Force Velocity Curve

Force-velocity curve: The force-velocity curve illustrates the inverse relationship between the force a muscle can generate and the velocity of joint movement. As movement velocity increases, the amount of force that a muscle can contribute to the motion decreases, and vice versa. This principle applies to both concentric and eccentric muscle actions, although force capabilities are generally higher during eccentric contractions.

In the context of power training, an athlete’s goal is to shift the force-velocity curve upward and to the right. This is an indication of improvements in the rate of force development (RFD). This suggests that greater force can be produced in less time, whether moving slowly with heavy loads (strength) or rapidly with light loads (speed).

• Examples: A heavy barbell back squat (slow velocity, high force) represents one extreme of the curve, while a counter-movement jump (e.g. box jump ) represents the opposite end. An athlete who trains for both strength and power may see improvements across the full curve, enhancing both strength and speed.

Related Topics: Power , Plyometric Exercise , Stretch-shortening Cycle , Force-velocity Curve , Amortization Phase , Rate of Force Development , Counter-movement Jump (CMJ)

Related Courses:

• Power (High-velocity) Training: Introduction
• Lower Body Power Exercises
• Upper Body Power Exercises and Total Body Power Exercises

Frequently Asked Questions:

What is the force-velocity curve in simple terms?

• It describes how the amount of force a muscle can produce changes depending on how fast the movement is. Typically, the faster you move, the less force you can apply—and the slower you move, the more force you can produce.

Why is the force-velocity curve important for training?

• It helps guide exercise selection and program design. Training at various points along the curve can improve strength, speed, or power depending on the athlete’s needs. For example, heavy lifts target the high-force/low-velocity end, while sprinting or jumping targets high-velocity/low-force.

What does it mean to “shift the force-velocity curve”?

• Shifting the curve upward and to the right means improving your ability to produce force quickly with a variety of loads. This typically reflects gains in both strength and speed, and is associated with enhanced athletic performance.

How does training affect the force-velocity curve?

• Strength training (high loads, slow velocity) can increase maximal force production. Plyometric or ballistic training (low loads, high velocity) improves movement speed and rate of force development. A combination is hypothesized to address the entire curve.

Is the force-velocity relationship the same for all muscle actions?

• No. The curve differs for concentric, eccentric, and isometric actions. Muscles can generally produce more force eccentrically than concentrically, and isometric force lies somewhere in between.

Who developed the force-velocity curve concept, or did the research that resulted in the graph that is now known as the force-velocity curve?

• The force-velocity curve was first developed by British physiologist A.V. Hill in 1938 through experiments on isolated frog muscle. Hill discovered an inverse relationship between the force a muscle can produce and the velocity of its shortening, which he described mathematically in what is now known as Hill’s equation. This foundational work was later supported by Andrew Huxley’s cross-bridge theory in 1957, providing a molecular explanation for Hill’s observations. Together, their research established the force-velocity curve as a core principle in muscle physiology and laid the groundwork for its application in exercise science and resistance training (1-7).

Sources:

1. Hill A.V. (1938). The heat of shortening and the dynamic constants of muscle. Proceedings of the Royal Society B 126, 136-195​cepcometti.com. (Classic paper introducing the force-velocity relationship in muscle).
2. Seow, C.Y. (2013). Hill’s equation of muscle performance and its hidden insight on molecular mechanisms. Journal of General Physiology 142(6): 561-573​pmc.ncbi.nlm.nih.gov ​pmc.ncbi.nlm.nih.gov . (Review connecting Hill’s equation to cross-bridge dynamics).
3. Cormie, P., McCaulley, G., & McBride, J. (2011). Developing maximal neuromuscular power: Part 1 – Biological basis. Sports Medicine 41(1): 17-38​cepcometti.com​cepcometti.com. (Review of muscle power, force-velocity relationship, and adaptations).
4. Ewing, J. et al. (1990). Effects of velocity of isokinetic training on strength, power, and quadriceps muscle fiber characteristics. Eur J Appl Physiol 61: 159-162​pubmed.ncbi.nlm.nih.gov . (Study demonstrating velocity-specific training effects on the F–V characteristics of muscle).
5. Samozino, P. et al. (2012). Optimal force-velocity profile in ballistic movements – Altius: Citius or Fortius? Med. Sci. Sports Exerc. 44(2): 313-322​pubmed.ncbi.nlm.nih.gov . (Study introducing individualized force-velocity profiling for jump performance).
6. Takei, S. et al. (2024). Portions of the force-velocity relationship targeted by weightlifting exercises. Sci Reports 14: 31021​pubmed.ncbi.nlm.nih.gov ​pubmed.ncbi.nlm.nih.gov . (Applied study comparing F–V characteristics of jump squats vs. weightlifting, illustrating exercise-specific differences).
7. Alcazar, J. et al. (2019). On the shape of the force-velocity relationship in skeletal muscles: The linear, the hyperbolic, and the double-hyperbolic. Frontiers in Physiology 10: 769​frontiersin.org . (Discussion of muscle F–V curve shape and implications).