Flywheel Kinetic Energy

Kinetic energy and moment of inertia of a flywheel

A flywheel is used to smooth the energy fluctuations in combustion engines and make the energy flow uniform. The flywheels store energy mechanically as kinetic energy.

Kinetic Energy

The kinetic energy of a flywheel can be expressed as

Ef = 1/2 I ω2         (1)

where

Ef = flywheel kinetic energy (Nm (Joule), ft lb)

I = moment of inertia (kg m2, lb ft2)

ω = angular velocity (rad/s)

Angular velocity converting units

  • 1 rad = 360o / 2 π =~ 57.29578o
  • 1 rad/s = 9.55 r/min (rpm) = 0.159 r/s (rps)

Moment of Inertia

Moment of inertia quantifies the rotational inertia of a rigid body and can be expressed as

I = k m r2         (2)

where

k = inertial constant - depends on the shape of the flywheel

m = mass of flywheel (kg, lbm)

r = radius (m, ft)

Inertial constants of some common types of flywheels

  • wheel loaded at rim like a bicycle tire - k =1
  • flat solid disk of uniform thickness - k = 0.606
  • flat disk with center hole - k = ~0.3
  • solid sphere - k = 2/5
  • thin rim - k = 0.5
  • radial rod - k = 1/3
  • circular brush - k = 1/3
  • thin-walled hollow sphere - k = 2/3
  • thin rectangular rod - k = 1/2

Moment of Inertia Converting Units

  • 1 kg m2 = 10000 kg cm2 = 54675 ounce in2 = 3417.2 lb in2 = 23.73 lb ft2

Flywheel Rotor Materials

Material Density
(kg/m3)
Design Stress
(MN/m2)
Specific Energy
(kWh/kg)
Aluminum alloy 2700    
Birch plywood 700 30  
Composite carbon fiber - 40% epoxy 1550 750 0.052
E-glass fiber - 40% epoxy 1900 250 0.014
Kevlar fiber - 40% epoxy 1400 1000 0.076
Maraging steel 8000 900 0.024
Titanium Alloy 4500 650 0.031
"Super paper" 1100    
S-glass fiber/epoxy 1900 350 0.020
  • Maraging steels are carbon free iron-nickel alloys with additions of cobalt, molybdenum, titanium and aluminum. The term maraging is derived from the strengthening mechanism, which is transforming the alloy to martensite with subsequent age hardening.

Example - Energy in a Rotating Bicycle Wheel

The typical 26-inch bicycle wheel rim has a diameter of 559 mm (22.0") and an outside tire diameter of about 26.2" (665 mm). For our calculation we approximate the radius - r - of the wheel to

r = ((665 mm) + (559 mm) / 2) / 2

  =  306 mm

  = 0.306 m

The weight of the wheel with tire is 2.3 kg and the inertial constant is k = 1.

The Moment of Inertia for the wheel can be calculated

I = (1) (2.3 kg) (0.306 m)2 

   = 0.22 kg m2

The speed of the bicycle is 25 km/h (6.94 m/s). The wheel circular velocity (rps, revolutions/s) - nrps - can be calculated as

nrps = (6.94 m/s) / (2 π (0.665 m) / 2)

     = 3.32 revolutions/s

The angular velocity of the wheels can be calculated as

ω = (3.32 revolutions/s) (2 π rad/revolution)

   = 20.9 rad/s

The kinetic energy of the rotating bicycle wheel can then be calculated to

Ef = 0.5 (0.22 kg m2) (20.9 rad/s)2    

  = 47.9 J

Related Topics

  • Dynamics - Dynamics Motion - velocity and acceleration
  • Mechanics - Kinematics, forces, vectors, motion, momentum, energy and the dynamics of objects

Related Documents

Tag Search

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  • es: volante energía cinética momento de inercia constante
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