FIVE-speed. Do you remember this decal that was pasted on the backs of new vehicles following the introduction of the extra ratio over four-speed transmissions? Back then, each gear increment was met with much media hype and enthusiasm from the motoring public. These days, the release of an extra ratio goes almost unnoticed. Porsche recently released a world-first seven-speed manual transmission (in the 911) and both Mercedes-Benz and ZF have developed nine-speed automatics.
The basics
Engine torque is delivered to the input shaft of a vehicle’s transmission. The output shaft carries the altered torque value to the input shaft of the differential, which in turn delivers the (again altered) torque to the driven wheels. A transmission ratio of 4,38:1 implies that the input shaft turns 4,38 times per full revolution of the output shaft (we’re using the transmission from the new Mercedes-Benz C250 to illustrate this feature; it’s driven on page 38). This can be accomplished, for example, by meshing a 21-tooth gear with a 92-tooth one because the tooth number directly translates to gear diameter and therefore gear ratio (92/21 = 4,38). The total reduction ratio at the rear wheels in first gear includes the final drive ratio (differential) of 3,07:1 and therefore equates to 4,38 x 3,07 = 13,45:1. This means that, when the C250 engine
rotates at 1 000 r/min, the rear axles (and wheels) rotate at approximately 74 r/min when travelling in a straight line in first gear.
Speed range
Internal-combustion engines generally have a fixed-speed operating range between idle and the maximum r/min (redline). The vehicle-speed range is very much application and market dependent; a sedan such as the C250 would be required to deal with stop/start traffic and reach a top speed of 250 km/h on the autobahn in Germany. A single total gear ratio (transmission and differential) connected to the engine is unable to power the car at walking speeds and obtain a top speed of 250 km/h. Either the gear will be too short to reach 250 km/h if adequate motive force for acceptable acceleration is provided (see the next section), or the motive force will be too small to accelerate the vehicle at acceptable levels at low speeds if it is geared for top speed. The idea is to establish a low ratio to cater for low-speed driving and a high ratio to enable the vehicle to reach the target top speed. The additional ratios in the transmission bridge the gap between the two extreme ratios (in case of the C250, five). Note that a clutch is needed to connect a turning powertrain (internal-combustion engine) to a static wheel (stationary vehicle). A clutch is not needed in electric powertrains because the electric motor can deliver maximum torque at zero r/min (see Electric powertrains below). The adjacent graph depicts the transmission ratios against vehicle speed for the C250 in the format given in our road tests.
Torque multiplication
A reduction gear set in essence reduces the rotational speed while multiplying the torque output by the same ratio (ignoring transmission losses). It is important to note that power stays constant and it is not multiplied, as is the case with torque. See the table in images above for maximum torque figures at the transmission and differential shafts of the C250. Note that the maximum engine torque at the flywheels is a claimed 350 N.m.
It’s clear the high motive forces (resulting from the traction between tyre and road) in the low gears aids acceleration and “grade-ability”, but maximum engine speed restricts maximum vehicle speed. This also explains why there is very little response when trying to accelerate in a high gear at low speed; the tractive force is limited. The constant speed line replicates that of a continuously variable transmission (CVT) when the engine speed is at 6 000 r/min (see The perfect transmission? below).
Fuel consumption
When engineers calculate the gear ratios of a new vehicle, they take the required performance requirements into consideration, as well as the brake-specific fuel consumption (BSFC) map for the engine (see example in images). The BSFC map looks at the specific fuel usage of the engine versus engine speed and load. This shows areas of constant fuel-consumption contours and the idea is to keep the operating point of the engine close to the optimum region to minimise fuel usage. It’s clear from the long final gearing of the C250 that the optimum operating point is found in the lower engine speed range. Therefore, the transmission calibration tries to keep engine speeds low when performance is not required.
The future
An infinite number of gear ratios, as replicated by a CVT, is the optimum solution. The problem is that the efficiency of a CVT is not as high as that of paired gear sets, which in turn negate the theoretical gains. Until a new mechanism of infinite gearing is found, we’ll see even more gear ratios added to conventional transmissions.
The Perfect Transmission?
From an engineering standpoint, a CVT appears to be the perfect solution. Infinite gear ratios allow engineers to optimise the engine to run effectively at constant engine speed (theoretically, no fancy variable valve timing and so on is needed). Normally, automakers run the engine around peak torque (lowest brake-specific fuel consumption) for best fuel consumption and peak power for performance.
Unfortunately, it isn’t that simple. The transmission belt (a special unit to withstand the torque) between the pulleys does not mean there’s point contact on the pulleys, but rather area contact. Therefore, the inner and outer radii of the contact area have to slip, which create heat and waste energy, and so negate the efficiency gains made with constant engine speed and infinite gear ratios. Furthermore, the actuation forces between the pulleys and belt are very high (to avoid complete slip), the result of which is a need for complex hydraulic/electric actuators and control systems.
Electric Powertrains
Electric motors are known to produce a flat torque curve from zero rotational speed up to about half their speed range, followed by a constant power region up to maximum rotational speed. As most EVs are optimised for city use and the accompanying low speed, they have fixed gear ratios and no clutch. We expect performance EVs of the future to add more gear ratios to enhance acceleration and lift the top speed.
