Force velocity relationship

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The force velocity relationship is the observation that muscle force and contraction velocity are inversely related. In shortening (concentric) muscle actions, where contraction velocity is high, muscle force must be low. Where muscle force is high, contraction velocity must be low.

In lengthening (eccentric) muscle actions, the force velocity relationship is the other way around. Where contraction velocity is high, muscle force can be high. Where muscle force is low, contraction velocity must be low.

The traditional, hyperbolic force velocity relationship properly describes the behavior of single muscle fibers but also seems to hold true for single joint movements. The force velocity relationship of both upper- and lower-body multi-joint (compound) movements is not hyperbolic, but is in fact linear.

Changing the force velocity curve as a result of training requires us to produce velocity-specific strength gains. This might be achieved by high-velocity strength training.

There is good evidence that high velocity isokinetic training leads to greater gains in strength when tested at high isokinetic velocities, and there is weaker evidence that the same effect occurs after constant load training.

Training with different types of external load could therefore be useful for emphasizing different ends of the force velocity curve. Using constant resistance or variable resistance could be helpful for improving force at higher velocities.

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CONTENTS

  1. Force-velocity relationship
  2. Changing the force-velocity relationship
  3. References
  4. Contributors

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THE FORCE-VELOCITY RELATIONSHIP

PURPOSE

The purpose of this section is to provide an explanation of the force velocity relationship in biomechanics.

BACKGROUND

Introduction

The force-velocity relationship is the observation that muscle force and contraction velocity are inversely related. Where contraction velocity is high, muscle force is low and vice versa. In practical terms, this means that when high levels of force are required (such as during powerlifting), the contraction velocity of the muscles involved is low. Similarly, when high velocities are required (such as during javelin throwing), the muscle force produced is much lower.

History

The discovery of the force velocity relationship in muscles is attributed to the famous English exercise science researcher, Archibald Hill (Hill, 1938), although it had also been observed by other researchers around the same time (Fenn and Marsh, 1935). Hill’s original formula includes two constants in addition to a measure of maximum isometric force and describes a hyperbolic relationship between muscle force and muscle contraction velocity when single muscle fibers shorten.

Hyperbolic relationship

The force velocity relationship observed when single muscle fibers shorten is hyperbolic, or non-linear. This is the famous force velocity relationship that is usually referred to in most popular articles. Being hyperbolic means that the rate of change of force alters with changing velocity. At low velocities, the rate of change of force is very high and it drops off quickly with small increments in speed. At higher velocities, the rate of change of force is quite low and alters little with each incremental change in speed. This hyperbolic force velocity relationship describes the relationship between muscle force production and contractile velocity in single muscles while shortening. Therefore, it does not necessarily explain the relationship between net joint moments and joint angular velocity, nor does it explain the relationship between muscle force production and contractile velocity in single muscles while lengthening.

CONCENTRIC AND ECCENTRIC JOINT ACTIONS

Correctly, the force-velocity relationship describes how the maximal force produced by single muscle fibers while they are shortening is inversely proportional to their contraction velocity. In other words, producing very high levels of force limits muscles to shortening slowly, while shortening limits muscles to producing a much smaller amount of force, even though the effort exerted is maximal in both cases. However, it is important to recognize that when studying lengthening (eccentric) contractions, we observe that the force-velocity relationship is the opposite way around, as can be seen in the chart below.

Force-Velocity relationship

The concentric and eccentric force-velocity relationships

As you can see from the chart, to produce high levels of force requires muscles to lengthen quickly, not lengthen slowly.

DIFFERENT EXTERNAL LOAD TYPES

Introduction

The force-velocity relationship is most commonly-measured using isokinetic resistance, which involves a dynamometer. In isokinetic movements, the dynamometer constantly adjusts the force resisting the joint movement so that the velocity remains constant. This allows force to be calculated at different points in the joint range of motion, as well as the mean force for the whole repetition. However, in practice, most strength coaches use other types of external load for training and testing, with the most common being constant loads (like free weights). Other training and testing equipment can include variable resistance (like machines using cams) or constant resistance, pneumatic machines (including Keiser machines).

Constant loads, variable resistance, and constant resistance

Constant loads do not produce a constant resistance over the whole joint angle range of motion. Because they involve exerting force against both weight and inertia, they require the greatest force at the beginning of the exercise (weight plus inertia), a moderate amount in the middle (just weight), and the smallest force at the end (weight minus inertia). In contrast, variable resistance tries to match the strength curve of the lifter with the applied resistance, which could vary depending on the exercise, but approximately reflects the external load type of the isokinetic dynamometer. Finally, constant resistance uses a very light mass in combination with a fixed pneumatic resistance so that inertia is minimal, and the force is constant throughout the whole repetition. The different types of external load are shown in the diagram below:

External load type

Different types of external load

As you can see from the chart, each type of external load will produce different types of force at different parts of the movement. This is especially important, at the beginning, where the individual is accelerating. And assuming that maximal bar speed is attempted, this produces a different peak velocity for the same force when using each external load type. For example, when comparing constant load (free weight) and constant resistance (pneumatic machine) bench presses, the constant resistance bench presses involve higher peak velocities, because they allow greater acceleration at the start of the movement (Frost et al. 2008). Constant resistance exercise therefore also increases peak power outputs, as you can see from the infographic below.

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Although we tend to think of free weights as being a "constant load" during each rep of a set, the force we exert is not actually constant over the duration of the concentric phase. In fact, the force that we exert on a barbell is equal to the weight due to gravity plus a force required to overcome the inertia associated with its mass. The weight due to gravity stays the same over the whole of the rep, while inertia works against us while we are accelerating the barbell in the first part of the concentric phase, and then helps us out (called momentum) in the later part. When we look at the force profile over a rep during a free weight lift, the force is therefore very high at the start as we get the bar moving, moderate in the middle, and low towards the end, as we let momentum carry us to lockout. Pneumatic resistance machines can be set to use air pressure to exert a constant force against the lifter. Since they have minimal mass, they don't display the same kind of force profile as a barbell. Instead, the force is similar over the whole rep, which means that accelerating is very easy, as there is no inertia to overcome. On the other hand, there is no momentum to ride to lockout, either. These differences between free weights and pneumatic resistance mean that the two types of external load display very different characteristics when we test the force produced at different percentages of the 1RM with each type of load. Pneumatic resistance consistently allows faster bar speeds for the same percentage of 1RM, while free weights tend to involve greater force production. This may imply that pneumatic resistance is better for producing velocity-specific adaptations, while free weights are better for producing force-specific adaptations, although there are of course many other factors involved.

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SINGLE-JOINT VS. MULTI-JOINT MOVEMENTS

Introduction

As noted above, the original force velocity relationship was calculated in order to explain the relationship between muscle force production and muscle contraction velocity in single muscle fibers. In such a system, the relationship appears to be hyperbolic, both in shortening (Wickiewicz et al. 1984; Sale et al. 1987; Hortobágyi & Katch, 1990; Westing et al. 1990) and in lengthening (Hortobágyi & Katch, 1990; Westing et al. 1990).

Single-joint movements

Although the original equations for the force-velocity relationship were not intended to describe the relationship between joint moments and angular velocity, the force velocity relationship of single joints does still appear to be hyperbolic and matches the behavior of single muscle fibers fairly closely (Hauraix et al. 2017). In these systems the force-velocity relationship is more accurately referred to as joint torque-angular velocity relationship.

Multi-joint movements

In multi-joint movements, the force velocity relationship seems to be linear (Bobbert, 2012; Cuk et al. 2014; Jaric, 2015). A linear force velocity relationship has been observed in the squat (Rahmani et al. 2001; Sheppard et al. 2008), leg press (Bobbert, 2012), loaded and unloaded vertical jumps (Samozino et al. 2014; Cuk et al. 2014), cycling (Vandewalle et al. 1987; Jaskolska et al. 1999; Driss et al. 2002), treadmill running (Jaskolska et al. 1999; Morin et al. 2010), arm cranking (Nikolaidis, 2012), in both bench presses and bench press throws (Rambaud et al. 2008; Sreckovic et al. 2015; García-Ramos et al. 2015), and during rowing (Sprague et al. 2007). Exactly why the force-velocity relationship is not hyperbolic in many multi-joint movements is not entirely clear. Musculoskeletal modeling indicates that this oddity is likely to be a biomechanical phenomenon and not a physiological one, resulting from segmental dynamics canceling increasingly more muscular force as movement velocity increases while external force reduces (Bobbert, 2012). However, interactions between the force velocity and length tension relationships have also been observed (Hahn et al. 2014), which remain to be clarified.

SECTION CONCLUSIONS

The force velocity relationship is the observation that muscle force and contraction velocity are inversely related. In shortening (concentric) muscle actions, where contraction velocity is high, muscle force must be low. Where muscle force is high, contraction velocity must be low.

In lengthening (eccentric) muscle actions, the force velocity relationship is the other way around. Where contraction velocity is high, muscle force can be high. Where muscle force is low, contraction velocity must be low.

The traditional, hyperbolic force velocity relationship properly describes the behavior of single muscle fibers but also seems to hold true for single joint movements. However, the force velocity relationship of both upper- and lower-body multi-joint (compound) movements is in fact linear.

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CHANGING THE FORCE VELOCITY RELATIONSHIP

PURPOSE

The purpose of this section is to describe how the force velocity relationship can be changed with training.

BACKGROUND

[Read more: velocity-specific strength training]

Introduction

Changing the force velocity curve as a result of training requires us to produce velocity-specific strength gains. Following the principle of specificity, we might expect to see the largest gains in strength when we test force production at the same movement speed as we use in training. This would lead to changes in the force velocity curve as shown in the diagram below.

Force-velocity response to training

If the principle of specificity applies to velocity, then when we train using a fast speed, we should see the greatest gains in strength when we test strength at a high velocity, and the smallest gains in strength when we test at a low velocity. Similarly, if we train using a slow speed, we should see the greatest gains in strength when we test strength at a low velocity, and the smallest gains in strength when we test at a high velocity. To prepare athletes for sport, are most interested in whether we can produce greater gains in strength at high velocities, by training using fast bar speeds.

The effect of “intent to move quickly”

In one very influential study, Behm & Sale (1993) tasked subjects to perform ankle dorsiflexion training either isometrically or isokinetically (300 degrees/s), but where both programs required the subjects to “move as rapidly as possible regardless of the imposed resistance.” Strength was tested at a range of angular velocities (0 – 300 degrees/s). There was no difference between the two training programs in respect of the changes in strength at any velocity. Yet, both training programs displayed velocity-specific strength gains, with the greatest gains in strength being at the highest velocities. On this basis, the researchers concluded that “intent to move quickly” is the only important factor for producing velocity-specific strength gains. However, the study used a within-subject design, where one leg was trained using the isometric training program, and the other used the isokinetic training program. A cross-over effect of strength gains from one limb to the other could therefore have occurred, and prevented the identification of velocity-specific strength gains.

Using high velocity strength training for velocity-specific strength gains

There is good evidence that high velocity isokinetic training leads to greater gains in strength when tested at high isokinetic velocities (Moffroid & Whipple, 1970; Caiozzo et al. 1981; Coyle et al. 1981; Jenkins et al. 1984; Garnica, 1986; Thomeé et al. 1987; Petersen et al. 1989; Bell et al. 1989; Ewing Jr et al. 1990), but it does not always happen (Farthing & Chilibeck, 2003). There is also weaker evidence that velocity-specificity occurs after constant load training (Kaneko et al. 1983; Aaagaard et al. 1994; 1996; Moss et al. 1997; Ingebrigtsen et al. 2009).

Effect of eccentric training velocity

Although it is not widely known, eccentric training also produces velocity-specific strength gains (Rocha et al. 2011), and this velocity-specificity even reaches across isometric strength and into slow-velocity concentric strength if the eccentric training velocity is slow.

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Strength is specific in many ways, including: 1️⃣ Muscle action (eccentric or concentric) 2️⃣ Velocity (fast or slow) 3️⃣ Range of motion (full or partial) or joint angle 4️⃣ Repetition range (maximum strength or muscular endurance) 5️⃣ Degree of stability (stable or unstable) 6️⃣ External load type (constant load or accommodating resistance) 7️⃣ Force vector (vertical or horizontal) 8️⃣ Muscle group Even so, it is not always clear whether all of these ways in which strength can be specific are independent of one another. This fascinating study set out to assess whether velocity-specificity would still occur when training with eccentric muscle actions at a moderate velocity (60 degrees/s). Interestingly, there was very clear evidence of velocity-specific transfer to the trained speed, and this transfer tapered away to either side of the trained speed, even though that zone included isometric strength at 0 degrees/s. This may imply that the mechanisms by which velocity-specific strength occur are actually independent of contraction type, and potentially also therefore independent of force (as faster eccentrics involve greater force than slower eccentrics). They may be solely dependent upon contraction velocity, which is an exciting possibility. —————— #sandcresearch #strengthandconditioning #strengthtraining #strength #sportsscience #biomechanics #eccentric #eccentrics #eccentrictraining #strengthispecific

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Using different external load types for velocity-specific strength gains

Training with different types of external load could therefore be useful for emphasizing different ends of the force velocity curve. Using constant loads such as free weights could be more valuable for increasing force-related strength qualities, including force at lower velocities. In contrast, using either constant resistance or variable resistance (which both increase peak bar speeds) could be helpful for improving force at higher velocities. Recent studies indicate that using different external loads in this way does indeed lead to differences in velocity-specific strength gains, and therefore also power outputs (Rivière et al. 2016; Frost et al. 2016).

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External load type is the way in which the external resistance changes over an exercise range of motion (ROM). External resistance can either stay constant, reduce, or remain the same over the exercise ROM. Free weights involve a reducing external resistance over the exercise ROM. They involve weight + inertia at the start of the exercise ROM, just weight in the middle, and weight less inertia at the end. In other words, free weights are hard to get moving, but once they are in motion, you can make use of momentum to finish the lift. Elastic bands or chains can be used to alter the external resistance provided by free weights, and make it more like a constant external resistance. By adding more loading throughout the lift, it is possible to compensate for the loss of inertia in the middle, and the effect of momentum at the end. Pneumatic resistance do a similar job to elastic bands and/or chains added to the barbell, by providing a constant external resistance with air pressure. Since there is little inertia, the lifter quickly reaches the constant external resistance and must exert force against this through the whole exercise ROM. There are 2 key differences between free weight and pneumatic resistances: 1️⃣ compared with pneumatic resistance, free weights involve a greater load at the start of the exercise ROM, which places more load on the muscle in a stretched position. This probably causes differences in joint angle-specific gains in strength between the two external load types. 2️⃣ compared with pneumatic resistance, free weights take longer to accelerate, because there is a high load at the start of the exercise ROM. So pneumatic resistance typically involves faster bar speeds for the same relative load. This probably causes differences in velocity-specific gains in strength between the two external load types. This important training study shows the specific effects of training with each external load type. ——————- #sandcresearch #strengthandconditioning #strengthtraining #strength #sportsscience #biomechanics #accommodatingresistance #power #speed

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Using individualized training based on the force-velocity profile

Very recent research has identified that for any given athlete, it is possible to establish a force-velocity profile in the vertical squat jump (Samazino et al. 2012; 2014) and countermovement jump (Jiménez-Reyes et al. 2014). This profile can be found by measuring mean force exerted into the ground and the mean velocity of the center of mass in jump squats with a range of loads. Plotting all of these values on a graph provides a line. The gradient of this line is the force-velocity profile. Since strength is velocity-specific, not everyone automatically has an optimal force-velocity profile for producing peak power output in a vertical jump. The difference between the optimal and the actual force-velocity profile can be expressed by the force-velocity imbalance. Having a force-velocity imbalance means either that high-velocity strength is small compared with low-velocity strength, or that low-velocity strength is small compared with high-velocity strength. This is important, because having a force-velocity imbalance means that the athlete is more likely to perform poorly at the vertical jump (Samazino et al. 2014).

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For any athlete, it is possible to establish a force-velocity profile (FV) during the vertical jumping movement. The FV profile can be found by measuring the mean force exerted into the ground, and the mean velocity of the center of mass, during both unweighted squat jumps and jump squats with a range of loads. Plotting all of these values on a graph provides a line. The gradient of this line is the FV profile. Using the formula derived from the line allows us to then produce theoretical maximal values for force and velocity, and also theoretical maximal power output. When performing a vertical jump, this theoretical power output may or may not be reached. If it is reached, then the FV profile is "optimal" and jump height is as high as it can be without increasing maximal power output. However, because strength is velocity-specific, not everyone has an optimal FV profile, and the difference between the optimal and the actual FV profile can be expressed by the FV imbalance. The FV imbalance is the difference between actual and optimal unweighted squat jump heights, expressed as a percentage of optimal unweighted squat jump height. This can be surprisingly large, as shown by this important study. ——————- #sandcresearch #strengthandconditioning #strengthtraining #strength #sportsscience #research #biomechanics #muscle #jump #jumping #vertical #verticaljumping #verticaljump #athlete #fast

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Interestingly, a recent long-term training study showed that training specifically using either high-velocity (ballistic) exercises or low-velocity (strength) exercises according to the individual force-velocity needs was superior to a general training program, for enhancing vertical jump height (Jiménez-Reyes et al. 2016).

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Strength is velocity-specific, which means that training with a light load and a faster bar speed leads to preferentially greater gains in high-velocity strength. In contrast, training with a heavy load and a slower bar speed leads to preferentially greater gains in low-velocity strength. Previous research has identified that there is an optimum balance of force and velocity during any athletic movement, for any given individual. Researchers can thereby calculate an optimal force-velocity profile for an athlete, as well as their current actual force-velocity profile. When the actual force-velocity profile is different from the optimal force-velocity profile, this leads to poor performance. Actual force-velocity profiles can differ from optimal force-velocity profiles EITHER by being too force-focused (there is a velocity deficit) OR by being too velocity-focused (there is a force deficit). Training to reduce the force deficit (by using heavy loads) or to reduce the velocity deficit (by using light loads) could therefore improve performance dramatically. This study investigated that question. ——————- #sandcresearch #strengthandconditioning #strengthtraining #strength #sportsscience #research #biomechanics #muscle #jump #jumping #vertical #verticaljumping #verticaljump #athlete #fast

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SECTION CONCLUSIONS

Changing the force velocity curve as a result of training requires us to produce velocity-specific strength gains. This might be achieved by high-velocity strength training.

There is good evidence that high velocity isokinetic training leads to greater gains in strength when tested at high isokinetic velocities, and there is weaker evidence that the same effect occurs after constant load training.

Training with different types of external load could therefore be useful for emphasizing different ends of the force velocity curve. Using constant resistance or variable resistance could be helpful for improving force at higher velocities.

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REFERENCES

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CONTRIBUTORS

Chris Beardsley performed the literature reviews, wrote the first draft of this page and was the primary author.


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