• a wheel winds up through some system of gears and then delivers rotational energy until friction dissipates it
  • stored energy = sum of kinetic energy of individual mass elements that comprise the flywheel

  • I = moment of inertia --> ability of an object to resist changes in its rotational velocity
  • w = rotational velocity (rpm)
  • I = k *M*R*R (M=mass; R=Radius); k = intertial constant (depends on shape)

    Inertial constants for different shapes:

  • Wheel loaded at rim (bicycle tire): k =1
  • solid disk of uniform thickness; k = 1/2
  • solid sphere; k = 2/5
  • spherical shell; k = 2/3
  • thin rectangular rod; k = 1/2

    To optimize the energy-to-mass ratio the flywheel needs to spin at the maximum possible speed. This is because kinetic energy only increases linerarly with Mass but goes as the square of the rotation speed.

    Rapidly rotating objects are subject to centrifugal forces that can rip them apart. Centrifugal force for a rotating object goes as:


    Thus, while dense material can store more energy it is also subject to higher centrifugal force and thus fails at lower rotation speeds than low density material.

    Tensile Strength is More important than density of material.

    Long rundown times are also required --> frictionless bearings and a vacuum to minimize air resistance can result in rundown times of 6 months --> steady supply of energy

    Flywheels are about 80% efficient (like hydro)

    Flywheels do take up much less land than pumped hydro systems

    Some Network Resources Related to Flywheels

    Example Calculation:

    Consider a solid disc flywheel of radius 50 cm and mass 140 kg. How fast would it have to spin to have a store the equivalent amount of energy that is stored in just 10 kg of gasoline when burned in an internal combustion engine:

    Compressed Air:

    Has high energy storage capacity compared to the alternatives. About 10 times higher per cubic meter than water.

    One example (in Germany) to date:

    For gases, Pressure is directly related to Temperature (Ideal Gas Law)

    If the temperature of the air at 1 atm is 20 C, how much will the temperature raise if we increase the pressure to 100 atm.

    For air, increase in T goes approximately as increase in P to the 1/4 power when T is measured in Kelvins

    100**1/4 is about 3.5, so the temperature of the air increases by a factor (20 +273) = 293 * 3.5. This is about 1100 K or 830 C --> which would melt the salt reservoir!

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