With a
this technology from motorsports guaranteed that the engines could handle sustained full throttle operation. continually monitored the operation of the entire exhaust system with catalytic converters and oxygen sensors, the functioning of the tank
All engines were
previously unknown minimum. Misfiring was also recorded. In 1974, 111 units of the Carrera RS were built with 3-litre engines as homologation vehicles for Group 3. Turbo for several years, because its engine was not configured for the use of a catalytic converter. For
It would return in 1985 with 210 kW (282 hp) of power. The two regulated turbines with integrated bypass flap generated a boost pressure of 0.8 bar. of the Porsche technical specialists could have foreseen that this engine type, in its basic form, would be continued up to the year 1998 or that its displacement would reach 3.8 litres. In the 911 Carrera, the engine produced 170 kW (231 hp) at 5900/min and delivered a torque of 284 Newton metres (for
Les Flat 6 sont chers aux passionnés de la marque. 1995: Bi-turbochargingThe 993 series 911 Turbo, presented in 1995, was given a 3.6-litre engine fitted with two small turbochargers, whose performance curve was not
À l’avant du flat 6, comme sur les blocs moteurs des précédentes générations de 911, l’arbre intermédiaire repose sur un palier sous pression d’huile, une technique tout à fait fiable et ayant fait ses preuves par le passé. Equipé de deux réservoir souple de 40 litres. Hans Mezger s’en est allé le jeudi 10 juin à l’âge de 90 ans. Le moteur dans le véhicules PORSCHE 911 est en charge de la génération de la puissance qui déplace le véhicule. Its torque was 520 Newton metres. Tout se fait sans collage ou peinture. [12](pp218,220), "The Wilson-Pilcher Petrol Cars", The Automotor Journal, April 16th, 1904, pp. The correct injection quantity and the exact ignition point were assigned to each
extensively modified that it was essentially a new design. move into new performance classes. of 80 hp per litre without any reduction in engine life. its higher rev reserves and more refined running properties one overhead camshaft per side. [10] Following a hiatus of flat-6 engine production for four years, the Subaru EZ30 engine was introduced in the 2000 Subaru Legacy/Outback. Early flat-six engines include the Franklin O-265 which began production in 1940, and the Lycoming O-435 which began production in 1942. The most notable use of flat-six engines is the Porsche 911 sports car, which has used flat-six engines continuously since 1963. Several other car manufacturers, including Subaru, have produced flat-six engines at times. The year 1990 saw a new edition of the 911 Turbo with a new engine. (320 hp) at 6800/min and a torque of 370 Newton metres. weight-to-power ratio of 3.5 kg per hp, the new 911 Carrera S is at the top of its competitive field. Reproduction du moteur plus qu'approximative, à faire fuir tous les porschistes. More engine displacement resulted in more power and torque; it was first increased to 2.2 litres in 1969, then to 2.4 litres two years later. In 1991, the Subaru EG33 engine was used in the Subaru Alcyone SVX, the replacement for the Subaru XT. Porsche 911 Moteur Boxer Flat 6 - 1/4 - Selection RS - YouTube One unique aspect was that it featured two spark plugs per combustion chamber to assure better combustion. S, for example, this initially boosted power to 132 kW (180 hp) and then to 140 kW (190 hp). (street version: 316 kW/430 hp). As per other six-cylinder engines, the overlapping power strokes of the cylinders (with a firing interval of 120 degrees in a four-stroke engine) reduces the pulsating power delivery seen on engines with fewer cylinders. time by a series production manufacturer. The
Its features included a different camshaft, reinforced connecting rods, pressed and coated
But in the view of automotive experts, the shift to water cooling did not by any means water down the total 911 package, rather just
À en juger par le son émis lors des changements de rapports, nous pensons que cette sportive embarque une boîte de vitesses à double embrayage, plutôt qu'une boîte manuelle. Then there was the GT3, whose naturally-aspirated engine was based on that of the GT1 but developed 265 kW (360 hp) at 7200/min. USA and Japan: 152 kW/207 hp and 260 Newton metres). kW (300 hp) at 6800/min and was much better at high revving than the previous naturally-aspirated engine. the 911 Carrera at first, one year later the new engine was also offered in the Carrera 4, and the Turbo was also switched over to water cooling. identifier 911 L, and later 911 E. Engineers were especially proud of having achieved this power boost in the 911 S and a power-to-displacement ratio
Cette maquette de qualité a été créé à partir des dessins originaux et comporte plus de 290 pièces partiellement mobiles. control system ensured "healthy" engine operating conditions. Carrera with 8.2 litres per 100 km and the 911 Carrera S (with 8.7 litres) each with Porsche Doppelkupplung once again exhibit top values. Starting in 1967, there was also the 911 T with reduced power output (81 kW/110 hp at 5800/min), which was designed as an entry-level model. At the
monitoring. that was also equipped with an intercooler. Its features included thermally optimised cylinders and cylinder head seals
The engine now developed 235 kW (320 hp) at 5750/min and a torque of 450 Newton metres from the same 3.3 litres of
(140 hp) at 6500/min, while the second produced 125 kW (170 hp). Now you can build a fully-functional 1: 4 model of an all-time classic motor - the flat-six engine from the Porsche 911. The most common type of flat-six engine is the boxer-six engine, where each pair of opposed cylinders moves inwards and outwards at the same time. In the year 1976, continually more stringent emissions regulations had to be satisfied, especially in the USA, Canada and Japan. The charge air cooler
Several other car manufacturers, including Subaru, have produced flat-six engines at times. Using direct petrol injection, combustion can be controlled more precisely according to specific operating states, which has resulted in significant fuel savings. 6800/min and 283 kW (385 hp) at 6500/min, respectively. In
En effet, le moteur comporte aussi quelques contraintes, notamment en termes de largeur et de refroidissement. ventilation system with activated charcoal filters, the secondary air system and the fuel system. La Porsche 718 GTS 4.0 en quelques chiffres Moteur: Flat 6, essence, 3.996cc ; 400ch à 7.000 tr/min ; 420Nm de 5.000 à 6.500 tr/min. La 911 est le modèle le plus célèbre de Porsche Il est important de bien lire et suivre la notice (inclue dans le livret) qui est dans l’ensemble assez claire. The 3.6-litre naturally-aspirated engine of the Carrera was preserved, while the
Carrera 2. Newton metres. Quand les gens pensent à Porsche, la première chose qui vient à lesprit est souvent la silhouette de la 911 et son moteur à plat. Accueil; PROMOS; Porsche Miniature. 1973, all engines were switched over to 2.7 litres displacement in the G model; at the same time, the use of regular unleaded petrol was enabled
Carrera S was distinguished by a new engine. Un moteur à plat (ou en V à 180°, en anglais flat ou boxer) est un moteur à pistons dans lequel les cylindres et pistons, normalement en nombre pair, sont sur un même plan (généralement horizontal) et disposés de part et d'autre du vilebrequin. [8] Both are rear-engined cars with rear-wheel drive. In 1972, the K-Jetronic made its debut, initially for the USA. Le problème vient de l’extrémité de l’IMS située à l’arrière du moteur. Le capot renferme un flat-six de 4,0 litres, on l'entend d'ailleurs très bien chanter dans la vidéo ci-dessus. The Wilson-Pilcher was a front-engined car with the crankshaft in-line with the chassis and the cylinders between the chassis rails. It facilitated early detection of faults or defects in the exhaust and fuel system. The six-cylinder flat engines had sodium-filled exhaust valves
Les cotes des modèles Porsche d’occasion fluctuent énormément suivant leur état et leur kilométrage. Moteur 6-cylindres à plat (flat-six) disposé en porte-à-faux arrière. The extensive measures
Its actual highlight was a low gross weight of 1120 kg (with manual gearbox) compared to the 1350 kg of a
advantages were better fuel consumption, cleaner combustion and therefore maximum power output. Le cas des Flat 6 à double allumage - moteurs de 964 et 993 : Lorsque c’est possible au niveau du règlement, ou en utilisation loisir, une gestion électronique MOTEC accouplée à des boitier papillon PMO ou JENVEY permet de tirer toute la quintessence de la préparation moteur en maximisant la puissance et en optimisant la consommation. Other Porsche models that use flat-six engines are the 1970-1972 Porsche 914/6 (mid-engine), the 1986-1993 Porsche 959 (rear-engine), and the 1996-2021 Porsche Boxster/Cayman (mid-engine). Each year, lots of small details on
Several examples of the Pietenpol Air Camper homebuilt monoplane aircraft have used the air-cooled engine from the Chevrolet Corvair compact car. The next GT3 (305 kW/415 hp) was also based on the 997 model series; it was presented at the Geneva International Motor Show in
Two American manufacturers briefly produced cars with flat-six engines— the 1948 Tucker 48 (water-cooled) and the 1959-1969 Chevrolet Corvair (air-cooled). Moteurs adulés à juste titre, mais redouté par la plupart des mécanos, les Flat 6 Porsche n’ont aucun secret pour Bourcier Auto Sport. The 993 Turbo also featured a ground-breaking flat six as it became the first twin turbocharged 911 (following the lead of the 959). 463-468, "The Physics of: Engine Cylinder-Bank Angles", "Pietenpol Official Pietenpol Air Camper Family Website", "The Lycoming O-540 Engine and Why We Use It", "Flat Sixy: The Evolution of Porsche 911 Engine Size, Technology, and Output in the U.S.", "7 Flat-Six-Powered Vehicles That Aren't Porsches", "Flat-6 Club: 1993 Subaru Impreza w/ Legacy 6-Cyl", "Subaru history in the USA: the models, the changes", https://en.wikipedia.org/w/index.php?title=Flat-six_engine&oldid=985372489, Creative Commons Attribution-ShareAlike License, This page was last edited on 25 October 2020, at 16:02. Japanese manufacturer Subaru produced water-cooled flat-6 engines from 1988–1996 and 2001–2019. Under
The camshafts were chain driven after bevel shafts or toothed belts were retired. A boxer-style flat-six engine is able to have perfect primary and secondary balance. Une fois le couvercle du coffret enlevé, la notice sous blister transparent qui est aussi un livre sur l’histoire de Porsche et notamment du moteur … [3] Compared with the engines used in cars, flat-six engines used by helicopters have large displacements and are low revving, producing more torque and less power. The
Its importance has increased in every model series ever since it was introduced. They achieved this by using two small turbochargers instead of one large one, whereby the low moment of inertia of
made of stainless steel. Under the leadership of the nephew of Ferry Porsche, Ferdinand Piëch, an air-cooled six-cylinder flat engine was created with an axial blower and – due to its higher rev reserves and more refined running properties – one overhead camshaft per side. From 3.8 litres displacement, it produced 261 kW (355 hp) at 6600/min and developed a torque of 400
That was sufficient for a power boost to 235 kW
Since the RS could not be registered in the USA, the RS America was sold in this market which featured engine technology of the Carrera 2
However, its key design properties were
Turbo re -ceived a new engine (309 kW/420 hp at 6000/min, 560 Newton metres) that was derived directly from the GT1. In 1992, the Turbo S was introduced of which only 86 units were produced; its engine developed 280 kW (381
emissions regulations, the engine's compression ratio was also reduced so that all 911 cars could continue to be driven with regular petrol worldwide. Du « vieux » 2L jusqu’au très récents 3,8 ou 4,0L, tous les Flat 6 Porsche peuvent faire l’objet de reconstruction partielles ou complètes. These characteristics result in low vibration for flat-six engines (as per straight-six engines), especially when compared with the imbalances that are present in V6 engines with a 90-degree bank angle. 1983: Digital engine electronicsDigital engine electronics (DEE) celebrated its debut in 1983 with the new naturally aspirated engine with 3.2-litre displacement. The first car to use a flat-six engine was the 1904–1907 Wilson-Pilcher 18/24 HP,[6] which used an engine based on a flat-four engine with two cylinders added. Ayant une solide expérience de la mécanique Porsche, vous pouvez confier votre auto pour des interventions techniques comme la réfection d'un moteur ou d'une boite de vitesses ou encore des prestations de fiabilisation moteurs sur Flat 6 Porsche. knowledge, Porsche developed new downsizing technology for the 911 of the 991 model series, which appeared in 2011: For example, the flat engine
the outset, their emissions behaviour was developed to meet the strictest regulations. At that time, none
Le kit du moteur Porsche Flat 6 à l’échelle 1:4 Le kit du moteur se présente dans une grande boîte de très bonne qualité à l’image des produits Porsche. "Downsizing" for improved fuel efficiency became a guiding design principle for engine engineers starting around 2008. [12](pp198,218) The limited edition 2004 Valkyrie Rune was based on the GL1800. Flat-six engines have also occasionally been used in aircraft and motorcycles. The
Cote Porsche 911 d'Occasion. motorsport, a short production run of the 911 GT2 was made; with two turbochargers its 3.6-litre engine could develop 316 kW (450 hp) at 5750/min
Some aircraft have used flat-six engines originally designed for cars. Porsche was the first company in Europe to install emission test benches for its development work. At the same engine displacements, they produced 254 kW (345 hp) at
Several manufacturers use the letter "O" in the model code for flat-six engines, as an abbreviation for the opposed cylinder layout. Its most important
Then engineers switched over to water cooling one benefit was that this let them
engine of the 911 Carrera RS 3.0, it produced 191 kW (260 hp) and a torque of 343 Newton metres and accelerated the car to a top speed of over 250 km/h. no fuel was consumed when the engine was overrunning, and
kit bon pour enfants en dessous de 8 ans et non intéressé par Porsche.prix sans rapport avec la prestation, autant acheter un kit du commerce qui lui sera fidèle, certes à une échelle moindre mais 5 à 6 fois moins cher. Only available in
To the great surprise of the experts, the turbo engine turned out to be the lowest
From as low as 2,000 rpm, the engine generated plenty of thrust which changed into
Another advantage is the improvement in antiknock properties excess temperatures causing the mixture to self-ignite is virtually ruled out. Cote Porsche d'Occasion. engine, with its 3.4 litres displacement, was significantly shorter (by 70 mm) and much lower (by 120 mm) than the previous engine. Cette superbe 911 S est née en 1973, en Allemagne et y a été livrée neuve. L'arrivée du Flat-6 sur le Cayman GTS permet au petit coupé Porsche de recomposer un trio devenu rare et pourtant délicieux : puissant six-cylindres atmosphérique, propulsion et boîte mécanique. It simultaneously served as the basis for the new GT2 (340 kW/442 hp at 5700/min, 620 Newton metres). The disadvantages are a large width (which can limit the maximum steering angle when used in a front-engined car), a large intake manifold being required when a central carburetor is used, and duplication of the inlet and outlet connections for water-cooled engines.[1]. [4], The flat-six engine is often associated with the Porsche 911, a rear-engined sports car which has used flat-six engines exclusively since 1963. torque of 310 Newton metres. The main features of the 911 Turbo, reworked in 1977, were an increased displacement of 3.3 litres and a charge air cooler
In the 911
1939 1.1 L (1,100 cc) 40 PS (29 kW; 39 bhp) or 50 PS (37 kW; 49 bhp) air-cooled boxer flat-four Porsche 356. Meanwhile, the types 924 and 928 appeared, and in 1977 the company reduced its 911
reduces the intake air temperature by up to 100 degrees Celsius, thus enabling the engine to achieve higher output and torque in all engine speed
La puissance passerait de 500 chevaux à environ 550 ch (410 kW). Caracteristiques techniques de la PORSCHE 936 flat 6 1976 compétition essence 700 kg : performance, consommation, prix, tarif, équipement, dimension, poids. The exhaust gas temperatures fall, as
Starting in model year 1967, the power-boosted 911 S version produced 118 kW (160 hp) at 6,600/min and the "normal" 911 soon carried the model
Flat engines largely replaced the historically more popular radial engines in small aircraft after World War II because they were less expensive to manufacture. Porsche succeeded in fulfilling emission
powerboosted to 191 kW (260 hp). unaltered: six-cylinder, seven-bearing crankshaft, dry sump lubrication, dual-mass flywheel and a longitudinally split engine housing. the 911 have been improved so that it has become closer and closer to Ferry Porsche's ideal image of a perfect sports car. whose signals were processed in a controller and were used directly for mixture control. Transmission: aux roues arrière. compared to that of an equivalent naturally-aspirated engine was primarily obtained from higher charge pressure and a modified ignition map. [9] Their first flat-6 engine, the Subaru ER27, was added to the model range of the Subaru XT coupe. This detailed replica features more than 280 components found in the real thing, and transparent casing so the moving parts can be seen when switched on. Carrera 2 introduced one year later which replaced the previous 911 with rear-wheel drive and a naturally-aspirated engine also got this engine. Le garage FLAT 06 CLASSIC Spécialiste Mécanique, Carrosserie et Restauration Porsche vous accueille au, Chemin de la Douane Prolongée, 06510 Carros. the smaller blades had the most significant effect. Il y a différentes classes de moteurs, il en y a le deux ou quatre temps, à essence, également appelé moteurs à explosion, ou de gasoil, connu sous le nom des moteurs à combustion. Most motorcycles use engines with four or fewer cylinders, however the Honda Gold Wing touring motorcycle has used a water-cooled flat-six engine since 1987. Carrera S (294 kW/400 hp at 7400/min, 440 Newton metres) retained its 3.8 litres of displacement. There was one disappointment, however: Customers in the USA had to do without the 911
Notre modèle a été entièrement révisé. Moteur Flat 6 boxer de Porsche avec pièces transparentesLa construction de la Porsche 911 avec son moteur boxer 6 cylindres est étroitement liée à l’histoire de Porsche AG. The advantages of the flat-six layout are good engine balance (for reduced vibration), a low center of gravity, short length (compared with an inline-six engine) and being well suited to air-cooling. At first, this shift met with scepticism by many enthusiasts, and for some purists it still represents a break with
1995: OBD II emissions control systemAnother technical highlight of the six-cylinder car was the new OBD (onboard diagnostics) II emissions monitoring system which was used for the first
hp) at 6000/min and a torque of 490 Newton metres. in the 911 Carrera (257 kW/350 hp at 7400/min, 390 Newton metres) was given a displacement of 3.4 litres instead of the previous 3.6 litres. + + This philosophy was also
Il possède des roues pluie + slic. OBD required a great deal of development work and an extremely complex engine management system. pistons, pressed alloy cylinders with surface coating and lengthened intake ports. All engines were used in front-engine cars with all-wheel drive, plus the XT and Alcyone SVX were also available with front-wheel drive. The result was a stable 300 hp at 5,500 rpm and a maximum
IL est équipé d’un 6 cylindre à plat Porsche 911S de 2L. En tout, moins de 10 voitures seront construites avec des moteurs de R8 Gordini de 1300 cm3 et 1 modèle avec un moteur Flat 6 de Porsche 906 Carrera 6. The Turbo also adopted the biturbo concept, and another global innovation was the OBD II emissions system
And in terms of NEDC fuel consumption, the 911
var addthis_config = {"data_track_clickback":true}; In coming up with the conceptual design for a new engine in the 356 successor, it was clear from the outset that it would be a rear engine. March 2006. which launched in 2003 and was primarily intended for motorsports, had a higher power output of 280 kW (381 hp) that was primarily due to its higher revving capabilities and an adjustable camshaft. electronic idle speed control when auxiliary components were activated were useful additions provided by the digital engine electronics. for reducing emissions were very effective on the 911 Turbo. Furthermore, the charge air cooling also reduces the thermal load on the engine. applied to the 911 Turbo. The camshafts were chain driven after bevel shafts or
AUTO MOTOR FLAT vous conseillera au mieux et dans votre seul intéret, envie de changement, visibilité maximale grâce à notre espace d'exposition trés bien situé, entièrement dédié aux véhicules de marque Porsche, nous contribuerons ainsi à la finalisation de votre projet. the opposite was the case. Both of these vehicles illustrate how the 991 model series has been reengineered for maximum fuel efficiency in a total package. Ce moteur fut conçu par l’ingénieur allemand Ferdinand Porsche qui crée sa propre marque et la célèbre Porsche 911, en 1964, avec un moteur flat-6. One year later, a fine delicacy for motorsport oriented customers made its appearance: the 911 Carrera RS, whose 3.6-litre engine was
Automotive engines Porsche 64. ranges cooler gases are denser and therefore charge the engine more effectively. In 2008, the 911 and 911 S
The initial specification called for 2 litres of displacement with a potential for increases up to 2.7 litres. The next generation 911 of the 997 model series appeared in 2004. 1997: The first water-cooled Porsche six-cylinder engine. engine speed, each accelerator position and temperature. The flat engine was air-cooled up to and including the type 993. Flat-six engines have also occasionally been used in aircraft and motorcycles. These modifications included a torsionally stiffer crankshaft, improved and lighter
The OBD
[12](p208), The Honda Valkyrie F6C (1997–2003) was a cruiser based on the GL1500 Gold Wing. Qui est en ligne ? Une restauration intégrale a été opérée entre 2005 et 2006, ce qui lui a valu un reportage dans le magazine Flat 6 (N°181). From
The first vehicles to feature engines with an emissions control system were offered in the USA in 1968. 911 de 1965 à 1973. launched, OBD II was already mandatory in the USA and other markets soon followed. Its successor followed in 1992: the 911 Turbo 3.6 with 265 kW (360 hp) whose higher power
A flat-six engine, also known as a horizontally opposed-six, is a six-cylinder piston engine with three cylinders on each side of a central crankshaft. Possesseurs de Porsche 911, 912, 914, 928, Cayman, Boxter, neuves ou anciennes, découvrez les avantages de notre offre d’assurance automobile 'Clubs Porsche' et … The GT3 RS,
SET & COFFRET PORSCHE; PORSCHE 356 550 718 804; PORSCHE 904 906 907 908 910; PORSCHE 911; PORSCHE PANAMERA ; PORSCHE CAYMAN regulations in the USA including especially strict rules in California without compromising car performance and with nearly identical ride comfort. simpler features than in the 911. plus sport chassis and a rear spoiler. completeness, a brief mention should also be made of the Porsche 912 here. One year later, the next GT2 appeared, whose biturbo engine produced 390 kW (530 hp) at 6500/min. For the sake of
Derived from the field of motor racing, it was a world first in a series production car. Initially, vehicles for
There were new engines for the 911 E and the 911 S the first produced 103 kW
Exploiting its bundled
these markets received complex emissions control systems. Emissions were controlled by exhaust gas recirculation in the induction manifold and by thermal reactors. In 2000, the
Moteur Flat 6 de Porsche avec pièces transparentes La construction de la réplique améliorée du moteur Flat 6 de la Porsche 911de 1966 est toujours assez agréable, prenant environ 3 heures. manufacturer had transferred its extensive experience with charged engines from motorsports to series production. now prepared for unleaded regular petrol this fuel was still unavailable in many European countries, so this modification would permit a flexible
The
The engines were air-cooled until 1999, when Porsche started using water-cooled engines.[5]. The smaller frontal area compared with a radial engine also results in less drag. positioned underneath the rear spoiler. In autumn 1968, Porsche introduced mechanical petrol injection. retaining the same engine displacement and compression ratio. Première génération 911 conçue en 1964. The supercharged 993 was also the first bi-turbo with air mass control in automotive history. In 1997, the 996 model series made a quantum leap in 911 history. reaction to its availability. 911 history. impressive, rousing velocity from 3,500 rpm and pressed the occupants into their seats. The Turbo got an engine with a higher 3.3 litres displacement
At the time it was
impressive increase in output and engine speed was also due to optimisation of the charge cycle, the high level of efficiency of the two charge air
A new six-cylinder model debuted in the same year: the Carrera RS with a 2.7-litre
The Porsche PFM 3200 engine, produced from 1985-1991, was based on the engine used in the Porsche 911 sports car. It was fitted with
The most notable use of flat-six engines is the Porsche 911 sports car, which has used flat-six engines continuously since 1963. Porsche was proving that sports cars could be eco-friendly as well. The
A new generation of naturally-aspirated engines was presented in 1983 with 3.2 litres of displacement and digital engine electronics. Cette cox' est une 1302 de 1971 qui fut équipée d'un moteur de Porsche 911 3.2l développant 231 chevaux. Cette auto est “matching numbers”, combinaison de couleurs d’origine, moteur … Prenez connaissance de la valeur de votre Porsche 911 d’occasion au regard de son état afin d’estimer son prix de vente. La … It produced 221
coolers and the knock control system that facilitated running the engine at optimum efficiency. Another legend made its debut in 1974 as well: Porsche introduced the 911 Turbo, the first production sports car with a turbocharger. dissimilar to a high-displacement naturally aspirated engine. In 1993, various modifications were made to the Carrera engine in the just introduced 993 model series to boost its power to 200 kW (272 hp) while
Reports on this car quote it as being "remarkably silent and smooth running" and "almost total absence of vibration".[7]. The results: a solid 221 kW (300 hp) at 5500/min and a torque of 412 Newton metres. 1977: Charge air coolingOne of the secrets of the success of the 911 series is that it has been enhanced constantly and systematically.