Stirling engine

Name and definitionheat from industrial processes.
Robert Stirling was the inventor of the firstA continuous combustion process can be used to
practical example of a closed cycle air engine insupply heat, so most types of emissions can be
1816, and it was suggested by Fleeming Jenkin asreduced.
early as 1884 that all such engines shouldMost types of Stirling engines have the bearing
therefore generically be called Stirling engines. Thisand seals on the cool side of the engine, and they
naming proposal found little favour, and therequire less lubricant and last longer than other
various types on the market continued to bereciprocating engine types.
known by the name of their individual designers orThe engine mechanisms are in some ways simpler
manufacturers, e.g. Rider's, Robinson's or Heinrici'sthan other reciprocating engine types. No valves
(hot) air engine. In the 1940s, the Philips companyare needed, and the burner system can be
was searching for a suitable name for its ownrelatively simple.
version of the 'air engine', which by that time itA Stirling engine uses a single-phase working fluid
had already been tested with other gases,which maintains an internal pressure close to the
eventually settling on 'Stirling engine' in April 1945.design pressure, and thus for a properly designed
However, nearly thirty years later Grahamsystem the risk of explosion is low. In
Walker was still bemoaning the fact that suchcomparison, a steam engine uses a two-phase
terms as 'hot air engine' continued to be usedgas/liquid working fluid, so a faulty relief valve can
interchangeably with 'Stirling engine' which itselfcause an explosion.
was applied widely and indiscriminately. TheIn some cases, low operating pressure allows the
situation has now improved somewhat, at least inuse of lightweight cylinders.
academic literature, and it is now generallyThey can be built to run quietly and without an air
accepted that 'Stirling engine' should refersupply, for air-independent propulsion use in
exclusively to a closed-cycle regenerative heatsubmarines.
engine with a permanently gaseous working fluid,They start easily (albeit slowly, after warmup)
where closed-cycle is defined as a thermodynamicand run more efficiently in cold weather, in
system in which the working fluid is permanentlycontrast to the internal combustion which starts
contained within the system and regenerativequickly in warm weather, but not in cold weather.
describes the use of a specific type of internalA Stirling engine used for pumping water can be
heat exchanger and thermal store, known as theconfigured so that the water cools the
regenerator. An engine working on the samecompression space. This is most effective when
principle but using a liquid rather than gaseous fluidpumping cold water.
existed in 1931 and was called the Malone heatThey are extremely flexible. They can be used as
engine.CHP (combined heat and power) in the winter and
It follows from the closed cycle operation thatas coolers in summer.
the Stirling engine is an external combustion engineWaste heat is easily harvested (compared to
that isolates its working fluid from the energywaste heat from an internal combustion engine)
input supplied by an external heat source. Theremaking Stirling engines useful for dual-output heat
are many possible implementations of the Stirlingand power systems.
engine most of which fall into the category ofDisadvantages
reciprocating piston engine.Size and cost issues
Functional descriptionStirling engine designs require heat exchangers for
The engine is designed so that the working gas isheat input and for heat output, and these must
generally compressed in the colder portion of thecontain the pressure of the working fluid, where
engine and expanded in the hotter portionthe pressure is proportional to the engine power
resulting in a net conversion of heat into work. Anoutput. In addition, the expansion-side heat
internal Regenerative heat exchanger increasesexchanger is often at very high temperature, so
the Stirling engine's thermal efficiency comparedthe materials must resist the corrosive effects of
to simpler hot air engines lacking this feature.the heat source, and have low creep
Key components(deformation). Typically these material
Cut-away diagram of a rhombic drive betarequirements substantially increase the cost of
configuration Stirling engine design:the engine. The materials and assembly costs for
Pink  Hot cylinder walla high temperature heat exchanger typically
Dark grey  Cold cylinder wall (with coolant inletaccounts for 40% of the total engine cost.
and outlet pipes in yellow)All thermodynamic cycles require large
Dark green  Thermal insulation separating thetemperature differentials for efficient operation. In
two cylinder endsan external combustion engine, the heater
Light green  Displacer pistontemperature always equals or exceeds the
Dark blue  Power pistonexpansion temperature. This means that the
Light blue  Linkage crank and flywheelsmetallurgical requirements for the heater material
Not shown: Heat source and heat sinks. In thisare very demanding. This is similar to a Gas
design the displacer piston is constructed withoutturbine, but is in contrast to an Otto engine or
a purpose-built regenerator.Diesel engine, where the expansion temperature
As a consequence of closed cycle operation thecan far exceed the metallurgical limit of the engine
heat that drives a Stirling engine must bematerials, because the input heat source is not
transmitted from a heat source to the workingconducted through the engine, so engine materials
fluid by heat exchangers and finally to a heat sink.operate closer to the average temperature of
A Stirling engine system has at least one heatthe working gas.
source, one heat sink and up to five heatDissipation of waste heat is especially complicated
exchangers. Some types may combine orbecause the coolant temperature is kept as low
dispense with some of these.as possible to maximize thermal efficiency. This
Heat sourceincreases the size of the radiators, which can
Point focus parabolic mirror with Stirling engine atmake packaging difficult. Along with materials cost,
its center and its solar tracker at Plataforma Solarthis has been one of the factors limiting the
de Almera (PSA) in Spainadoption of Stirling engines as automotive prime
The heat source may be combustion of a fuelmovers. For other applications such as ship
and, since the combustion products do not mixpropulsion and stationary microgeneration systems
with the working fluid (that is, externalusing combined heat and power (CHP) high power
combustion) and come into contact with thedensity is not required.
internal moving parts of the engine, a StirlingPower and torque issues
engine can run on fuels that would damage otherStirling engines, especially those that run on small
(that is, internal combustion) engines' internals,temperature differentials, are quite large for the
such as landfill gas which contains siloxane.amount of power that they produce (i.e., they
Some other suitable heat sources arehave low specific power). This is primarily due to
concentrated solar energy, geothermal energy,the heat transfer coefficient of gaseous
nuclear energy, waste heat, or even biological. Ifconvection which limits the heat flux that can be
the heat source is solar power, regular solarattained in a typical cold heat exchanger to about
mirrors and solar dishes may be used. Also,500 W/(m2K), and in a hot heat exchanger to
fresnel lenses have been advocated to be usedabout 5005000 W/(m2K). Compared with internal
(for example, for planetary surface exploration).combustion engines, this makes it more challenging
Solar powered Stirling engines are becomingfor the engine designer to transfer heat into and
increasingly popular, as they are a veryout of the working gas. Increasing the
environmentally sound option for producing power.temperature differential and/or pressure allows
Also, some designs are economically attractive inStirling engines to produce more power, assuming
development projects.the heat exchangers are designed for the
Recuperatorincreased heat load, and can deliver the
An optional heat exchanger is the recuperatorconvected heat flux necessary.
used when high efficiency is desired fromA Stirling engine cannot start instantly; it literally
combustion fuel input to mechanical power output.needs to "warm up". This is true of all external
As the heater of a fuel-fired engine with highcombustion engines, but the warm up time may
efficiency must operate at a nearly uniform highbe longer for Stirlings than for others of this type
temperature, there is considerable heat loss fromsuch as steam engines. Stirling engines are best
the combustion gases exiting the burner unlessused as constant speed engines.
this can be cooled by preheating the air neededPower output of a Stirling tends to be constant
for combustion. Engines used within combined heatand to adjust it can sometimes require careful
and power systems can instead cool the exhaustdesign and additional mechanisms. Typically,
gases at the "cold" side of the engine.changes in output are achieved by varying the
Heaterdisplacement of the engine (often through use of
In small, low power engines this may simplya swashplate crankshaft arrangement), or by
consist of the walls of the hot space(s) butchanging the quantity of working fluid, or by
where larger powers are required a greateraltering the piston/displacer phase angle, or in
surface area is needed in order to transfersome cases simply by altering the engine load.
sufficient heat. Typical implementations are internalThis property is less of a drawback in hybrid
and external fins or multiple small bore tubeselectric propulsion or "base load" utility generation
Designing Stirling engine heat exchangers is awhere constant power output is actually desirable.
balance between high heat transfer with lowGas choice issues
viscous pumping losses and low dead space. WithThe used gas should have a low heat capacity, so
engines operating at high powers and pressures,that a given amount of transferred heat leads to
the heat exchangers on the hot side must bea large increase in pressure. Considering this issue,
made of alloys retaining considerable strength athelium would be the best gas because of its very
temperature and also not corrode or creep.low heat capacity. Air is a viable working fluid, but
Regeneratorthe oxygen in a highly pressurized air engine can
Main article: Regenerative heat exchangercause fatal accidents caused by lubricating oil
In a Stirling engine, the regenerator is an internalexplosions. Following one such accident Philips
heat exchanger and temporary heat store placedpioneered the use of other gases to avoid such
between the hot and cold spaces such that therisk of explosions.
working fluid passes through it first in oneHydrogen's low viscosity and high thermal
direction then the other. Its function is to retainconductivity make it the most powerful working
within the system that heat which wouldgas, primarily because the engine can run faster
otherwise be exchanged with the environment atthan with other gases. However, due to hydrogen
temperatures intermediate to the maximum andabsorption, and given the high diffusion rate
minimum cycle temperatures, thus enabling theassociated with this low molecular weight gas,
thermal efficiency of the cycle to approach theparticularly at high temperatures, H2 will leak
limiting Carnot efficiency defined by those maximathrough the solid metal of the heater. Diffusion
and minima.through carbon steel is too high to be practical,
The primary effect of regeneration in a Stirlingbut may be acceptably low for metals such as
engine is to greatly increase the thermal efficiencyaluminum, or even stainless steel. Certain ceramics
by 'recycling' internally heat which would otherwisealso greatly reduce diffusion. Hermetic pressure
pass through the engine irreversibly. As avessel seals are necessary to maintain pressure
secondary effect, increased thermal efficiencyinside the engine without replacement of lost gas.
promises a higher power output from a given setFor HTD engines, auxiliary systems may need to
of hot and cold end heat exchangers (since it isbe added to maintain high pressure working fluid.
these which usually limit the engine's heatThese systems can be a gas storage bottle or a
throughput), though, in practice this additionalgas generator. Hydrogen can be generated by
power may not be fully realized as the additionalelectrolysis of water, the action of steam on red
"dead space" (unswept volume) and pumping losshot carbon-based fuel, by gasification of
inherent in practical regenerators tends to havehydrocarbon fuel, or by the reaction of acid on
the opposite effect.metal. Hydrogen can also cause the embrittlement
The regenerator works like a thermal capacitor.of metals. Hydrogen is a flammable gas, which is a
The ideal regenerator has very high thermalsafety concern, although the quantity used is
capacity, very low thermal conductivity parallel tovery small, and it is arguably safer than other
fluid flow, very high thermal conductivitycommonly used flammable gases.
perpendicular to fluid flow, almost no volume, andMost technically advanced Stirling engines, like
introduces no friction to the working fluid. As thethose developed for United States government
regenerator approaches these ideal limits, Stirlinglabs, use helium as the working gas, because it
engine efficiency increases.functions close to the efficiency and power
The design challenge for a Stirling enginedensity of hydrogen with fewer of the material
regenerator is to provide sufficient heat transfercontainment issues. Helium is inert, which removes
capacity without introducing too much additionalall risk of flammability, both real and perceived.
internal volume ('dead space') or flow resistance,Helium is relatively expensive, and must be
both of which tend to reduce power andsupplied as bottled gas. One test showed
efficiency. These inherent design conflicts are onehydrogen to be 5% (absolute) more efficient than
of many factors which limit the efficiency ofhelium (24% relatively) in the GPU-3 Stirling engine.
practical Stirling engines. A typical design is a stackThe researcher Allan Organ demonstrated that a
of fine metal wire meshes, with low porosity towell-designed air engine is theoretically just as
reduce dead space, and with the wire axesefficient as a helium or hydrogen engine, but
perpendicular to the gas flow to reducehelium and hydrogen engines are several times
conduction in that direction and to maximizemore powerful per unit volume.
convective heat transfer.Some engines use air or nitrogen as the working
The regenerator is the key component inventedfluid. These gases have much lower power
by Robert Stirling and its presence distinguishes adensity (which increases engine costs), but they
true Stirling engine from any other closed cycleare more convenient to use and they minimize
hot air engine. However, many engines with nothe problems of gas containment and supply
apparent regenerator may still be correctly(which decreases costs). The use of compressed
described as Stirling engines as in the simple betaair in contact with flammable materials or
and gamma configurations with a 'loose fitting'substances such as lubricating oil, introduces an
displacer, the surfaces of the displacer and itsexplosion hazard, because compressed air
cylinder will cyclically exchange heat with thecontains a high partial pressure of oxygen.
working fluid providing a significant regenerativeHowever, oxygen can be removed from air
effect particularly in small, low-pressure engines.through an oxidation reaction or bottled nitrogen
The same is true of the passage connecting thecan be used, which is nearly inert and very safe.
hot and cold cylinders of an alpha configurationOther possible lighter-than-air gases include:
engine.methane, and ammonia.
CoolerApplications
In small, low power engines this may simplyIt has been suggested that this section be split
consist of the walls of the cold space(s), butinto a new article titled applications of the Stirling
where larger powers are required a cooler using aengine. (Discuss)
liquid like water is needed in order to transferA desktop alpha Stirling engine. The working fluid
sufficient heat.in this engine is air. The hot heat exchange is the
Heat sinkglass cylinder on the right, and the cold heat
The heat sink is typically the environment atexchanger is the finned cylinder on the top. This
ambient temperature. In the case of medium toengine uses a small alcohol burner (bottom right)
high power engines, a radiator is required toas a heat source
transfer the heat from the engine to the ambientHeating and cooling
air. Marine engines can use the ambient water. InIf supplied with mechanical power, a Stirling engine
the case of combined heat and power systems,can function in reverse as a heat pump for
the engine's cooling water is used directly orheating or cooling. Experiments have been
indirectly for heating purposes.performed using wind power driving a Stirling
Alternatively, heat may be supplied at ambientcycle heat pump for domestic heating and air
and the heat sink maintained at a lowerconditioning. In the late 1930s, the Philips
temperature by such means as cryogenic fluidCorporation of the Netherlands successfully utilized
(see Liquid nitrogen economy) or ice water.the Stirling cycle in cryogenic applications.
ConfigurationsCombined heat and power
There are two major types of Stirling enginesThermal power stations on the electric grid use
that are distinguished by the way they move thefuel to produce electricity, however there are
air between the hot and cold sides of the cylinder:large quantities of waste heat produced which
The two piston alpha type design has pistons inoften go unused. In other situations, high-grade
independent cylinders, and gas is driven betweenfuel is burned at high temperature for a low
the hot and cold spaces.temperature application. According to the second
The displacement type Stirling engines, known aslaw of thermodynamics, a heat engine can
beta and gamma types, use an insulatedgenerate power from this temperature difference.
mechanical displacer to push the working gasIn a CHP system, the high temperature primary
between the hot and cold sides of the cylinder.heat enters the Stirling engine heater, then some
The displacer is large enough to thermally insulateof the energy is converted to mechanical power
the hot and cold sides of the cylinder and displacein the engine, and the rest passes through to the
a large quantity of gas. It must have enough of acooler, where it exits at a low temperature. The
gap between the displacer and the cylinder wall to"waste" heat actually comes from engine's main
allow gas to easily flow around the displacer.cooler, and possibly from other sources such as
Alpha Stirlingthe exhaust of the burner, if there is one.
An alpha Stirling contains two power pistons inIn a combined heat and power (CHP) system,
separate cylinders, one hot and one cold. The hotmechanical or electrical power is generated in the
cylinder is situated inside the high temperatureusual way, however, the waste heat given off by
heat exchanger and the cold cylinder is situatedthe engine is used to supply a secondary heating
inside the low temperature heat exchanger. Thisapplication. This can be virtually anything that uses
type of engine has a high power-to-volume ratiolow temperature heat. It is often a pre-existing
but has technical problems due to the usually highenergy use, such as commercial space heating,
temperature of the hot piston and the durabilityresidential water heating, or an industrial process.
of its seals. In practice, this piston usually carries aThe power produced by the engine can be used
large insulating head to move the seals awayto run an industrial or agricultural process, which in
from the hot zone at the expense of someturn creates biomass waste refuse that can be
additional dead space.used as free fuel for the engine, thus reducing
Action of an alpha type Stirling enginewaste removal costs. The overall process can be
The following diagrams do not show internal heatefficient and cost effective.
exchangers in the compression and expansionDisenco, a UK based company are going through
spaces, which are needed to produce power. Athe final stages of development of their
regenerator would be placed in the pipeHomePowerPlant. Unlike other m-CHP appliances
connecting the two cylinders. The crankshaft hascoming to market the HPP generates 3 kW of
also been omitted.electrical and 15 kW of thermal energy, making
1. Most of the working gas is in contact with thethis appliance suitable for both the domestic and
hot cylinder walls, it has been heated andSME markets.
expansion has pushed the cold piston to theWhisperGen, a New Zealand firm with offices in
bottom of its travel in the cylinder. The expansionChristchurch, has developed an "AC Micro
continues in the hot cylinder, which is 90 behindCombined Heat and Power" Stirling cycle engine.
the cold piston in its cycle, extracting more workThese microCHP units are gas-fired central heating
from the hot gas.boilers which sell unused power back into the
2. The gas is now at its maximum volume. Theelectricity grid. WhisperGen announced in 2004
hot cylinder piston begins to move most of thethat they were producing 80,000 units for the
gas into the cold cylinder, where it cools and theresidential market in the United Kingdom. A
pressure drops.20 unit trial in Germany started in 2006.
3. Almost all the gas is now in the cold cylinderSolar power generation
and cooling continues. The cold piston, powered byPlaced at the focus of a parabolic mirror a Stirling
flywheel momentum (or other piston pairs on theengine can convert solar energy to electricity with
same shaft) compresses the remaining part ofan efficiency better than non-concentrated
the gas.photovoltaic cells, and comparable to
4. The gas reaches its minimum volume, and it willConcentrated Photo Voltaics. On August 11, 2005,
now expand in the hot cylinder where it will beSouthern California Edison announced an
heated once more, driving the hot piston in itsagreement with Stirling Energy Systems to
power stroke.purchase electricity created using over 30,000
The complete alpha type Stirling cycleSolar Powered Stirling Engines over a twenty year
Beta Stirlingperiod sufficient to generate 850 MW of
A beta Stirling has a single power piston arrangedelectricity. These systems, on an 8,000 acre
within the same cylinder on the same shaft as a(19 km2) solar farm will use mirrors to direct and
displacer piston. The displacer piston is a loose fitconcentrate sunlight onto the engines which will in
and does not extract any power from theturn drive generators. Construction is expected to
expanding gas but only serves to shuttle thebegin on the farm in 2010, although there are
working gas from the hot heat exchanger to thedisputes over the project due to concerns of
cold heat exchanger. When the working gas isenvironmental impact on animals living on the site.
pushed to the hot end of the cylinder it expandsStirling cryocoolers
and pushes the power piston. When it is pushedAny Stirling engine will also work in reverse as a
to the cold end of the cylinder it contracts andheat pump; when a motion is applied to the shaft,
the momentum of the machine, usually enhanceda temperature difference appears between the
by a flywheel, pushes the power piston the otherreservoirs. The essential mechanical components
way to compress the gas. Unlike the alpha type,of a Stirling cryocooler are identical to a Stirling
the beta type avoids the technical problems ofengine. In both the engine and the heat pump,
hot moving seals.heat flows from the expansion space to the
Action of a beta type Stirling enginecompression space; however, input work is
Again, the following diagrams do not show internalrequired in order for heat to flow against a
heat exchangers or a regenerator, which wouldthermal gradient, specifically when the
be placed in the gas path around the displacer.compression space is hotter than the expansion
1. Power piston (dark grey) has compressed thespace. The external side of the expansion-space
gas, the displacer piston (light grey) has moved soheat exchanger may be placed inside a thermally
that most of the gas is adjacent to the hot heatinsulated compartment such as a vacuum flask.
exchanger.Heat is in effect pumped out of this
2. The heated gas increases in pressure andcompartment, through the working gas of the
pushes the power piston to the farthest limit ofcryocooler and into the compression space. The
the power stroke.compression space will be above ambient
3. The displacer piston now moves, shunting thetemperature, and so heat will flow out into the
gas to the cold end of the cylinder.environment.
4. The cooled gas is now compressed by theOne of their modern uses is in cryogenics, and to
flywheel momentum. This takes less energy, sincea lesser extent, refrigeration. At typical
when it is cooled its pressure dropped.refrigeration temperatures, Stirling coolers are
The complete beta type Stirling cyclegenerally not economically competitive with the
Gamma Stirlingless expensive mainstream Rankine cooling
A gamma Stirling is simply a beta Stirling in whichsystems, even though they are typically 20%
the power piston is mounted in a separatemore energy efficient. However, below about
cylinder alongside the displacer piston cylinder, but40  to 30 C, Rankine cooling is not effective
is still connected to the same flywheel. The gas inbecause there are no suitable refrigerants with
the two cylinders can flow freely between themboiling points this low. Stirling cryocoolers are able
and remains a single body. This configurationto "lift" heat down to 200 C (73 K), which is
produces a lower compression ratio but issufficient to liquefy air (oxygen, nitrogen and
mechanically simpler and often used inargon). They can go as low as 4060 K,
multi-cylinder Stirling engines.depending on the particular design. Cryocoolers for
Other typesthis purpose are more or less competitive with
Other Stirling configurations continue to interestother cryocooler technologies. The coefficient of
engineers and inventors. Tom Peat conceived of aperformance at cryogenic temperatures is
configuration that he likes to call a "Delta" type,typically 0.040.05 (corresponding to a 45%
although currently this designation is not widelyefficiency). Empirically, the devices show a linear
recognized, having a displacer and two powertrend, where typically the COP = 0.0015 Tc 
pistons, one hot and one cold.0.065, where Tc is the cryogenic temperature. At
There is also the rotary Stirling engine whichthese temperatures, solid materials have lower
seeks to convert power from the Stirling cyclevalues for specific heat, so the regenerator must
directly into torque, similar to the rotarybe made out of unexpected materials, such as
combustion engine. No practical engine has yetcotton.[citation needed]
been built but a number of concepts, models andThe first Stirling cycle cryocooler was developed
patents have been produced, such as theat Philips in the 1950s and commercialized in such
Quasiturbine engine.places as liquid air production plants. The Philips
Another alternative is the Fluidyne engine (FluidyneCryogenics business evolved until it was split off in
heat pump), which use hydraulic pistons to1990 to form the Stirling Cryogenics BV, The
implement the Stirling cycle. The work producedNetherlands. This company is still active in the
by a Fluidyne engine goes into pumping the liquid.development and manufacturing of Stirling
In its simplest form, the engine contains a workingcryocoolers and cryogenic cooling systems.
gas, a liquid and two non-return valves.A wide variety of smaller size Stirling cryocoolers
The Ringbom engine concept published in 1907 hasare commercially available for tasks such as the
no rotary mechanism or linkage for the displacer.cooling of electronic sensors and sometimes
This is instead driven by a small auxiliary piston,microprocessors. For this application, Stirling
usually a thick displacer rod, with the movementcryocoolers are the highest performance
limited by stops.technology available, due to their ability to lift heat
Free piston enginesefficiently at very low temperatures. They are
Various Free-Piston Stirling Configurations... F."freesilent, vibration-free, and can be scaled down to
cylinder", G. Fluidyne, H. "double-acting" Stirlingsmall sizes, and have very high reliability and low
(typically 4 cylinders)maintenance. As of 2009, cryocoolers are
"Free piston" Stirling engines include those withconsidered to be the only commercially successful
liquid pistons and those with diaphragms asStirling devices.[citation needed]
pistons. In a "free piston" device, energy may beHeat pump
added or removed by an electrical linearA Stirling heat pump is very similar to a Stirling
alternator, pump or other coaxial device. Thiscryocooler, the main difference being that it
sidesteps the need for a linkage, and reduces theusually operates at room temperature and its
number of moving parts. In some designs frictionprincipal application to date is to pump heat from
and wear are nearly eliminated by the use ofthe outside of a building to the inside, thus cheaply
non-contact gas bearings or very preciseheating it.
suspension through planar springs.As with any other Stirling device, heat flows from
In the early 1960s, W.T. Beale invented a freethe expansion space to the compression space;
piston version of the Stirling engine in order tohowever, in contrast to the Stirling engine, the
overcome the difficulty of lubricating the crankexpansion space is at a lower temperature than
mechanism. While the invention of the basic freethe compression space, so instead of producing
piston Stirling engine is generally attributed towork, an input of mechanical work is required by
Beale, independent inventions of similar types ofthe system (in order to satisfy the second law of
engines were made by E.H. Cooke-Yarboroughthermodynamics). When the mechanical work for
and C. West at the Harwell Laboratories of thethe heat pump is provided by a second Stirling
UKAERE. G.M. Benson also made important earlyengine, then the overall system is called a
contributions and patented many novel free-piston"heat-driven heatpump".
configurations.The expansion side of the heat pump is thermally
What appears to be the first mention of a Stirlingcoupled to the heat source, which is often the
cycle machine using freely moving components isexternal environment. The compression side of
a British patent disclosure in 1876. This machinethe Stirling device is placed in the environment to
was envisaged as a refrigerator (i.e., the reversedbe heated, for example a building, and heat is
Stirling cycle). The first consumer product to utilize"pumped" into it. Typically there will be thermal
a free piston Stirling device was a portableinsulation between the two sides so there will be a
refrigerator manufactured by Twinbirdtemperature rise inside the insulated space.
Corporation of Japan and offered in the US byHeat pumps are by far the most energy-efficient
Coleman in 2004.types of heating systems. Stirling heat pumps also
Thermoacoustic cycleoften have a higher coefficient of performance
Thermoacoustic devices are very different fromthan conventional heat pumps. To date, these
Stirling devices, although the individual pathsystems have seen limited commercial use;
travelled by each working gas molecule doeshowever, use is expected to increase along with
follow a real Stirling cycle. These devices includemarket demand for energy conservation, and
the thermoacoustic engine and thermoacousticadoption will likely be accelerated by technological
refrigerator. High-amplitude acoustic standingrefinements.
waves cause compression and expansionMarine engines
analogous to a Stirling power piston, whileThe Swedish shipbuilder Kockums has built 8
out-of-phase acoustic travelling waves causesuccessful Stirling powered submarines since the
displacement along a temperature gradient,late 1980s. They carry compressed oxygen to
analogous to a Stirling displacer piston. Thus aallow fuel combustion whilst submerged that
thermoacoustic device typically does not have aprovides heat for the Stirling engine. They are
displacer, as found in a beta or gamma Stirling.currently used on submarines of the Gotland and
HistorySdermanland classes. They are the first
Illustration to Robert Stirling's 1816 patentsubmarines in the world to feature a Stirling
application of the air engine design which laterengine air-independent propulsion (AIP) system,
came to be known as the Stirling Enginewhich extends their underwater endurance from a
The Stirling engine (or Stirling's air engine as it wasfew days to two weeks. This capability has
known at the time) was invented and patentedpreviously only been available with nuclear
by Robert Stirling in 1816. It followed earlierpowered submarines.
attempts at making an air engine but wasA similar system also powers the Japanese Sry
probably the first to be put to practical use whenclass submarine.
in 1818 an engine built by Stirling was employedNuclear power
pumping water in a quarry. The main subject ofThere is a potential for nuclear-powered Stirling
Stirling's original patent was a heat exchangerengines in electric power generation plants.
which he called an "economiser" for itsReplacing the steam turbines of nuclear power
enhancement of fuel economy in a variety ofplants with Stirling engines might simplify the plant,
applications. The patent also described in detail theyield greater efficiency, and reduce the
employment of one form of the economiser in hisradioactive byproducts. A number of breeder
unique closed-cycle air engine design in whichreactor designs use liquid sodium as coolant. If the
application it is now generally known as aheat is to be employed in a steam plant, a water
'regenerator'. Subsequent development by Robertsodium heat exchanger is required, which raises
Stirling and his brother James, an engineer,some concern as sodium reacts violently with
resulted in patents for various improvedwater. A Stirling engine eliminates the need for
configurations of the original engine includingwater anywhere in the cycle.
pressurization which had by 1843 sufficientlyUnited States government labs have developed a
increased power output to drive all the machinerymodern Stirling engine design known as the Stirling
at a Dundee iron foundry.Radioisotope Generator for use in space
Though it has been disputed it is widely supposedexploration. It is designed to generate electricity
that as well as saving fuel the inventors werefor deep space probes on missions lasting
motivated to create a safer alternative to thedecades. The engine uses a single displacer to
steam engines of the time, whose boilersreduce moving parts and uses high energy
frequently exploded causing many injuries andacoustics to transfer energy. The heat source is a
fatalities. The need for Stirling engines to run atdry solid nuclear fuel slug and the heat sink is
very high temperatures to maximize power andspace itself.
efficiency exposed limitations in the materials ofAutomotive engines
the day and the few engines that were built inIt is often claimed that the Stirling engine has too
those early years suffered unacceptably frequentlow a power/weight ratio, too high a cost, and
failures (albeit with far less disastroustoo long a starting time for automotive
consequences than a boiler explosion) - forapplications. They also have complex and
example, the Dundee foundry engine wasexpensive heat exchangers. A Stirling cooler must
replaced by a steam engine after three hotreject twice as much heat as an Otto engine or
cylinder failures in four years.Diesel engine radiator. The heater must be made
Later nineteenth centuryof stainless steel, exotic alloy or ceramic to
A typical late nineteenth/early twentieth centurysupport high heater temperatures needed for high
water pumping engine by the Rider-Ericssonpower density, and to contain hydrogen gas that
Engine Companyis often used in automotive Stirlings to maximize
Subsequent to the failure of the Dundee foundrypower. The main difficulties involved in using the
engine there is no record of the Stirling brothersStirling engine in an automotive application are
having any further involvement with air enginestartup time, acceleration response, shutdown
development and the Stirling engine never againtime, and weight, not all of which have
competed with steam as an industrial scale powerready-made solutions. However, a modified Stirling
source (steam boilers were becoming safer andengine has been recently introduced that uses
steam engines more efficient, thus presenting lessconcepts taken from a patented
of a target to rival prime movers). However,internal-combustion engine with a sidewall
from about 1860 smaller engines of the Stirlingcombustion chamber (U.S. patent 7,387,093) that
hot air type were produced in substantial numberspromises to overcome the deficient
finding applications wherever a reliable source ofpower-density and specific-power problems, as
low to medium power was required, such aswell as the slow acceleration-response problem
raising water or providing air for church organs.inherent in all Stirling engines. However, it could be
These generally operated at lower temperaturespossible to use these in co-generation systems
so as not to tax available materials, so werethat use waste heat from a conventional piston
relatively inefficient. But their selling point was that,or gas turbine engine's exhaust and use this either
unlike a steam engine, they could be operatedto power the ancillaries (eg: the alternator) or
safely by anybody capable of managing a fire.even as a turbo-compound system that adds
Several types remained in production beyond thepower and torque to the crankshaft.
end of the century, but apart from a few minorAt least two automobiles exclusively powered by
mechanical improvements the design of theStirling engines were developed by NASA, as well
Stirling engine in general stagnated during thisas earlier projects by the Ford Motor Company
period.and American Motors Corporation. The NASA
Twentieth century revivalvehicles were designed by contractors and
During the early part of the twentieth century thedesignated MOD I and MOD II. The MOD II
role of the Stirling engine as a "domestic motor"replaced the normal spark-ignition engine in a 1985
was gradually taken over by the electric motor4-door Chevrolet Celebrity Notchback. In the 1986
and small internal combustion engines. By the lateMOD II Design Report (Appendix A) the results
1930s it was largely forgotten, only produced forshow that highway gas mileage was increased
toys and a few small ventilating fans. At this timefrom 40 to 58 mpg and urban mileage from 26
Philips was seeking to expand sales of its radiosto 33 mpg with no change in vehicle gross
into areas where electricity was unavailable andweight. Startup time in the NASA vehicle maxed
the supply of batteries uncertain. Philips'out at 30 seconds,[citation needed] while Ford's
management decided that a low-power portableresearch vehicle used an internal electric heater to
generator would facilitate such sales and tasked ajump-start the vehicle, allowing it to start in only a
group of engineers at the company's research labfew seconds.
in Eindhoven to evaluate alternatives.Electric vehicles
After a systematic comparison of various primeMany people believe that Stirling engines as part
movers, the Stirling engine's quiet operation (bothof a hybrid electric drive system can bypass all of
audibly and in terms of radio interference) andthe perceived design challenges or disadvantages
ability to run on a variety of heat sourcesof a non-hybrid Stirling automobile.
(common lamp oil  "cheap and availableIn November 2007, a prototype hybrid car using
everywhere"  was favoured), the team pickedsolid biofuel and a Stirling engine was announced
Stirling. They were also aware that, unlike steamby the Precer project in Sweden.
and internal combustion engines, virtually noThe Manchester Union Leader reports that Dean
serious development work had been carried outKamen has developed a series plug-in hybrid car
on the Stirling engine for many years andusing a Ford Think. DEKA, Kamen's technology
asserted that modern materials and know-howcompany in the Manchester Millyard, has recently
should enable great improvements.demonstrated an electric car, the DEKA Revolt,
Philips MP1002CA Stirling generator of 1951that can go approximately 60 miles (97 km) on
Encouraged by their first experimental engine,a single charge of its lithium battery.
which produced 16 W of shaft power from aAircraft engines
bore and stroke of 30mm 25mm, Philips began aStirling engines may hold theoretical promise as
development program. This work continuedaircraft engines, if high power density and low
throughout World War II and by the late 1940scost can be achieved. They are quieter, less
handed over the Type 10 to Philips' subsidiarypolluting, gain efficiency with altitude due to lower
Johan de Witt in Dordrecht to be "productionised"ambient temperatures, are more reliable due to
and incorporated into a generator set. The result,fewer parts and the absence of an ignition
rated at 200 W from a bore and stroke of 55system, produce much less vibration (airframes
mm x 27 mm, was designated MP1002CAlast longer) and safer, less explosive fuels may be
(known as the "Bungalow set"). Production of anused. However, the Stirling engine often has low
initial batch of 250 began in 1951, but it becamepower density compared to the commonly used
clear that they could not be made at aOtto engine and Brayton cycle gas turbine. This
competitive price and the advent of transistorissue has been a point of contention in
radios with their much lower power requirementsautomobiles, and this performance characteristic is
meant that the original rationale for the set waseven more critical in aircraft engines.
disappearing. Approximately 150 of these setsLow temperature difference engines
were eventually produced. Some found their wayA low temperature difference Stirling Engine
into university and college engineeringshown here running on the heat from a warm
departments around the world giving generationshand
of students a valuable introduction to the StirlingA low temperature difference (Low Delta T, or
engine.LTD) Stirling engine will run on any low
Philips went on to develop experimental Stirlingtemperature differential, for example the
engines for a wide variety of applications anddifference between the palm of a hand and room
continued to work in the field until the late 1970s,temperature or room temperature and an ice
but only achieved commercial success with thecube. A record of only 0.5 K was achieved in
'reversed Stirling engine' cryocooler. They did1990. See which also shows an animated drawing
however take out a large number of patents andof this type. Usually they are designed in a
amass a wealth of information which they licensedgamma configuration, for simplicity, and without a
to other companies and which formed the basisregenerator, although some have slits in the
of much of the development work in the moderndisplacer typically made of foam, for partial
era.regeneration. They are typically unpressurized,
Towards the end of the century, severalrunning at pressure close to 1 atmosphere. The
companies developed research prototypes ofpower produced is less than 1 W, and they are
medium-power engines and in some cases smallintended for demonstration purposes only. They
production series. A mass market was neverare sold as toys and educational models.
achieved because the unit costs were very highLarger (typically 1 m square) low temperature
and some technical problems remained unsolved.engines have been built for pumping water using
Now in the twenty-first century, somedirect sunlight with minimal or no magnification.
commercial success is starting to become feasible,Other recent applications
notably with combined heat and power units.Acoustic Stirling Heat Engine
In the field of low-power engines, many plans, kitsLos Alamos National Laboratory has developed an
and finished engines are available commercially."Acoustic Stirling Heat Engine" with no moving
Apart from traditional small models and someparts. It converts heat into intense acoustic
larger machines for real use, a new type waspower which (quoted from given source) "can be
introduced in the 1980s: the low-temperature flatused directly in acoustic refrigerators or
plate type.pulse-tube refrigerators to provide heat-driven
Theoryrefrigeration with no moving parts, or ... to
Main article: Stirling cyclegenerate electricity via a linear alternator or other
A pressure/volume graph of the idealized Stirlingelectro-acoustic power transducer".
cycleMicroCHP
The idealised Stirling cycle consists of fourWhisperGen, a New Zealand based company has
thermodynamic processes acting on the workingdeveloped stirling engines that can be powered by
fluid:natural gas or diesel. Recently an agreement has
Isothermal Expansion. The expansion-space andbeen signed with Mondragon Corporacin
associated heat exchanger are maintained at aCooperativa, a Spanish firm, to produce
constant high temperature, and the gasWhisperGen's microCHP and make them available
undergoes near-isothermal expansion absorbingfor the domestic market in Europe. Some time
heat from the hot source.ago E.ON UK announced a similar initiative for the
Constant-Volume (known as isovolumetric orUK. Stirling engines would supply the client with hot
isochoric) heat-removal. The gas is passed throughwater, space heating and a surplus electric power
the regenerator, where it cools transferring heatthat could be fed back into the electric grid.
to the regenerator for use in the next cycle.However the preliminary results of an Energy
Isothermal Compression. The compression spaceSaving Trust review of the performance of the
and associated heat exchanger are maintained atWhisperGen microCHP units suggested that their
a constant low temperature so the gasadvantages were marginal at best in most homes.
undergoes near-isothermal compression rejectingHowever another author shows that that Stirling
heat to the cold sinkengined microgeneration is the most cost
Constant-Volume (known as isovolumetric oreffective of various microgeneration technologies
isochoric) heat-addition. The gas passes backin terms of reducing CO2.
through the regenerator where it recovers muchChip cooling
of the heat transferred in 2 to 3, heating up onMSI (Taiwan) recently developed a miniature
its way to the expansion space.Stirling engine cooling system for personal
Theoretical thermal efficiency equals that of thecomputer chips that uses the waste heat from
hypothetical Carnot cycle - i.e. the highestthe chip to drive a fan.
efficiency attainable by any heat engine. However,Alternatives
though it is useful for illustrating general principles,Alternative thermal energy harvesting devices
the text book cycle it is a long way frominclude the Thermogenerator. Thermogenerators
representing what is actually going on inside aallow less efficient conversion (5-10%) but may
practical Stirling engine and should not be regardedbe useful in situations where the end product
as a basis for analysis. In fact it has been arguedneeds to be electricity and where a small
that its indiscriminate use in many standard booksconversion device is a critical factor.
on engineering thermodynamics has done aPhoto gallery
disservice to the study of Stirling engines inPreserved examples of antique Rider hot air
general.engines - an alpha configuration Stirling
Other real-world issues reduce the efficiency ofSee also
actual engines, due to limits of convective heatThermomechanical generator
transfer, and viscous flow (friction). There areBeale Number
also practical mechanical considerations, forWest Number
instance a simple kinematic linkage may beSchmidt number
favoured over a more complex mechanismFluidyne engine
needed to replicate the idealized cycle, andStirling radioisotope generator
limitations imposed by available materials such asRelative cost of electricity generated by different
non-ideal properties of the working gas, thermalsources
conductivity, tensile strength, creep, ruptureDistributed generation
strength, and melting point.References
Operation^ "Stirling Engines", G. Walker (1980), Clarenden
Since the Stirling engine is a closed cycle, itPress, Oxford, page 1: "A Stirling engine is a
contains a fixed mass of gas called the "workingmechanical device which operates on a *closed*
fluid", most commonly air, hydrogen or helium. Inregenerative thermodynamic cycle, with cyclic
normal operation, the engine is sealed and no gascompression and expansion of the working fluid at
enters or leaves the engine. No valves aredifferent temperature levels."
required, unlike other types of piston engines. The^ T. Finkelstein; A.J. Organ (2001), Chapters
Stirling engine, like most heat engines, cycles2&3
through four main processes: cooling, compression,^ Sleeve notes from A.J. Organ (2007)
heating and expansion. This is accomplished by^ F. Starr (2001)
moving the gas back and forth between hot and^ C.M. Hargreaves (1991), Chapter 2.5
cold heat exchangers, often with a regenerator^ "A new Prime Mover", J.F.J. Malone, Journal of
between the heater and cooler. The hot heatthe Royal Society of Arts, June 12, 1931,
exchanger is in thermal contact with an externalreprinted with further material as "Secrets of the
heat source, such as a fuel burner, and the coldMalone Heat Engine, Richard A. Ford (1983),
heat exchanger being in thermal contact with anLindsay Publications, Bradley IL
external heat sink, such as air fins. A change in^ W.R. Martini (1983), p.6
gas temperature will cause a corresponding^ W.H. Brandhorst; J.A. Rodiek (2005)
change in gas pressure, while the motion of the^ B. Kongtragool; S. Wongwises (2003)
piston causes the gas to be alternately expanded^ A.J. Organ (1992), p.58
and compressed.^ Y. Timoumi; I. Tlili; S. Ben Nasrallah (2007)
The gas follows the behaviour described by the^ K. Hirata (1998)
gas laws which describe how a gas' pressure,^ M.Keveney (2000a)
temperature and volume are related. When the^ M. Keveney (2000b)
gas is heated, because it is in a sealed chamber,^ D.Liao (a)
the pressure rises and this then acts on the^ Quasiturbine Agence (a)
power piston to produce a power stroke. When^ "Ringbom Stirling Engines", James R. Senft,
the gas is cooled the pressure drops and this1993, Oxford University Press
means that less work needs to be done by the^ "Free-Piston Stirling Engines", G. Walker et
piston to compress the gas on the return stroke,al.,Springer 1985, reprinted by Stirling Machine
thus yielding a net power output.World, West Richland WA
When one side of the piston is open to the^ "The Thermo-mechanical Generator...", E.H.
atmosphere, the operation is slightly different. AsCooke-Yarborough, (1967) Harwell Memorandum
the sealed volume of working gas comes inNo. 1881 and (1974) Proc. I.E.E., Vol. 7, pp. 749-751
contact with the hot side, it expands, doing work^ G.M. Benson (1973 and 1977)
on both the piston and on the atmosphere. When^ D. Postle (1873)
the working gas contacts the cold side, its^ R. Sier (1999)
pressure drops below atmospheric pressure and^ T. Finkelsteinl; A.J. Organ (2001), Chapter 2.2
the atmosphere pushes on the piston and does^ English patent 4081 of 1816 Improvements for
work on the gas.diminishing the consumption of fuel and in
To summarize, the Stirling engine uses theparticular an engine capable of being applied to the
temperature difference between its hot end andmoving (of)machinery on a principle entirely new.
cold end to establish a cycle of a fixed mass ofas reproduced in part in C.M. Hargreaves (1991),
gas, heated and expanded, and cooled andAppendix B, with full transcription of text in R. Sier
compressed, thus converting thermal energy into(1995), p.??
mechanical energy. The greater the temperature^ R. Sier (1995), p. 93
difference between the hot and cold sources, the^ A.J. Organ (2008a)
greater the thermal efficiency. The maximum^ Excerpt from a paper presented by James
theoretical efficiency is equivalent to the CarnotStirling in June 1845 to the Institute of Civil
cycle, however the efficiency of real engines isEngineers. As reproduced in R. Sier (1995), p.92.
less than this value due to friction and other^ A. Nesmith (1985)
losses.^ R. Chuse; B. Carson (1992), Chapter 1
Video showing the compressor and displacer of a^ R. Sier (1995), p.94
very small Stirling Engine in action^ T. Finkelstein; A.J. Organ (2001), p.30
Very low-power engines have been built which will^ Hartford Steam Boiler (a)
run on a temperature difference of as little as 0.5^ T. Finkelstein; A.J. Organ (2001), Chapter 2.4
K.^ The 1906 Rider-Ericsson Engine Co. catalog
Pressurizationclaimed that "any gardener or ordinary domestic
In most high power Stirling engines, both thecan operate these engines and no licensed or
minimum pressure and mean pressure of theexperienced engineer is required".
working fluid are above atmospheric pressure.^ T. Finkelstein; A.J. Organ (2001), p.64
This initial engine pressurization can be realized by^ T. Finkelstein; A.J. Organ (2001), p.34
a pump, or by filling the engine from a^ T. Finkelstein; A.J. Organ (2001), p.55
compressed gas tank, or even just by sealing the^ C.M. Hargreaves (1991), pp.2830
engine when the mean temperature is lower than^ Philips Technical Review Vol.9 No.4 page 97
the mean operating temperature. All of these(1947)
methods increase the mass of working fluid in the^ C.M. Hargreaves (1991), Fig. 3
thermodynamic cycle. All of the heat exchangers^ C.M. Hargreaves (1991), p.61
must be sized appropriately to supply the^ Letter dated March 1961 from Research and
necessary heat transfer rates. If the heatControl Instruments Ltd. London WC1 to North
exchangers are well designed and can supply theDevon Technical College, offering "remaining
heat flux needed for convective heat transfer,stocks...... to institutions such as yourselves..... at a
then the engine will in a first approximationspecial price of 75 nett"
produce power in proportion to the mean^ C.M. Hargreaves (1991), p.77
pressure, as predicted by the West number, and^ T. Finkelstein; A.J. Organ (2001), Page 66 &
Beale number. In practice, the maximum pressure229
is also limited to the safe pressure of the^ A.J. Organ (1992), Chapter 3.1 - 3.2
pressure vessel. Like most aspects of Stirling^ "An Introduction to Low Temperature
engine design, optimization is multivariate, andDifferential Stirling Engines", James R. Senft, 1996,
often has conflicting requirements.Moriya Press
Lubricants and friction^ a b A.J. Organ (1997), p.??
A modern Stirling engine and generator set with^ a b c C.M. Hargreaves (1991), p.??
55 kW electrical output, for combined heat and^ a b WADE (a)
power applications^ Krupp and Horn. Earth: The Sequel. p. 57
At high temperatures and pressures, the oxygen^ a b Kockums (a)
in air-pressurized crankcases, or in the working^ Z. Herzog (2008)
gas of hot air engines, can combine with the^ K. Hirata (1997)
engine's lubricating oil and explode. At least one^ BBC News (2003), "The boiler is based on the
person has died in such an explosion.Stirling engine, dreamed up by the Scottish
Lubricants can also clog heat exchangers,inventor Robert Stirling in 1816. [...] The technical
especially the regenerator. For these reasons,name given to this particular use is Micro
designers prefer non-lubricated, low-coefficient ofCombined Heat and Power or Micro CHP."
friction materials (such as rulon or graphite), with^ A.J. Organ (2008b)
low normal forces on the moving parts, especially^ L.G. Thieme (1981)
for sliding seals. Some designs avoid sliding^ C.M. Hargreaves (1991), p.63
surfaces altogether by using diaphragms for^ a b by: admin (2008-11-06). "What is
sealed pistons. These are some of the factorsMicrogeneration? And what is the most cost
that allow Stirling engines to have lowereffective in terms of CO2 reduction | Claverton
maintenance requirements and longer life thanGroup". Retrieved 2009-07-24. 
internal-combustion engines.^ Pure Energy Systems (2005)
Analysis^ "Tessera Solar World-Scale Power Projects".
Comparison with internal combustion enginesTessera Solar. Retrieved 2010-01-21. 
In contrast to internal combustion engines, Stirling^ "Battle Brewing Over Giant Desert Solar Farm".
engines have the potential to use renewable heatNew York Times. 2009-08-05. Retrieved
sources more easily, to be quieter, and to be2010-01-21. 
more reliable with lower maintenance. They are^ "The Kockums Stirling AIP system - proven in
preferred for applications that value these uniqueoperational service". Kockums. Retrieved
advantages, particularly if the cost per unit energy2009-11-12. 
generated ($/kWh) is more important than the^
capital cost per unit power ($/kW). On this basis,^ J. Hasci (2008)
Stirling engines are cost competitive up to about^ Precer Group (a)
100 kW.^ a b S.K. Wickham (2008)
Compared to an internal combustion engine of the^
same power rating, Stirling engines currently have^
a higher capital cost and are usually larger and^ S. Backhaus; G. Swift (2003)
heavier. However, they are more efficient than^ Carbon Trust (2007)
most internal combustion engines. Their lower^ MSI (2008)
maintenance requirements make the overallBibliography
energy cost comparable. The thermal efficiency isS.D. Allan (2005). "World's Largest Solar Installation
also comparable (for small engines), ranging fromto use Stirling Engine Technology". Pure Energy
15% to 30%. For applications such as micro-CHP,Systems News. Retrieved 2009-01-19. 
a Stirling engine is often preferable to an internalS. Backhaus; G. Swift (2003). "Acoustic Stirling
combustion engine. Other applications includeHeat Engine: More Efficient than Other
water pumping, astronautics, and electricalNo-Moving-Parts Heat Engines". Los Alamos
generation from plentiful energy sources that areNational Laboratory. Retrieved 2009-01-19. 
incompatible with the internal combustion engine,BBC News (2003-10-31). "Power from the people".
such as solar energy, and biomass such asRetrieved 2009-01-19. 
agricultural waste and other waste such asW.T. Beale (1971). "Stirling Cycle Type Thermal
domestic refuse. Stirlings have also been used asDevice", US patent 3552120. Granted to Research
a marine engine in Swedish Gotland classCorp, 5 January 1971.
submarines. However, Stirling engines are generallyG.M. Benson (1977). "Thermal Oscillators", US
not price-competitive as an automobile engine, duepatent 4044558. Granted to New Process Ind, 30
to high cost per unit power, low power densityAugust 1977 .
and high material costs.G.M. Benson (1973). "Thermal Oscillators".
Basic analysis is based on the closed-formProceedings of the 8th IECEC. Philadelphia: ASME.
Schmidt analysis.pp. 182189. 
AdvantagesH.W. Brandhorst; J.A. Rodiek (2005). "A 25 kW
Stirling engines can run directly on any availableSolar Stirling Concept for Lunar Surface
heat source, not just one produced byExploration". in International Astronautics
combustion, so they can run on heat from solar,Federation (PDF). Procedings of the 56th
geothermal, biological, nuclear sources or wasteInternational Astronautical Co...