The Force-Velocity Relationship

Introduction

Skeletal muscle contractions begin when an action potential from a motor neuron reaches the muscle fiber and signals it to contract. This isolated contraction is called a twitch, which can last from a few milliseconds to 100 milliseconds depending on the muscle. Each twitch undergoes three distinct phases; 

1. The latent period: action potential propagates along the sarcolemma and calcium ions (Ca²⁺) are released from the sarcoplasmic reticulum.
2. The contraction phase: Ca²⁺ ions bind to troponin, causing tropomyosin to move and expose the actin binding sites. This allows actin and myosin form cross-bridges and shorten the sarcomere.
3. The relaxation phase: Ca²⁺ ions are pumped out of the sarcoplasm into the sarcoplasmic reticulum. Cross-bridge cycling stops and the muscles return to their resting length (see: muscle contraction).

A single twitch produces little tension because the muscle relaxes before reaching maximal force potential. Therefore, muscles need a series of action potentials to produce movement. If an additional action potential were to stimulate a muscle contraction prior to the full relaxation of a twitch, the successive twitch would sum onto the previous one. Thus, a progressively higher frequency of action potentials increases the force produced by the muscle. This phenomenon is known as wave summation, which allows muscles to produce varying levels of force (graded muscle response). When the frequency of action potentials is high enough to prevent muscles from relaxing between two successive stimuli, the muscle will become fully contracted. This is known as tetanic contraction, or tetanus. 

The force generated by a muscle is dependent on its length and shortening velocity. Together, these two factors have an impact on the muscle’s biomechanical properties, and thus, physical performance (strength, power, etc.). The force-velocity relationship demonstrates that muscles generate the greatest amount of force when at their resting length, whereas the least amount of force is produced when muscles are shortened or stretched. Force production is also controlled by 1) the velocity and 2) the force of muscle contraction. The optimal power output takes place at approximately 1/3 of maximum velocity.

This post explains the basics of the force-velocity relationship, and its implications in physical performance and training.

The basics of the force-velocity relationship

The force-velocity relationship describes the speed at which a muscle changes length in relation to the force of the contraction and the resulting power output (force x velocity = power). This is often displayed in a force-velocity curve, where the x-axis (i.e horizontal axis) indicates velocity of movement (measured in meters per second), and the y-axis (i.e. vertical axis) indicates the amount of force produced (measured in Newtons). The curve shows an inverse relationship between force and velocity – an increase in force results in a decrease in velocity and vice versa. For example, a countermovement jump (CMJ) produces low levels of force at a high movement velocity, whereas a squat generates high levels of force at a slow movement velocity. This tradeoff between force and velocity is thought to be a result of reduced time available for cross-bridge formation between actin (thin) and myosin (thick) filaments. The more time is available, the more cross-bridges are formed, and thus, more contractile force is produced. 

At maximum velocity, actin and myosin filaments are unable to form cross-bridges. Thus, no force is generated, and no power is produced (right edge of graph). Interestingly, the opposite is true when the muscle is stretched. Even though the muscle’s ability to produce force is increased, there is no velocity of contraction. Therefore, no power is generated (left edge of graph). The maximum amount of power is generated at roughly one-third of maximum shortening velocity.