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How It Works
The spring rate equation k = Gd4/(8D3n) describes how stiff a helical coil spring is. Wire diameter (d) has the biggest impact because it is raised to the fourth power. The torsional modulus (G) depends on the material: about 11.5 × 106 psi for music wire and 10.6 × 106 psi for stainless steel.
Example Problem
A music-wire spring has G = 11.5×106 psi, wire diameter 0.1 in, mean coil diameter 1.0 in, and 10 active coils. What is the spring rate?
- d4 = 0.14 = 0.0001
- D3 = 1.03 = 1.0
- k = (11,500,000 × 0.0001) / (8 × 1.0 × 10) = 1,150 / 80 = 14.375 lb/in
Frequently Asked Questions
Why does wire diameter have such a large effect on spring rate?
Wire diameter appears as d4, so increasing it by just 10% raises the spring rate by about 46%. This makes wire gauge selection the most critical decision in spring design.
What are active coils vs total coils?
Active coils are the ones that deflect under load. Closed and ground ends add inactive coils that do not contribute to stiffness. Subtract 2 from the total for closed and ground ends, or 1 for closed ends only.
How do I choose a spring rate for a car suspension?
Start with the vehicle weight per corner and desired ride frequency (1–2 Hz for street, 2–3 Hz for track). Spring rate (lb/in) ≈ (weight × (2π × frequency)²) / 386.4. A 750 lb corner at 1.5 Hz needs about 173 lb/in.
Related Calculators
- Horsepower Calculator — HP, torque, and RPM for automotive applications.
- Gear Equations Calculator — vehicle speed from RPM and gear ratio.
- Hooke's Law Calculator — calculate spring force and potential energy from spring constant.
- Stress & Strain Calculator — analyze shear stress in spring wire material.
- Force Unit Converter — convert spring force between pounds, newtons, and kilograms-force.
Reference: Wahl, A.M. 1963. Mechanical Springs. McGraw-Hill. 2nd ed.