Outer Radius of Flywheel Disk Calculator

Formula Used:

\[ R = \left( \frac{2 \times I}{\pi \times t \times \rho} \right)^{1/4} \]

Moment of Inertia of Flywheel (I):

kg·m²

Thickness of Flywheel (t):

Mass Density of Flywheel (ρ):

kg/m³

Outer Radius of Flywheel (R):

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1. What is the Outer Radius of Flywheel Disk?

The outer radius of a flywheel disk is the distance from the center to the outermost edge of the flywheel. It is a critical parameter in flywheel design that affects the moment of inertia and energy storage capacity of the system.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ R = \left( \frac{2 \times I}{\pi \times t \times \rho} \right)^{1/4} \]

Where:

\( R \) — Outer Radius of Flywheel (m)
\( I \) — Moment of Inertia of Flywheel (kg·m²)
\( t \) — Thickness of Flywheel (m)
\( \rho \) — Mass Density of Flywheel Material (kg/m³)
\( \pi \) — Mathematical constant (approximately 3.1416)

Explanation: This formula calculates the outer radius based on the flywheel's moment of inertia, thickness, and material density, assuming a solid disk configuration.

3. Importance of Outer Radius Calculation

Details: Accurate calculation of the outer radius is essential for proper flywheel design, ensuring optimal energy storage, rotational stability, and mechanical performance in various applications.

4. Using the Calculator

Tips: Enter the moment of inertia in kg·m², thickness in meters, and mass density in kg/m³. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: Why is the outer radius important in flywheel design?
A: The outer radius significantly affects the moment of inertia and energy storage capacity. Larger radii generally provide higher energy storage but may present structural challenges.

Q2: What materials are commonly used for flywheels?
A: Common materials include steel, aluminum, carbon fiber composites, and other high-strength materials with appropriate density and strength characteristics.

Q3: How does thickness affect the outer radius calculation?
A: Thicker flywheels require smaller outer radii to achieve the same moment of inertia, while thinner flywheels require larger outer radii.

Q4: Are there limitations to this formula?
A: This formula assumes a solid, homogeneous disk flywheel. Different geometries or material distributions would require different calculation methods.

Q5: How accurate is this calculation for real-world applications?
A: While the formula provides a good theoretical estimate, real-world factors like material imperfections, mounting considerations, and safety factors should be accounted for in final designs.