But first to finish up with electric vehicles:

The Key of course is marketing people have to buy the product

- Performance people need to change their driving habits
- Range not a problem for in town use. City ordinance to make city limits and internal combustion free zone would clearly help
- Price Probably needs to come down to 10K before people would seriously consider this "glorified golf cart"
- Safety Lightweight materials --> carbon fiber. High tensile strength but not a Farady Cage (thunderstorm problem!). Also braking is a concern.

California Mandate:

- 1998: 2% of all vehicles offered for sale must be zero emission vehicles (meaning electric cars)
- 2003: 10% must be zero emission
- As of Fall 1995 the Mandate has been
rolled back
Some Prototypes:

- Ford Ecostar two-passenger electric mini-van used by Post-Office and UPS sodium-sulfur batteries
- Chrysler TEVan nickel-iron batteries
- $500,000 given to Yosemite to replace diesel buses with electric buses
- $500,000 given to General Motors to loan 50 vehicles to 1000 people nationwide for test drive results

Why is Energy Storage Important:?

Energy Density of Some Materials (KHW/kg)

Energy density storage drives the choices that can be made:

At the turn of the century electric vehicles were commonplace (using basically lead-acid batteries). Since gasoline has much higher energy density it quickly dominated the way vehicles were propelled.

In fact, gasoline has one of the highest energy density storage capacities known. This makes it very difficult to duplicate the convenience that gasoline has traditionally provided (e.g. 350 kg of batteries is equivalent to 1 kg of gasoline !).

Pumped Hydroelectric Energy Storage:

Simple in concept use excess energy to pump water uphill pump from lower reservoir (natural or artifical) to upper reservoir.

Energy recovery depends on total volume of water and its height above the turbine

- need at least 100-meters this is a stringent limit on locations
- artificial lower reserviors can made via excavation can achieve higher energy density due to large vertical distance (up to 1000 feet!)
- facility does not impact free flowing stream
- sediment build-up at dam base is minimized
- Hydropower is 80% efficient (uphill or downhill). So to pump uphill and the get energy downhill, efficiency is 0.8x0.8 = 64%

Cost Issues:

Suppose a company has a coal fired plant which operates at 36% efficiency and uses excess power to pump water uphill. The overall efficiency of recovering that to deliver to the consumer is 0.36 x 0.64 = 0.23 (23%)

- So stored energy is more expensive what's the incentive?
- Need to balance this cost against the costs of building a power planet with capacity to meet some theoretical maximum demand but the rest of the time doesn't operate at this level

Real Life Facility in Michigan

- Use Lake Michigan as Lower Reservoir
- Upper reservoir is 75 meters higher
- Peak capacity is 2000 MW (!)
- Stored energy is 15 million KWH`

- Kinetic Energy = 1/2*Iw

Inertial constants for different shapes:

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:

MRw^{2}

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

- Turbine Flywheel Cars
- Flywheel Physics
- Flywheels and Electric Vehicles
- High-Power Density Lightweight Flywheels

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:

- 10 kg of gasoline = 140 KWH
- Engine has 15% efficiency --> 21 KWH of useable energy
- Flywheel has a conversion efficiency of 80%
- Flywheel must therefore store 21/.8 = 26.25 KWH
- Kinetic Energy goes as 1/2*Iw
^{2}. For flywheels I =1/2MR^{2}. - A revolution means an object moves 2 pi radians (360 degrees)
- So
Stored Energy = 1/2*Iw ^{2}= 1/2*1/2MR^{2}* (2 pi* w)^{2}= pi

^{2}MR^{2}* w(RPS)^{2} - If we measure w in revolutions per second then the
stored energy of a flywheel is approximately 10MR
^{2}x w(RPS)^{2} - For M=140 kg and R=50cm this yields a required w of 500 RPS or
30,000 RPM
- The required energy storage is 26 KWH/140 Kg = .18 KWH/kg which excees the energy storage density of steel - hence such a flywheel requires construction out of carbon fiber.

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:

- Storage reservoir is underground cavity in a natural salt deposit
- The storage volume is 300,000 cubic meters
- Sheer weight of the salt deposit is able to pressure confine the air reservoir
- Air is compressed to 70 atm (1000 lbs per square inch)
- Compression is done by electrically driven air compressors
- System delivers 300 Megawatts for 2 hours by using the compressed air to drive a turbine
- Difficult to measure the efficiency of this system. Two
major contribution to the inefficiency:
- Energy required to cool the air as it is being put into storage --> this is a critical requirement (see below)
- Energy required (usually from fuel) to expand the cool air taken from storage as it entires the turbine.

- Desireable design feature would be recycle the waste heat from the compression stage and use it to reheat the air during expansion stage