Flywheel Energy Storage Calculator
Calculate energy storage capacity, power density, and performance characteristics of flywheel systems
Calculate Flywheel Energy Storage
Total mass of the rotating flywheel
Reference radius of the flywheel
Rotational speed of the flywheel
Shape-dependent constant for moment of inertia
Flywheel Energy Storage Results
Moment of Inertia: 0.0000 kg·m²
Formula: I = k × m × r²
Energy Formula: E = ½ × I × ω²
Angular Velocity: 0.00 rad/s
NASA G2 Flywheel Example
System Parameters
Mass: 250 lb (113.4 kg)
Radius: 12 in (0.305 m)
Geometry: Hollow disk (k = 0.333)
Angular Velocity: 60,000 RPM
Calculation Steps
I = 0.333 × 113.4 × (0.305)² = 3.52 kg·m²
ω = 60,000 × 2π/60 = 6,283 rad/s
E = ½ × 3.52 × (6,283)² = 69.25 MJ
Result: 19,236 Wh (19.2 kWh)
Common Flywheel Materials
Steel
σ: 400-1000 MPa, ρ: 7850 kg/m³
Carbon Fiber
σ: 3500-5000 MPa, ρ: 1600 kg/m³
Titanium Alloy
σ: 900-1200 MPa, ρ: 4500 kg/m³
Aluminum
σ: 200-600 MPa, ρ: 2700 kg/m³
Geometric Constants
Design Tips
Higher speed stores more energy (ω² relationship)
Larger radius increases energy storage capacity
Material strength limits maximum speed
Carbon fiber offers best energy density
Vacuum chambers reduce energy losses
Understanding Flywheel Energy Storage
What is Flywheel Energy Storage?
Flywheel energy storage systems (FESS) store energy in the form of rotational kinetic energy. A massive rotating element (flywheel) spins at high speed to store energy and can release it by connecting to an electrical generator when power is needed.
Key Advantages
- •Long operational lifespan (20+ years)
- •High power density and rapid response
- •Temperature resistant operation
- •Environmentally friendly (no chemicals)
Energy Storage Formula
E = ½ × I × ω²
I = k × m × r²
- E: Stored energy (Joules)
- I: Moment of inertia (kg·m²)
- ω: Angular velocity (rad/s)
- k: Geometric constant
- m: Mass (kg)
- r: Radius (m)
Alternative Formula: E = k × (σ/ρ) for material-based calculations, where σ is tensile strength and ρ is density.
Applications & Future
Grid Storage
Frequency regulation and peak shaving for electrical grids, especially with renewable energy integration.
Transportation
Electric vehicles, trains, and buses for regenerative braking and rapid energy delivery during acceleration.
Space Applications
Spacecraft attitude control and energy storage where battery degradation is problematic in harsh environments.