# Energy Storage

Specific power versus specific energy of what can be achieved with modern (2022) technology for various energy storage technologies.

Science fiction is full of flashy technology. Incandescent beams. Hover sleds. Menacing robots. Spaceships with obscure engines pumping rocket plasma into the void of space. Unexplained glowing things cluttering up engineering bays and mad scientist's workshops. But all these things need energy. And if you are not making use of the energy as soon as it is generated, you need to store it. Here, we'll discuss some of the ways that energy can be stored in order to power all of these wacky tech ideas.

## Electrical energy storage

### Supercapacitors

Also called ultracapacitors, supercapacitors store energy in the separation of charge that occurs at interfaces via various complicated mechanisms like redox reactions, formation of electric double layers, or intercalcation. They can discharge much faster than batteries but can store less energy, so if you are limited by power rather than energy you might choose supercapacitors over batteries - you'll be able to shoot your laser blaster more rapidly, but with fewer shots. Supercapacitors can also survive many more recharging cycles than modern batteries, but lose their charge faster (losing most of their charge in a few weeks). The very best modern (2021) commercial supercapacitors store somewhere around 50 kJ/kg and discharge at a rate of about 15 kW/kg. So for high power pulsed applications (like many directed energy weapons) you will still want to accumulate that electrical energy in a solenoid or dielectric capacitor for a higher power but brief discharge that lets you reach the peak power needs of your device. However, laboratories around the world keep hinting at even higher capacity supercapacitors that can store even more energy, so who knows what the future will bring.

### Batteries

Batteries store energy in chemical reactions or aqueous ion migrations that drive currents of electrons. Batteries store more energy than supercapacitors, but release it more slowly. To get a reasonable rate of fire out of something like a directed energy weapon, you will need large battery packs to meet the average power requirements – but that large battery pack will give you a very large number of shots. Like supercapacitors, a battery for a pulsed laser will almost certainly be energizing a faster discharging electrical circuit element like a dielectric capacitor or an inductor. Alternately, you might use a battery to charge a supercapacitor. This could get you several shots at rapid fire at a time from the supercapacitor, with an overall high number of shots from the battery but with a waiting time to charge up the supercapacitor after you empty it. As usual, the supercapacitor would need to discharge into a more rapidly discharging circuit element for pulsed applications.

#### Lithium-ion battery

The modern standard is the lithium-ion (Li-ion) battery. These batteries store lithium ions packed between the atomically thin layers of a graphite anode. When the battery discharges, the ions migrate through an electrolyte to be absorbed into a metal oxide cathode layer (usually cobalt oxide, for the high energy storage, but iron phosphate or manganese oxide are also used). When the battery is recharged, the lithium ions are dragged back out of the cathode material and pushed back into the graphite. As of 2021, commercially available Li-ion batteries can store somewhere between a third and one MJ/kg (so 6 to 20 times more than the best modern supercapacitors), and discharge at a rate of about a quarter to a third of a kW/kg (or roughly 100 times less than a supercapacitor). They have a self-discharge rate of about 2% per month, a charge-discharge efficieny of 80 to 90%, and last for something like 1000 charge-discharge cycles.

#### Lithium metal batteries

Lithium metal batteries are a potential near future battery technology. They replace the graphite anode of the Li-ion battery with a layer of lithium metal. In combination with a solid state electrolyte, they might get specific energies of about 2 MJ/kg, or twice as much as a Li-ion battery. We can make lithium metal batteries today, but they can only handle several dozen charge-discharge cycles before shorting out (and potentially catching fire!). There's a lot of research trying to find ways to make them last longer and be safer. By the time we're ready to equip our troops with laser rifles, we might have ironed out these difficulties.

#### Lithium sulfur batteries

Lithium sulfur batteries replace the cobalt oxide cathode of a Li-ion battery with sulfur. Sulfur weighs less than cobalt, so you can cut down on the weight even more. How much more? We don't know yet. Most of the research these days involve ways of keeping the batteries from getting clogged up with unwanted lithium-sulfur compounds, greatly limiting their life. Maybe some sort of lithium metal sulfur battery with a solid electrolyte could reach 2.5 or even 3 MJ/kg? We'll eventually figure it out, but in the meantime we'll need to be patient and wait for the researchers to do their stuff (or, you know, because we are making science fiction, make something up).

#### Lithium-air batteries

Lithium-air batteries might be the ultimate in battery technology. You would have lithium metal at the anode and lithium oxide at the cathode, with a current of lithium ions being passed between them through the electrolyte and the current of electrons giving you your electric power is what balances the charges. Up to 6 MJ/kg has been demonstrated in the lab (as of 2021); but the theoretical maximum specific energy is 40 MJ/kg! This, of course, is excluding the weight of the oxygen, which is assumed to be freely available from the air. But for all their promises, there are many challenges. Both their charging cycle lifetime and charge-discharge efficiency are disappointingly low, meaning that they will probably remain in the laboratory rather than store shelves for some time to come.

#### Flow batteries

Sometimes you are not mass-limited in your application. You don't care about super-high specific energy but just want the most energy storage for your dollar. A common application like this is grid-level energy storage, where your batteries won't be moving anywhere but just sitting in a shed someplace so no one really cares how big they are as long as they are cheap. Flow batteries are a strong contender for applications like this. They have tanks of two kinds of liquid electrode that can be pumped past an ion exchange membrane. The capacity of the flow battery can be easily scaled up by just adding bigger tanks. They also tend to have high charging cycle lifetimes and if the electrode liquid gets degraded anyway it can be replaced without throwing away the entire battery.

### Superconductive magnetic energy storage

A cutaway view of a toroidal superconductive magnetic energy storage solenoid. The electric current (green) flows around an inner toroidal winding of superconductive wire. This generates a powerful magnetic field in the empty space inside the winding (magenta) that stores the energy of the device. The action of the magnetic field on the very same current that creates it gives a powerful outward force (red) on that current and the substance through which it flows. To counteract this force and keep the superconductive winding from bursting, a thick supportive jacket of strong material is wrapped around the winding.

Main article: Superconductive_Magnetic_Energy_Storage

Inductors, like capacitors, are electrical components that can directly store electrical energy and discharge it quickly[1]. Unlike a capacitor, which stores electrical charge, an inductor stores electrical current which is maintained by electromagnetic induction opposing any changes in the current. In the real world, electrical resistance means the current will decrease over time and eventually fade away to zero – unless you can get rid of the resistance! This is possible with exotic materials known as superconductors, which have no electrical resistance at all. In this way, a superconductive inductor can store a persistent supercurrent that does not fade with time until it is connected to an exterior load and its energy is used. This is called Superconductive Magnetic Energy Storage (or SMES) because the energy can be considered to be stored in the magnetic field produced by the currents flowing in the inductor.

All known superconductors can only remain superconductive at cryogenic temperatures, generally requiring liquid nitrogen or liquid helium to work. Room temperature and pressure superconductors may be possible, but we haven't discovered any yet and it is also possible that none may exist at all. If room temperature superconductors do exist, you could run a SMES unit without any additional cooling.

One of the strengths of SMES is that they can discharge their energy nearly instantly, giving them exceptional specific power. Merely switch the current path from looping endlessly through the inductor to flow through the thing you are trying to power. SMES is limited in its ability to store energy by the usual material limits imposed by the strength of the stuff used to hold the SMES unit together – the currents and fields in the inductor act to try to blow the inductor apart and you need material strength to hold it together.

If you are confining yourself to modern tech, SMES made from REBCO superconductors held together with the best carbon fiber backing material may be able achieve a specific energy of between 2 and 4 MJ/kg. Switching equipment, insulation, refrigerator pumps, helium recovery systems, quench protection, and other equipment will reduce these values somewhat, but if a low mass, compact SMES was desired, performance in the range of 2 MJ/kg and 0.5 MJ/liter may be achievable. This will invariably result in some energy loss as refrigerator pumps are used to keep the superconductors cool, but with large systems this energy loss can be reasonably tolerable for many applications.

In the far future, you might imagine that room temperature superconductors have been discovered. This will likely increase the energy density by at least an order of magnitude. So you might have between 3 and 20 MJ/liter, or even much higher! The ultimate limit of the specific energy will be given by the tensile strength of the backing material, which for atomically perfect graphene or hexagonal boron nitride might get you 60 or so MJ/kg. You might want to include a safety factor in this, to prevent it bursting on you if anything jostles or slightly weakens or damages it, however!

## Mechanical energy storage

### Flywheels

Flywheels use the inertia of a spinning disk to drive a mechanical load[2]. To recharge, a motor is used to spin the disk back up. The limit to how much energy it can store is when the centrifugal force at the rim exceeds the strength of the flywheel material and the flywheel tears itself apart. The specific energy of the flywheel is thus limited by the material limits of the disk. But that's just for the spinning disk. For applications requiring electricity, you also need your electric motor/generator. For pure mechanical applications, you will need a clutch and driveshaft and gearbox and transmission. On top of that, you will need a housing (to reduce losses due to air friction by keeping it in vacuum, and to protect the outside world in the event of a failure) and low-friction bearings to allow the flywheel to keep spinning as long as possible. Self-discharge is quite high. With magnetically levitated bearings, self discharge rates are typically about 1% per hour (compared to 10 to 50% per hour for mechanical bearings). Superconductive bearings (which with today's materials must be cryogenically cooled - another source of loss with the addition of a cryogenic liquid logistics train) can reduce this to about 0.1% per hour (or something like 2% per day). But this all assumes that the bearings are only supporting the weight of the flywheel, not any gyroscopic precession torques. Any motion that tends to move the spin axis will lead to gyroscopic effects that will make the flywheel very hard to point and maneuver and also greatly increase the self-discharge rate. Mounting the flywheels in counter-spinning pairs will solve the first of these two problems, but not the second. If you are designing for any kind of mobile application, you will need to put the flywheel energy storage system in gimbals to allow the spin axis to remain constant. Even for stationary applications, you need to be sure the flywheel spin axis is aligned with the planetary spin axis to avoid daily precession cycles. On the plus side, flywheels allow for nearly unlimited charge-discharge cycles without any degradation.

### Springs

Hypothetically, something like a watch spring could be used to drive a mechanical device or run an electric generator[3][4]. To recharge, a motor would wind the spring back up again. Springs are subject to material limits on specific energy, but they are more restrictive than for technologies like SMES or flywheels. The energy density you can store in a distorted solid is one half the stress ${\displaystyle \sigma }$ (pressure, tension, shear, etc.) times the strain ${\displaystyle \epsilon }$ (fractional change in length)

${\displaystyle {\frac {E}{V}}={\frac {1}{2}}\sigma \epsilon }$.

The specific energy is the energy density divided by the mass density ${\displaystyle \rho }$

${\displaystyle {\frac {E}{M}}={\frac {1}{2}}{\frac {\sigma \epsilon }{\rho }}}$.

For example, a hypothetical material with a yield strength of ${\displaystyle \sigma =1}$ GPa and a mass of ${\displaystyle \rho =1000}$ kg/m² could store a specific energy of 1 MJ/kg when used to build a flywheel rim, if it could only elongate by 10% before failure then as a spring it could store at most 5% of that, or 50 kJ/kg. While this example is highly simplified (springs are going to involve tension, compression, and shear, each of which will have different yield strengths) it shows that for good spring storage what you want are high yield strengths, low densities, and high elongations before failure. A high quality spring steel might be able to store about 10 kJ/kg as a spring, Kevlar might store about 45 kJ/kg, while a hypothetical perfect carbon nanotube yarn might be able to support around 7 MJ/kg. Springs also have the usual specific power limits from the electric motor or mechanical drivetrain. You have the benefit of nearly no self-discharge, and no need to worry about gyroscopic forces. However, this is a largely untested technology and its limitations are not well understood yet.

### Compressed gas

One way to store energy is to use it to pump a gas into a container to hold that gas at higher pressure. Then, when you need to get the energy back, you can let the gas squirt back out and turn a turbine to generate energy again.

When you compress a gas, its temperature increases. Some of the work you do will go into increasing the gas's pressure, while some will go into increasing its temperature. So you end up with a hot pressurized container compared to the external environment. For small systems or long time storage, this means that heat will eventually leak out into the surrounding environment and you won't be able to get that heat energy back.

When you allow the gas to expand again to extract its energy, its temperature decreases. If there hasn't been enough time for a significant amount of the initial heat of compression to leak out of the system you can get nearly all your energy back (minus details like turbine and pump efficiencies) and the gas will come out at nearly the same temperature as it went in. If the heat of compression has leaked out, the gas will come out much colder than ambient temperature, which means that fittings and equipment will need to be able to handle cryogenic temperatures and ice build-up.

For large scale storage, you can often use tricks for storing the heat produced by compression in a material that can hold the heat for a long time which is highly insulated from the environment. Another way around heat energy losses is to continually exchange heat between the gas and its environment during the compression and expansion process in order to keep it the same temperature, although this method limits the power you can get to the power your heat exchanger can handle.

The pressure vessel that contains the compressed gas has a specific energy that depends on the material limits of the stuff used to make it. But the gas itself also contributes to the mass of the storage, and can be significant when the material strength of the pressure vessel is high.

There is a limit to how much you can compress a gas. At about 700 atmospheres or so for simple molecules, you have squished all the molecules together enough that they are nearly touching, at which point they stop behaving like a gas. Big complex molecules start touching at even lower pressures. This places an upper limit on How much compression you can get, beyond this you won't be storing very much additional energy by pressurizing it further.

If you want to figure out the actual specs for your compressed gas storage, you can make an estimate based on ideal gas behavior. At high pressures this will not be perfect! Hydrogen exhibits about 50% deviation from ideal gas properties at 700 atmospheres and room temperatures[5], but it can at least get us in the ballpark. You will need to know the molar mass ${\displaystyle m}$ of your gas molecules and the number of degrees of freedom ${\displaystyle n}$ of the gas molecules (${\displaystyle n=3}$ for monoatomic molecules like helium, ${\displaystyle n=5}$ for diatomic molecules like hydrogen, oxygen, and nitrogen). You will also need to know the ambient pressure ${\displaystyle P_{1}}$ from which you will start compressing from, and which the gas will eventually expand back to, the pressure ${\displaystyle P_{2}}$ you are compressing the gas to, the volume ${\displaystyle V_{2}}$ of your pressure container, the ambient temperature ${\displaystyle T_{0}}$ that you start at whether you are compressing or expanding the gas, the efficiency ${\displaystyle \epsilon }$ of your compressor and engine, and probably also the strength ${\displaystyle S}$ and density ${\displaystyle \rho }$ of your container material. You will also use the gas constant ${\displaystyle R=8.3144621}$ J/mol/K.

Compute

${\displaystyle \alpha ={\frac {n}{2}}}$
${\displaystyle \gamma ={\frac {n+2}{n}}}$ (adiabatic index)
${\displaystyle V_{1}=\left({\frac {P_{2}}{P_{1}}}\right)^{1/\gamma }}$ (volume of the expanded gas)
${\displaystyle r=\left({\frac {P_{2}}{P_{1}}}\right)^{(1-\gamma )/\gamma }}$ (ratio of the temperature of expanded gas to compressed gas)
${\displaystyle N={\frac {P_{2}\,V_{2}}{T_{0}\,R}}}$ (amount of gas molecules, in moles)
${\displaystyle M_{g}=m\,N}$ (mass of gas)
${\displaystyle M_{c}={\frac {\rho \,P_{2}\,V_{2}}{S}}}$ (estimate for mass of container)
${\displaystyle W=\alpha \left(P_{2}\,V_{2}-P_{1}\,V_{1}\right)}$ (work needed to compress gas, work done by expanding gas)

The energy you can get out of your container of compressed gas is ${\displaystyle E=\epsilon \,W}$. The specific energy is ${\displaystyle E/(M_{g}+M_{c})}$ for the storage alone, neglecting any piping, regulators, compressors, turbines, and generators. When you compress the gas from your initial temperature of ${\displaystyle T_{0}}$ it will rise to a temperature of ${\displaystyle T_{0}/r}$; when you expand it from the ambient temperature ${\displaystyle T_{0}}$ it will cool to a temperature of ${\displaystyle T_{0}\,r}$. The ratio of amount of work you can get back out compared to the amount of energy you have to put in, if you let the gas cool back down to temperature ${\displaystyle T_{0}}$, and neglecting efficiency losses, is ${\displaystyle r}$.

Let's work an example. We will use a ${\displaystyle V_{2}=1}$ m³ pressure vessel to compress hydrogen to 700 atmospheres (${\displaystyle P_{2}=7.09\times 10^{7}}$ Pa) from an initial 1 atmosphere (${\displaystyle P_{1}=1.01\times 10^{5}}$ Pa) and ${\displaystyle T_{0}=290}$ K. Hydrogen has ${\displaystyle n=5}$ and ${\displaystyle m=2.016\times 10^{3}}$ kg/mol. We will make the container out of high tech carbon composites with ${\displaystyle S=3.6\times 10^{9}}$ Pa and ${\displaystyle \rho =1.8\times 10^{3}}$ kg/m³. We find ${\displaystyle \alpha =5/2}$ and ${\displaystyle \gamma =7/5}$. The volume of expanded gas that we can fit in to the container is ${\displaystyle V_{1}=108}$ m³ before the gas cools back down to ambient temperature; this is also the volume of expanded gas we get from a fully pressurized tank at room temperature before it has time to warm back up to ambient temperature (the volume of expanded gas at the same temperature as the compressed gas is just the volume of the container times the ratio of the pressures, or 700 m³ in this case). The temperature ratio of expanded to compressed gas is ${\displaystyle r=0.154}$, so if you start with ambient pressure and temperature hydrogen it will end up at ${\displaystyle T_{2}=1880}$ K and if the compressed hydrogen is at ambient temperature it will end up at a temperature of ${\displaystyle T_{1}=44.6}$ K after it is expanded. You need to do ${\displaystyle W=150}$ MJ of work to compress the ambient 1 atmosphere pressure and 290 K temperature hydrogen from a volume of 108 m³ to its final 700 atmospheres pressure at 1880 K. Then the tank starts to cool off, its pressure drops, and you need to keep pumping more hydrogen in to keep the pressure up. Ultimately in order to get the tank up to its design pressure of 700 atmospheres at 290 K you will need to expend a total energy of ${\displaystyle W/r=974}$ MJ. With the compressor efficiency factored in, this is an expenditure of 1145 MJ of energy that you put in to the process. When you let the gas back out, it will do 150 MJ of work; with your motor efficiency you will be able to get 128 MJ of energy back out. The mass of the stored hydrogen is ${\displaystyle M_{g}=59.3}$ kg, the mass of the container is ${\displaystyle M_{c}=35.5}$ kg for a total mass of 94.8 kg. This gives you a specific energy of 1.35 MJ/kg, at a charge-discharge efficiency of 13.1%. This is a bit better than a modern high-end Li-ion battery in terms of specific energy, but not by much; and the charge-discharge efficiency is much worse. Hydrogen is as good as you can possibly get for compressed gas energy storage, if you use something like helium or nitrogen or air the performance will be worse. So compressed gas storage probably will not be used for compact energy storage in weight or mass limited applications like vehicles or zap gun energy packs. At least, not on its own - that same hydrogen run through a fuel cell might get you something like 4 GJ of energy back out! But for grid scale energy storage at lower pressures with tricks for storing heat or equalizing the heat during pumping compressed gas can start to look promising compared to other options.

### Gravitational

Pushing a mass to a higher location is one way to store energy, when the mass is let back down it can deliver mechanical energy. In modern (2021) times, the main form of gravitational energy storage is pumped hydro – an impeller pumps water from a lower altitude source into a higher altitude reservoir. When the water is let back down, it can drive a turbine. There have been proposals for other gravitational energy storage devices like pulling a train full of rocks up a tall, steep mountain, or raising heavy concrete blocks up tall towers, but these have not yet been commonly implemented.

## Chemical energy storage

Energy stored in chemical form is usually called fuel. It includes things like gasoline, kerosene, and Diesel fuel, as well as natural gas (methane), ammonia, and hydrogen. In our modern (2021) world, most fuel is turned into useful work by burning it in a heat engine – producing heat from its combustion and using that heat to run through various thermodynamic cycles to extract part of it as work. However, some of them are used in fuel cells, that directly react the fuel to create electricity. Note that both of these methods introduce substantial inefficiencies into the process of using the energy – you won't be able to use the full energy of combustion released as heat that is reported here directly in your device.

### Liquid hydrocarbons

Liquid hydrocarbons are things like gasoline, kerosene, and Diesel fuel. There are various and very important differences about what kind of engines they can burn in, but those are beyond the scope of this article. The main important thing is that burning 1 kg of liquid hydrocarbons in oxygen (such as that from the air) will produce about 45 MJ of heat.

### Gaseous hydrocarbons

This includes things like methane, natural gas, and propane. They must be stored in pressurized bottles, often under enough pressure to turn the gas into a liquid for storage. When burned, methane produces about 55 MJ/kg of heat compared to the 50 MJ/kg of propane or butane, but the latter two are easier to store and transport.

### Hydrogen

Hydrogen has the highest specific energy of any chemical fuel – about 120 MJ per kg of hydrogen burned. Unfortunately, hydrogen is also the hardest of these common fuels to store. In modern times (2021), in needs to be stored as a high pressure gas at very low density, or as a low density liquid that needs to be kept at cryogenic temperatures. However, there are research programs looking into hydrogen storage with the hydrogen adsorbed into chemical sponges or in the form of metal superhydrides that could potentially store hydrogen more safely and conveniently. Hydrogen is the easiest gas to burn in a fuel cell, and fuel cells are emerging as the preferred way to extract hydrogen energy for their efficiency, reliability, lack of emissions, and low maintenance.

### High explosives

High explosives are sometimes considered when the need to extract energy quickly is more important than storing energy compactly. TNT releases about 4.2 MJ/kg of heat and work upon detonation, while more modern explosives like PETN release more like 6.7 MJ/kg. PETN is particularly interesting because very small diameters of the stuff can support a detonation wave, allowing it to be used in compact pulsed power applications that don't require a good fraction of a megajoule at a time. While this energy storage pales in comparison to that of hydrocarbons and hydrogen, it is convenient because modern high explosives are generally easy and safe to transport and store, and can release their energy in a very short period of time – with detonation speeds of around 7 to 8 km/s, high explosives will generally release all their energy in under a millisecond (with exceptions for things like very long strings of PETN det cord). High explosives are pretty hard on the motors and generators that use them as fuel, though – almost all are single use items.

## Material limits

Most things that store energy rely on the chemical bonds between atoms to either actively shuffle the electrons around, provide heat through chemical reactions that is fed into a heat engine, or to simply hold the energized structure together. The first two of these are generally well appreciated – a battery or fuel is no better than the ability of its chemical reactions to supply energy. The stresses imposed on the materials by the energy circulating inside the device is often less considered, but poses the ultimate limit for many of the devices described here. Consequently, to get the highest specific energy you want to use the highest possible specific strength (strength-to-weight ratio) material for making the storage device. The best performing steels (maraging steels) can get you around 0.2 to 0.3 MJ/kg. Carbon fiber can reach 2.5 to 4 MJ/kg, depending on type, with some recent samples promising 6 MJ/kg. The ultimate limit for materials held together by chemical bonds is the carbon-carbon bond found in things like atomically perfect graphene or carbon nanotubes (the boron-nitrogen bond offers similar strength). In principle, these could reach 45 to 60 MJ/kg if they could be made defect free (or in configurations that are resistant to crack propagation because there will inevitably be defects) and in bulk samples. And remember that if you run your energy storage device right up to the limits of its material strength, it will be on the verge of failure – a very explosive failure. So be sure to incorporate an adequate safety margin into your design.

To get around the limits of the chemical bond, you will need to go to energy storage methods that rely on different kinds of reactions such as nuclear or matter-antimatter reactions. These will not be constrained by the energy they can store by material strength. They will, however, be limited in the rate at which they can extract that energy by material constraints – confining the high pressure steam generated by the heat of a nuclear reactor, resisting the centrifugal forces of a spinning turbine driven by that steam, confining the magnetic fields of a magnetohydrodynamic generator or magnetic nozzle; all these require strong materials to hold the machinery together. The obvious exception is for explosives, where there is nothing confining the energy. But if you try to contain the explosion and use it to generate useful work, you are back to material strength limits again.

## Converting between energy types

Often, you have energy stored in some form and you need to use it in a different form. For example, if you are storing the energy for your laser gun in a flywheel, the mechanical energy that the flywheel puts out won't do you any good unless you can turn it into electrical energy to pump your laser. The mass and cost of the converters can be a significant factor in your design considerations – if you have an ultra-compact source of energy but need a big bulky motor to make use of it, it starts to look less attractive than one that gives you energy in the same form you need.

### Electric to mechanical and back – motors and generators

An electric motor takes electrical energy and transforms it into mechanical energy. When you mechanically spin the shaft it becomes a generator, taking mechanical energy and turning it into electrical energy. Note that these are the same machine – any electric motor can be run backwards as a generator and vice versa. With modern (2021) tech, electric motors generally have an efficiency of 90 to 95%, with 99% efficiencies reported for experimental superconducting designs. Most modern electric motors have specific energies in the 1 to 2 kW/kg range, with a few that have been engineered to hell and back for ultra-high performance bleeding edge mass reduction to just barely break past 15 kW/kg[6].

#### Explosively pumped flux compression generator

While there are many different kinds of electric motors and generators, one kind stands out as being particularly unusual and unique with a specific application that cannot easily be met by anything else. This is the explosively pumped flux compression generator (FCG), which is technically a combination of heat engine and electric motor in one. There are different configurations, but a typical FCG operates as follows: A cylinder of high explosive is surrounded by a sheet of copper. This tube is wound with a solenoid electromagnet and energized with a pulse of electric current supplied by a capacitor bank. The explosive is then detonated on one end, producing a detonation wave that sweeps down the cylinder. As the detonation wave passes, it pushes the copper sheath outward, confining the magnetic flux from the electromagnet into a smaller and smaller area. This induces an increase in electrical current in the electromagnet, ultimately delivering much more energy than was initially input by the capacitor bank discharge[7]. As you might imagine, detonating a large quantity of high explosive inside of it (or, in some designs, surrounding it as a sleeve or jacket) is hard on the generator – these are single-use only devices, being exploded with each use. Their main application is to provide very high pulses of power, taking the substantial portion of the energy of detonation that is produced by the explosive on the order of a millisecond and turning it into a pulse of electrical energy with the same duration. Reported efficiencies for FCGs tend to run around 10% to 20%[8][9] Specific energies reported have been on the order of a few kJ/kg[10][11], with specific powers on the order of several MW/kg.

### Chemical to mechanical – Heat engines

Technically, a heat engine is any device that takes in energy and entropy at high temperature and exhausts the entropy along with a certain portion of the energy at lower temperature and uses the rest of the energy to do work. This definition technically includes things like photovoltaic solar panels (which take in energy and entropy from the 6000 kelvin hot sun and exhaust the entropy at the 300 kelvin ambient temperature typical of Earth and produce electrical work in the process). But usually when people think of a heat engine, they imagine a device that takes hot gases from combustion, runs those gases through various expansion, compression, and heat exchange cycles, uses these cycles to extract mechanical work, and then exhausts the entropy as a lower temperature gas. These run from the earliest Watt steam engines all the way to modern jet turbines and combined cycle steam turbines at power plants.

#### Internal combustion piston engines

These are the machines that power our cars. They include both gasoline engines and Diesel engines. For the latter half of the 20th century, they generally ran about 20% efficient at turning heat energy into work, with the occasional commercial design topping 25% when they wanted to advertise fuel efficiency. Fuel efficiency regulations in the early 21st century driven by climate worries drove the efficiencies up to around 30% or 35% with some advanced models achieving 50% efficiency. [12] Specific powers of modern (2021) piston engines tend to run at about 1 to 2 kW/kg, with very high performance turbocharged or supercharged models approaching 10 kW/kg. High performance piston engines can maintain these specific powers down to at least somewhat less than 100 kg of mass. [13]

#### Stirling piston engines

Stirling cycle engines are closed-cycle engines that re-use the same working fluid over and over again. They take in heat from an external source (such as concentrated solar, burning a fuel, or from radioactive decay), couple it to the working fluid with a heat exchanger, and use that to drive the piston cycles that generate mechanical power. Compared to internal combustion engines, Stirling engines tend to have a lower specific power and higher specific cost, but require less maintenance and can run on any available source of heat rather than only highly refined fuels. For combustion engines or other heat sources providing a similar high input temperature, the efficiencies of a Stirling engine are similar to those of an internal combustion engine.

#### Turbines

Turbines use a flow of fluid past a radial array of fan blades to spin a shaft; that shaft can be used for mechanical power or to drive an electrical generator. If you are looking for a turbine engine for power rather than just as a propulsive jet, you get a turboshaft engine (or, if you are using the mechanical energy to drive a propeller, a turboprop). These usually burn a liquid hydrocarbon to generate heat and pressure, and the hot, high pressure gas spins the turbine as it squirts out. They can, however, also be designed to burn gaseous hydrocarbons, hydrogen, or other fuels. Turbines take some time to spin up to full speed, and are not very efficient when not working near their optimal spin rate, so they are best for applications that require a constant power. In addition, they spin really fast but at low torque, so you will usually need a gearbox to trade speed for torque. Compared to piston engines, they are more expensive and ill-suited to applications requiring rapidly changing loads or variable power (like automotive engines) but are lower maintenance, lower vibration, can burn less volatile (and thus safer) fuels, and generally have a much higher specific energy – usually in the 5 to 12 kW/kg range. Typical designs for helicopter or maritime powerplants run at about 30 to 40% efficiency at extracting mechanical energy from the thermal energy of combustion [14] [15]. Unfortunately, turbines don't scale down very well. Below many hundreds of kilowatts, they start to lose efficiency and specific power.

A non-gaseous source of heat (like a nuclear reaction, or sunlight) can be used to boil water. The high pressure steam can then spin a turbine to generate power.

The most efficient turbines are combined cycle turbines, where the output heat from a gas turbine can be used to generate steam to run a steam turbine. These can reach efficiencies in the 60% range, and are often used for large, stationary applications like grid-scale power.

### Chemical to electrical – fuel cells

A fuel cell directly extracts an electrical current from a chemical reaction. It is typically run somewhat like a battery with the fuel diffusing through an electrolyte between an anode and a cathode, and the extra electrons required to make the reaction work drive the electric current. Almost all modern (2021) fuel cells use take hydrogen as fuel and react it with atmospheric oxygen, or perhaps stored oxygen from a separate tank. Fuel cells are generally between 40 and 60% efficient. There are many different kinds of fuel cell. Some kinds only work at elevated temperatures (although they can use the heat produced by the reaction to help maintain those temperatures once they are operational). The anode of most modern (2021) fuel cells require platinum as a catalyst to break up the fuel, which is not only expensive but can cause problems when not using hydrogen as a fuel source because the platinum catalyst can get clogged up with carbon monoxide and stop working. Because they have no working parts, fuel cells are very reliable and low maintenance. Fuel cells for automotive use generally deliver about 1 to 2 kW/kg specific power.

### Mechanical to mechanical – drivetrains

Usually, the mechanical energy you are getting out of your energy source isn't quite what you need for your application. Maybe it has the wrong RPM or the wrong torque. Or maybe it is in the wrong place or you need to be able to idle the engine or something. So just about any source of mechanical energy being used for a mechanical application will need a collection of gearboxes, transmissions, differentials, clutches, and driveshafts. This can be minimal, like for turboprops, or extensive, like for automobiles. Drivetrains will introduce an additional source of efficiency loss - you might expect only about 80% to 90% of the input power of an automotive engine to reach the wheels, for example (depending on many details, such as type of transmission, front-wheel vs. rear wheel drive, and so on). [16] [17]

### Electrical to electrical – rectifiers, inverters, and transformers

Sometimes, the electrical energy you get from your power source doesn't have the right voltage, current, or frequency that you need for your application. An inverter takes direct current (DC) and turns it into alternating current (AC). A transformer takes AC power and changes its voltage, with a reciprocal change to the current (for example, a step-up transformer might increase the voltage by a factor of 6 but decrease the current to 1/6 of it's input value). A rectifier takes AC electricity and gives you DC electricity back out. Using these tools, you can convert your electricity from the kind you get to the kind you need. However, depending on the application, you may need additional massaging of your electricity. To change the wave form, for example, or shape high energy pulses, to what is required.

## Credit

Author: Luke Campbell

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