The classical Carnot heat engine
The Atkinson cycle engine is a type of internal combustion engine invented by James Atkinson in 1882. The Atkinson cycle is designed to provide efficiency at the expense of power density, or total power extracted per unit of displacement per rotation. A modern variation of this approach is used in some modern automobile engines. While originally seen exclusively in hybrid electric applications such as the Toyota Prius, some non-hybrid automobiles now feature engines that can run in the Atkinson-cycle as a part-time operating regime, giving good economy while running in Atkinson cycle, and conventional power density when running as a normal-cycle engine. Mazda Skyactiv models offering this capability include the Mazda 3 and MX-5.
Atkinson produced 3 different designs that had a short compression stroke and a longer expansion stroke. The first Atkinson-cycle was named the "Differential Engine". This engine used opposed pistons, The second, and most well known, design was called the "Cycle Engine" which used an over center arm to create 4 piston strokes in one revolution of the crankshaft. piston engine allowed the intake, compression, power, and exhaust strokes of the four-stroke cycle to occur in a single turn of the crankshaft and was designed to avoid infringing certain patents covering Otto-cycle engines. Atkinson's third and final engine was called the "Utilite Engine" and it operated much like any 2-stroke engine. The common thread throughout Atkinson's designs is the engines have an expansion stroke that is longer than compression stroke and by this method the engine can achieve greater thermal efficiency than a traditional piston engine. Atkinson's engines were produced by the British Gas Engine Company and also licensed to other overseas manufacturers. Many modern engines now use unconventional valve timing to produce the effect of a shorter compression stroke/longer power stroke, Miller applied this technique to the 4 stroke engine and so it is sometimes referred as the Atkinson / Miller cycle. US patent 2817322 dated Dec 24, 1957. In 1888 Charon filed a French patent and displayed an engine at the Paris Exhibition in 1889 . The Charon gas engine (4 stroke) also used a similar cycle to Miller but without a supercharger. It is referred to as the "Charon Cycle"  Modern engine designers are realizing the potential fuel-efficiency improvements the Atkinson type cycle can provide. 
Atkinson "Differential Engine"
The first implementation of the Atkinson cycle was in 1882; unlike later versions, it was arranged as an opposed piston engine, the Atkinson differential engine. In this, a single crankshaft was connected to two opposed pistons through a toggle jointed linkage that had a non-linearity; for half a revolution one piston remained almost stationary while the other approached it and returned, and then for the next half revolution the pistons changed over which piston was almost stationary and which piston approached and returned. Thus, in each revolution, one piston provided a compression stroke and a power stroke, and then the other piston provided an exhaust stroke and a charging stroke. As the power piston remained withdrawn during exhaust and charging, it was practical to provide exhaust and charging using valves behind a port that was covered during the compression stroke and the power stroke, and so the valves did not need to resist high pressure and could be of the simpler sort used in many steam engines, or even reed valves.
Atkinson "Cycle Engine"
The next engine designed by Atkinson in 1887 was named the "Cycle Engine" This engine used poppet valves a cam and an over center arm to produce 4 piston strokes for every one revolution of the crankshaft. The intake and compression stroke were significantly shorter than the Expansion and exhaust stroke. The "Cycle" engines were produced and sold for several years by the British Engine Company. Atkinson also licensed production to other manufactures. Sizes ranged form a few H.P. up to 100 H.P.
Atkinson "Utilite' Engine"
Atkinson's third design was named the "Utilite' engine". Atkinson realized an improvement was needed to make his cycle more applicable to a high speed engine. The final engine produced by The British Gas Engine company was the Utilite' engine. With this design Atkinson was able to make a more conventional engine yet preserve the efficiency of having a short compression stroke and a long expansion stroke in a rather ingenious way. It operates much like a standard 2 stroke except that the exhaust port is located at about the middle of the stroke. During the expansion stroke a valve (which remains closed until the piston reaches the end of the stroke) prevents pressure from escaping as the piston moves past the exhaust port. Once the valve is opened it remains open as the piston heads back toward compression letting fresh air charge the cylinder and exhaust escape until the port is covered. a rich fuel /air mixture is injected by a small piston pump after the start of compression. This resulted in a 2 stroke engine with a short compression and longer expansion stroke. The Utilite' engines were tested and found to be even more efficient than Atkinson's previous designs. Very few Utilite' engines were produced and none are known to survive. The British patent is from 1892 #2492 There is no known US patent for the Utilite' engine.
Ideal thermodynamic cycle
The ideal Atkinson cycle consists of following operations:
- 1–2 Isentropic, or reversible, adiabatic compression
- 2–3 Isochoric heating (Qp)
- 3–4 Isobaric heating (Qp')
- 4–5 Isentropic expansion
- 5–6 Isochoric cooling (Qo)
- 6–1 Isobaric cooling (Qo')
Modern Atkinson-cycle engines
Recently, the term "Atkinson cycle" has been used to describe a modified Otto-cycle engine in which the intake valve is held open longer than normal to allow a reverse flow of intake air into the intake manifold. The effective compression ratio is reduced (for a time the air is escaping the cylinder freely rather than being compressed), but the expansion ratio is unchanged. This means the compression ratio is smaller than the expansion ratio. Heat gained from burning fuel increases the pressure, thereby forcing the piston to move, expanding the air volume beyond the volume when compression began. The goal of the modern Atkinson cycle is to allow the pressure in the combustion chamber at the end of the power stroke to be equal to atmospheric pressure; when this occurs, all the available energy has been obtained from the combustion process. For any given portion of air, the greater expansion ratio allows more energy to be converted from heat to useful mechanical energy, meaning the engine is more efficient.
The disadvantage of the four-stroke Atkinson-cycle engine versus the more common Otto-cycle engine is reduced power density. Due to a smaller portion of the compression stroke being devoted to compressing the intake air, an Atkinson-cycle engine does not take in as much air as would a similarly designed and sized Otto-cycle engine.
Rotary Atkinson-cycle engine
The Atkinson cycle can be used in a rotary engine. In this configuration an increase in both power and efficiency can be achieved when compared to the Otto cycle. This type of engine retains the one power phase per revolution, together with the different compression and expansion volumes of the original Atkinson cycle. Exhaust gases are expelled from the engine by compressed-air scavenging. This modification of the Atkinson cycle allows the use of alternative fuels like diesel and hydrogen. Disadvantages of this design include the requirement that rotor tips seal very tightly on the outer housing wall and the mechanical losses suffered through friction between rapidly oscillating parts of irregular shape. See external links below for more information.
Vehicles using Atkinson-cycle engines
While a modified Otto-cycle piston engine using the Atkinson cycle provides good fuel efficiency, it is at the expense of a lower power-per-displacement as compared to a traditional four-stroke engine. If demand for more power is intermittent, the power of the engine can be supplemented by an electric motor during times when more power is needed. This forms the basis of an Atkinson-cycle-based hybrid electric drivetrain. These electric motors can be used independently of, or in combination with, the Atkinson-cycle engine, to provide the most efficient means of producing the desired power. This drive-train first entered production in late 1997 in the Japanese-market Toyota Prius.
- Chevrolet Volt
- Chrysler Pacifica (front-wheel drive) plug-in hybrid model minivan
- Ford C-Max (front-wheel drive / US market) hybrid & plug-in hybrid models
- Ford Escape/Mercury Mariner/Mazda Tribute electric (front- and four-wheel drive) with a compression ratio of 12.4:1
- Ford Fusion Hybrid/Mercury Milan Hybrid/Lincoln MKZ Hybrid electric (front-wheel drive) with a compression ratio of 12.3:1
- Honda Accord Plug-in Hybrid
- Honda Accord Hybrid (front-wheel drive)
- Hyundai Sonata Hybrid (front-wheel drive)
- Hyundai Elantra Atkinson cycle models
- Infiniti M35h Hybrid (rear-wheel drive)
- Kia Optima Hybrid (front-wheel drive) with a compression ratio of 13:1
- Lexus CT 200h (front-wheel drive)
- Lexus ES 300h (front-wheel drive)
- Lexus GS 450h hybrid electric (rear-wheel drive) with a compression ratio of 13:1
- Lexus GS F (rear-wheel drive)
- Lexus RC F (rear-wheel drive)
- Lexus HS 250h (front-wheel drive)
- Lexus IS 200t (2016)
- Lexus NX hybrid electric (four-wheel drive)
- Lexus RX 450h hybrid electric (four-wheel drive)
- Mazda Mazda6 (2014 and newer in North America, 2013 rest of world)
- Mercedes ML450 Hybrid (four-wheel drive) electric
- Mercedes S400 Blue Hybrid (rear-wheel drive) electric
- Toyota Camry Hybrid electric (front-wheel drive) with a compression ratio of 12.5:1
- Toyota Highlander Hybrid (2011 and newer)
- Toyota Prius hybrid electric (front-wheel drive) with a (purely geometric) compression ratio of 13.0:1
- Toyota Yaris Hybrid (front-wheel drive) with a compression ratio of 13.4:1
- Toyota Auris Hybrid (front-wheel drive)
- Toyota Tacoma V6 (beginning in 2015 for the 2016 model year)
Summary of the patent
The 1887 patent (US 367496 ) describes the mechanical linkages necessary to obtain all four strokes of the four-stroke cycle for a gas engine within one revolution of the crankshaft. There is also a reference to an 1886 Atkinson patent (US 336505 ) which describes an opposed-piston gas engine. The British patent for the "Utilite" is from 1892 #2492 There is no known US patent for the Utilite' engine.
- US 367496, J. Atkinson, "Gas Engine", issued 1887-08-02
- A text-book on gas, oil and air engines: or, Internal combustion motors ... By Bryan Donkin 1896 https://books.google.com/books?id=XQEUAAAAYAAJ&pg=PR22&lpg=PR22&dq=charon+cycle+engine&source=bl&ots=I7rragM6KP&sig=uDXprUG5xGHItZ_Enpqwrroe_eA&hl=en&sa=X&ved=0ahUKEwjrq-_elrbOAhVB3mMKHVJ7ACkQ6AEIKTAE#v=onepage&q=charon%20cycle%20engine&f=false page 152
- "Auto Tech: Atkinson Cycle engines and Hybrids". Autos.ca. 2010-07-14. Retrieved 2013-02-23.
- Gingery, Vincent. Building the Atkinson Differential Engine. David J. Gingery Publishing, LLC. ISBN 1878087231.
- Clerk, Dugald (1913). The gas, petrol, and oil engine, Volume 2. J. Wiley. p. 210.
- Heywood, John B. Internal Combustion Engine Fundamentals, p. 184-186.
- Gauthier, Michael (2013-01-21). "Honda Accord Plug-in Hybrid earns the title for being the most fuel-efficient sedan in America". worldcarfans.com. Retrieved 2013-01-22.
- "2016 Lexus IS – Performance". US: Lexus. Retrieved 2016-08-09.
- Edmunds, Dan (2010-09-24). "2011 Toyota Highlander Hybrid Road Test". Edmunds.com. Retrieved 2012-07-04.
- US 336505, J. Atkinson, "Gas Engine", issued 1886-02-16
- Comparison of Prime Movers Suitable for USMC Expeditionary Power Sources, Oak Ridge National Laboratory
- Libralato Engines - developing a rotary Atkinson cycle engine
- Rotary Atkinson cycle engine - gives details of this engine as well as comparisons with conventional and Wankel engines
- The Prius's Not So Secret Gas-Mileage Secrets - how the Prius uses the Atkinson cycle to get better results than an Otto cycle engine