc.

      • PolyisTCOandbanned says:

        Bret:

        You are so polite when you call me on the carpet. 😉

        http://exrx.net/forum/viewtopic.php?p=56488&highlight=machine#56488

        • Definitely not calling you out on the carpet Poly! I’m truly very interested in this topic and have my own theories that I’d love to research down the road if I ever find the time and am in the position to do so. Thanks for the links.

      • Mark Young says:

        Hey Nick,

        – Just a few thoughts…

        “You’re right, of course, that training for your sport is a priority. But, there are not a lot of athletes who don’t need more power.”

        – I agree. I think there should definitely be power training for most sports. But to me it is more about how much time you allocate to specific areas (i.e., power, strength, lateral speed, etc). Each should be dictated by the sport.

        “OH, and Oly lifting is ‘cool’ for the same reason a high protein diet is cool for athletes – it works.”

        – Being that Oly lifting is usually used in combination with the rest of a S&C program I think it is very hard to attribute any specific benefits to those lifts. If you took them out would the power be less? Maybe. Would it affect performance on a measurable level? Who knows?

        I have my thoughts on protein, but I won’t get into it here as it will be lenghty. Suffice it to say, science doesn’t back the super high protein claims that most make.

        In the end, I agree that power movements are important for most sports, but I think the degree to which the influence performance is probably overrated.

      • Mark Young says:

        PolyisTCOandbanned – Exactly!

    • Thanks Mark, I’ve seen a couple of studies that show high correlations with overhead medball/shot tests, so there’s definitely something to that motion as far as testing explosiveness.

      Obviously Oly lifts aren’t necessary if you still do other things (jump squats, sprints, different types of medball throws and tosses, vertical and horizontal plyos, etc.). But I like them for several reasons and think that many coaches duck out on account of laziness.

      As for training for power, I completely agree if we’re talking about non-athletes. I don’t do much power work with my physique-based clients.

      Thoughts?

      • Mark Young says:

        Bret – Just to be clear, I LOVE oly lifts.

        With physique clients I’ll sometimes use power variations such as med ball work so that this quality is at least maintained. They don’t NEED oly lifts and I find that the time could be better spent doing something that directly improves appearance. Since power decreases with age I think it is important to maintain this in older clients.

        • Mark and Nick,

          I think we could all agree on this:

          1. There is no good research to show that heavy training + plyos and sprints is better or worse than heavy training + Oly lifts + plyos and sprints.
          2. If you omitted them but still went heavy on some exercises and did sprints/plyos, there probably wouldn’t be much of a difference.
          3. Variety is good.
          4. Oly lifts cover a lot of bases at once (triple ext., RFD, reactive strength, shoulder and core stability, hip/ankle/t-spine mobility, etc.).
          5. They’re very teaching-intensive, take a ton of patience, and time.
          6. At the end of the day it’s up to the trainer/coach to determine whether or not to use them but the coach shouldn’t be judged for his/her position as there isn’t much research to go with and a good argument could be presented either way.

          Agree?

    • PolyisTCOandbanned says:

      I would love your thoughts on how to self teach oneself anatomy and stuff. I google a lot of stuff and look at wikipedia and all. But it’s hard to absorb things that way. A good desk referece would help me (could still google in addition to that). Also, wonder how you access studies and all. I’m thinking of becoming a friend of the library (50 buck) at my local state medical school. Then I still have to go down there, though, to use their databases and hard copies. But beats buying articles ad hoc, when behind paywalls.

      • Nick Horton says:

        Haha! When I said “high protein” I meant higher than 30 grams a day – which is what most high school “athletes” are coming in to me eating. I certainly did not mean the 700 times bodyweight stuff that the Bodybuilders eat.

        As I said, regarding Oly lifts, they aren’t the end-all be-all of a S&C program. They certainly COULD be kept out, and still the athletes could be made to be just as explosive. They aren’t magical.

        But, they ARE more time efficient than most exercises. They hit the body in more places than most exercises, and have a very high carryover to power production.

        By using a power snatch or power clean, you cover a lot of bases really fast, and can spend more time on other stuff that still needs to get done. Since a lot of our athletes have limited time with us as it is, this is a priority.

        Also, as Bret and I both stated, the reason a lot of coaches don’t bother with them is out of shear laziness, not because there are good logical reasons not too.

      • Poly, I’m taking a class at ASU so I have access to their library…I can get pdf’s of tons of different journal articles. This is huge for me as I get a ton out of this service (but classes cost a fortune these days).

        As for anatomy, etc., the combination of 1) textbooks, 2) Google, and 3) talking to Physical therapists, etc. works best. I took the 2 semesters on my own for the hell of it after I finished undergrad because I was so interested in Anatomy & Physiology.

        The public libary would probably be invaluable.

      • Mark Young says:

        Poly – Just wanted to mention that access to online journals for 50 bucks is a HUGE score. If you can get this…take it.

      • PolyisTCOandbanned says:

        Mark: Thanks for the motivation. I will go ahead and sign up. Of course, I have to go down to the library to use their terminals. And pay for the copying.

        Actually I think I might even get access just as a member of the general public. Not sure. I know I can’t check books out, though. I’ll just sign up for the membership, so I don’t have things that bug me about not having total access.

    • PolyisTCOandbanned says:

      Brett: the study in bullet three is the best of my post. I did not do a thorough search. Just a quick google really (just being honest about the limitation).

      P.s. I hate threading of comments. It never works…

  • Travis says:

    Bret,

    Great post!

    I agree with you that different lifts or movements work better with different loads all depending on what you’re training for.

  • Kyle Barbour says:

    Great read Bret, Thanks.

  • Truet says:

    As always, very informative without the fluff!

  • Tim Egerton says:

    Great stuff as always Bret!

    Another thought is that perhaps we should be looking to maximise power output in our sport rather than in a particular exercise.

    Is the load that maximises power output in an exercise (whatever that load as a percentage of maximum might be) always going to be the most appropriate for developing maximum power within the athletes sport?

    Might it be better to select loads that result in the lift being performed with the same or similar joint angular velocities to those associated with the sporting movement they are training for? Assuming this is always possible of course.

    cheers,

    Tim

    • Great points of course Tim! I like to consider “general” strength/power and “specific” strength/power as some lifts are just so conducive to power training that many athletes would benefit from doing them even if they’re not so biomechanically similar to their sport. When we try to get more specific, sometimes we end up trying lifts that make sense in theory but don’t hold up in the real-world. But I do agree with you!

    • Peter Mundy says:

      Currently, certain departments are already attempting to look at this:

      http://www.ncbi.nlm.nih.gov/pubmed/21240030

      However, it must be noted that this is only realistically pilot data. Lifts with greater joint moments, angular velocities etc must be correlated with sporting movements before intervention studies are conducted. This area has a lot of potential but is in a relatively infant phase with regards to the current literature.

      I have also collected similar data across similar loads but over a greater range of exercises, however, it is currently unanalysed. When I get round to this project I will post my findings.

      Regards,
      Peter

      • Bret says:

        Very interesting abstract Peter. This is great stuff. We should definitely look at the load that maximizes power at each joint during compound movements. Thanks for the link!!! And definitely keep me posted.

        • Peter Mundy says:

          No problem, I am in love with this area of research – I could speak about it all day!

          Here is another link on the theme of the original post that I think you will find very informative:

          http://www.ncbi.nlm.nih.gov/pubmed/21244105

          Bear in mind though, it doesn’t really discuss how for highvelo-highload sporting movements that there is no sig dif between JS and PC (and my studies also show Vs mtpc and push press) between 50-70% (movement specific) 1RM. Furthermore, in elite rugby players VGRF and RFD (Unpublished/in press I think PPO as well) @ 60% (PC) 1RM are sig higher in the mid-thigh versions of the PC when compared to conventional and hang variations (Comfort, Allen & Graham-Smith, 2011), however, a greater spectrum of loads (while accounting for system load) must be analysed.

          My pilot data showed that PPO and VGRF is non-sig greater than the MTPC and PP at 50-70%, however, RFD is maximised non-sig in the MTPC. I also noticed a linear increase in PPO in the MTPC, while an inverse linear decline in the JS. Cognisant to the limitations of my pilot data (only 3 loads, strength trained (2y) sample group and not athletes, 1rm pc for mtpc and not 1rm mtpc), this may suggest that, as changes to the load-velo relationship occur at the %RM trained at and both movements present an intra-individual response at moderate loads, that practitioners should periodise across a number of loads and exercises in order to elicit adaptations across the entire continuum.

          While Cormie (see her 2007 work) has analysed the JS vs the PC, Comfort’s research suggests that the mid-thigh variations, which also show an intra-individual response across large loading conditions (30-120% no sig, Kawamori et al. 2006), may be more beneficial to athletes (less technical, more bang for the buck etc). Subsequently, it is axiomatic that more comparative research is produced. However, obviously longitudinal comparative analysis is required (do they actually result in adaptations to the l-v curve and where?!). Unfortunately, we all know that this is hardly pragmatic and often problematic in elite training populations!

          Sorry for the long, un-organised post – I’ve just woken up! I hope you allow post author corrections :p

          Regards,
          Peter

        • Peter Mundy says:

          (Please delete the above post Bret!)

          No problem, I am in love with this area of research – I could speak about it all day!

          Here is another link on the theme of the original post that I think you will find very informative:

          http://www.ncbi.nlm.nih.gov/pubmed/21244105

          Bear in mind though, it doesn’t really discuss how for highvelo-highload sporting movements that there is no sig dif between JS and PC (and my studies also show Vs mtpc and push press) between 50-70% (movement specific) 1RM. Furthermore, in elite rugby players VGRF and RFD (Unpublished/in press I think PPO as well) @ 60% (PC) 1RM are sig higher in the mid-thigh versions of the PC when compared to conventional and hang variations (Comfort, Allen & Graham-Smith, 2011), however, a greater spectrum of loads (while accounting for system load) must be analysed.

          While Cormie (see her 2007 work) has analysed the JS vs the PC, Comfort’s research suggests that the mid-thigh variations, which also show an intra-individual response across large loading conditions (30-120% no sig, Kawamori et al. 2006), may be more beneficial to athletes (less technical, more bang for the buck etc). Subsequently, it is axiomatic that more comparative research is produced. However, obviously longitudinal comparative analysis is required (do they actually result in adaptations to the l-v curve and where?!). Unfortunately, we all know that this is hardly pragmatic and often problematic in elite training populations!

          My pilot data showed that PPO and VGRF is non-sig greater than the MTPC and PP at 50-70%, however, RFD is maximised non-sig in the MTPC. I also noticed a linear increase in PPO in the MTPC, while an inverse linear decline in the JS. Cognisant to the limitations of my pilot data (only 3 loads, strength trained (2y) sample group and not athletes, 1rm pc for mtpc and not 1rm mtpc), this may suggest that, as changes to the load-velo relationship occur at the %RM trained at and both movements present an intra-individual response at moderate loads, that practitioners should periodise across a number of loads and exercises in order to elicit adaptations across the entire continuum.

          Sorry for the long, un-organised post – I’ve just woken up! I hope you allow post author corrections :p

          Regards,

          • Bret says:

            Since you’ve just woken up I’ll let you off the hook! 🙂 I agree…we don’t know enough about this topic…and we really need to look at individual responses instead of averages, both in terms of peak power output at various %’s in various exercises, as well as the adaptations to training at various %’s in various exercises. Thanks Peter!

  • Eric Buratty says:

    Hey Bret,

    Awesome post! . . . AND you included the actual research links! . . .

    Usually people are quick to fire the old “recent studies have shown…” without showing where they found the information.

    Keep ’em coming!

    -Eric

  • Howard Gray says:

    A topic that gets me going too Bret!

    Just because peak power (tends) to be reached with 30% loads, does not necessarily mean that is what best develops power. As with training for any goal – we have to expose our body to a variety of loads and forms of training in a periodized plan that will bring about phase potentiation.

    Also I am sure many of your readers heard Prue Cormie speak about improving power in athletes and that the majority of athletes (everyone but the very strong) can develop power with heavy loads as well as they can with more typical “power” methods. These athletes will also develop strength with heavy strength training.

    Keep it coming!

  • Ben Bruno says:

    Great post Bret. Thanks for including those studies. It is always nice to read the science behind what we intuitively think to be true.

  • Mel Siff states in Supertraining: “Exercise with small loads (with approximately 20% of 1RM) is the principal method of developing speed-strength.” (p. 263).

    Are you saying he’s wrong?

    • Yes I am. In general it’s probably safe to generalize and throw out a number such as 20% or 30%, but as shown above each lift has it’s own specific percentage for max power. Furthermore, from a practical perspective some lifts aren’t very conducive to training with 20% of 1RM. Exericses like squats, bench press, and deadlifts when performed at 20% would involve a brief ROM involving rapid acceleration followed by a long ROM involving deceleration. With exercises like jump squats, med ball throws, plyo push ups, etc. it’s also impossible to measure a 1RM. So some things are great in theory but when considering the practical side of things we have to make adjustments.

  • I agree bret, thanks for the informative article! And cant wait for those explosive test results to come through.

  • Jon says:

    Great article, Bret! Came across your site via fitmarker, and I’m glad I did!

  • Joe says:

    Do you guys know of any resources for developing a periodized hang clean program…as far as working with 1 RM’s. Im working with track athletes. Thanks

  • I think you misunderstand the meaning of 30%. That is meant in the context of the Force-Velocity relationship. Look a the relationship in Wikipedia and the graph on the right-hand side
    https://en.wikipedia.org/wiki/Muscle_contraction#Force-length_and_force-velocity_relationships

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