Length–tension and force–velocity relationships !
- Concept
- Exam priority: medium
A muscle is strongest at a middle length and when it moves slowly; stretched too much, squeezed too short or moving fast, it pulls less.
Updated 2026-11-01
Also called: Length–tension curve, Hill curve
See it in 3D: Gastrocnemius (inner head) · Soleus
What it is
Active force depends on how many myosin heads can reach actin, which depends on sarcomere length (length–tension). Force also depends on shortening speed: the faster a muscle shortens, the less force it can hold (force–velocity). Together they explain joint angles where we are weakest, why lifting fast feels harder, and why the heart works on the rising limb of its curve (Frank–Starling).
Key facts
- Total tension = active + passive tension; muscles in the body usually work near the plateau of the active curve.
- Power = force × velocity; it peaks at about one-third of maximum velocity.
- Cardiac sarcomeres normally work below their optimum, so more filling stretches them toward it and raises force (Frank–Starling).
Key points (skeletal muscle)
| Parameter | Value | Note |
|---|---|---|
| Optimal sarcomere length | ≈ 2.0–2.2 µm | |
| Active force falls to zero | ≈ 3.6 µm (no overlap) | short end ≈ 1.3 µm |
| Peak power | ≈ 1/3 of maximum shortening velocity |
Approximate values for a healthy adult at rest; each laboratory sets its own ranges.
Clinical notes
- Tendon transfers and joint immobilization change resting sarcomere length; surgeons try to set the new length near the plateau of the curve.
- Eccentric work (walking downhill, landing) loads the gastrocnemius strongly and is a common cause of soreness and calf strains.
Test yourself
Think of the answer, then tap the question to see it.
Why does active force fall when a sarcomere is stretched beyond about 3 µm?
Thin filaments are pulled away from the thick filaments, so fewer myosin heads overlap actin and fewer cross-bridges can form.
Why can you lower a weight slowly that you are unable to lift?
During lengthening, attached cross-bridges are forcibly stretched and resist detachment, so eccentric force exceeds maximum isometric force.
How does the length–tension relationship underlie the Frank–Starling mechanism?
Cardiac sarcomeres at rest sit below optimal length. Greater filling stretches them toward optimum and increases Ca²⁺ sensitivity, so stroke volume rises.
Why does a cyclist shift to a lower gear on a climb, using the force–velocity curve?
Power peaks at moderate shortening speed. A lower gear lets the leg muscles contract at a velocity near that peak instead of working slowly against a very high load.
See it in 3D
The structures of Durgical's 3D anatomy where it happens.
Related topics
- Sliding filaments and the cross-bridge cycle
- The Frank–Starling mechanism
- Motor units, recruitment and summation
- Muscle spindle and Golgi tendon organ
Educational physiology content; not a diagnostic or treatment guide and no substitute for a health professional's advice. Values are approximate references. No doses are given.
Sources: 10.3 Muscle Fiber Contraction and Relaxation (OpenStax (Rice University), 2022); 10.4 Nervous System Control of Muscle Tension (OpenStax (Rice University), 2022); Anatomy, Bony Pelvis and Lower Limb: Gastrocnemius Muscle (StatPearls (NCBI Bookshelf), 2024); Hall JE. Guyton and Hall Textbook of Medical Physiology, 13th ed. (ch. 6). Reference book used to check facts; its text and figures are not reproduced (Elsevier, 2016).
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Representative model, for educational purposes only.