Flywheel
A flywheel is a mechanical device designed to store and release energy, ensuring that machines operate smoothly and without interruptions. It achieves this by storing potential energy, which can be converted into kinetic energy, specifically in the form of rotational energy as the wheel spins. In practical applications, such as in car engines, flywheels help maintain engine momentum even when the engine is not actively receiving fuel. The efficiency of a flywheel is enhanced by its large moment of inertia, allowing it to resist rapid changes in speed and stabilize energy outputs, which is particularly useful in systems reliant on intermittent power sources like solar and wind energy.
Flywheels also play a crucial role in various engine designs, such as in diesel engines, where they optimize fuel usage, and in steam engines, where they help regulate rotational motion. Moreover, they are employed in spacecraft as reaction wheels, assisting in maneuvering by utilizing the principles of inertia and torque. Overall, flywheels offer a robust alternative to conventional energy storage methods, providing benefits such as longevity and efficiency while enabling smoother operations in diverse applications.
Flywheel
FIELDS OF STUDY: Classical Mechanics
ABSTRACT: This article examines the uses and the physics of flywheels. Flywheels were essential to the Industrial Revolution and are still used in a variety of machines, from roller coasters to spaceships. The physics behind them is classical rotational dynamics. This article will examine the kinematics of rotation and how to calculate the energy stored.
principal terms
- inertia: a body’s resistance to change in its motion.
- kinetic energy: the energy a body possesses due to its motion
- potential energy: the energy held in a system due to the positions of its elements in relation to various forces.
- rotational energy: the kinetic energy of a spinning object.
- rotational speed: the rate at which an object spins.
- torque: a force that causes a rotation, or the measure of such a force.
What Is a Flywheel?
A flywheel is a device that keeps a machine running without interruption. In a car engine, flywheels keep the engine running even when it is in neutral or is not receiving gasoline. Flywheels are able to keep machines running smoothly by storing potential energy, which is energy that depends on the position of a device’s parts within a system or force field. Potential energy can be stored in chemical bonds, an electric field, or a gravitational field. The flywheel can then convert this stored energy to kinetic energy, which is the energy of motion. Specifically, a flywheel’s kinetic energy is rotational energy (Er), generated by the spinning of the wheel. The International System of Units (SI) unit of energy is the joule (J), equal to one kilogram–square meter per second squared (kg·m2/s2).
A potter’s wheel is a type of flywheel in which a stepping on a foot pedal causes a stone to spin. The spinning stone causes a table to rotate, allowing a potter to shape and mold clay atop the table as it spins. The force is applied to the pedal is at intervals, but the action of the flywheel delivers a constant flow of energy to the rotating table.
Another type of flywheel might be a length of metal shaped into a coil and housed within an apparatus that keeps it from springing out. As energy is needed, the coil inside the housing is allowed to release its stored potential energy, resulting in a smooth flow of energy to the machine or objects involved.
The faster a flywheel spins, the more energy is involved. According to Isaac Newton’s (1642–1727) first law of motion, an object in motion will remain in motion until a force acts on it. It is for this reason that even if a spaceship traveling through a vacuum suddenly loses all propulsion, it will keep moving in the same direction at the same speed indefinitely.
Rotational Dynamics
A top is a sort of flywheel. In order to make a top spin, an initial impulse must be applied to it such that it moves. This sort of force is called torque. It works against an object’s inertia, which is the amount of resistance it has to a change in its motion.
In a spinning object such as a flywheel, the effects of inertia are more complex because everything occurs with reference to the axis of rotation. Torque is applied at a distance from this axis. This distance works as a lever does, trading the force required at any given moment for distance. The further the force is applied from the center part of the top, the more torque is required to make it spin.
The top’s rotational speed is the rate at which it spins and is proportional to its rotational energy. It is measured in cycles or revolutions per second. The SI unit of rotational speed is the hertz (Hz), equal to one revolution per second. Meanwhile, rotational velocity, also called angular velocity, is a vector quantity. It is the object’s rotational speed in a defined direction of motion, given in SI units of radians per second (rad/s). One radian is the section of a circle described by an arclength that is equal to the circle’s radius (r), and the circumference of a circle is 2πr, so the number of radians in a circle is 2πr/r, or 2π. Thus, to convert from rotational speed to angular velocity, multiply the speed by 2π to convert from hertz to radians per second.
Angular velocity (ω) can also be calculated according to the linear speed (v) in meters per second and the radius (r) of the rotational path in meters:
ω = v/r
Flywheels have a large moment of inertia (I), also called rotational inertia, measured in SI units of kilogram–square meters (kg·m2). It can be calculated with the equation
I = kmr2
where k is the inertial constant, determined by the shape of the flywheel; m is the mass of the flywheel; and r is its radius. If the flywheel is shaped like a bicycle wheel, with a tire on the outer edge, k is equal to 1; if it is shaped like a flat, solid disk, k equals 0.606; and if it is shaped like a disk with a hole in the center, k equals about 0.3. The flywheel’s moment of inertia and its rotational speed can then be used to calculate its rotational energy (Er), according to the following equation:
Sample Problem
If a flywheel has a moment of inertia (I) of 300 kg·m2 and an angular velocity (ω) of 5 rad/s, what is its rotational energy (Er) in joules?
Answer:
Use the equation for rotational energy, given above:
Plug in the given values for moment of inertia and angular velocity and solve, paying close attention to units:
The radian is a dimensionless unit, equal to 1, so it can be discarded:
Er = 3,750 kg·m2/s2 = 3,750 J
The flywheel generates 3,750 J of rotational energy.
Uses of Flywheels
One of the primary advantages of flywheels over chemical batteries is that flywheels can be used over and over again. While chemical batteries wear out over time and lose their ability to hold charge, a flywheel does not have this problem. Flywheels do lose energy to friction, but scientists have been studying ways to design new, lower-friction flywheels. Eventually, very large flywheels could store and stabilize power grids based on solar and wind power, both of which have a high variance in their output.
Having a large moment of inertia allows flywheels to resist sudden changes to their rotation. As a result, they can be used to maintain a continuous power supply from an intermittent current. If current cuts out, the wheel will continue to rotate. One of the most familiar uses of this feature is in the piston engine, where the flywheel on the crankshaft continues spinning through the upstroke. A car engine’s piston is powered by a small explosion in a gas-air mixture. This explosion forces the shaft down the piston, powering the wheel. The momentum of the rotating mass carries the piston into the upstroke. Diesel engines use the energy stored in the wheel to ignite the next gas mix, ensuring maximal fuel use, which is why they are more efficient than gasoline engines.
Flywheels are also used to govern rotational motion, as in the steam engine, which has little balls that spin on top of the rotational governor. The energy required to accelerate the governor keeps the engine accelerating evenly. In complex engine design, the rate at which the governor spins can be used to regulate fuel flow into the engine, basically allowing the machine to self-regulate and maintain a constant output. Such systems have been critical both in large engines, such as steam locomotives, and in power plants.
The rotational momentum of the flywheel resists sudden changes in motion and can be used to stabilize objects as well. This is commonly seen in spacecraft, often in the form of a reaction wheel, which uses the force of a wheel trying to right itself to turn the spacecraft about its axis.
Bibliography
Dresig, Hans, and Franz Holzweißig. Dynamics of Machinery: Theory and Applications. Berlin: Springer, 2010. Print.
Gregory, R. Douglas. Classical Mechanics: An Undergraduate Text. New York: Cambridge UP, 2006. Print.
Gross, Dietmar, et al. Engineering Mechanics 3: Dynamics. 2nd ed. Berlin: Springer, 2014. Print.
Levi, Mark. The Mathematical Mechanic: Using Physical Reasoning to Solve Problems. Princeton: Princeton UP, 2009. Print.
Nave, Carl R. "Angular Momentum of a Particle." HyperPhysics. Georgia State U, n.d. Web. 26 June 2015.
Nave, Carl R. "Rotational-Linear Parallels." HyperPhysics. Georgia State U, n.d. Web. 26 June 2015.