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The V10 is essentially the result of mating two even-firing straight-5 engines together. The straight-5 engine shows first and second order rocking motion. Here it should be assumed that the crankshaft with low second-order vibration is used and the first order is balanced by a balance shaft. By mating the straight-5 banks at 90 degrees and using five throws, the balance shafts balance each other and become null. The firing sequence is odd (BMW S85, Dodge Viper, Volkswagen Touareg). Using an 18° split journal crankshaft the firing order can be made even, and the two balanced shaft do not balance each other completely, but are combined into a single very small balance shaft (Lamborghini V10, Porsche Carrera GT). Using a five-throw crankshaft and 72° bank angle the firing order can be made even, and the two balanced shafts do not balance each other completely, but are combined into a single small balance shaft (Toyota 1LR-GUE engine). A 36° degree bank angle and a 108° flying arm crankshaft would allow even firing without a balance shaft and smaller counterweights, but would be impractical.
The V10 configuration is not an inherently balanced design like a straight-6, V-12, flat-6, or V-8 (ignoring the counterweights) and does still have a small second order rocking motion, which can only be compensated by two additional balance shafts.
Until recently, the V10 configuration was not a common configuration for road cars; a V12 is only slightly more complicated and runs more smoothly, while a V8 is less complex and more economical. For the Lexus LFA, the engineers selected a V10 engine over an equivalent displacement V8 because they could not get the V8 to rev as high as the V10, and over a V12 for its lower reciprocating mass, allowing for more rapid engine response. For Audi in their Audi R8 5.2 FSI quattro, the V10 was a compromise between a V12 which would be too long and suffer more internal friction due to extra cylinders and valves, and a V8 which would be more compact but have larger heavier pistons and produce lower revs. 
The Dodge V10 engine saw its first production use in substantially revised form in the Dodge Viper sports car, while the truck version of the engine was used starting with the 2nd generation Dodge Ram. It discontinued in that application after 2003. However, 2003 also saw the introduction of the Dodge Ram SRT-10, a performance model meant to rival Ford's successful V8 powered F-150 SVT Lightning. The Viper engine (a 90-degree engine with odd firing order to obviate the need for a balance shaft) has been tweaked through the years, and for the fifth-generation Viper produces 640 hp (477 kW; 649 PS) in a standard state of tune from its 8.4 liter displacement. The previous generation engine is used by Bristol, in tuned form, in their two-seat Fighter coupe, where it can produce upward of 630 hp (470 kW; 639 PS).
Ford also developed a heavy-duty V10 version of their Triton engine to replace the 460 big block in truck applications. It was introduced in the E-Series/Econoline full-size van. The F-Series Super Duty and Excursion SUV furthered the engines popularity. The Triton 6.8 V10 is still in production today.
European marques were slower to adopt the V10 configuration. However, high-revving V10 power-plants were incorporated into supercars from Lamborghini and Porsche. BMW and Audi later unveiled ten-cylinder versions of their mid-range saloons (the BMW 5-Series and Audi A6 families, respectively). Audi here profited from their Lamborghini ownership, which allowed them to source the Gallardo's V10 for their own cars. Volkswagen also developed a turbodiesel V10; their Volkswagen Phaeton was the first production sedan to have a V10.
A list of post-war V10-engined production cars (sorted alphabetically by manufacturer, sub-sorted by year of introduction):
The most widespread use of the V10 has been in Formula One racing. Alfa Romeo made the first modern Formula One V10 in 1986, although it was never used in a Formula One car. Later the configuration was introduced by Honda and Renault before the 1989 season. The introduction of the 3.5 liter rule after turbos were outlawed following 1988 made the V10 seem the best compromise between the V8 and V12. V10 engines became commonplace after the reduction from 3.5 to 3 liters in 1995, and were used exclusively by teams from 1998 to 2005. Renault had a more flat 110° angle in 2002 and 2003, but reverted to a more conventional 72° following the change in rules which dictated that an engine must last two race weekends. In a further change to the rules, V10s were banned for the 2006 season onwards in favor of 2.4 liter V8s, however a concession was made in that season for teams to use significantly rev limited V10s; Scuderia Toro Rosso being the only team to use this option.
The Audi R15 LMP1 Uses a TDI V10 Diesel Engine which made its debut in 2009 12 Hours of Sebring
There are also cars with V10 engines in sports car racing, usually with Judd power plants with 4 or 5 liter engines, made available for customers, although the first V10 was seen in the works Peugeot 905, in the two final races of the 1990 World Sportscar Championship season. It was also seen in the works Toyota TS010 that appeared at the end of 1991.
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