# Changing the spring wire diameter

Mechanics study · 2024-11-15

English translation of the Portuguese source. The ratio assumes the remaining spring geometry and material stay fixed. This is a calculation from the design discussion.

---

Spring stiffness (\(k\)) depends on wire diameter (\(d\)) to the **fourth power**:

\[
k \propto d^4
\]

To calculate the reduction in stiffness when changing from **2 mm** to **1.6 mm**, use the ratio:

\[
\text{Reduction in stiffness} = \left( \frac{1.6}{2} \right)^4
\]

### Calculation:
\[
\frac{1.6}{2} = 0.8
\]
\[
(0.8)^4 = 0.4096
\]

### Result:
The spring's stiffness will be **40.96% of the original**, a reduction of approximately **59.04%**.

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### Practical interpretation:
- The spring will be **significantly more flexible**.
- The force needed to compress it by the same distance will be **59% lower** than with 2 mm wire.