⚡ Flywheel Energy Storage Calculator
Calculate stored energy
How to Use This Calculator
Enter Moment of Inertia
Input the moment of inertia (I) in kg·m². This is the rotational mass of the flywheel, measuring its resistance to changes in rotation. For a solid disk flywheel, I = ½mr². You can calculate this separately or use the mass moment of inertia calculator.
Enter Angular Velocity
Input the angular velocity (ω) in radians per second (rad/s). This is how fast the flywheel is rotating. If you have RPM, convert it: ω = 2π × (RPM / 60). For example, 3000 RPM = 314.16 rad/s.
Calculate and Review
Click the "Calculate" button to compute the stored energy in joules (J). This energy can be extracted when the flywheel slows down. Flywheels are used for energy storage because they can store and release energy efficiently, making them useful for applications like regenerative braking and grid energy storage.
Formula
E = ½Iω²
Where:
• E = Stored energy (J)
• I = Moment of inertia (kg·m²)
• ω = Angular velocity (rad/s)
For a solid disk flywheel: I = ½mr², so E = ¼mr²ω²
Example 1: Small Flywheel
A flywheel with moment of inertia 0.5 kg·m² rotates at 100 rad/s. Calculate the stored energy.
Given:
• Moment of inertia (I) = 0.5 kg·m²
• Angular velocity (ω) = 100 rad/s
Solution:
E = ½Iω²
E = ½ × 0.5 × 100²
E = ½ × 0.5 × 10,000
E = 2,500 J
Example 2: Large Flywheel System
An energy storage flywheel has moment of inertia 50 kg·m² and rotates at 500 rad/s. What energy is stored?
Given:
• Moment of inertia (I) = 50 kg·m²
• Angular velocity (ω) = 500 rad/s
Solution:
E = ½Iω²
E = ½ × 50 × 500²
E = ½ × 50 × 250,000
E = 6,250,000 J = 6.25 MJ
This is equivalent to approximately 1.74 kWh of energy.
Frequently Asked Questions
What is flywheel energy storage?
Flywheel energy storage is a method of storing energy in the rotational kinetic energy of a spinning flywheel. Energy is stored by spinning the flywheel faster and extracted when it slows down. Flywheels can charge and discharge quickly, making them useful for applications requiring rapid energy delivery or absorption.
How does flywheel energy storage work?
When energy is supplied to a flywheel, it accelerates (stores energy as rotational kinetic energy). When energy is needed, the flywheel's rotation drives a generator or motor, converting rotational energy back to electrical energy. The energy stored is proportional to the square of angular velocity, so doubling the speed quadruples the stored energy.
What are the advantages of flywheel energy storage?
Flywheels offer: very fast charge/discharge rates (milliseconds), high power density, long cycle life (millions of cycles), no chemical degradation, high efficiency (90-95%), and environmental friendliness. They're particularly useful for power quality applications, regenerative braking, and grid frequency regulation.
How does moment of inertia affect stored energy?
Energy is directly proportional to moment of inertia - doubling the moment of inertia doubles the stored energy (at the same angular velocity). The moment of inertia depends on the mass distribution: more mass farther from the axis means higher moment of inertia and more energy storage capacity.
Why is angular velocity squared in the formula?
The energy depends on the square of angular velocity because both kinetic energy and the rotational motion contribute quadratically. This means small increases in speed result in large increases in stored energy. For example, doubling the angular velocity quadruples the stored energy, making high-speed flywheels very energy-dense.
Where are flywheel energy storage systems used?
Flywheel energy storage is used in: regenerative braking systems (trains, buses, race cars), uninterruptible power supplies (UPS), grid frequency regulation, power quality applications, spacecraft attitude control systems, and hybrid vehicles. Modern flywheels use magnetic bearings and vacuum chambers to minimize friction losses.
About Flywheel Energy Storage Calculator
The flywheel energy storage calculator computes the rotational kinetic energy stored in a flywheel using E = ½Iω². Flywheel energy storage is an efficient method for storing mechanical energy, particularly useful for applications requiring rapid energy transfer.
This calculator is essential for engineers designing energy storage systems, researchers studying regenerative energy technologies, and anyone analyzing rotational energy systems. Understanding flywheel energy storage helps in designing efficient systems for applications ranging from electric vehicles to grid-scale energy storage.