{{Short description|Energy recovery mechanism}} {{Use dmy dates|date=November 2024}} {{more citations needed |date=February 2026}} [[File:Skoda 03 T roof.jpg|thumb|Mechanism for regenerative brake on the roof of a [[Škoda 03 T|Škoda Astra]] tram]] [[File:S stock northwood.JPG|thumb|The [[London Underground S7 and S8 Stock|S7/8 Stock]] on the [[London Underground]] can return around 20% of its energy usage to the power supply.<ref name=TfL200807>{{cite web|url=http://www.tfl.gov.uk/assets/downloads/transforming-the-tube-brochure.pdf |title=Transforming the Tube |date=July 2008 |publisher=Transport for London |access-date=28 May 2009 |url-status=dead |archive-url=https://web.archive.org/web/20110605002808/http://www.tfl.gov.uk/assets/downloads/transforming-the-tube-brochure.pdf |archive-date=5 June 2011}}</ref>]]
'''Regenerative braking''' is an [[energy recovery]] mechanism that slows down a moving vehicle or object by converting its [[kinetic energy]] or [[potential energy]] into a form that can be either used immediately or stored until needed.
Typically, regenerative [[brakes]] work by driving an [[electric motor]] in reverse to recapture energy that would otherwise be lost as heat during braking, effectively turning the [[traction motor]] into an [[electric generator]]. Feeding power backwards through the system like this allows the energy harvested from [[Acceleration|deceleration]] to resupply an [[energy storage]] solution such as a [[Electric battery|battery]] or a [[capacitor]]. Once stored, this power can then be later used to aid forward [[propulsion]]. Because of the electrified vehicle architecture required for such a braking system, automotive regenerative brakes are most commonly found on [[Hybrid electric vehicle|hybrid]] and [[electric vehicles]].
This method contrasts with conventional braking systems, where excess kinetic energy is converted to unwanted and wasted heat due to friction in the [[brake]]s. Similarly, with [[rheostatic brake]]s, energy is recovered by using electric motors as generators but is immediately dissipated as heat in [[resistors]].
In addition to improving the overall efficiency of the vehicle, regeneration can significantly extend the life of the braking system. This is because the traditional mechanical parts like discs, calipers, and pads – included for when regenerative braking alone is insufficient to safely stop the vehicle – will not wear out as quickly as they would in a vehicle relying solely on traditional brakes.
== General principle == The most common form of regenerative brake involves an [[electric motor]] functioning as an electric generator. In electric [[rail transport|railways]], the electricity generated is fed back into the [[railway electrification system|traction power supply]]. In [[battery electric vehicle|battery electric]] and [[hybrid vehicle|hybrid electric]] vehicles, the energy is stored chemically in a [[electric battery|battery]], electrically in a bank of [[capacitor]]s, or mechanically in a rotating [[flywheel energy storage|flywheel]]. [[Hydraulic hybrid]] vehicles use hydraulic motors to store energy in the form of [[compressed air energy storage|compressed air]]. In a hydrogen [[fuel cell]] powered vehicle, the electrical energy generated by the motor is stored chemically in a battery, similar to battery and hybrid electric vehicles.<ref>{{cite web |title=How Do Fuel Cell Electric Vehicles Work Using Hydrogen? |url=https://afdc.energy.gov/vehicles/how-do-fuel-cell-electric-cars-work |website=Alternative Fuels Datacenter |publisher=U.S. Department of Energy |access-date=22 March 2021}}</ref>
===Practical regenerative braking=== Regenerative braking is not by itself sufficient as the sole means of safely bringing a vehicle to a standstill, or slowing it as required, so it must be used in conjunction with another braking system such as [[friction]]-based braking.
* The regenerative braking effect drops off at lower speeds and cannot bring a vehicle to a complete halt reasonably quickly with current technology. However, some cars, like the [[Chevrolet Bolt]], can bring the vehicle to a complete stop on level surfaces when the driver knows the vehicle's regenerative braking distance. This is referred to as One Pedal Driving (OPD). * Some current regenerative brakes do not immobilize a stationary vehicle; [[Parking brake|physical locking]] is required, for example, to prevent vehicles from rolling down hills. Some cars, like the Chevrolet Bolt, can remain stationary on small slopes using only the motor. * Many road vehicles with regenerative braking do not have drive motors on all wheels (as in a [[two-wheel drive]] car); regenerative braking is normally only applicable to wheels with motors. For safety, the ability to brake all wheels is required. * The regenerative braking effect available is limited, and mechanical braking is still necessary for substantial speed reductions or to bring a vehicle to a stop. * On steep hills with real traffic speeds, the magnitude of potential energy recoverable during the descent of a vehicle at a slower speed than its terminal speed is substantially greater than that recoverable by bringing the vehicle from even the terminal speed to a complete stop. An example used by bicyclists is that during the descent of a hill, approximately three hair dryers' worth of power or some two horsepower is lost to Air drag at terminal speeds. {{Citation needed|date=May 2024}}
Regenerative and friction braking must both be used, creating the need to control them to produce the required total braking. The GM [[General Motors EV1|EV-1]] was the first commercial car to do this. In 1997 and 1998, engineers Abraham Farag and Loren Majersik were issued two patents for this ''[[brake-by-wire]]'' technology.<ref>GM patent [https://patents.google.com/patent/US5775467A/en?oq=5775467 5775467] – ''Floating electromagnetic brake system- Erik Knuth, Abraham Farag, Loren Majersik, William Borchers''.</ref><ref>GM patent [https://patents.google.com/patent/US5603217A/en?oq=5603217 5603217] – ''Compliant master cylinder- Loren Majersik, Abraham Farag''.</ref>
Early applications commonly suffered from a serious safety hazard: in many early electric vehicles with regenerative braking, the same controller positions were used to apply power and to apply the regenerative brake, with the functions being swapped by a separate manual switch. This led to a number of serious accidents when drivers accidentally accelerated when intending to brake, such as the [[List of rail accidents (1930–49)#1948|runaway train accident]] in [[Wädenswil, Switzerland]] in 1948, which killed twenty-one people.
In the 2020s, most vehicles equipped with regenerative braking can completely halt reasonably quickly in One Pedal Driving mode. Some car models do not illuminate the braking light when engaging in regenerative braking, leading to safety concerns. Most regulations do not mandate the illumination of a braking light when the vehicle decelerates through regenerative braking.<ref>{{cite web|url=https://www.consumerreports.org/cars/car-safety/brake-lights-can-fail-to-provide-fair-warning-on-some-evs-a9533519285/ |title= Brake Lights Can Fail to Provide Fair Warning on Some Electric Vehicles |website=Consumer Reports |date=26 June 2023 |first=Mike |last=Monticello }}</ref> The One Pedal Driving (OPD) mode also lead to concerns over [[sudden unintended acceleration]] (SUA), as the driver could confuse the accelerator as the brake in stressful situations when the latter is seldomly used during OPD operation.<ref>{{cite web|url=https://www.autoevolution.com/news/china-to-ban-one-pedal-driving-mode-that-was-widely-blamed-for-tesla-sua-crashes-234766.html |title=China To Ban One-Pedal Driving Mode That Was Widely Blamed for Tesla SUA Crashes |website=Auto Evolution |date=31 May 2024 |first=Cristian |last=Agatie }}</ref> The GB 21670-2025 vehicle standard later mandated that [[brake light]]s must turn on during regenerative braking when deceleration exceeds 1.3 m/s<sup>2</sup>.<ref>{{cite web|url=https://carnewschina.com/2025/07/08/chinas-new-auto-standard-curbs-single-pedal-driving/ |title=China’s new auto standard curbs single-pedal driving |website=CarNewsChina |date=8 July 2025 |last=Liu |first=Miao }}</ref>
[[File:Tesla Model S P85+ 60 kW Regenerative Braking (cropped).jpg|thumb|A Tesla Model S P85+ recovering regenerative braking power in excess of 60 kW. During regenerative braking the power indicator is green.]]
== History == In 1886 the Sprague Electric Railway & Motor Company, founded by [[Frank J. Sprague]], introduced two important inventions: a constant-speed, non-sparking motor with fixed brushes, and regenerative braking.
Early examples of this system in road vehicles were the [[front-wheel drive]] conversions of horse-drawn [[cabriolet (carriage)|cabs]] by [[Louis Antoine Krieger]] in Paris in the 1890s. The Krieger electric [[Landaulet (car)|landaulet]] had a drive motor in each front wheel with a second set of parallel windings ([[bifilar coil]]) for regenerative braking.<ref>{{cite web|url=http://www.shorpy.com/node/5734%23comment-58487|author=Dave|title=Horseless Carriage: 1906|publisher=Shorpy|date=16 March 2009|access-date=14 August 2010|url-status=live|archive-url=https://web.archive.org/web/20110725214152/http://www.shorpy.com/node/5734%23comment-58487|archive-date=25 July 2011}}</ref> The Orwell Electric Truck introduced by [[Ransomes, Sims & Jefferies]] in England during WW1 used regenerative braking switched in by the driver.
In England, "automatic regenerative control" was introduced to tramway operators by John S. Raworth's Traction Patents 1903–1908, offering them economic and operational benefits<ref>{{Cite journal |doi = 10.1049/jiee-1.1907.0020|title = Regenerative control of electric tramcars and locomotives|journal = Journal of the Institution of Electrical Engineers|volume = 38|issue = 182|pages = 374–386|year = 1907|last1 = Raworth|first1 = A.}}</ref> <ref>{{cite journal|url= https://books.google.com/books?id=ki4SAAAAIAAJ&q=%22raworth+system%22&pg=PA68 |title=Discussion on the 'Regenerative braking of electric vehicles' (Hellmund) Pittsburgh, PA |journal=Transactions of the American Institute of Electrical Engineers |volume=36 |page=68 |year=1917 |access-date=11 March 2014}}</ref> <ref name="Jno">{{cite book|first1=Struan |last1=Jno |first2=T. |last2=Robertson |first3=John D. |last3=Markham |title=The Regenerative Braking Story |publisher=Scottish Tramway & Transport Society |year=2007}}</ref> as explained in some detail by his son [[Southern Railway (UK)#Other engineers|Alfred Raworth]]. These included tramway systems at Devonport (1903), [[Rawtenstall Corporation Tramways|Rawtenstall]], [[Birmingham Corporation Tramways|Birmingham]], Crystal Palace-Croydon (1906), and many others. Slowing the speed of the cars or keeping it in control on descending gradients, the motors worked as generators and braked the vehicles. The tram cars also had wheel brakes and track slipper brakes which could stop the tram should the electric braking systems fail. In several cases the tram car motors were shunt wound instead of series wound, and the systems on the Crystal Palace line utilized series-parallel controllers.{{Clarify|date=January 2012}}<ref>{{cite book|url= https://books.google.com/books?id=fjApAAAAYAAJ&q=%22raworth+system%22&pg=PA20 |title=Transport World The Tramway and Railway World |volume=XX |date=July–December 1906 |page=20 |publisher=Carriers Publishing |access-date=11 March 2014}}</ref> Following a serious accident at Rawtenstall, an embargo was placed on this form of traction in 1911;<ref>{{Cite journal |last=John |first=Prentice |date=January–February 2016 |title=The Raworth Demi-car |url=https://tramwayinfo.com/tramways/Download/Raworth.pdf |journal=Tramfare |publisher=Tramway & Light Railway Society |issue=288 |pages=5}}</ref> the regenerative braking system was reintroduced twenty years later.<ref name="Jno"/>
Regenerative braking has been in extensive use on railways for many decades. The Baku-Tbilisi-Batumi railway ([[Transcaucasus Railway]] or Georgian railway) started utilizing regenerative braking in the early 1930s. This was especially effective on the steep and dangerous [[Surami Pass]].<ref>{{cite web|url=http://forum.axishistory.com/viewtopic.php?f=34&t=91987&start=645|author=Bigpanzer|title=Susrami Type Locomotoive at Surami Pass|publisher=Shorpy|date=30 April 2006|access-date=31 January 2011|url-status=live|archive-url=https://web.archive.org/web/20111123134107/http://forum.axishistory.com/viewtopic.php?f=34&t=91987&start=645|archive-date=23 November 2011}}</ref> In Scandinavia the Kiruna to Narvik electrified railway, known as [[Malmbanan]] on the Swedish side and [[Ofoten Line]] on the Norwegian, carries iron ore on the steeply-graded route from the mines in [[Kiruna]], in the north of Sweden, down to the port of [[Narvik]] in Norway to this day. The rail cars are full of thousands of tons of [[iron ore]] on the way down to Narvik, and these trains generate large amounts of electricity by regenerative braking, with a maximum recuperative braking force of 750 [[Newton (force)|kN]]. From [[Riksgränsen]] on the national border to the Port of Narvik, the trains<ref>[https://library.e.abb.com/public/b53e94802c75e541c125789a00290729/Railvolution02-11-Traction-transformer-Kiruna.pdf Railvolution magazine, 2/11, Kiruna Locomotives, Part 1] {{webarchive|url=https://web.archive.org/web/20160129071806/https://library.e.abb.com/public/b53e94802c75e541c125789a00290729/Railvolution02-11-Traction-transformer-Kiruna.pdf|date=29 January 2016}}<!--Source for electrified railway, steeply-graded, description of locomotives, 750kN--></ref> use only a fifth of the power they regenerate.{{failed verification|date=December 2016}}<!---SOURCE ONLY SAYS THAT TIMING SYSTEM REDUCES ENERGY CONSUMPTION BY 20%, IT SAYS NOTHING ABOUT GENERATIVE BRAKING---> The regenerated energy is sufficient to power the empty trains back up to the national border.<ref>{{cite news |title=Evighetsmaskiner |last=Næss |first=Per |work=[[Fremover]] |date=3 August 2007 |page=28 |language=no}}</ref>{{failed verification|date=December 2016}} Any excess energy from the railway is pumped into the power grid to supply homes and businesses in the region, and the railway is a net generator of electricity.{{citation needed|date=December 2016}}
Electric cars used regenerative braking since the earliest experiments, but this initially required the driver to flip switches between various operational modes in order to use it. The [[Baker Motor Vehicle|Baker Electric Runabout]] and the [[Owen Magnetic]] were early examples, which used many switches and modes controlled by an expensive "black box" or "drum switch" as part of their electrical system.<ref>{{cite web |url=http://www.sunrise-ev.com/Controllers.htm |title=EV Motor Controllers |first=Lee A. |last=Hart |date=28 December 2013 |access-date=4 May 2014 |url-status=dead |archive-url=https://web.archive.org/web/20140504204906/http://www.sunrise-ev.com/Controllers.htm |archive-date=4 May 2014}}</ref><ref>{{cite web |url=http://www.popularmechanics.com/cars/jay-leno/vintage/4215940 |title=The 100-Year-Old Electric Car |first=Jay |last=Leno |publisher=Popular Mechanics |date=1 May 2007 |access-date=4 May 2014 |url-status=live |archive-url=https://web.archive.org/web/20140504191755/http://www.popularmechanics.com/cars/jay-leno/vintage/4215940 |archive-date=4 May 2014}}</ref> These, like the Krieger design, could only practically be used on downhill portions of a trip, and had to be manually engaged.
Improvements in electronics allowed this process to be fully automated, starting with 1967's [[AMC Amitron]] experimental electric car.<ref>{{cite web |last=Voelcker |first=John |date=10 January 2014 |title=Electric-Car Trivia: When Was Regenerative Braking First Used? |url=https://www.greencarreports.com/news/1089510_electric-car-trivia-when-was-regenerative-braking-first-used |website=Green Car Reports}}</ref> Designed by Gulton Industries<ref>{{cite book|url= https://archive.org/details/alternativestoin00robe |url-access= registration |page=[https://archive.org/details/alternativestoin00robe/page/219 219] |chapter=The Electric Car |title=Alternatives to the internal combustion engine: impacts on environmental quality |first1=Robert U. |last1=Ayres |first2=Richard P. |last2=McKenna |publisher=Johns Hopkins University Press |year=1972 |isbn= 978-0-8018-1369-6 |access-date=4 May 2014}}</ref> the motor controller automatically began battery charging when the brake pedal was applied. Many modern hybrid and electric vehicles use this technique to extend the range of the battery pack, especially those using an AC drive train (most earlier designs used DC power).
An AC/DC rectifier and a very large capacitor may be used to store the regenerated energy, rather than a battery. The use of a capacitor allows much more rapid peak storage of energy, and at higher voltages. [[Mazda]] used this system in some 2018 cars, where it is branded i-ELOOP.
== Electric railways == During braking, the [[traction motor]] connections are altered to turn them into electrical generators. The motor fields are connected across the main traction generator (MG) and the motor armatures are connected across the load. The MG now excites the motor fields. The rolling locomotive or multiple unit wheels turn the motor armatures, and the motors act as generators, either sending the generated current through onboard resistors ([[dynamic braking]]) or back into the supply (regenerative braking). Compared to electro-pneumatic friction brakes, braking with the traction motors can be regulated faster improving the performance of [[wheel slide protection]].
For a given direction of travel, current flow through the motor armatures during braking will be opposite to that during motoring. Therefore, the motor exerts [[torque]] in a direction that is opposite from the rolling direction.
Braking effort is proportional to the product of the magnetic strength of the field windings, multiplied by that of the armature windings.
Savings of 17%, and less wear on friction braking components, are claimed for [[British Rail Class 390]]s.<ref>{{cite web |title=Regenerative braking boosts green credentials |url=http://www.railwaygazette.com/news/single-view/view/regenerative-braking-boosts-green-credentials.html |publisher=[[Railway Gazette International]] |date=2 July 2007 |access-date=11 March 2014 |url-status=live |archive-url=https://web.archive.org/web/20140311153140/http://www.railwaygazette.com/news/single-view/view/regenerative-braking-boosts-green-credentials.html |archive-date=11 March 2014}}</ref> [[Caltrain]] claims 23% of the energy used by its [[Stadler KISS]] electric trains are recaptured and returned to the grid.<ref>{{cite press release|url=https://www.caltrain.com/news/caltrains-electric-fleet-more-efficient-expected|title=Caltrain’s Electric Fleet More Efficient than Expected|date=January 23, 2025|access-date=October 30, 2025|publisher=Caltrain}}</ref> The [[Delhi Metro]] reduced the amount of [[carbon dioxide]] ({{CO2}}) released into the atmosphere by around 90,000 tons by regenerating 112,500 megawatt hours of electricity through the use of regenerative braking systems between 2004 and 2007. It was expected that the Delhi Metro would reduce its emissions by over 100,000 tons of {{CO2}} per year once its phase II was complete, through the use of regenerative braking.<ref>{{cite news|title=Delhi Metro prevents 90,000 tons of CO<sub>2</sub> |url=http://economictimes.indiatimes.com/Earth/Delhi-Metro-Cuts-90000-tons-of-CO2/articleshow/4176147.cms |work=India Times|date=23 February 2009 |access-date=14 August 2010 |url-status=dead |archive-url=https://web.archive.org/web/20090226201221/http://economictimes.indiatimes.com/Earth/Delhi-Metro-Cuts-90000-tons-of-CO2/articleshow/4176147.cms |archive-date=26 February 2009 }}</ref>
Electricity generated by regenerative braking may be fed back into the traction power supply; either offset against other electrical demand on the network at that instant, used for [[head end power]] loads, or stored in [[Kinetic Traction Systems|lineside storage systems]] for later use.<ref>{{cite web |url=http://www.railwaygazette.com/nc/news/single-view/view/flywheel-firm-launches.html |date=20 January 2011 |work=Railway Gazette|title=Flywheel firm launches |access-date=11 March 2014 |url-status=live |archive-url=https://web.archive.org/web/20120618183110/http://www.railwaygazette.com/nc/news/single-view/view/flywheel-firm-launches.html |archive-date=18 June 2012}}</ref>
A form of what can be described as regenerative braking is used on some parts of the [[London Underground]], achieved by having small slopes leading up and down from stations. The train is slowed by the climb, and then leaves down a slope, so kinetic energy is converted to [[gravitational energy|gravitational potential energy]] in the station.<ref>{{cite web |url=http://www.londonreconnections.com/2011/milestones-reached-on-the-jubilee-and-victoria-lines/ |title=Milestones Reached on the Jubilee and Victoria Lines |publisher=London Reconnections |date=2 August 2011 |access-date=11 March 2014 |url-status=live |archive-url=https://web.archive.org/web/20140311154424/http://www.londonreconnections.com/2011/milestones-reached-on-the-jubilee-and-victoria-lines/ |archive-date=11 March 2014}}</ref> This is normally found on the deep tunnel sections of the network and not generally above ground or on the [[Tunnel#Cut-and-cover|cut and cover]] sections of the Metropolitan and District Lines.
== Comparison of dynamic and regenerative brakes == [[File:NSLocoNo.5348.jpg|thumb|The box extending sideways from the roof directly over the word "operation" allows air to freely flow through the resistors of the dynamic brakes on this diesel-electric locomotive.]] What are described as dynamic brakes ("[[rheostatic brake]]s" in British English) on electric traction systems, unlike regenerative brakes, dissipate electric energy as heat rather than using it, by passing the current through large banks of [[resistor]]s. Vehicles that use dynamic brakes include [[forklift truck]]s, [[Diesel-electric transmission|diesel-electric]] [[locomotive]]s, and [[tram]]s. This heat can be used to warm the vehicle interior, or dissipated externally by large [[radiator]]-like cowls to house the resistor banks.
General Electric's experimental 1936 [[GE steam turbine locomotives|steam turbine locomotives]] featured true regeneration. These two locomotives ran the steam water over the resistor packs, as opposed to air cooling used in most dynamic brakes. This energy displaced the oil normally burned to keep the water hot, and thereby recovered energy that could be used to accelerate again.<ref>{{cite book |first= Brian |last= Solomon |url=https://books.google.com/books?id=sTRcBAAAQBAJ&pg=PA59 |title= GE and EMD Locomotives |publisher=Voyageur Press |year=2014 |pages=59–61|isbn= 9781627883979 }}</ref>
The main disadvantage of regenerative brakes when compared with dynamic brakes is the need to closely match the generated current with the supply characteristics and increased maintenance cost of the lines. With DC supplies, this requires that the voltage be closely controlled. The AC power supply and frequency converter pioneer Miro Zorič and his first AC power electronics have also enabled this to be possible with AC supplies.{{citation needed|date=February 2019}} The supply frequency must also be matched (this mainly applies to locomotives where an AC supply is [[rectifier|rectified]] for DC motors).
In areas where there is a constant need for power unrelated to moving the vehicle, such as electric train heat or [[air conditioning]], this load requirement can be utilized as a sink for the recovered energy via modern [[Variable-frequency drive|AC traction systems]]. This method has become popular with North American passenger railroads where [[head end power]] loads are typically in the area of 500 kW year round. Using HEP loads in this way has prompted recent electric locomotive designs such as the [[ALP-46]] and [[ACS-64]] to eliminate the use of dynamic brake resistor grids and also eliminates any need for any external power infrastructure to accommodate power recovery allowing self-powered vehicles to employ regenerative braking as well.
A small number of [[steep grade railway]]s have used [[three-phase|3-phase]] power supplies and [[induction motor]]s. This results in a near constant speed for all trains, as the motors rotate with the supply frequency both when driving and braking.
== Kinetic energy recovery systems == {{main|Kinetic energy recovery system}} Kinetic energy recovery systems (KERS) were used for the motor sport [[Formula One]]'s [[2009 Formula One World Championship|2009 season]], and are under development for road vehicles. KERS was abandoned for the [[2010 Formula One World Championship|2010 Formula One season]], but re-introduced for the [[2011 Formula One World Championship|2011 season]]. By [[2013 Formula One World Championship|2013]], all teams were using KERS with [[Marussia F1]] starting use for the 2013 season.<ref name="3teams">{{cite news |url=http://www.autoevolution.com/news/team-lotus-virgin-hrt-f1-to-start-2011-without-kers-30389.html |title=Team Lotus, Virgin, HRT F1 to Start 2011 Without KERS |newspaper=Autoevolution |date=28 January 2011 |access-date=1 June 2011 |url-status=live |archive-url=https://web.archive.org/web/20110204162818/http://www.autoevolution.com/news/team-lotus-virgin-hrt-f1-to-start-2011-without-kers-30389.html |archive-date=4 February 2011|last1=Panzariu |first1=Ovidiu }}</ref> One of the main reasons that not all cars used KERS immediately is because it raises the car's center of gravity, and reduces the amount of [[ballast weight|ballast]] that is available to balance the car so that it is more predictable when turning.<ref>BBC TV commentary on German Grand Prix 2009</ref> FIA rules also limit the exploitation of the system. The concept of transferring the vehicle's kinetic energy using [[flywheel energy storage]] was postulated by physicist [[Richard Feynman]] in the 1950s<ref>Selected Papers of Richard Feynman: (With Commentary) edited by Laurie M Brown p952</ref> and is exemplified in such systems as the [[Zytek]], Flybrid,<ref>{{cite web |author=Flybrid Systems LLP |url=http://www.flybridsystems.com/Technology.html |title=Flybrid Systems |publisher=Flybrid Systems |date=10 September 2010 |access-date=17 September 2010 |url-status=dead |archive-url=https://web.archive.org/web/20100713210303/http://www.flybridsystems.com/Technology.html |archive-date=13 July 2010}}</ref> Torotrak<ref>{{cite web|url= http://www.torotrak.com/IVT/works/ |title=Overview of the IVT system |work=Torotrak |archive-url= https://web.archive.org/web/20081014225121/http://www.torotrak.com/IVT/works/ |archive-date=14 October 2008 |access-date=4 October 2019}}</ref><ref>{{cite web |url=http://www.xtrac.com/pdfs/Torotrak_Xtrac_CVT.pdf |title=Torotrak, Xtrac & CVT pdf |access-date=17 September 2010 |url-status=dead |archive-url=https://web.archive.org/web/20110516084534/http://www.xtrac.com/pdfs/Torotrak_Xtrac_CVT.pdf |archive-date=16 May 2011}}</ref> and Xtrac used in F1. [[Differential (mechanical device)|Differential]] based systems also exist such as the Cambridge Passenger/Commercial Vehicle Kinetic Energy Recovery System (CPC-KERS).<ref>{{cite web |author=BHR Technology. |url=http://www.bhr-technology.com/CPC-KERS.pps |title=Cpc-Kers |publisher=Bhr-technology.com |access-date=17 September 2010 |url-status=dead |archive-url=https://web.archive.org/web/20110707232035/http://www.bhr-technology.com/CPC-KERS.pps |archive-date=7 July 2011}}</ref>
Xtrac and Flybrid are both licensees of Torotrak's technologies, which employ a small and sophisticated ancillary gearbox incorporating a [[continuously variable transmission]] (CVT). The CPC-KERS is similar as it also forms part of the driveline assembly. However, the whole mechanism including the flywheel sits entirely in the vehicle's hub (looking like a drum brake). In the CPC-KERS, a differential replaces the CVT and transfers torque between the [[flywheel]], drive wheel and road wheel.
== Motor sports == <!-- Order by History, FIA, and the carmakers -->
[[File:Flybrid Systems Kinetic Energy Recovery System.jpg|thumb|right|A Flybrid Systems kinetic energy recovery system]]
The first of these systems to be revealed was the Flybrid. This system weighs 24 kg and has an energy capacity of 400 kJ after allowing for internal losses. A maximum power boost of {{convert|60|kW|PS hp|abbr=on}} for 6.67 seconds is available. The 240 mm diameter flywheel weighs 5.0 kg and revolves at up to 64,500 rpm. Maximum torque is 18 Nm (13.3 ftlbs). The system occupies a volume of 13 litres.{{Citation needed|date=July 2011}}
=== Formula One === [[File:KERS flywheel.jpg|thumb|right|A KERS flywheel]]
[[Formula One]] have stated that they support responsible solutions to the world's environmental challenges,<ref>{{cite web|url=http://www.fia.com/en-GB/mediacentre/pressreleases/mobility/2008/Pages/f1_environment.aspx|title=Teams Comment on F1's Environmental Future|publisher=FIA|date=8 October 2008|access-date=14 January 2009|url-status=dead|archive-url=https://web.archive.org/web/20081228022048/http://www.fia.com/en-GB/mediacentre/pressreleases/mobility/2008/Pages/f1_environment.aspx|archive-date=28 December 2008}}</ref> and the [[Fédération Internationale de l'Automobile|FIA]] allowed the use of {{convert|60|kW|PS hp|abbr=on}} KERS in the regulations for the [[2009 Formula One season]].<ref>{{cite web | url =http://www.fia.com/resources/documents/1151088479__2009_F1_TECHNICAL_REGULATIONS.pdf | title =2009 Formula One Technical Regulations | publisher =FIA | date =22 December 2006 | access-date =22 December 2006 | url-status =dead | archive-url =https://web.archive.org/web/20080625190106/http://www.fia.com/resources/documents/1151088479__2009_F1_TECHNICAL_REGULATIONS.pdf | archive-date =25 June 2008}}</ref> Teams began testing systems in 2008: energy can either be stored as mechanical energy (as in a [[flywheel]]) or as electrical energy (as in a battery or [[supercapacitor]]).<ref>{{cite web|url=http://www.fia.com/resources/documents/1151088479__2009_F1_TECHNICAL_REGULATIONS.pdf|title=2009 FORMULA ONE TECHNICAL REGULATIONS|publisher=FIA|author=FIA management|date=22 December 2006|access-date=8 July 2008|url-status=dead|archive-url=https://web.archive.org/web/20080625190106/http://www.fia.com/resources/documents/1151088479__2009_F1_TECHNICAL_REGULATIONS.pdf|archive-date=25 June 2008}}</ref>
Prior to the introduction of KERS, [[McLaren]] had already deployed an early regenerative braking system in their 1998 [[McLaren MP4/13|MP4/13]] race car. This system didn't send power to the wheels directly, and instead used energy from the brakes to run auxiliary pumps on the engine to combat parasitic losses, resulting in an extra 30 to 40 horsepower for a limited period.<ref name=F1Technical>{{Cite web |title=McLaren MP4-13 Mercedes |url=https://www.f1technical.net/f1db/cars/810/mclaren-mp4-13 |publisher=F1Technical.net |access-date=26 July 2025}}</ref>
Two minor incidents were reported during testing of KERS systems in {{F1|2008}}. The first occurred when the [[Red Bull Racing]] team tested their KERS battery for the first time in July: it malfunctioned and caused a fire scare that led to the team's factory being evacuated.<ref>{{cite news| title =KERS failure caused Red Bull fire scare| publisher =autosport.com| url =http://www.autosport.com/news/report.php/id/69199| date =17 July 2008| access-date =22 July 2008| url-status =live| archive-url =https://web.archive.org/web/20080722162339/http://www.autosport.com/news/report.php/id/69199| archive-date =22 July 2008}}</ref> The second was less than a week later when a [[Sauber Motorsport|BMW Sauber]] mechanic was given an electric shock when he touched [[Christian Klien]]'s KERS-equipped car during a test at the [[Circuito de Jerez|Jerez circuit]].<ref>{{cite news| title =BMW mechanic escapes KERS scare| publisher =autosport.com| url =http://www.autosport.com/news/report.php/id/69391| date =22 July 2008| access-date =22 July 2008| url-status =live| archive-url =https://web.archive.org/web/20080724005938/http://www.autosport.com/news/report.php/id/69391| archive-date =24 July 2008}}</ref>
With the introduction of KERS in the 2009 season, four teams used it at some point in the season: [[Scuderia Ferrari|Ferrari]], [[Renault F1|Renault]], [[Sauber Motorsport|BMW]], and [[McLaren]]. During the season, Renault and BMW stopped using the system. [[McLaren|McLaren Mercedes]] became the first team to win a F1 GP using a KERS equipped car when [[Lewis Hamilton]] won the [[2009 Hungarian Grand Prix]] on 26 July 2009. Their second KERS equipped car finished fifth. At the following race, Lewis Hamilton became the first driver to take pole position with a KERS car, his teammate, [[Heikki Kovalainen]] qualifying second. This was also the first instance of an all KERS front row. On 30 August 2009, [[Kimi Räikkönen]] won the Belgian Grand Prix with his KERS equipped Ferrari. It was the first time that KERS contributed directly to a race victory, with second placed [[Giancarlo Fisichella]] claiming "Actually, I was quicker than Kimi. He only took me because of KERS at the beginning".<ref>{{cite news|url=https://news.bbc.co.uk/sport1/hi/motorsport/formula_one/8229449.stm|title=Raikkonen wins exciting Spa duel|publisher=BBC|date=30 August 2009|access-date=30 August 2009|first=Chris|last=Whyatt|url-status=live|archive-url=https://web.archive.org/web/20140517122254/http://news.bbc.co.uk/sport1/hi/motorsport/formula_one/8229449.stm|archive-date=17 May 2014}}</ref>
Although KERS was still legal in Formula 1 in the 2010 season, all the teams had agreed not to use it.<ref>{{cite web |url= http://www.formula1.com/inside_f1/understanding_the_sport/8763.html |title=Kinetic Energy Recovery Systems (KERS) |publisher=Formula1.com |access-date=14 August 2010 |url-status=dead |archive-url= https://web.archive.org/web/20100706214811/http://www.formula1.com/inside_f1/understanding_the_sport/8763.html |archive-date=6 July 2010}}</ref> New rules for the 2011 F1 season which raised the minimum weight limit of the car and driver by 20 kg to 640 kg,<ref>{{cite web|url= http://www.formula1.com/news/headlines/2010/12/11603.html |title = formula1.com/ |publisher = formula1.com|access-date = 4 December 2010|url-status = live|archive-url = https://web.archive.org/web/20101216011345/http://www.formula1.com/news/headlines/2010/12/11603.html |archive-date = 16 December 2010}}</ref> along with the FOTA teams agreeing to the use of KERS devices once more, meant that KERS returned for the 2011 season.<ref>{{cite news|url= https://news.bbc.co.uk/sport2/hi/motorsport/formula_one/8756430.stm|title=Changes made to F1l|publisher=BBC|date=23 June 2010|access-date=23 June 2010|first=Andrew|last=Benson|url-status=live|archive-url=https://web.archive.org/web/20100623185054/http://news.bbc.co.uk/sport2/hi/motorsport/formula_one/8756430.stm|archive-date=23 June 2010}}</ref> This is still optional as it was in the 2009 season; in the 2011 season 3 teams elected not to use it.<ref name="3teams"/> For the [[2012 Formula One World Championship|2012 season]], only Marussia and [[HRT Formula 1 Team|HRT]] raced without KERS, and by 2013, with the withdrawal of HRT, all 11 teams on the grid were running KERS.
In the [[2014 Formula One World Championship|2014 season]], the power output of the MGU-K (The replacement of the KERS and part of the ERS system that also includes a [[turbocharger]] [[waste heat recovery unit|waste heat recovery]] system) was increased from 60 kW to 120 kW and it was allowed to recover 2 [[mega-]] [[joules]] per lap. This was to balance the sport's move from 2.4-litre V8 engines to 1.6-litre V6 engines.<ref>{{cite news|url=https://www.bbc.co.uk/sport/formula1/13878359 |title=Formula 1 delays introduction of 'green' engines until 2014 |publisher=bbc.co.uk |date= 29 June 2011|access-date=27 June 2011}}</ref> The fail-safe settings of the [[brake-by-wire]] system that now supplements KERS came under examination as a contributing factor in the fatal crash of [[Jules Bianchi#FIA reaction and investigation|Jules Bianchi]] at the [[2014 Japanese Grand Prix]].
=== Autopart makers === [[Robert Bosch GmbH|Bosch]] Motorsport Service is developing a KERS for use in motor racing. These electricity storage systems for hybrid and engine functions include a [[lithium-ion battery]] with scalable capacity or a [[flywheel]], a four to eight kilogram [[electric motor]] (with a maximum power level of {{convert|60|kW|abbr=on|disp=or}}), as well as the KERS controller for power and battery management. Bosch also offers a range of electric hybrid systems for commercial and light-duty applications.<ref>{{cite web | publisher = Green Car Congress | title = Bosch Developing Modular KERS Systems for Range of Motorsport Applications | url = http://www.greencarcongress.com/2008/11/bosch-developin.html | date = 18 November 2008 | access-date = 27 April 2010 | url-status = live | archive-url = https://web.archive.org/web/20100905151239/http://www.greencarcongress.com/2008/11/bosch-developin.html | archive-date = 5 September 2010}}</ref>
=== Car makers === Automakers including [[Honda]] have been testing KERS systems.<ref>{{cite web |url=http://www.carmondo.de/blog/2008/07/03/honda-und-bmw-mit-formel-1-hybriden/ |title=Sixt Car Sales | Gebrauchtwagen günstig kaufen |access-date=15 December 2010 |url-status=live |archive-url=https://web.archive.org/web/20090929044738/http://www.carmondo.de/blog/2008/07/03/honda-und-bmw-mit-formel-1-hybriden/ |archive-date=29 September 2009|language=de}}</ref> At the [[2008 1000 km of Silverstone|2008 1,000 km of Silverstone]], Peugeot Sport unveiled the [[Peugeot 908 HDi FAP|Peugeot 908 HY]], a [[hybrid electric vehicle|hybrid electric]] variant of the diesel 908, with KERS. Peugeot planned to campaign the car in the [[2009 Le Mans Series season]], although it was not capable of scoring championship points.<ref name="908HY">{{cite web | url = http://www.racecar-engineering.com/news/people/273697/peugeot-reveal-hybrid-racer-for-2009.html | title = Peugeot Sport Hybrid | publisher = Racecar Engineering | date = 13 September 2008 | access-date = 13 September 2008 | url-status = dead | archive-url = https://web.archive.org/web/20090113183348/http://www.racecar-engineering.com/news/people/273697/peugeot-reveal-hybrid-racer-for-2009.html | archive-date = 13 January 2009}}</ref> Peugeot plans also a compressed air regenerative braking powertrain called Hybrid Air.<ref>{{cite web | url = http://www.psa-peugeot-citroen.com/en/featured-content/automotive-innovation/hybrid-air-engine-full-hybrid-gasoline | title = Hybrid Air, an innovative full hybrid gasoline system | publisher = PSA-Peugeot-Citroen | access-date = 4 May 2014 | url-status = dead | archive-url = https://web.archive.org/web/20140504141546/http://www.psa-peugeot-citroen.com/en/featured-content/automotive-innovation/hybrid-air-engine-full-hybrid-gasoline | archive-date = 4 May 2014}}</ref><ref>{{cite web | url = http://www.popsci.com/article/cars/car-runs-air | title = The Car That Runs on Air | publisher = Popular Science | date = 25 February 2014 | access-date = 4 May 2014 | url-status = live | archive-url = https://web.archive.org/web/20140302192529/http://www.popsci.com/article/cars/car-runs-air | archive-date = 2 March 2014}}</ref>
[[McLaren]] began testing of their KERS in September 2008 at the Jerez test track in preparation for the 2009 F1 season, although at that time it was not yet known if they would be operating an electrical or mechanical system.<ref>{{cite web |author=Lawrence Butcher |url=http://www.racecar-engineering.com/news/people/274178/mclaren-on-track-with-kers.html |title=F1 KERS; McLaren on track with KERS | People |publisher=Racecar Engineering |date=18 September 2008 |access-date=14 August 2010 |url-status=dead |archive-url=https://web.archive.org/web/20080922221623/http://www.racecar-engineering.com/news/people/274178/mclaren-on-track-with-kers.html |archive-date=22 September 2008}}</ref> In November 2008 it was announced that [[Freescale Semiconductor]] would collaborate with [[McLaren Electronic Systems]] to further develop its KERS for McLaren's Formula One car from 2010 onwards. Both parties believed this collaboration would improve McLaren's KERS system and help the system filter down to road car technology.<ref>[http://www.autosport.com/news/report.php/id/72085 McLaren to work with Freescale on KERS] {{webarchive|url=https://web.archive.org/web/20110608155041/http://www.autosport.com/news/report.php/id/72085 |date=8 June 2011 }} 12 November 2008</ref>
[[Toyota]] has used a [[electric double-layer capacitor|supercapacitor]] for regeneration on a [[Toyota Supra|Supra]] HV-R hybrid race car that won the [[Tokachi 24 Hours]] race in July 2007.<ref>{{cite web |url=http://www.greencarcongress.com/2007/07/toyota-hybrid-r.html |title=Toyota Hybrid Race Car Wins Tokachi 24-Hour Race; In-Wheel Motors and Supercapacitors |publisher=Green Car Congress |date=17 July 2007 |access-date=17 September 2010 |url-status=live |archive-url=https://web.archive.org/web/20110517211826/http://www.greencarcongress.com/2007/07/toyota-hybrid-r.html |archive-date=17 May 2011}}</ref>
BMW has used regenerative braking on their E90 3 Series as well as in current models like F25 5 Series under the EfficientDynamics moniker.<ref>{{Cite web|title = BMW EfficientDynamics : Brake Energy Regeneration|url = http://www.bmw.com/com/en/insights/technology/efficient_dynamics/phase_2/technologies/brake_energy_regeneration.html|website = www.bmw.com|access-date = 3 January 2016|url-status = live|archive-url = https://web.archive.org/web/20160106044548/http://www.bmw.com/com/en/insights/technology/efficient_dynamics/phase_2/technologies/brake_energy_regeneration.html|archive-date = 6 January 2016}}</ref> Volkswagen have regenerative braking technologies under the [[BlueMotion]] brand in such models as the [[Volkswagen Golf Mk7]] and Mk7 Golf Estate / Wagon models, other VW group brands like [[SEAT]], [[Škoda Auto|Skoda]] and [[Audi]].<ref>{{Cite web|title = BlueMotion Technology – Technical glossary – Volkswagen Technology & Service {{!}} VW Australia|url = http://www.volkswagen.com.au/en/technology_and_service/technical-glossary/bluemotion-technologies.html|website = www.volkswagen.com.au|access-date = 3 January 2016|url-status = live|archive-url = https://web.archive.org/web/20160304070433/http://www.volkswagen.com.au/en/technology_and_service/technical-glossary/bluemotion-technologies.html|archive-date = 4 March 2016}}</ref>
=== Motorcycles === [[KTM]] racing boss [[Harald Bartol]] has revealed that the factory raced with a secret kinetic energy recovery system (KERS) fitted to [[Tomoyoshi Koyama|Tommy Koyama]]'s motorcycle during the 2008 season-ending 125cc [[Valencian Community motorcycle Grand Prix|Valencian Grand Prix]]. This was against the rules, so they were banned from doing it afterwards.<ref>{{cite web |url=http://www.crash.net/MotoGP/News/142605/1/ktm_beats_f1_with_secret_kers_debut.html |title=KTM beats F1 with secret KERS debut! | MotoGP News | February 2009 |publisher=Crash.Net |date=4 February 2009 |access-date=14 August 2010 |url-status=live |archive-url= https://web.archive.org/web/20110523172718/http://www.crash.net/MotoGP/News/142605/1/ktm_beats_f1_with_secret_kers_debut.html |archive-date=23 May 2011}}</ref>
=== Races === [[Automobile Club de l'Ouest]], the organizer behind the annual [[24 Hours of Le Mans]] event and the [[Le Mans Series]], was "studying specific rules for [[Le Mans Prototype|LMP1]] that will be equipped with a kinetic energy recovery system" in 2007.<ref>{{cite web | url =http://www.lemans.org/sport/sport/reglements/ressources/auto_2008/cdc_reglement_lmp_fr_gb_2008.pdf |title =ACO Technical Regulations 2008 for Prototype "LM"P1 and "LM"P2 classes, page 3| publisher =Automobile Club de l'Ouest (ACO) | date =20 December 2007 | access-date =20 January 2008 |archive-url = https://web.archive.org/web/20080625190107/http://www.lemans.org/sport/sport/reglements/ressources/auto_2008/cdc_reglement_lmp_fr_gb_2008.pdf <!-- Bot retrieved archive --> |archive-date = 25 June 2008}}</ref> Peugeot was the first manufacturer to unveil a fully functioning LMP1 car in the form of the 908 HY at the 2008 Autosport 1000 km race at Silverstone.<ref>{{cite web |author=Sam Collins |url=http://www.racecar-engineering.com/news/people/273697/peugeot-reveal-hybrid-racer-for-2009.html |title=Peugeot Sport Hybrid | People |publisher=Racecar Engineering |date=13 September 2008 |access-date=14 August 2010 |url-status=dead |archive-url=https://web.archive.org/web/20090113183348/http://www.racecar-engineering.com/news/people/273697/peugeot-reveal-hybrid-racer-for-2009.html |archive-date=13 January 2009}}</ref>
== Civilian transport ==
=== Bicycles === On electric bicycles, regenerative braking can be used in principle. However, as of 2024 it is rarely used on bicycles, mainly because it requires a direct-drive [[hub motor]] (while many bicycles use a mid-drive motor which drives the chain), and because it cannot be combined with a [[freewheel]] mechanism. Also, the amount of energy regenerated is typically too low to be worthwhile.<ref>{{Cite web |title=Why Don't More Bikes Use Regenerative Braking? |url=https://evelo.com/blogs/learn/why-don-t-more-bikes-use-regenerative-braking |access-date=15 May 2023 |website=EVELO |date=8 September 2020 |language=en}}</ref>
Regenerative braking is also possible on a non-electric bicycle. The [[United States Environmental Protection Agency]], working with students from the [[University of Michigan]], developed the [[Hydraulics|hydraulic]] Regenerative Brake Launch Assist (RBLA).<ref>{{cite web|url=http://www.epa.gov/otaq/technology/research/research-hhb.htm|title=Hydraulic Hybrid Bicycle Research|publisher=[[United States Environmental Protection Agency|EPA]]|archive-url=https://web.archive.org/web/20131017083619/http://epa.gov/otaq/technology/research/research-hhb.htm|archive-date=17 October 2013|url-status=dead}}</ref>
=== Cars === Many hybrid electric and fully electric vehicles employ regenerative braking in conjunction with friction braking,<ref>{{cite web|url= https://auto.howstuffworks.com/auto-parts/brakes/brake-types/regenerative-braking.htm/printable |first=Christopher |last=Lampton |title=How Regenerative Braking Works |date=23 January 2009 |work=HowStuffWorks.com |access-date=4 October 2019}}</ref> Regenerative braking systems (RBS) are not able to fully emulate conventional brake function for drivers, but there are continuing advancements.<ref>{{cite web |title=Where are regenerative brakes headed? |url=https://greeninginc.com/blog/new-tech/where-are-regenerative-brakes-headed/ |website=greeninginc.com |date=27 December 2018}}</ref> The calibrations used to determine when energy will be regenerated and when friction braking is used to slow down the vehicle affects the way the driver feels the braking action.<ref>{{cite web |last=Berman |first=Bradley |title=Best And Worst Electric Cars For Regenerative Braking |url= https://insideevs.com/reviews/342108/best-and-worst-electric-cars-for-regenerative-braking/ |website=InsideEVs |date=15 January 2019 |access-date=4 October 2019}}</ref><ref>{{cite web |last=Varocky |first=B.J. |title=Benchmarking of Regenerative Braking for a Fully Electric Car |url=http://www.mate.tue.nl/mate/pdfs/12673.pdf |publisher=Technische Universiteit Eindhoven (TU/e) |access-date=10 October 2019 |date=January 2011 |archive-date=26 November 2019 |archive-url=https://web.archive.org/web/20191126174903/http://www.mate.tue.nl/mate/pdfs/12673.pdf |url-status=dead }}</ref>
The RBS is a key mechanism for electric vehicles to obtain braking energy. This technology seriously affects the economy, emissions, safety and other functions of electric vehicles. By improving the RBS, the kinetic energy recovery rate of the vehicle can be significantly increased, and the driving stability of the vehicle can be improved.<ref>{{Cite journal |last1=Mei |first1=Peng |last2=Karimi |first2=Hamid Reza |last3=Yang |first3=Shichun |last4=Xu |first4=Bin |last5=Huang |first5=Cong |date=February 2022|title=An adaptive fuzzy sliding-mode control for regenerative braking system of electric vehicles |journal=International Journal of Adaptive Control and Signal Processing |language=en |volume=36 |issue=2 |pages=391–410 |doi=10.1002/acs.3347 |issn=0890-6327|doi-access=free }}</ref>
===Streetcars/trams=== Power consumption is reduced by regenerative braking on streetcars ({{abbr|AE|American English}}) or [[Trams in Oranjestad, Aruba|trams]] ({{abbr|CE|Commonwealth English}}) in [[Oranjestad, Aruba]]. Designed and built by TIG/m Modern Street Railways in [[Chatsworth, California|Chatsworth]], USA,<ref name="LATimes-May2015">{{cite news|url=http://www.latimes.com/business/la-fi-made-in-california-trolleymaker-20150527-story.html |title=Chatsworth trolley maker is going places|newspaper=[[Los Angeles Times]]|date=27 May 2015|last=White|first=Ronald D.|access-date=28 May 2016}}</ref> the vehicles use [[hydrail|hybrid/electric]] technology: they do not take their power from external sources such as overhead wires when running but are self-powered by [[Battery (electricity)|lithium batteries]] augmented by [[hydrogen]] [[fuel cell]]s.<ref>{{cite web|url=https://www.altenergymag.com/news/2013/03/27/tigm-modern-street-railways-delivering-world39s-greenest-streetcars-to-aruba-in-island39s-transition-to-100-sustainability/28761 |title=TIG/m Modern Street Railways delivering world's greenest streetcars to Aruba in island's transition to 100% sustainability |author=<!--Not stated--> |date=27 March 2013 |website=altenergymag.com |access-date=29 May 2024 }}</ref>
== Thermodynamics ==
=== KERS flywheel === The energy of a flywheel can be described by this general energy equation, assuming the flywheel is the system: :<math> E_\text{in}-E_\text{out}= \Delta E_\text{system}</math>
where :*<math>E_\text{in}</math> is the energy into the flywheel. :*<math>E_\text{out}</math> is the energy out of the flywheel. :*<math>\Delta E_\text{system}</math> is the change in energy of the flywheel.
An assumption is made that during braking there is no change in the potential energy, [[enthalpy]] of the flywheel, pressure or volume of the flywheel, so only kinetic energy will be considered. As the car is braking, no energy is dispersed by the flywheel, and the only energy into the flywheel is the initial kinetic energy of the car. The equation can be simplified to: :<math>\frac{mv^2} {2} = \Delta E_\text{fly}</math>
where :*<math>m</math> is the mass of the car. :*<math>v</math> is the initial velocity of the car just before braking.
The flywheel collects a percentage of the initial kinetic energy of the car, and this percentage can be represented by <math>\eta_\text{fly}</math>. The flywheel stores the energy as rotational kinetic energy. Because the energy is kept as kinetic energy and not transformed into another type of energy this process is efficient. The flywheel can only store so much energy, however, and this is limited by its maximum amount of rotational kinetic energy. This is determined based upon the inertia of the flywheel and its [[angular velocity]]. As the car sits idle, little rotational kinetic energy is lost over time so the initial amount of energy in the flywheel can be assumed to equal the final amount of energy distributed by the flywheel. The amount of kinetic energy distributed by the flywheel is therefore:
:<math>KE_\text{fly}=\frac{\eta_\text{fly} mv^2} {2} </math>
=== Regenerative brakes === Regenerative braking has a similar energy equation to the equation for the mechanical flywheel. Regenerative braking is a two-step process involving the motor/generator and the battery. The initial kinetic energy is transformed into electrical energy by the generator and is then converted into chemical energy by the battery. This process is less efficient than the flywheel. The efficiency of the generator can be represented by: :<math> \eta_\text{gen}=\frac{W_\text{out}}{W_\text{in}}</math>
where :*<math>W_\text{in}</math> is the work into the generator. :*<math>W_\text{out}</math> is the work produced by the generator.
The only work into the generator is the initial kinetic energy of the car and the only work produced by the generator is the electrical energy. Rearranging this equation to solve for the power produced by the generator gives this equation: :<math>P_\text{gen}= \frac{\eta_\text{gen} mv^2}{2 \, \Delta t} </math>
where :*<math>\Delta t</math> is the amount of time the car brakes. :*<math>m</math> is the mass of the car. :*<math>v</math> is the initial velocity of the car just before braking.
The efficiency of the battery can be described as: :<math> \eta_\text{batt}=\frac{P_\text{out}} {P_\text{in}} </math>
where :*<math>P_\text{in}=P_\text{gen}</math> :*<math>P_\text{out}=\frac{W_\text{out}}{\Delta t}</math> The work out of the battery represents the amount of energy produced by the regenerative brakes. This can be represented by: : <math> W_\text{out}=\frac{\eta_\text{batt} \eta_\text{gen} mv^2}{2}</math>
=== In cars === [[File:Energy flows in car.svg|thumb|400px|Energy efficiency of cars in towns and on motorways according to the [[United States Department of Energy|DoE]]]] [[File:Energy flow in cars (recuperation in green).pdf|thumb|Energy efficiency of electric cars in towns and on motorways according to the [[United States Department of Energy]]]]
A diagram by the [[United States Department of Energy]] (DoE) shows cars with internal combustion engines as having efficiency of typically 13% in urban driving, 20% in highway conditions. Braking in proportion to the useful mechanic energy amounts to 6/13 i.e. 46% in towns, and 2/20 i.e. 10% on motorways.
The DoE states that electric cars convert over 77% of the electrical energy from the grid to power at the wheels.<ref>{{Cite web |title=All-Electric Vehicles |author= |website=Office of Energy Efficiency & Renewable Energy - US Department of Energy |date= |access-date=29 January 2021 |url= https://www.fueleconomy.gov/feg/evtech.shtml}}</ref> The efficiency of an electric vehicle, taking into account losses due to the electric network, heating, and air conditioning is about 50% according to [[Jean-Marc Jancovici]]<ref>{{Cite web |title=Is the electric car an ideal solution for tomorrow's mobility?|author=Jean-Marc Jancovici |work=jancovici.com |date=1 October 2017 |access-date=29 January 2021 |url= https://jancovici.com/transition-energetique/transports/la-voiture-electrique-est-elle-la-solution-aux-problemes-de-pollution-automobile/|language=en}}</ref> (however for the overall conversion see [[Embodied energy#Embodied energy in the energy field]]).
Consider the electric motor efficiency <math>\eta_\text{eng}=0.5</math> and the braking proportion in towns <math>p=0.46</math> and on motorways <math>p=0.1</math>.
Let us introduce <math>\eta_\text{recup}</math> which is the recuperated proportion of braking energy. Let us assume <math>\eta_\text{recup}=0.6</math>.<ref>{{Cite web |title=Bremsenergierückgewinnung und ihr Wirkungsgrad |trans-title=Brake energy recovery and its efficiency |last=Schwarzer |first=Christoph M. |website=heise online - heise Autos |date=21 March 2019 |url= https://www.heise.de/autos/artikel/Bremsenergierueckgewinnung-und-ihr-Wirkungsgrad-4340576.html |language=de}}</ref>
[[File:Regenerative brake.png|thumb|Description of the energy flux in the case of regenerative braking]] Under these circumstances, <math>E</math> being the energy flux arriving at the electric engine, <math>E_\text{braking}</math> the energy flux lost while braking and <math>E_\text{recup}</math> the recuperated energy flux, an equilibrium is reached according to the equations
<math>E_\text{braking}=(E + E_\text{recup}) \cdot \eta_\text{eng} \cdot p</math> and <math>E_\text{recup}=\eta_\text{recup} \cdot E_\text{braking}</math>
thus <math>E_\text{braking}=\frac {E \cdot \eta_\text{eng} \cdot p} {1-\eta_\text{eng} \cdot p \cdot \eta_\text{recup}}</math>
It is as though the old energy flux <math>E</math> was replaced by a new one <math>E \cdot (1-\eta_\text{eng} \cdot p \cdot \eta_\text{recup})</math>
The expected gain amounts to <math>\eta_\text{eng} \cdot p \cdot \eta_\text{recup}</math>
The higher the recuperation efficiency, the higher the recuperation.
The higher the efficiency between the electric motor and the wheels, the higher the recuperation.
The higher the braking proportion, the higher the recuperation.
On motorways, this figure would be 3%, and in cities it would amount to 14%.
== See also == {{Div col|colwidth=22em}} * {{Annotated link |Kinetic energy recovery system}} * {{Annotated link |Brake (railway)}} * {{Annotated link |Electromagnetic brake}} * {{Annotated link |Regenerative (design)}} * {{Annotated link |Regenerative shock absorber}} * {{Annotated link |Hybrid Synergy Drive}} * {{Annotated link |Ram air turbine}} * {{Annotated link |Dynamic braking}} * {{Annotated link |Electric motor}} * {{Annotated link |Self-winding watch}} * {{Annotated link |Brake run}} * {{Annotated link |Electromagnetic clutch}} * {{Annotated link |Eddy current brake}} {{div col end}}
== References == {{reflist|colwidth=30em}} {{reflist|group=Note}}
{{Powertrain}} {{Railway brakes}}{{Electric vehicles}} [[Category:Dynamic braking]] [[Category:Electric vehicle technologies]] [[Category:Energy recovery]] [[Category:Railway brakes]] [[Category:Electric motors]]