4.1 The Need for Storage

Despite the continuing challenges with using electrochemical batteries for long-term, bulk, or large vehicular propulsion power, they are still favored in many applications. These applications can range from small vehicles to computer power, because of their inherent simplicity in configuration and because they provide direct output power in electrical form.

Immense attention and support has been expended on energy matters in recent decades, mostly with regard to its sources or production, i.e., wind, solar, methanol fuels, etc. Relatively little resources have been devoted to the storage of energy. In fact, a significant number of the problems with which we are faced could be resolved with more effective storage. Energy is frequently available to the user, but often not at the needed time or location.

Usually, until a technology shows imminent promise as practical, industrial and/or commercial products, they are not supported by commercial enterprises, which must realize a return on investment in the predictable future. A recent exception to this is the lithium-ion or polymer-based technology, which has found widespread use in portable devices such as computers, navigation equipment, cameras, etc., and use as auxiliary power for electric hybrid cars. Despite its limited life and rather high cost, it presents an opportunity for making some progress in areas in which other batteries cannot be applied.

Let us take a brief look at the overall energy situation about which there is so much scientific discussion. The broad view certainly encompasses not only the issue of storage but also the matter of primary energy sources. In actuality, we have very few options. From a very practical standpoint there are only two primary sources, and they are either solar or nuclear energy. More will be discussed in later chapters.

The position that seems to predominate in any discussion these days about the environment and energy favors alternative energy sources. What are these alternatives? Unfortunately, there are precious few alternatives that we are, at present, aware of to “solve the world’s energy problems.” In Chapter 5 we will examine these options more closely. For the present, the options can be summed up as being either fossil fuel (petroleum products) processes or nuclear processes. All others, such as wind, solar photovoltaic, geo-thermal, lunar, etc., are at best only supplementary sources when one considers the immense amount of energy that we use and will increasingly continue to use on a global scale. We are no longer at the level of one manpower to one horsepower per person that was predominant well before 1900 in Western civilizations. Now we are at the tens to hundreds of horsepower machinery at the disposal of each person. To sustain the level of accommodations in travel, living comforts, and convenience that modern societies enjoy will require increasing amounts of readily available energy. Meanwhile, our oil reserves are surely dwindling because they are finite (no new oil deposits are being created on Earth at this rate of usage), and the demand is increasing.

At present, wind and solar, other than solar thermal, provide small amounts of intermittent and usually unpredictable power to the user. There are no large-scale, practical, and economic means available as yet to store vast quantities of energy to make their extensive use practical. In most instances, windmills and solar collector field outputs are connected to a nearby electric power utility to “level” the power in a continuous fashion.

We certainly don’t want to be in a situation where our electrical appliances work well only when the sun is shining brightly or only when there is enough wind. Hence, we must either store this energy when the source is producing more than we need at that moment, or we sell our excess wind-generated power at windy times to a power grid, and then buy some back when the local moving air mass (wind) is insufficient to power our home, office, or factory. That situation ties everything inexorably to available power lines. That restriction reduces the places where alternative sources such as these can be employed effectively. Hence, no remote, stand-alone wind or solar power is practical without storage.

All of the above are fine as auxiliary power for perhaps reducing the use of and our dependence upon fossil fuels. However, unless we drastically change our way of life in the more civilized and prosperous parts of the world, these measures will not solve our overall energy needs for the future. So far, the only two sources with universal applicability are fossil fuels and nuclear. Nuclear along with hydro can run virtually all of our stationary power needs. However, portable nuclear power is very limited to large vehicles such as ocean-going ships. There has been much speculation about developing nuclear-powered aircraft and large land-going vehicles. Unfortunately, the issues of fissionable mass criticality, controls, safety, radiation, and shielding greatly limit its applicability to moving conveyances. Certainly, we cannot look forward to street buses and private cars being powered this way.

That leaves us with the situation of how to power all the various vehicles and industrial equipment even if we have universal nuclear power for power-generating plants. Should we use gasoline, diesel fuel, or propane? Perhaps, but there may be a time in the not so distant future when science will have found either a new source of portable energy or an entirely new approach (mechanism) for the creation of available energy, in much the same fashion that, prior to 1900, nuclear energy was inconceivable. Knowledge of the atomic nucleus, with all of its associated subatomic particle physics, gamma radiation, relativity theory, and quantum mechanics, didn’t exist. Thus, there was no way to even think constructively about such matters before that time.

Similarly, there may indeed be a whole way of attacking the energy question if we could be armed with new knowledge of the nature of things in the Universe. Then again, there may not be any other alternatives beyond what we now know about matter, energy, space, time, etc.

If there is some qualitatively new approach that utilizes new principles of physics in generating usable energy to satisfy our needs, and if we find it in time, the limited availability of fossil fuels may just buy us that needed time and we will not have to change our lifestyles too drastically.

However, storing energy effectively would make all primary energy sources available for many applications, including load leveling. It would also enable us to physically transport available energy from one place to another without wires. In addition, electric vehicle propulsion could become practical.

Storing energy in a directly useable, electrical form, as distinguished from compressed gas, would be ideal. Batteries and some forms of regenerable fuel cells offer that opportunity. They are able to store energy provided electrically from a source (e.g., generators, solar photo-voltaic) by changing oxidation states of ionic materials. Then they are able to deliver the major portion of that energy at a later time directly in the form of electrical output.

Virtually all of the complexities and inefficiencies of converting from one form of energy to another is avoided. Converting, for example, from mechanically moving components, such as expanding gas or rotating flywheels, requires a generator and regulation. An electrochemical device requires little ancillary equipment. The basic simplicity of such systems make them quite attractive, even though in most instances there is the necessity for electronic circuitry to manage the power and probably convert from ac to dc and back again.

4.2 The Need for Secondary Energy Systems

The ability to store energy from a primary source for later use is important in many situations, especially when that primary source of energy is from an uncontrollable and variable source, such as solar radiation through the atmosphere at the Earth’s surface.

Even in those instances where the primary source is controllable, such as in petroleum-fueled gas turbines, there may be a need for peak bursts of power at random or scheduled times. Also, the ability to store energy would provide uninterrupted power delivery to the electrical load in those instances where a temporary breakdown or malfunction is encountered at the primary source.

The diagram of Figure 4.1 illustrates the idea of the multiple functions that storage might provide in a total energy system. The storage stage shown can serve the following purposes:

• Provide uninterrupted power
• Briefly provide peak power exceeding that of the primary source
• Smoothing function in those instances where the power from the source is not constant
• Standby, emergency source.

4.3 Sizing Power Requirements of Familiar Activities

Examining the energy needed to perform a number of familiar activities may prove informative. Some of these activities are common, everyday actions. The illustrations that follow emphasize the familiar in order to gain some perspective on the range of energy and power required to perform various common tasks.

One of the most common activities with which many can identify is the act of throwing a ball. A hardball baseball weighs approximately 1/2 lb, and when thrown by an adult with some practice, it achieves velocities in excess of 50 to 60 miles per hour. Speeds of over 80 mph have been reported. Consider the case of a 60 mph ball speed. That corresponds to 88 feet per second. To calculate the energy of motion, we use the formula 1/2mv², with m being in units of slugs in the English system.

The exercise in estimating the energy and power associated with throwing the ball is as follows:

(4.1)

Remember, the mass units have been converted to slugs by dividing the weight by the acceleration of gravity. That amount of energy would be equal to, for instance, the impact energy of dropping a 1 lb weight from a height of 60 feet.

Now consider the power involved. It will be recalled that power is the rate of doing work, or expending or transferring energy.

A simple estimate of the power that a human arm can develop for a brief period of time is found by taking the above information and making a few realistic assumptions. The swing or arc of the pitcher’s arm from the beginning of the throw to the moment the ball is released will be approximated as 180°, or half of a full circle. The radius of the pitcher’s arm is about 2.5 feet. Hence, the total distance through which the ball is accelerated to its release velocity is

(4.2)

Next, if we assume that the ball is linearly accelerated through the throw, an average speed of the ball through the arc while still in the hand of the pitcher is about 44 ft/sec. The time then spent in accelerating the ball is 8ft/44ft/sec = 0.2 sec.

During this short time, about 60 ft-lb of energy was imparted on the ball, corresponding to 300 ft-lb per second as the average rate of doing work, or power output of the pitcher’s arm. Converting this number to other, more familiar units, we get

(4.3)

or

(4.4)

So, it seems that a human can generate significant amounts of power, but only for very brief periods of time.

4.3.1 Examples of Directly Available Human Manual Power Mechanically Unaided

4.3.1.1 Arm Throwing

An experienced baseball player can easily pitch a ball at 60 mph. Taking the data available for a typical ball pitching, the following information is generated:

• Ball weight ~ 8 oz
• Propelled velocity ~ 88 ft/sec
• Kinetic energy ~ 60 ft-lbs
• Power Out for 0.2 sec ~ 1/2hp ~ 400 watts.

4.3.1.2 Vehicle Propulsion by Human Powered Leg Muscles

As an addendum to the above, consider the amount of energy a human can generate on a sustained, but limited, basis with leg muscles only. This is illustrated below in the form of bicycling uphill. Employing the same mathematics as before in ball pitching, we can see how much power is required to pedal at different speeds up hills with different inclinations.

A 180 lb man with a 20 lb bicycle, pedaling at the speed of 3 mph, moves vertically at the rate of grade fraction × speed. In the steepest case shown in Table 4.2, a speed of 5 mph is 88×5/60 = 7 ft/sec. At a 5% grade, that would be 0.05 × 7 = 0.35 ft/sec in the vertical direction. Lifting 200 lbs at a rate of 0.35 ft/sec requires about 70 ft-lb/sec of power. Assuming a 100% efficiency of the bicycle mechanisms and no friction loss to the road surface, converting to hp and watts results in almost 100 watts.

3% grade at 3 mph	~50 watts
5% grade at 3 mph	~100 watts
10% grade at 5 mph	~200 watts

Using similar arithmetic, the numbers for a bicyclist climbing different hills at different rates are shown below. As we know from experience, it is possible to sustain such effort for only brief periods, perhaps limited to minutes rather than hours of such power outputs.

Before leaving the realm of human muscle power capabilities in transforming one form of energy into another, we will make an estimate of the sort of performance that can be achieved with the use of mechanical aids that enable us to store some energy over a short time to be released in an even more brief interval of time.

The use of spring-like materials, such as resilient wood and steel, have enabled us to hurl objects much further and with greater speeds than are possible by efforts of directly throwing. A classic example of this is afforded by the bow-and-arrow of antiquity and modern times. The limit to the storable energy is, of course, the arm and shoulder strength of the archer.

As a sample calculation, let us assume that the archer is capable of exerting a 100 lb pull on a bow string, and that the string is pulled back a full 2 feet from its rest position. In addition, if we assume the arrow weighs about 4 oz (while these figures may not be completely accurate, they are sufficient for illustrative purposes), then the computations below follow.

There is a constant force term, k, that one can assume for the bow that expresses the force as a function of the tension or stretch of the bowstring. That distance, x, at the center of the bow is the difference from the zero point of the string when there is no pulling force to the position of the string center at maximum extension, or pull. The incremental force, dF, is then

(4.5)

4.3.1.3 Mechanical Storage: Archer’s Bow and Arrow

The energy, E, stored in the bow string upon extending it a distance, x, from the relaxed position and normal to the string is

(4.6)

where k is the “spring constant” of the bow. If we assume that k is constant over the string extension, then E = (1/2)kx². For a bow and arrow with the properties given below, we obtain the results shown for energy and speed of the projectile:

• Full Bow Pull ~ 100 lb
• Total string displacement ~ 2 feet
• Arrow weight ~ 4 oz
• Energy imparted to arrow ~ 100 ft-lb
• Exit velocity ~ 112 ft/sec ~ 76 mph
• Power out for 0.018 sec ~ 1 hp.

The energy with which the arrow leaves the archer’s bow is quite high, and the speed exceeds that which throwing can attain. This was a formidable distance weapon in its time, and it still is employed for silent or stealth operations. The exit energies of other projectiles, such as bullets propelled by gunpowder, is mentioned elsewhere in this book. Among the more commonly found forms of portable energy sources for general use are the myriad electrochemical cells and batteries that are available everywhere and are used for almost every imaginable purpose. These applications range from the flashlight to large batteries that are used to start internal combustion engines and to power electric vehicles. These are all secondary devices in the sense that the capacity for releasing or making energy available to the user has been provided by some primary source at an earlier time. In the case of a primary battery, its energy deposit is made at the time of manufacture. In the case of a rechargeable battery, its ability to repeatedly store energy upon electrical recharging has also been provided at the time of its manufacture. At the other extreme is the hydroelectric generating station or dam. Here also, the system is secondary because the water at a useable elevation in the reservoir was provided by the sun as accumulated rainfall.

These two secondary sources have the energy characteristics given below:

• Flash light with 2 D-cells ~ 0.5 to 1 watt over 5 to 10 hours intermittent
• Hydro-electric Generation (water fall) at 40 gallons per minute from 100 foot elevation ~ 1 hp (746 watts).

There is a huge difference in the economics, the life, and the practicality of all the various means of storing and making available energy for practical purposes. A quick look at the costs of the energy from these two sources is pertinent in our overall views on the subject.

Let’s assume that the price of a D-cell alkaline battery with a useable capacity of around 6 watt-hours is $1. That would make the cost of energy on a larger scale about $160/kwh. Compare that to the figure of about $0.10 per kWh for energy from an electric power utility. This should help explain why we don’t use primary batteries to power electric cars or our homes.

However, the convenience factor of having a small amount of portable energy and power when needed for lights, computers, and other electronic apparatus makes it well worth the cost – as long as we are not using large amounts of energy at that cost rate.

The single shortcoming of an electrochemical battery is its inability to deliver high, short-term bursts of power that one can obtain from chemical reactions like explosions or mechanical contraptions like catapults and large springs.

4.4 On-the-Road Vehicles

Now, we will turn our attention from human powered efforts to devices that are capable of doing greater amounts of work, such as the internal combustion engine in passenger cars.

Consider the amount of energy and power required to propel an automobile in its different modes of operation. The least amount of energy per unit time is needed to maintain cruise speeds, but much more power is required in accelerating and hill climbing. And, of course, passing on an upgrade hill is the most demanding on power from the engine. Most modern cars are designed with engines that will deliver the type of performance that motorists demand under the worst conditions. That means that the purchaser is buying a vehicle with a power plant significantly larger than what is needed to more slowly climb hills and that perhaps doesn’t accelerate from 0 to 60 mph in less than 10 seconds.

4.4.1 Land Vehicle Propulsion Requirements Summary

A typical or test vehicle that weighs about 3,000 lb when loaded with passengers is used here for illustrative purposes. The calculations below show a few of the energies and power levels required to accomplish the cited performances. At 60 mph the kinetic energy of the vehicle is

(4.7)

If the vehicle were to accelerate from full stop to 60 mph in 10 seconds, the power requirement of the engine would be

(4.8)

In order to maintain a speed of 25 to 35 mph, about 25 to 35 hp is required to overcome road friction, drive train losses, and wind resistance.

These calculations indicate that almost twice the engine power is required to climb hills and accelerate at the rates shown than what is needed to propel the car along a level road to overcome the frictional forces, etc., encountered in machinery and wind and road contact. It should be noted here that cruise power must be added to the hill climbing power because those cruise losses still pertain.

4.5 Rocket Propulsion Energy Needs Comparison

For rocket propulsion, the equation for thrust force versus mass and energy of the propellant is

(4.9)

where φ = fuel energy density m = mass of fuel

M = total mass of expelled material.

Gasoline as fuel, with liquid oxygen, gives 12,000 pounds of thrust per gallon burned per second. All the above applications of portable power sources have both power and energy density requirements far outside the current or future battery capabilities.