Non-Drag Racing Transmission tuning guide
- Thread starter Otaliema
- 120 comments
- 21,279 views
- 2,643
- Finland
- OdeFinn
Whole gearing ideology depends on that info, like on my quick example FD35 gearing is using gearing to get high torque on low gears, kicking torque on start of middle gears and using higher rev(hp) to pull speed higher till there's no power/torque left and squeezing last bit of engine on power(hp) peak on last gear.
Example box is not fine tuned and polished, altering final and polishing gearing it will make it faster/better, but it's just an example. Would that go faster with only one overdrive gear? Maybe, but would it make lower gears harder to use on circuit racing, probably, those are things what should also keep in mind, final gear affects a lot car overall handling and grip during cornering, it's not just for adjusting speed as many people are using it on flipped trannies.
- 2,643
- Finland
- OdeFinn
Few quotes from net, when reading don't fall on usual error as stick on stable rpm when making comparison between hp and torque - your rpm is rising during acceleration and you need quite long piece of powerband to do proper acceleration.
http://craig.backfire.ca/pages/autos/transmissions
http://craig.backfire.ca/pages/autos/horsepower
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Transmissions
Introduction
In this article, I will be looking at the transmissions found in cars, and how they affect performance and economy.
Table of Contents
For the majority of this article, I will be using a 2006 Nissan 350z Coupe as an examplevehicle. In stock form, it comes with a 6-speed manual transmission and a 3.538:1 rear axle ratio. Below is a graph showing the torque and power curves of the engine, a 3.5L 287hp VQ35DE V6.
Nissan VQ35DE torque curve.
Transmission Formulae
Ratio Spread
The ratio spread is the ratio of two different gear's ratios, such as second gear and third gear, or first gear and top gear. The overall ratio spread directly affects the range of speeds that the transmission can allow thevehicle to travel at, and the ratio spread between each gear affects the change inacceleration force after each gear change.
Ideally, the ratio spread between first gear and top gear would be very high, so that the car would have high acceleration at low speeds, and a high top speed without causing the engine to redline. Also, the ratio spread between each gear should be low, so that the engine can be kept revving near its power peak while the vehicle passes through a wide range of speeds.
The only way to have a large overall ratio spread and a small ratio spread between each gear is to have numerous gears.
A close-ratio transmission will have a small overall ratio spread, by definition. Likewise, a wide-ratio transmission will have a large ratio spread.
Ratio spread formula.
RPM Change When Shifting Gears
When a higher gear is selected in the transmission, the engine RPM drops. The RPM after the shift can be calculated if both gear ratios and the RPM before the shift are known. The process can be reversed to determine the RPM after gearing down.
The formulae for calculating the ratio spread and RPM change are shown below.
RPM change formula.
Gear Ratio Selection
The gear ratios in a transmission are chosen based on what rev range the engine makes power, and the speeds the vehicle will most often be traveling at.
Typically, first gear has a very high ratio, which allows the engine to rev up quickly and get into its power band. This is especially true in trucks where a high gear ratio is needed to get heavy loads moving, or to climb a very steep hill.
The remaining gear ratios are chosen in such a way that the vehicle can have highacceleration at various vehicle speeds. The ratio spread between each gear decreases from first gear to top gear. This is because the engine's ability to exert a force at a certain speed follows a curve which flattens with increasing speed.
On regular production road cars, the top gear ratio is usually set to keep the engine revving at an ideal RPM for good fuel economy at freeway speeds.
A wide-ratio transmission is normally used in applications where the vehicle will be traveling at a wide range of speeds, while a close-ratio transmission will be used where the speed range of the vehicle is fairly narrow, such as a race track. A wide-ratio six speed transmission can do what a wide-ratio three speed a close-ratio three speed can do, at the same time.
Below is a plot of the gear ratios of the following transmissions:
Gear ratios of various transmissions. Note that Supra's 6-speed does not have the same ratios as the 6-speed in the Mustang GT500.
Overall ratio spread for each transmission. Note that the 3-speed does not have nearly the same ratio spread as the 6-speeds.
3-Speed Versus 6-Speed
It is intuitive that a transmission with more gears than another will be better, but it may not be totally clear as to why that is. To make the comparison, I will use the stock 6-speed manual in the 350z, along with an old 3-speed manual from an older Nissan vehicle. Below is a table showing the gear ratios of each transmission.
Gear Ratios (x:1)
6 Speed 3 Speed
1st 3.794 3.380
2nd 2.234 1.730
3rd 1.624 1.000
4th 1.271 -
5th 1.000 -
6th 0.794 -
Below is a graph showing the force that the 350z puts to the pavement versus the speed that the car is traveling. Each arc represents a selected gear in the transmission. First gear is the highest, narrowest curve, and top gear is the lowest, widest curve. The beginning of the arc is when the engine is at 1600RPM (chosen by me to keep the graphs clean) in that particular gear, and the end of the arc is when the engine hits its redline of 6600RPM. A higher force implies a higher accelerationat that speed.
Road force with the VQ35DE turning the 3 speed and 6 speed transmissions. Note that at 75mph, there are 4 gears to choose from with the 6 speed, while the 3 speed offers only two.
The above graph clearly shows the superiority of the 6-speed in terms ofacceleration. The 6-speed has significantly better acceleration than the 3-speed at numerous vehicle speeds, especially at 45-60mph and 85-100mph.
The graph below shows the engine RPM versus the speed of the car. Note that the 6-speed is much better at keeping the engine revving high than the 3-speed. This is because the ratio spread between each gear is much lower. The fact that the engine can be kept revving high allows much moreaverage power to be put to the road while the car accelerates. This was already seen in the previous graph.
Engine RPM versus vehicle speed for both transmissions. The large RPM drops on the 3-speed's gear changes are from the high ratio spread between the gears.
It can be seen in the above graph that at 60mph, the 6-speed can have the engine turning as low as 2150rpm, while the 3-speed can only bring it down to 2700rpm. To correct this, I will change the gears in the 3-speed car's rear axle from the stock 3.538:1 to 2.809:1. Below is a graph showing the effect of changing the rear axle gear on the 3-speed.
Road force with the VQ35DE turning the 3 speed and 6 speed transmissions. Note that in order to have the same top gear cruise RPM as the 6-speed, the 3-speed has had to sacrifice acceleration all across the board.
It can clearly be seen that the 3-speed is now very far behind the 6-speed in terms ofacceleration. This shows that transmissions with very few gears can give a car goodacceleration or good fuel economy, but not both at the same time.
Continuously Variable Transmissions
A continuously variable transmission is a transmission that uses a belt on two conic pulleys or a set of rollers to provide an infinite number of ratios. An ideal CVT has an infinite ratio spread, meaning that it could allow the engine to run while the vehicle is at rest (∞:1) and allow the vehicle to drive at an infinitely high speed (0:1). Real CVTs have a finite ratio spread, and use an engagement similar to a torque converter in an automatic transmission to allow the car to be at rest and drive at low speeds.
The ideal CVT can put the engine's peak power to the road at all speeds. It is superior to the 6-speed.
Cornering
When going around a corner, there is a maximum speed that the car can go around it. It is therefore important that the transmission can keep the engine revving at a suitable RPM at that speed. Below is adiagram showing the 3-speed car and 6-speed car going around a corner at 80mph.
When the cars are going around a corner at 80mph, the 6-speed has the advantage because it can keep the engine revving fairly high without redlining. The 3-speed can either redline in 2nd gear, or lug in 3rd gear.
Drag Racing
In drag racing, the time it takes to shift gears is very significant. The faster the vehicle is, the more significant the gear change time becomes relative to the elapsed time down the strip. Because of this, most high performance drag cars only go through three gears (two changes) when going down the ¼ mile. The fastest drag cars do not shift gears at all, but rather have a hydraulic drive system that varies the transfer of power from the engine to the drivetrain. A drag race engine must be tuned to provide a high amount of power at any RPM to provide the necessaryacceleration while pulling through so few gears. Transmissions with fewer gears also tend to have less friction, which allows more of the engine's power to make it to the pavement.
Conclusion
Transmissions have a direct effect on a vehicle's ability to accelerate. An ideal transmission can keep the engine revving near its power peak when the vehicle is driving at various speeds. The gear ratios are chosen based on what speeds the vehicle will be traveling, and having more gears raises the speed range that the vehicle can accelerate most quickly.
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Horsepower and torque
Introduction
An engine's horsepower and torque numbers are two things that are often talked about in automotive circles, but may be misunderstood. In this article, I will be looking at how those numbers affect a car's ability to accelerate. Carroll Shelby once said: "Horsepower sells cars, torque wins races." Let's see if that is actually true.
Table of Contents
In this article, some assumptions will be made, as seen below.
Torque
Torque is a force that tends to cause a rotation. A force applied at a non-zero distance from an object's centre will tend to rotate the object. This is easily seen in real life. If a wrench is placed on a bolt and a force is applied to the end of the wrench, the bolt will turn. If the same pulling force was applied directly to the bolt, it would not turn because the force's direction passes through the object's centre. The amount of torque is determined by multiplying the magnitude of the force by the force's distance from centre.
Diagram showing torque.
Torque can be used to create a force at a distance, as seen below. On a car, this is how the wheel and tire apply force to the pavement.
Torque can be used to create a force at a distance.
Work
Work is not something that is brought up often when talking about cars. Work is defined as the transfer of energy from one system to another, such as a person pushing a cart. Mathematically, work is the product of force and distance, and has units such as foot-pounds or Newton-metres. The direction of force (or at least a component of it) must match the direction of motion for the force to be considered to have done work. Also, if there is no motion, no work has been done.
Work is done on the object by applying a force along a distance.
Difference Between Torque and Work
Note that the units for both torque and work are the product of force and distance, yet torque and work are two different things. Torque is a force that tends to cause a rotation, which means that it does not actually cause an object to move along a distance. Work is a measure of energy transfer between systems, which may or may not have been done by a force from torque.
The difference between torque and work.
On a rotating shaft, work is done by the force from torque. Torque is a force that tends to cause a rotation, and the shaft is rotating. The force is going round and round, and so is the shaft, so if the shaft was "unrolled", there would be a force traveling along a distance, which is work.
On a rotating shaft, the torque is doing the work.
Power
Power is the amount of work that can be done in a certain amount of time, or "the rate of work", or "the rate of energy transfer between systems". The formula for calculating power is shown below:
Power is the product of force and distance over a period of time.
The above equation can be rewritten in terms offorce and speed, as seen below:
Using the definition of speed, power can be expressed in terms of force and speed.
Shaft Power
On a rotating shaft, the force from torque is doing work. The rate of work is dependent upon the shaft's rotational speed. Therefore, the amount of power that a rotating shaft has is the product of its rotational speed and its torque. Using arbitrary units, the power formula for a rotating shaft is:
Shaft power using arbitrary units.
Units of Shaft Power
When using pound-feet as units of torque,revolutions per minute (RPM) for rotational speed, and horsepower for power, shaft power can be expressed with the following formula:
Shaft power in horsepower.
The above power formula is often misinterpreted as showing that power and torque are the same thing, or that they somehow trade hands with each other at 5252RPM. This mistake is from the fact that a graph of torque in pound-feet andpower in horsepower versus engine RPM has crossing lines at 5252RPM. Torque and power play the same role whether an engine is revving below, at, or above 5252RPM. Many dieselengines, and even some gas engines, are not even capable of revving that high at all.
5252RPM is not a significant point in a physical sense. It is merely the RPM at which a graph of torque in pound-feetand power in horsepower would cross when drawn on the same piece of paper. If different units were used, the curves would cross at a different point, yet the principles of operation would remain unchanged.
The above statements can be proven by changing the units for power and torque. Australians often use kilowatts for units of power, and Newton-metres for torque. With that, the shaft powerformula becomes:
Shaft power in metric units.
Using metric units, the unit conversion constant is 9549, not 5252 like it was whenpound-feet and horsepower were being used. This means that a graph of power and torque versus revs using metric units would have crossing curves at 9549RPM instead of 5252RPM.
Australian engines obey the exact same laws of physics as American engines. The only real distinction between the two is that Aussie engines are designed to run upside down.
Gears
Gears are used to change the torque and rotational speed of a part of a system of rotating shafts, or to change the direction of the transmitted motion. An example of the former would be the car's transmission, while an example of the latter would be the rear axle gears.
An ideal (lossless) gear set transmits an equal amount of power to the output shaft as it received from the input shaft. This means that if a gearbox has a 2:1 gear ratio, the output shaft will be rotating half as fast as the input shaft, but will have double the torque. Below is a drawing that shows the effects of a gear set, using an abitrary ratio, GR.
The gearbox is given a certain amount of power, in the form of torque and revs. It then puts out an equal amount of power, with the revs and torque adjusted according to the gear ratio.
Formulae used for gears.
It is interesting to point out that gears and electrical transformers are very similar. Gears change the torque and speed, while transformers change voltage and current. Both gears and transformers put out as much power as they receive.
A car battery produces 12 volts and a lot of current, but a spark plug needs up to 50,000 volts and very little current. An ignition coil, which is a transformer, trades away the excess current from the battery to make the high voltage needed for the spark plugs.
Drivetrain Gearing
A car's drivetrain uses multiple sets of gears to control how much of the engine's total power is going to torque, and how much is going to the rotational speed of the wheels.
All gasoline piston engines produce too little torque and too many revs to properly turn the wheels of a typical road car. With 27 inch tires, 6000RPM at the wheels would be 450mph. It also takes a lot more than a few hundred pounds of force to even move something as heavy as a passenger car. This is why all cars have drivetrains which are setup to divide the revs and multiply the torque.
Most cars are fitted with two sets of gearing between the engine and the wheels. The first set is the transmission, which multiplies the torque a certain amount, depending on what gear it is in. Typically, first gear has a ratio near 3:1, while the top gear has a ratio near 0.8:1. After the transmission, there is another set of gears which usually have a ratio of around 2.5:1 through 6.0:1, depending on the vehicle. Below is a diagramof a typical drivetrain found in most cars.
The drivetrain of a car is fitted with a transmission and final drive gearing to adjust the engine's torque and revs to accelerate the car.
The wheel torque and revs vary with the engine torque and revs, and the gear ratios in between.
The reason that cars have transmissions with multiple gears is so that the engine can be kept within its operating rev range while the vehicle accelerates from rest to possibly over 200mph. In first gear, there is plenty of acceleration because of the torque multiplication, but very little speed before the engine revs to its redline. In second gear, there is slightly less acceleration, but a slightly higher speed before hitting the redline. This trend of higher speed and lower acceleration continues through each gear in the transmission.
Each transmission gear provides a different amount of acceleration and speed. The combination of speed and acceleration is related to the power from the engine.
Accelerating a Car
Newton's second law of motion states that the acceleration of a body is related to the force being applied and the mass of the body, as seen below:
According to Newton's second law of motion, a greater force or a lower mass will result in a greater acceleration.
In order for there to be any acceleration, the force must be applied at the same speed that the object is traveling, for a non-zero length of time. A force being applied at a certain speed for a period of time is power, therefore, the acceleration force on a moving object is determined by the power being applied at that speed.
The wheels receive torque and rotational speed from the engine, and lay down a force onto the pavement. It is this force which accelerates the vehicle. The car's speed is directly related to the rotational speed of the wheel.
The acceleration of a moving object is equal to the power divided by the speed and the mass. The product of speed and mass is known as momentum.
The acceleration force that the tire puts to the road comes from the torque at the wheels. This is why the acceleration force is often calculated by passing the engine torque through the drivetrain gearing and wheels, as seen in the formula below. I will refer to this method of calculating the acceleration force as the torque method.
The acceleration force can be calculated by passing the engine torque through the entire drivetrain and down the tire radius on to the road.
If the vehicle's speed and the power of its engine are known at a given instant, the force of acceleration can be calculated without knowing anything about the drivetrain gearing, tire diameter, or even the engine torque. I will refer to this method of calculating the acceleration force as the power method. Below is the formula for the power method when using imperial units.
When the power and speed are known, the acceleration force can be calculated directly without knowing anything about the drivetrain.
The torque method and the power method will both produce the same results, as seen in the example below.
The calculated acceleration force is the same when using the torque method or the power method.
A Simple Example
To demonstrate the effects of power and torque, I will put three different engines into the same car. The car's speed will be the same for each of the three tests, so that the differences in the acceleration force can be seen clearly.
A sample car will be used for the comparison.
The car has tires with a 24-inch diameter, which gives a radius of 1 foot. The tire will be turning at 500 RPM, which means the car is traveling at 35.7 mph. The transmission will be in a gear which has a gear ratio of 2 : 1. The final drive ratio will be chosen in a way that satisfies the driveshaft RPM and the wheel RPM.
Details of the drivetrain layout.
Blue Engine
The blue engine is running at 2000 RPM and making 200 lb-ft of torque, which is 76 horsepower. The final drive ratio has to be 2 : 1 to match up with the wheel RPM and the driveshaft RPM. With this setup, the car puts 800 lbf to the road.
The blue engine makes 76 hp, and puts down 800 lbf to the road.
Green Engine
The green engine is running at 4000 RPM and making 100 lb-ft of torque, which is also 76 horsepower. It is revving twice as high as the blue engine, but making only half the torque. The final drive ratio has to be 4 : 1 to match up with the wheel RPM and the driveshaft RPM. With this setup, the car puts 800 lbf to the road, which is the same as the force made by the blue engine.
The green engine makes 76 hp and puts down 800 lbf to the road, just like the blue engine.
Red Engine
The red engine is running at 4000 RPM and making 200 lb-ft of torque, which is 152 horsepower. It is making just as much torque as the blue engine, and revving just as high as the green engine. The final drive ratio has to be 4 : 1 to match up with the wheel RPM and the driveshaft RPM. With this setup, the car puts 1600 lbf to the road, which is twice the force that the other two engines made.
The red engine makes 152 horsepower, which is twice the power of the other two engines. It is putting a 1600 lb force to the road, which is also twice as high as the other two engines.
It can be seen from the comparison of the above three engines that the most powerful one gave the highest force, and the two which made the same power as each other made the same force as each other as well. The two engines with the same power had a different amount of torque and revs, but the acceleration force was equalized by the final drive gear. This clearly shows that the engine's power, regardless of how much torque it is making or how high it is revving, determines the car's acceleration force.
Power Curves and Power Bands
Engine performance is often described by the peak power figure. A good engine will produce high peak power, and have a very high average power level as well. A graph of power with respect to engine RPM is known as a power curve, and holds important information about an engine's performance across its rev range.
It is possible for one engine to have more average power than another, even with a lower peak power figure, as seen in the example below.
The power curves above are for one engine with 400hp, and another with 375hp. While the 400hp engine has a higher peak power figure, the 375hp engine has a much higher average power throughout the rev range. In most cases, especially on the street or in drag racing, the 375hp engine seen above would make for a faster car.
The power band is the rev range where the engine is producing an arbitrary percentage of its peak power figure. For example, the 80% power band of an engine with 500hp would be the rev range where it makes 400hp or more. A wide power band implies high average power. This will be seen later in the article.
An engine's power band can be predicted as wideor narrow based on certain characteristics. Some examples are shown in the table below.
Wider Power Band Narrower Power Band
Large displacement Small displacement
High Torque Low Torque
>2 valves/cyl 2 valves/cyl
Variable Valve Timing No VVT
Supercharged or Turbocharged Naturally Aspirated
Peak HP, Peak TQ, Redline
far from each other in the rev range Peak HP, Peak TQ, Redline
very close to each other in the rev range
An engine's power band can be predicted to be wide or narrow based on certain characteristics. There are many exceptions.
Comparing Two Cars
Let's compare two cars with two different engines that have the same peak power output, but different power bands.
Both cars have the same curb weight, transmission, tire radius, and so on. In fact, the only difference between the two cars will be the engines. One car will be equipped with a 500hp V8, and the other will have a 500hp turbocharged 4 cylinder engine.
The car with the V8 will be named Redneck , and the car with the 4 cylinder will be named Ricer . The V8 can rev to 6000RPM and produce a ton of torque, while 4 cylinder can to rev way up to 9000RPM and produce a fair bit of torque. To keep the math very simple, the V8 idles at 600RPM, and the I4 idles at 900RPM.
Below are plots of the two fictitious engine's torque and power curves.
Figure 1: Torque versus RPM for Redneck and Ricer. These are unrealistic curves which have been exaggerated to help illustrate certain concepts.
Figure 2: Horsepower versus RPM for Redneck and Ricer. This is calculated from the torque at each RPM.
Both engines produce a peak of 500hp, as specified earlier. The V8 produces 500hp at 5000RPM, and 573tq at 4250RPM, while the I4 produces 500hp at 8000RPM, and 337tq at 7500RPM.
Ricer Redneck Difference
Rev Range 900 - 9000RPM 600 - 6000RPM 50% more for Ricer
Peak Torque 337tq 573tq 70% more for Redneck
Peak Power 500hp 500hp Equal
Since the V8 was revving low, it needed to produce a lot more torque than the I4 to reach 500hp. At the same time, the I4 needed to rev higher than the V8 to produce 500hp, because it offers up less torque. Below is a comparison of the two engines' power bands.
Figure 3: Power band comparison of both engines. Note that the Redneck's average power production (area under the curve) is higher, and that the peak power is the same, at 500hp.
If the x-axis on the above graph seems unusual, there is a separate page on comparing power curves which explains why the rev ranges are not compared directly.
Notice that while both engines have the same peak power figures, the Redneck's engine has a much wider 80% power band. This situation is a considerable advantage for the Redneck. Between the two cars, the one with the made-up V8 is going to be faster than the one with the made-up I4, because the V8 has a higher average power level throughout its rev range.
Ricer Redneck
Peak Power
500hp = 500hp
Average Power
(Entire Rev Range) 263hp < 338hp
Average Power
(Idle to Redline/2) 106hp < 166hp
Average Power
(Redline/2 to Redline) 385hp < 460hp
Average Power
(80% Power Band) 462hp < 471hp
Both vehicles have a curb weight of 3000 lb, which gives both cars a peak power-to-weight ratio of 330 hp per ton. A final drive (axle) ratio of 3.55:1 has been chosen for the Redneck, and a 5.325:1 ratio has been chosen for the Ricer. The Ricer uses a higher ratio to match the high-revving engine.
Ricer Redneck
Transmission Ratios 2.52,1.52,1.00 2.52,1.52,1.00
Final Drive Ratio 5.325:1 3.55:1
Curb Weight 3000 lb 3000 lb
With all of the above data, a velocity-versus time graph can be created for both cars. It is important to remember that aerodynamic drag, initial launch conditions, and other losses have been ignored for this comparison. Below is a graph of the Redneck and Ricer's acceleration data.
Figure 4: Velocity versus time for Redneck and Ricer. The slope of the curve represents acceleration.
Low-Speed Acceleration
The results of the race between the Redneck and Ricer shows that the Redneck had a significant advantage from start to 60 mph. Above 60 mph, the Ricer was revving closer to its power band, and both cars had similar acceleration to the top speed of approximately 135 mph. In drag racing, the Ricer would have lost the race, but on a racetrack, the difference could be quite minor. Therefore, it can be said that a vehicle which is subject to widely varying speeds must have a very wide power band to be competitive, while a vehicle operating in a narrow range of speeds does not.
Shift Points
When the Ricer and Redneck were racing, they were shifting gears at their engine's redlines. In many real-life cases, shifting gears earlier may be advantageous for acceleration. An engine with a power curve that begins to "fall off" at very high RPM should be shifted earlier, if doing so would bring the engine to an RPM where it is making more power. Gear shift points should always be chosen in such a way that the engine is putting out the highest average power to the wheels.
In the race between the Ricer and Redneck, both cars were fitted with a three-speed, wide-ratio transmission. A high-revving engine with a narrow power band would benefit greatly from a transmission with closer ratios, and additional gears so that the engine can be revved much more closely to its power peak as the vehicle's speed changes. For a more detailed analysis of the effects of transmissions on vehicle performance, refer to the transmissions article.
Driveability
Driveability is a subjective term used to describe the ability to "access" an engine's power. A naturally-aspirated engine with a wide power band will have very good driveability; putting the pedal to the floor at any speed in any gear should yield reasonable acceleration. On the other hand, a car with a narrow power band would not be considered as "driveable". Passing cars while cruising on the highway often requires dropping a gear to bring the engine's revs up to access the power. This is one of the reasons that luxury cars often come with large, naturally-aspirated or supercharged engines, while small, turbocharged engines are not as common and often found in more "focused" sportscars where outstanding driveability is not expected or required.
Engines are sometimes described as being "torquey". This is slang for having good driveability, a wide power band, or a lot of power at low RPM.
Streetability is another term which is often used to describe engines with the aforementioned characteristics, along with good road manners, such as a smooth idle and the ability to start in very cold temperatures.
High Torque Engines versus High Revving Engines
The torque that an engine can produce is somewhat related to the displacement of the engine. Larger displacement engines are likely to be much bigger and heavier, making them unsuitable for certain types of vehicles. This is why many small race cars have engines with small displacement, high-revving, and sometimes equipped with forced induction to produce high horsepower. Also, race cars are often given limits on displacement, which means their only chance at producing a lot of power is to rev very high or use forced induction. A large engine may be able to produce power more reliably than a smaller one, but not necessarily. There are plenty of big, gutless engines that don't last.
Heavy vehicles are almost always equipped with large displacement engines because they require more low-RPM power to accelerate from rest (and very low speeds). As the weight of a vehicle goes up, the ability to accelerate from rest becomes increasingly significant.
Conclusion
In order to quickly accelerate a vehicle, the engine must be able to make a large force at the speed that the vehicle is traveling. The amount of power determines the force that the engine can create at a given speed, whether it is a very low speed or a very high speed. It does not matter if the engine makes power by revving high or making a lot of torque, because drivetrain gearing can be used to adjust the torque and revs proportionally.
“ Peak power sells cars. High average power wins races. ”
A vehicle's peak torque and power figures can only give a general idea of performance. The best way to make a good comparison between vehicles is to go racing!
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http://craig.backfire.ca/pages/autos/transmissions
http://craig.backfire.ca/pages/autos/horsepower
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Transmissions
Introduction
In this article, I will be looking at the transmissions found in cars, and how they affect performance and economy.
Table of Contents
For the majority of this article, I will be using a 2006 Nissan 350z Coupe as an examplevehicle. In stock form, it comes with a 6-speed manual transmission and a 3.538:1 rear axle ratio. Below is a graph showing the torque and power curves of the engine, a 3.5L 287hp VQ35DE V6.
Nissan VQ35DE torque curve.
Transmission Formulae
Ratio Spread
The ratio spread is the ratio of two different gear's ratios, such as second gear and third gear, or first gear and top gear. The overall ratio spread directly affects the range of speeds that the transmission can allow thevehicle to travel at, and the ratio spread between each gear affects the change inacceleration force after each gear change.
Ideally, the ratio spread between first gear and top gear would be very high, so that the car would have high acceleration at low speeds, and a high top speed without causing the engine to redline. Also, the ratio spread between each gear should be low, so that the engine can be kept revving near its power peak while the vehicle passes through a wide range of speeds.
The only way to have a large overall ratio spread and a small ratio spread between each gear is to have numerous gears.
A close-ratio transmission will have a small overall ratio spread, by definition. Likewise, a wide-ratio transmission will have a large ratio spread.
Ratio spread formula.
RPM Change When Shifting Gears
When a higher gear is selected in the transmission, the engine RPM drops. The RPM after the shift can be calculated if both gear ratios and the RPM before the shift are known. The process can be reversed to determine the RPM after gearing down.
The formulae for calculating the ratio spread and RPM change are shown below.
RPM change formula.
Gear Ratio Selection
The gear ratios in a transmission are chosen based on what rev range the engine makes power, and the speeds the vehicle will most often be traveling at.
Typically, first gear has a very high ratio, which allows the engine to rev up quickly and get into its power band. This is especially true in trucks where a high gear ratio is needed to get heavy loads moving, or to climb a very steep hill.
The remaining gear ratios are chosen in such a way that the vehicle can have highacceleration at various vehicle speeds. The ratio spread between each gear decreases from first gear to top gear. This is because the engine's ability to exert a force at a certain speed follows a curve which flattens with increasing speed.
On regular production road cars, the top gear ratio is usually set to keep the engine revving at an ideal RPM for good fuel economy at freeway speeds.
A wide-ratio transmission is normally used in applications where the vehicle will be traveling at a wide range of speeds, while a close-ratio transmission will be used where the speed range of the vehicle is fairly narrow, such as a race track. A wide-ratio six speed transmission can do what a wide-ratio three speed a close-ratio three speed can do, at the same time.
Below is a plot of the gear ratios of the following transmissions:
- Getrag V160 6-speed manual, found in 1993-1998Toyota Supra Turbos.
- Tremec TR6060 6-speed manual, found in 2007+ FordMustang GT500s.
- Borg-Warner T5 5-speed manual, found in 3rd-generation Chevy Camaros.
- TorqueFlite 727 3-speed automatic, found in various Chrysler vehicles over the years.
Gear ratios of various transmissions. Note that Supra's 6-speed does not have the same ratios as the 6-speed in the Mustang GT500.
Overall ratio spread for each transmission. Note that the 3-speed does not have nearly the same ratio spread as the 6-speeds.
3-Speed Versus 6-Speed
It is intuitive that a transmission with more gears than another will be better, but it may not be totally clear as to why that is. To make the comparison, I will use the stock 6-speed manual in the 350z, along with an old 3-speed manual from an older Nissan vehicle. Below is a table showing the gear ratios of each transmission.
Gear Ratios (x:1)
6 Speed 3 Speed
1st 3.794 3.380
2nd 2.234 1.730
3rd 1.624 1.000
4th 1.271 -
5th 1.000 -
6th 0.794 -
Below is a graph showing the force that the 350z puts to the pavement versus the speed that the car is traveling. Each arc represents a selected gear in the transmission. First gear is the highest, narrowest curve, and top gear is the lowest, widest curve. The beginning of the arc is when the engine is at 1600RPM (chosen by me to keep the graphs clean) in that particular gear, and the end of the arc is when the engine hits its redline of 6600RPM. A higher force implies a higher accelerationat that speed.
Road force with the VQ35DE turning the 3 speed and 6 speed transmissions. Note that at 75mph, there are 4 gears to choose from with the 6 speed, while the 3 speed offers only two.
The above graph clearly shows the superiority of the 6-speed in terms ofacceleration. The 6-speed has significantly better acceleration than the 3-speed at numerous vehicle speeds, especially at 45-60mph and 85-100mph.
The graph below shows the engine RPM versus the speed of the car. Note that the 6-speed is much better at keeping the engine revving high than the 3-speed. This is because the ratio spread between each gear is much lower. The fact that the engine can be kept revving high allows much moreaverage power to be put to the road while the car accelerates. This was already seen in the previous graph.
Engine RPM versus vehicle speed for both transmissions. The large RPM drops on the 3-speed's gear changes are from the high ratio spread between the gears.
It can be seen in the above graph that at 60mph, the 6-speed can have the engine turning as low as 2150rpm, while the 3-speed can only bring it down to 2700rpm. To correct this, I will change the gears in the 3-speed car's rear axle from the stock 3.538:1 to 2.809:1. Below is a graph showing the effect of changing the rear axle gear on the 3-speed.
Road force with the VQ35DE turning the 3 speed and 6 speed transmissions. Note that in order to have the same top gear cruise RPM as the 6-speed, the 3-speed has had to sacrifice acceleration all across the board.
It can clearly be seen that the 3-speed is now very far behind the 6-speed in terms ofacceleration. This shows that transmissions with very few gears can give a car goodacceleration or good fuel economy, but not both at the same time.
Continuously Variable Transmissions
A continuously variable transmission is a transmission that uses a belt on two conic pulleys or a set of rollers to provide an infinite number of ratios. An ideal CVT has an infinite ratio spread, meaning that it could allow the engine to run while the vehicle is at rest (∞:1) and allow the vehicle to drive at an infinitely high speed (0:1). Real CVTs have a finite ratio spread, and use an engagement similar to a torque converter in an automatic transmission to allow the car to be at rest and drive at low speeds.
The ideal CVT can put the engine's peak power to the road at all speeds. It is superior to the 6-speed.
Cornering
When going around a corner, there is a maximum speed that the car can go around it. It is therefore important that the transmission can keep the engine revving at a suitable RPM at that speed. Below is adiagram showing the 3-speed car and 6-speed car going around a corner at 80mph.
When the cars are going around a corner at 80mph, the 6-speed has the advantage because it can keep the engine revving fairly high without redlining. The 3-speed can either redline in 2nd gear, or lug in 3rd gear.
Drag Racing
In drag racing, the time it takes to shift gears is very significant. The faster the vehicle is, the more significant the gear change time becomes relative to the elapsed time down the strip. Because of this, most high performance drag cars only go through three gears (two changes) when going down the ¼ mile. The fastest drag cars do not shift gears at all, but rather have a hydraulic drive system that varies the transfer of power from the engine to the drivetrain. A drag race engine must be tuned to provide a high amount of power at any RPM to provide the necessaryacceleration while pulling through so few gears. Transmissions with fewer gears also tend to have less friction, which allows more of the engine's power to make it to the pavement.
Conclusion
Transmissions have a direct effect on a vehicle's ability to accelerate. An ideal transmission can keep the engine revving near its power peak when the vehicle is driving at various speeds. The gear ratios are chosen based on what speeds the vehicle will be traveling, and having more gears raises the speed range that the vehicle can accelerate most quickly.
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Horsepower and torque
Introduction
An engine's horsepower and torque numbers are two things that are often talked about in automotive circles, but may be misunderstood. In this article, I will be looking at how those numbers affect a car's ability to accelerate. Carroll Shelby once said: "Horsepower sells cars, torque wins races." Let's see if that is actually true.
Table of Contents
- Assumptions
- Torque
- Work
- Difference Between Torque and Work
- Power
- Shaft Power
- Units of Shaft Power
- Gears
- Drivetrain Gearing
- Accelerating a Car
- A Simple Example
- Power Curves and Power Bands
- Comparing Two Cars
- Low-Speed Acceleration
- Shift Points
- Driveability
- High Torque versus High Revving
- Conclusion
- See Also
In this article, some assumptions will be made, as seen below.
- There is no road friction, or friction anywhere for that matter.
- There are no aerodynamic effects acting on the vehicles.
- The vehicles are on flat ground.
- There are no drivetrain losses. The transmission and rear axle are ideal.
- The vehicles are always moving at some non-zerospeed.
- Gear changes take place instantaneously.
- The vehicles are at full throttle at all times.
- There is no turbo lag.
Torque
Torque is a force that tends to cause a rotation. A force applied at a non-zero distance from an object's centre will tend to rotate the object. This is easily seen in real life. If a wrench is placed on a bolt and a force is applied to the end of the wrench, the bolt will turn. If the same pulling force was applied directly to the bolt, it would not turn because the force's direction passes through the object's centre. The amount of torque is determined by multiplying the magnitude of the force by the force's distance from centre.
Diagram showing torque.
Torque can be used to create a force at a distance, as seen below. On a car, this is how the wheel and tire apply force to the pavement.
Torque can be used to create a force at a distance.
Work
Work is not something that is brought up often when talking about cars. Work is defined as the transfer of energy from one system to another, such as a person pushing a cart. Mathematically, work is the product of force and distance, and has units such as foot-pounds or Newton-metres. The direction of force (or at least a component of it) must match the direction of motion for the force to be considered to have done work. Also, if there is no motion, no work has been done.
Work is done on the object by applying a force along a distance.
Difference Between Torque and Work
Note that the units for both torque and work are the product of force and distance, yet torque and work are two different things. Torque is a force that tends to cause a rotation, which means that it does not actually cause an object to move along a distance. Work is a measure of energy transfer between systems, which may or may not have been done by a force from torque.
The difference between torque and work.
On a rotating shaft, work is done by the force from torque. Torque is a force that tends to cause a rotation, and the shaft is rotating. The force is going round and round, and so is the shaft, so if the shaft was "unrolled", there would be a force traveling along a distance, which is work.
On a rotating shaft, the torque is doing the work.
Power
Power is the amount of work that can be done in a certain amount of time, or "the rate of work", or "the rate of energy transfer between systems". The formula for calculating power is shown below:
Power is the product of force and distance over a period of time.
The above equation can be rewritten in terms offorce and speed, as seen below:
Using the definition of speed, power can be expressed in terms of force and speed.
Shaft Power
On a rotating shaft, the force from torque is doing work. The rate of work is dependent upon the shaft's rotational speed. Therefore, the amount of power that a rotating shaft has is the product of its rotational speed and its torque. Using arbitrary units, the power formula for a rotating shaft is:
Shaft power using arbitrary units.
Units of Shaft Power
When using pound-feet as units of torque,revolutions per minute (RPM) for rotational speed, and horsepower for power, shaft power can be expressed with the following formula:
Shaft power in horsepower.
The above power formula is often misinterpreted as showing that power and torque are the same thing, or that they somehow trade hands with each other at 5252RPM. This mistake is from the fact that a graph of torque in pound-feet andpower in horsepower versus engine RPM has crossing lines at 5252RPM. Torque and power play the same role whether an engine is revving below, at, or above 5252RPM. Many dieselengines, and even some gas engines, are not even capable of revving that high at all.
5252RPM is not a significant point in a physical sense. It is merely the RPM at which a graph of torque in pound-feetand power in horsepower would cross when drawn on the same piece of paper. If different units were used, the curves would cross at a different point, yet the principles of operation would remain unchanged.
The above statements can be proven by changing the units for power and torque. Australians often use kilowatts for units of power, and Newton-metres for torque. With that, the shaft powerformula becomes:
Shaft power in metric units.
Using metric units, the unit conversion constant is 9549, not 5252 like it was whenpound-feet and horsepower were being used. This means that a graph of power and torque versus revs using metric units would have crossing curves at 9549RPM instead of 5252RPM.
Australian engines obey the exact same laws of physics as American engines. The only real distinction between the two is that Aussie engines are designed to run upside down.
Gears
Gears are used to change the torque and rotational speed of a part of a system of rotating shafts, or to change the direction of the transmitted motion. An example of the former would be the car's transmission, while an example of the latter would be the rear axle gears.
An ideal (lossless) gear set transmits an equal amount of power to the output shaft as it received from the input shaft. This means that if a gearbox has a 2:1 gear ratio, the output shaft will be rotating half as fast as the input shaft, but will have double the torque. Below is a drawing that shows the effects of a gear set, using an abitrary ratio, GR.
The gearbox is given a certain amount of power, in the form of torque and revs. It then puts out an equal amount of power, with the revs and torque adjusted according to the gear ratio.
Formulae used for gears.
It is interesting to point out that gears and electrical transformers are very similar. Gears change the torque and speed, while transformers change voltage and current. Both gears and transformers put out as much power as they receive.
A car battery produces 12 volts and a lot of current, but a spark plug needs up to 50,000 volts and very little current. An ignition coil, which is a transformer, trades away the excess current from the battery to make the high voltage needed for the spark plugs.
Drivetrain Gearing
A car's drivetrain uses multiple sets of gears to control how much of the engine's total power is going to torque, and how much is going to the rotational speed of the wheels.
All gasoline piston engines produce too little torque and too many revs to properly turn the wheels of a typical road car. With 27 inch tires, 6000RPM at the wheels would be 450mph. It also takes a lot more than a few hundred pounds of force to even move something as heavy as a passenger car. This is why all cars have drivetrains which are setup to divide the revs and multiply the torque.
Most cars are fitted with two sets of gearing between the engine and the wheels. The first set is the transmission, which multiplies the torque a certain amount, depending on what gear it is in. Typically, first gear has a ratio near 3:1, while the top gear has a ratio near 0.8:1. After the transmission, there is another set of gears which usually have a ratio of around 2.5:1 through 6.0:1, depending on the vehicle. Below is a diagramof a typical drivetrain found in most cars.
The drivetrain of a car is fitted with a transmission and final drive gearing to adjust the engine's torque and revs to accelerate the car.
The wheel torque and revs vary with the engine torque and revs, and the gear ratios in between.
The reason that cars have transmissions with multiple gears is so that the engine can be kept within its operating rev range while the vehicle accelerates from rest to possibly over 200mph. In first gear, there is plenty of acceleration because of the torque multiplication, but very little speed before the engine revs to its redline. In second gear, there is slightly less acceleration, but a slightly higher speed before hitting the redline. This trend of higher speed and lower acceleration continues through each gear in the transmission.
Each transmission gear provides a different amount of acceleration and speed. The combination of speed and acceleration is related to the power from the engine.
Accelerating a Car
Newton's second law of motion states that the acceleration of a body is related to the force being applied and the mass of the body, as seen below:
According to Newton's second law of motion, a greater force or a lower mass will result in a greater acceleration.
In order for there to be any acceleration, the force must be applied at the same speed that the object is traveling, for a non-zero length of time. A force being applied at a certain speed for a period of time is power, therefore, the acceleration force on a moving object is determined by the power being applied at that speed.
The wheels receive torque and rotational speed from the engine, and lay down a force onto the pavement. It is this force which accelerates the vehicle. The car's speed is directly related to the rotational speed of the wheel.
The acceleration of a moving object is equal to the power divided by the speed and the mass. The product of speed and mass is known as momentum.
The acceleration force that the tire puts to the road comes from the torque at the wheels. This is why the acceleration force is often calculated by passing the engine torque through the drivetrain gearing and wheels, as seen in the formula below. I will refer to this method of calculating the acceleration force as the torque method.
The acceleration force can be calculated by passing the engine torque through the entire drivetrain and down the tire radius on to the road.
If the vehicle's speed and the power of its engine are known at a given instant, the force of acceleration can be calculated without knowing anything about the drivetrain gearing, tire diameter, or even the engine torque. I will refer to this method of calculating the acceleration force as the power method. Below is the formula for the power method when using imperial units.
When the power and speed are known, the acceleration force can be calculated directly without knowing anything about the drivetrain.
The torque method and the power method will both produce the same results, as seen in the example below.
The calculated acceleration force is the same when using the torque method or the power method.
A Simple Example
To demonstrate the effects of power and torque, I will put three different engines into the same car. The car's speed will be the same for each of the three tests, so that the differences in the acceleration force can be seen clearly.
A sample car will be used for the comparison.
The car has tires with a 24-inch diameter, which gives a radius of 1 foot. The tire will be turning at 500 RPM, which means the car is traveling at 35.7 mph. The transmission will be in a gear which has a gear ratio of 2 : 1. The final drive ratio will be chosen in a way that satisfies the driveshaft RPM and the wheel RPM.
Details of the drivetrain layout.
Blue Engine
The blue engine is running at 2000 RPM and making 200 lb-ft of torque, which is 76 horsepower. The final drive ratio has to be 2 : 1 to match up with the wheel RPM and the driveshaft RPM. With this setup, the car puts 800 lbf to the road.
The blue engine makes 76 hp, and puts down 800 lbf to the road.
Green Engine
The green engine is running at 4000 RPM and making 100 lb-ft of torque, which is also 76 horsepower. It is revving twice as high as the blue engine, but making only half the torque. The final drive ratio has to be 4 : 1 to match up with the wheel RPM and the driveshaft RPM. With this setup, the car puts 800 lbf to the road, which is the same as the force made by the blue engine.
The green engine makes 76 hp and puts down 800 lbf to the road, just like the blue engine.
Red Engine
The red engine is running at 4000 RPM and making 200 lb-ft of torque, which is 152 horsepower. It is making just as much torque as the blue engine, and revving just as high as the green engine. The final drive ratio has to be 4 : 1 to match up with the wheel RPM and the driveshaft RPM. With this setup, the car puts 1600 lbf to the road, which is twice the force that the other two engines made.
The red engine makes 152 horsepower, which is twice the power of the other two engines. It is putting a 1600 lb force to the road, which is also twice as high as the other two engines.
It can be seen from the comparison of the above three engines that the most powerful one gave the highest force, and the two which made the same power as each other made the same force as each other as well. The two engines with the same power had a different amount of torque and revs, but the acceleration force was equalized by the final drive gear. This clearly shows that the engine's power, regardless of how much torque it is making or how high it is revving, determines the car's acceleration force.
Power Curves and Power Bands
Engine performance is often described by the peak power figure. A good engine will produce high peak power, and have a very high average power level as well. A graph of power with respect to engine RPM is known as a power curve, and holds important information about an engine's performance across its rev range.
It is possible for one engine to have more average power than another, even with a lower peak power figure, as seen in the example below.
The power curves above are for one engine with 400hp, and another with 375hp. While the 400hp engine has a higher peak power figure, the 375hp engine has a much higher average power throughout the rev range. In most cases, especially on the street or in drag racing, the 375hp engine seen above would make for a faster car.
The power band is the rev range where the engine is producing an arbitrary percentage of its peak power figure. For example, the 80% power band of an engine with 500hp would be the rev range where it makes 400hp or more. A wide power band implies high average power. This will be seen later in the article.
An engine's power band can be predicted as wideor narrow based on certain characteristics. Some examples are shown in the table below.
Wider Power Band Narrower Power Band
Large displacement Small displacement
High Torque Low Torque
>2 valves/cyl 2 valves/cyl
Variable Valve Timing No VVT
Supercharged or Turbocharged Naturally Aspirated
Peak HP, Peak TQ, Redline
far from each other in the rev range Peak HP, Peak TQ, Redline
very close to each other in the rev range
An engine's power band can be predicted to be wide or narrow based on certain characteristics. There are many exceptions.
Comparing Two Cars
Let's compare two cars with two different engines that have the same peak power output, but different power bands.
Both cars have the same curb weight, transmission, tire radius, and so on. In fact, the only difference between the two cars will be the engines. One car will be equipped with a 500hp V8, and the other will have a 500hp turbocharged 4 cylinder engine.
The car with the V8 will be named Redneck , and the car with the 4 cylinder will be named Ricer . The V8 can rev to 6000RPM and produce a ton of torque, while 4 cylinder can to rev way up to 9000RPM and produce a fair bit of torque. To keep the math very simple, the V8 idles at 600RPM, and the I4 idles at 900RPM.
Below are plots of the two fictitious engine's torque and power curves.
Figure 1: Torque versus RPM for Redneck and Ricer. These are unrealistic curves which have been exaggerated to help illustrate certain concepts.
Figure 2: Horsepower versus RPM for Redneck and Ricer. This is calculated from the torque at each RPM.
Both engines produce a peak of 500hp, as specified earlier. The V8 produces 500hp at 5000RPM, and 573tq at 4250RPM, while the I4 produces 500hp at 8000RPM, and 337tq at 7500RPM.
Ricer Redneck Difference
Rev Range 900 - 9000RPM 600 - 6000RPM 50% more for Ricer
Peak Torque 337tq 573tq 70% more for Redneck
Peak Power 500hp 500hp Equal
Since the V8 was revving low, it needed to produce a lot more torque than the I4 to reach 500hp. At the same time, the I4 needed to rev higher than the V8 to produce 500hp, because it offers up less torque. Below is a comparison of the two engines' power bands.
Figure 3: Power band comparison of both engines. Note that the Redneck's average power production (area under the curve) is higher, and that the peak power is the same, at 500hp.
If the x-axis on the above graph seems unusual, there is a separate page on comparing power curves which explains why the rev ranges are not compared directly.
Notice that while both engines have the same peak power figures, the Redneck's engine has a much wider 80% power band. This situation is a considerable advantage for the Redneck. Between the two cars, the one with the made-up V8 is going to be faster than the one with the made-up I4, because the V8 has a higher average power level throughout its rev range.
Ricer Redneck
Peak Power
500hp = 500hp
Average Power
(Entire Rev Range) 263hp < 338hp
Average Power
(Idle to Redline/2) 106hp < 166hp
Average Power
(Redline/2 to Redline) 385hp < 460hp
Average Power
(80% Power Band) 462hp < 471hp
Both vehicles have a curb weight of 3000 lb, which gives both cars a peak power-to-weight ratio of 330 hp per ton. A final drive (axle) ratio of 3.55:1 has been chosen for the Redneck, and a 5.325:1 ratio has been chosen for the Ricer. The Ricer uses a higher ratio to match the high-revving engine.
Ricer Redneck
Transmission Ratios 2.52,1.52,1.00 2.52,1.52,1.00
Final Drive Ratio 5.325:1 3.55:1
Curb Weight 3000 lb 3000 lb
With all of the above data, a velocity-versus time graph can be created for both cars. It is important to remember that aerodynamic drag, initial launch conditions, and other losses have been ignored for this comparison. Below is a graph of the Redneck and Ricer's acceleration data.
Figure 4: Velocity versus time for Redneck and Ricer. The slope of the curve represents acceleration.
Low-Speed Acceleration
The results of the race between the Redneck and Ricer shows that the Redneck had a significant advantage from start to 60 mph. Above 60 mph, the Ricer was revving closer to its power band, and both cars had similar acceleration to the top speed of approximately 135 mph. In drag racing, the Ricer would have lost the race, but on a racetrack, the difference could be quite minor. Therefore, it can be said that a vehicle which is subject to widely varying speeds must have a very wide power band to be competitive, while a vehicle operating in a narrow range of speeds does not.
Shift Points
When the Ricer and Redneck were racing, they were shifting gears at their engine's redlines. In many real-life cases, shifting gears earlier may be advantageous for acceleration. An engine with a power curve that begins to "fall off" at very high RPM should be shifted earlier, if doing so would bring the engine to an RPM where it is making more power. Gear shift points should always be chosen in such a way that the engine is putting out the highest average power to the wheels.
In the race between the Ricer and Redneck, both cars were fitted with a three-speed, wide-ratio transmission. A high-revving engine with a narrow power band would benefit greatly from a transmission with closer ratios, and additional gears so that the engine can be revved much more closely to its power peak as the vehicle's speed changes. For a more detailed analysis of the effects of transmissions on vehicle performance, refer to the transmissions article.
Driveability
Driveability is a subjective term used to describe the ability to "access" an engine's power. A naturally-aspirated engine with a wide power band will have very good driveability; putting the pedal to the floor at any speed in any gear should yield reasonable acceleration. On the other hand, a car with a narrow power band would not be considered as "driveable". Passing cars while cruising on the highway often requires dropping a gear to bring the engine's revs up to access the power. This is one of the reasons that luxury cars often come with large, naturally-aspirated or supercharged engines, while small, turbocharged engines are not as common and often found in more "focused" sportscars where outstanding driveability is not expected or required.
Engines are sometimes described as being "torquey". This is slang for having good driveability, a wide power band, or a lot of power at low RPM.
Streetability is another term which is often used to describe engines with the aforementioned characteristics, along with good road manners, such as a smooth idle and the ability to start in very cold temperatures.
High Torque Engines versus High Revving Engines
The torque that an engine can produce is somewhat related to the displacement of the engine. Larger displacement engines are likely to be much bigger and heavier, making them unsuitable for certain types of vehicles. This is why many small race cars have engines with small displacement, high-revving, and sometimes equipped with forced induction to produce high horsepower. Also, race cars are often given limits on displacement, which means their only chance at producing a lot of power is to rev very high or use forced induction. A large engine may be able to produce power more reliably than a smaller one, but not necessarily. There are plenty of big, gutless engines that don't last.
Heavy vehicles are almost always equipped with large displacement engines because they require more low-RPM power to accelerate from rest (and very low speeds). As the weight of a vehicle goes up, the ability to accelerate from rest becomes increasingly significant.
Conclusion
In order to quickly accelerate a vehicle, the engine must be able to make a large force at the speed that the vehicle is traveling. The amount of power determines the force that the engine can create at a given speed, whether it is a very low speed or a very high speed. It does not matter if the engine makes power by revving high or making a lot of torque, because drivetrain gearing can be used to adjust the torque and revs proportionally.
“ Peak power sells cars. High average power wins races. ”
A vehicle's peak torque and power figures can only give a general idea of performance. The best way to make a good comparison between vehicles is to go racing!
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- 5,489
- mid west USA
- Otaliema
Thank you for the information, I would like to ask that if you want contribute to the guide with relevant information send it to me in PM so we can sort out repute information and add it to the correct part(s) of the guide. Thank you.Few quotes from net, when reading don't fall on usual error as stick on stable rpm when making comparison between hp and torque - your rpm is rising during acceleration and you need quite long piece of powerband to do proper acceleration.
http://craig.backfire.ca/pages/autos/transmissions
http://craig.backfire.ca/pages/autos/horsepower
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Transmissions
Introduction
In this article, I will be looking at the transmissions found in cars, and how they affect performance and economy.
Table of Contents
The Vehicle
For the majority of this article, I will be using a 2006 Nissan 350z Coupe as an examplevehicle. In stock form, it comes with a 6-speed manual transmission and a 3.538:1 rear axle ratio. Below is a graph showing the torque and power curves of the engine, a 3.5L 287hp VQ35DE V6.
Nissan VQ35DE torque curve.
Transmission Formulae
Ratio Spread
The ratio spread is the ratio of two different gear's ratios, such as second gear and third gear, or first gear and top gear. The overall ratio spread directly affects the range of speeds that the transmission can allow thevehicle to travel at, and the ratio spread between each gear affects the change inacceleration force after each gear change.
Ideally, the ratio spread between first gear and top gear would be very high, so that the car would have high acceleration at low speeds, and a high top speed without causing the engine to redline. Also, the ratio spread between each gear should be low, so that the engine can be kept revving near its power peak while the vehicle passes through a wide range of speeds.
The only way to have a large overall ratio spread and a small ratio spread between each gear is to have numerous gears.
A close-ratio transmission will have a small overall ratio spread, by definition. Likewise, a wide-ratio transmission will have a large ratio spread.
Ratio spread formula.
RPM Change When Shifting Gears
When a higher gear is selected in the transmission, the engine RPM drops. The RPM after the shift can be calculated if both gear ratios and the RPM before the shift are known. The process can be reversed to determine the RPM after gearing down.
The formulae for calculating the ratio spread and RPM change are shown below.
RPM change formula.
Gear Ratio Selection
The gear ratios in a transmission are chosen based on what rev range the engine makes power, and the speeds the vehicle will most often be traveling at.
Typically, first gear has a very high ratio, which allows the engine to rev up quickly and get into its power band. This is especially true in trucks where a high gear ratio is needed to get heavy loads moving, or to climb a very steep hill.
The remaining gear ratios are chosen in such a way that the vehicle can have highacceleration at various vehicle speeds. The ratio spread between each gear decreases from first gear to top gear. This is because the engine's ability to exert a force at a certain speed follows a curve which flattens with increasing speed.
On regular production road cars, the top gear ratio is usually set to keep the engine revving at an ideal RPM for good fuel economy at freeway speeds.
A wide-ratio transmission is normally used in applications where the vehicle will be traveling at a wide range of speeds, while a close-ratio transmission will be used where the speed range of the vehicle is fairly narrow, such as a race track. A wide-ratio six speed transmission can do what a wide-ratio three speed a close-ratio three speed can do, at the same time.
Below is a plot of the gear ratios of the following transmissions:
- Getrag V160 6-speed manual, found in 1993-1998Toyota Supra Turbos.
- Tremec TR6060 6-speed manual, found in 2007+ FordMustang GT500s.
- Borg-Warner T5 5-speed manual, found in 3rd-generation Chevy Camaros.
- TorqueFlite 727 3-speed automatic, found in various Chrysler vehicles over the years.
Gear ratios of various transmissions. Note that Supra's 6-speed does not have the same ratios as the 6-speed in the Mustang GT500.
Overall ratio spread for each transmission. Note that the 3-speed does not have nearly the same ratio spread as the 6-speeds.
3-Speed Versus 6-Speed
It is intuitive that a transmission with more gears than another will be better, but it may not be totally clear as to why that is. To make the comparison, I will use the stock 6-speed manual in the 350z, along with an old 3-speed manual from an older Nissan vehicle. Below is a table showing the gear ratios of each transmission.
Gear Ratios (x:1)
6 Speed 3 Speed
1st 3.794 3.380
2nd 2.234 1.730
3rd 1.624 1.000
4th 1.271 -
5th 1.000 -
6th 0.794 -
Below is a graph showing the force that the 350z puts to the pavement versus the speed that the car is traveling. Each arc represents a selected gear in the transmission. First gear is the highest, narrowest curve, and top gear is the lowest, widest curve. The beginning of the arc is when the engine is at 1600RPM (chosen by me to keep the graphs clean) in that particular gear, and the end of the arc is when the engine hits its redline of 6600RPM. A higher force implies a higher accelerationat that speed.
Road force with the VQ35DE turning the 3 speed and 6 speed transmissions. Note that at 75mph, there are 4 gears to choose from with the 6 speed, while the 3 speed offers only two.
The above graph clearly shows the superiority of the 6-speed in terms ofacceleration. The 6-speed has significantly better acceleration than the 3-speed at numerous vehicle speeds, especially at 45-60mph and 85-100mph.
The graph below shows the engine RPM versus the speed of the car. Note that the 6-speed is much better at keeping the engine revving high than the 3-speed. This is because the ratio spread between each gear is much lower. The fact that the engine can be kept revving high allows much moreaverage power to be put to the road while the car accelerates. This was already seen in the previous graph.
Engine RPM versus vehicle speed for both transmissions. The large RPM drops on the 3-speed's gear changes are from the high ratio spread between the gears.
It can be seen in the above graph that at 60mph, the 6-speed can have the engine turning as low as 2150rpm, while the 3-speed can only bring it down to 2700rpm. To correct this, I will change the gears in the 3-speed car's rear axle from the stock 3.538:1 to 2.809:1. Below is a graph showing the effect of changing the rear axle gear on the 3-speed.
Road force with the VQ35DE turning the 3 speed and 6 speed transmissions. Note that in order to have the same top gear cruise RPM as the 6-speed, the 3-speed has had to sacrifice acceleration all across the board.
It can clearly be seen that the 3-speed is now very far behind the 6-speed in terms ofacceleration. This shows that transmissions with very few gears can give a car goodacceleration or good fuel economy, but not both at the same time.
Continuously Variable Transmissions
A continuously variable transmission is a transmission that uses a belt on two conic pulleys or a set of rollers to provide an infinite number of ratios. An ideal CVT has an infinite ratio spread, meaning that it could allow the engine to run while the vehicle is at rest (∞:1) and allow the vehicle to drive at an infinitely high speed (0:1). Real CVTs have a finite ratio spread, and use an engagement similar to a torque converter in an automatic transmission to allow the car to be at rest and drive at low speeds.
The ideal CVT can put the engine's peak power to the road at all speeds. It is superior to the 6-speed.
Cornering
When going around a corner, there is a maximum speed that the car can go around it. It is therefore important that the transmission can keep the engine revving at a suitable RPM at that speed. Below is adiagram showing the 3-speed car and 6-speed car going around a corner at 80mph.
When the cars are going around a corner at 80mph, the 6-speed has the advantage because it can keep the engine revving fairly high without redlining. The 3-speed can either redline in 2nd gear, or lug in 3rd gear.
Drag Racing
In drag racing, the time it takes to shift gears is very significant. The faster the vehicle is, the more significant the gear change time becomes relative to the elapsed time down the strip. Because of this, most high performance drag cars only go through three gears (two changes) when going down the ¼ mile. The fastest drag cars do not shift gears at all, but rather have a hydraulic drive system that varies the transfer of power from the engine to the drivetrain. A drag race engine must be tuned to provide a high amount of power at any RPM to provide the necessaryacceleration while pulling through so few gears. Transmissions with fewer gears also tend to have less friction, which allows more of the engine's power to make it to the pavement.
Conclusion
Transmissions have a direct effect on a vehicle's ability to accelerate. An ideal transmission can keep the engine revving near its power peak when the vehicle is driving at various speeds. The gear ratios are chosen based on what speeds the vehicle will be traveling, and having more gears raises the speed range that the vehicle can accelerate most quickly.
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Horsepower and torque
Introduction
An engine's horsepower and torque numbers are two things that are often talked about in automotive circles, but may be misunderstood. In this article, I will be looking at how those numbers affect a car's ability to accelerate. Carroll Shelby once said: "Horsepower sells cars, torque wins races." Let's see if that is actually true.
Table of Contents
Assumptions
- Assumptions
- Torque
- Work
- Difference Between Torque and Work
- Power
- Shaft Power
- Units of Shaft Power
- Gears
- Drivetrain Gearing
- Accelerating a Car
- A Simple Example
- Power Curves and Power Bands
- Comparing Two Cars
- Low-Speed Acceleration
- Shift Points
- Driveability
- High Torque versus High Revving
- Conclusion
- See Also
In this article, some assumptions will be made, as seen below.
Obviously, none of these assumptions apply to real life, but they will make explanation of many concepts much simpler. Power will be measured in Horsepower. Power and Horsepower will be used interchangeably in this article. Torque will be measured in pound-feet, which will be abbreviated as lb-ft or just tq.
- There is no road friction, or friction anywhere for that matter.
- There are no aerodynamic effects acting on the vehicles.
- The vehicles are on flat ground.
- There are no drivetrain losses. The transmission and rear axle are ideal.
- The vehicles are always moving at some non-zerospeed.
- Gear changes take place instantaneously.
- The vehicles are at full throttle at all times.
- There is no turbo lag.
Torque
Torque is a force that tends to cause a rotation. A force applied at a non-zero distance from an object's centre will tend to rotate the object. This is easily seen in real life. If a wrench is placed on a bolt and a force is applied to the end of the wrench, the bolt will turn. If the same pulling force was applied directly to the bolt, it would not turn because the force's direction passes through the object's centre. The amount of torque is determined by multiplying the magnitude of the force by the force's distance from centre.
Diagram showing torque.
Torque can be used to create a force at a distance, as seen below. On a car, this is how the wheel and tire apply force to the pavement.
Torque can be used to create a force at a distance.
Work
Work is not something that is brought up often when talking about cars. Work is defined as the transfer of energy from one system to another, such as a person pushing a cart. Mathematically, work is the product of force and distance, and has units such as foot-pounds or Newton-metres. The direction of force (or at least a component of it) must match the direction of motion for the force to be considered to have done work. Also, if there is no motion, no work has been done.
Work is done on the object by applying a force along a distance.
Difference Between Torque and Work
Note that the units for both torque and work are the product of force and distance, yet torque and work are two different things. Torque is a force that tends to cause a rotation, which means that it does not actually cause an object to move along a distance. Work is a measure of energy transfer between systems, which may or may not have been done by a force from torque.
The difference between torque and work.
On a rotating shaft, work is done by the force from torque. Torque is a force that tends to cause a rotation, and the shaft is rotating. The force is going round and round, and so is the shaft, so if the shaft was "unrolled", there would be a force traveling along a distance, which is work.
On a rotating shaft, the torque is doing the work.
Power
Power is the amount of work that can be done in a certain amount of time, or "the rate of work", or "the rate of energy transfer between systems". The formula for calculating power is shown below:
Power is the product of force and distance over a period of time.
The above equation can be rewritten in terms offorce and speed, as seen below:
Using the definition of speed, power can be expressed in terms of force and speed.
Shaft Power
On a rotating shaft, the force from torque is doing work. The rate of work is dependent upon the shaft's rotational speed. Therefore, the amount of power that a rotating shaft has is the product of its rotational speed and its torque. Using arbitrary units, the power formula for a rotating shaft is:
Shaft power using arbitrary units.
Units of Shaft Power
When using pound-feet as units of torque,revolutions per minute (RPM) for rotational speed, and horsepower for power, shaft power can be expressed with the following formula:
Shaft power in horsepower.
The above power formula is often misinterpreted as showing that power and torque are the same thing, or that they somehow trade hands with each other at 5252RPM. This mistake is from the fact that a graph of torque in pound-feet andpower in horsepower versus engine RPM has crossing lines at 5252RPM. Torque and power play the same role whether an engine is revving below, at, or above 5252RPM. Many dieselengines, and even some gas engines, are not even capable of revving that high at all.
5252RPM is not a significant point in a physical sense. It is merely the RPM at which a graph of torque in pound-feetand power in horsepower would cross when drawn on the same piece of paper. If different units were used, the curves would cross at a different point, yet the principles of operation would remain unchanged.
The above statements can be proven by changing the units for power and torque. Australians often use kilowatts for units of power, and Newton-metres for torque. With that, the shaft powerformula becomes:
Shaft power in metric units.
Using metric units, the unit conversion constant is 9549, not 5252 like it was whenpound-feet and horsepower were being used. This means that a graph of power and torque versus revs using metric units would have crossing curves at 9549RPM instead of 5252RPM.
Australian engines obey the exact same laws of physics as American engines. The only real distinction between the two is that Aussie engines are designed to run upside down.
Gears
Gears are used to change the torque and rotational speed of a part of a system of rotating shafts, or to change the direction of the transmitted motion. An example of the former would be the car's transmission, while an example of the latter would be the rear axle gears.
An ideal (lossless) gear set transmits an equal amount of power to the output shaft as it received from the input shaft. This means that if a gearbox has a 2:1 gear ratio, the output shaft will be rotating half as fast as the input shaft, but will have double the torque. Below is a drawing that shows the effects of a gear set, using an abitrary ratio, GR.
The gearbox is given a certain amount of power, in the form of torque and revs. It then puts out an equal amount of power, with the revs and torque adjusted according to the gear ratio.
Formulae used for gears.
It is interesting to point out that gears and electrical transformers are very similar. Gears change the torque and speed, while transformers change voltage and current. Both gears and transformers put out as much power as they receive.
A car battery produces 12 volts and a lot of current, but a spark plug needs up to 50,000 volts and very little current. An ignition coil, which is a transformer, trades away the excess current from the battery to make the high voltage needed for the spark plugs.
Drivetrain Gearing
A car's drivetrain uses multiple sets of gears to control how much of the engine's total power is going to torque, and how much is going to the rotational speed of the wheels.
All gasoline piston engines produce too little torque and too many revs to properly turn the wheels of a typical road car. With 27 inch tires, 6000RPM at the wheels would be 450mph. It also takes a lot more than a few hundred pounds of force to even move something as heavy as a passenger car. This is why all cars have drivetrains which are setup to divide the revs and multiply the torque.
Most cars are fitted with two sets of gearing between the engine and the wheels. The first set is the transmission, which multiplies the torque a certain amount, depending on what gear it is in. Typically, first gear has a ratio near 3:1, while the top gear has a ratio near 0.8:1. After the transmission, there is another set of gears which usually have a ratio of around 2.5:1 through 6.0:1, depending on the vehicle. Below is a diagramof a typical drivetrain found in most cars.
The drivetrain of a car is fitted with a transmission and final drive gearing to adjust the engine's torque and revs to accelerate the car.
The wheel torque and revs vary with the engine torque and revs, and the gear ratios in between.
The reason that cars have transmissions with multiple gears is so that the engine can be kept within its operating rev range while the vehicle accelerates from rest to possibly over 200mph. In first gear, there is plenty of acceleration because of the torque multiplication, but very little speed before the engine revs to its redline. In second gear, there is slightly less acceleration, but a slightly higher speed before hitting the redline. This trend of higher speed and lower acceleration continues through each gear in the transmission.
Each transmission gear provides a different amount of acceleration and speed. The combination of speed and acceleration is related to the power from the engine.
Accelerating a Car
Newton's second law of motion states that the acceleration of a body is related to the force being applied and the mass of the body, as seen below:
According to Newton's second law of motion, a greater force or a lower mass will result in a greater acceleration.
In order for there to be any acceleration, the force must be applied at the same speed that the object is traveling, for a non-zero length of time. A force being applied at a certain speed for a period of time is power, therefore, the acceleration force on a moving object is determined by the power being applied at that speed.
The wheels receive torque and rotational speed from the engine, and lay down a force onto the pavement. It is this force which accelerates the vehicle. The car's speed is directly related to the rotational speed of the wheel.
The acceleration of a moving object is equal to the power divided by the speed and the mass. The product of speed and mass is known as momentum.
The acceleration force that the tire puts to the road comes from the torque at the wheels. This is why the acceleration force is often calculated by passing the engine torque through the drivetrain gearing and wheels, as seen in the formula below. I will refer to this method of calculating the acceleration force as the torque method.
The acceleration force can be calculated by passing the engine torque through the entire drivetrain and down the tire radius on to the road.
If the vehicle's speed and the power of its engine are known at a given instant, the force of acceleration can be calculated without knowing anything about the drivetrain gearing, tire diameter, or even the engine torque. I will refer to this method of calculating the acceleration force as the power method. Below is the formula for the power method when using imperial units.
When the power and speed are known, the acceleration force can be calculated directly without knowing anything about the drivetrain.
The torque method and the power method will both produce the same results, as seen in the example below.
The calculated acceleration force is the same when using the torque method or the power method.
A Simple Example
To demonstrate the effects of power and torque, I will put three different engines into the same car. The car's speed will be the same for each of the three tests, so that the differences in the acceleration force can be seen clearly.
A sample car will be used for the comparison.
The car has tires with a 24-inch diameter, which gives a radius of 1 foot. The tire will be turning at 500 RPM, which means the car is traveling at 35.7 mph. The transmission will be in a gear which has a gear ratio of 2 : 1. The final drive ratio will be chosen in a way that satisfies the driveshaft RPM and the wheel RPM.
Details of the drivetrain layout.
Blue Engine
The blue engine is running at 2000 RPM and making 200 lb-ft of torque, which is 76 horsepower. The final drive ratio has to be 2 : 1 to match up with the wheel RPM and the driveshaft RPM. With this setup, the car puts 800 lbf to the road.
The blue engine makes 76 hp, and puts down 800 lbf to the road.
Green Engine
The green engine is running at 4000 RPM and making 100 lb-ft of torque, which is also 76 horsepower. It is revving twice as high as the blue engine, but making only half the torque. The final drive ratio has to be 4 : 1 to match up with the wheel RPM and the driveshaft RPM. With this setup, the car puts 800 lbf to the road, which is the same as the force made by the blue engine.
The green engine makes 76 hp and puts down 800 lbf to the road, just like the blue engine.
Red Engine
The red engine is running at 4000 RPM and making 200 lb-ft of torque, which is 152 horsepower. It is making just as much torque as the blue engine, and revving just as high as the green engine. The final drive ratio has to be 4 : 1 to match up with the wheel RPM and the driveshaft RPM. With this setup, the car puts 1600 lbf to the road, which is twice the force that the other two engines made.
The red engine makes 152 horsepower, which is twice the power of the other two engines. It is putting a 1600 lb force to the road, which is also twice as high as the other two engines.
It can be seen from the comparison of the above three engines that the most powerful one gave the highest force, and the two which made the same power as each other made the same force as each other as well. The two engines with the same power had a different amount of torque and revs, but the acceleration force was equalized by the final drive gear. This clearly shows that the engine's power, regardless of how much torque it is making or how high it is revving, determines the car's acceleration force.
Power Curves and Power Bands
Engine performance is often described by the peak power figure. A good engine will produce high peak power, and have a very high average power level as well. A graph of power with respect to engine RPM is known as a power curve, and holds important information about an engine's performance across its rev range.
It is possible for one engine to have more average power than another, even with a lower peak power figure, as seen in the example below.
The power curves above are for one engine with 400hp, and another with 375hp. While the 400hp engine has a higher peak power figure, the 375hp engine has a much higher average power throughout the rev range. In most cases, especially on the street or in drag racing, the 375hp engine seen above would make for a faster car.
The power band is the rev range where the engine is producing an arbitrary percentage of its peak power figure. For example, the 80% power band of an engine with 500hp would be the rev range where it makes 400hp or more. A wide power band implies high average power. This will be seen later in the article.
An engine's power band can be predicted as wideor narrow based on certain characteristics. Some examples are shown in the table below.
Wider Power Band Narrower Power Band
Large displacement Small displacement
High Torque Low Torque
>2 valves/cyl 2 valves/cyl
Variable Valve Timing No VVT
Supercharged or Turbocharged Naturally Aspirated
Peak HP, Peak TQ, Redline
far from each other in the rev range Peak HP, Peak TQ, Redline
very close to each other in the rev range
An engine's power band can be predicted to be wide or narrow based on certain characteristics. There are many exceptions.
Comparing Two Cars
Let's compare two cars with two different engines that have the same peak power output, but different power bands.
Both cars have the same curb weight, transmission, tire radius, and so on. In fact, the only difference between the two cars will be the engines. One car will be equipped with a 500hp V8, and the other will have a 500hp turbocharged 4 cylinder engine.
The car with the V8 will be named Redneck , and the car with the 4 cylinder will be named Ricer . The V8 can rev to 6000RPM and produce a ton of torque, while 4 cylinder can to rev way up to 9000RPM and produce a fair bit of torque. To keep the math very simple, the V8 idles at 600RPM, and the I4 idles at 900RPM.
Below are plots of the two fictitious engine's torque and power curves.
Figure 1: Torque versus RPM for Redneck and Ricer. These are unrealistic curves which have been exaggerated to help illustrate certain concepts.
Figure 2: Horsepower versus RPM for Redneck and Ricer. This is calculated from the torque at each RPM.
Both engines produce a peak of 500hp, as specified earlier. The V8 produces 500hp at 5000RPM, and 573tq at 4250RPM, while the I4 produces 500hp at 8000RPM, and 337tq at 7500RPM.
Ricer Redneck Difference
Rev Range 900 - 9000RPM 600 - 6000RPM 50% more for Ricer
Peak Torque 337tq 573tq 70% more for Redneck
Peak Power 500hp 500hp Equal
Since the V8 was revving low, it needed to produce a lot more torque than the I4 to reach 500hp. At the same time, the I4 needed to rev higher than the V8 to produce 500hp, because it offers up less torque. Below is a comparison of the two engines' power bands.
Figure 3: Power band comparison of both engines. Note that the Redneck's average power production (area under the curve) is higher, and that the peak power is the same, at 500hp.
If the x-axis on the above graph seems unusual, there is a separate page on comparing power curves which explains why the rev ranges are not compared directly.
Notice that while both engines have the same peak power figures, the Redneck's engine has a much wider 80% power band. This situation is a considerable advantage for the Redneck. Between the two cars, the one with the made-up V8 is going to be faster than the one with the made-up I4, because the V8 has a higher average power level throughout its rev range.
Ricer Redneck
Peak Power
500hp = 500hp
Average Power
(Entire Rev Range) 263hp < 338hp
Average Power
(Idle to Redline/2) 106hp < 166hp
Average Power
(Redline/2 to Redline) 385hp < 460hp
Average Power
(80% Power Band) 462hp < 471hp
Both vehicles have a curb weight of 3000 lb, which gives both cars a peak power-to-weight ratio of 330 hp per ton. A final drive (axle) ratio of 3.55:1 has been chosen for the Redneck, and a 5.325:1 ratio has been chosen for the Ricer. The Ricer uses a higher ratio to match the high-revving engine.
Ricer Redneck
Transmission Ratios 2.52,1.52,1.00 2.52,1.52,1.00
Final Drive Ratio 5.325:1 3.55:1
Curb Weight 3000 lb 3000 lb
With all of the above data, a velocity-versus time graph can be created for both cars. It is important to remember that aerodynamic drag, initial launch conditions, and other losses have been ignored for this comparison. Below is a graph of the Redneck and Ricer's acceleration data.
Figure 4: Velocity versus time for Redneck and Ricer. The slope of the curve represents acceleration.
Low-Speed Acceleration
The results of the race between the Redneck and Ricer shows that the Redneck had a significant advantage from start to 60 mph. Above 60 mph, the Ricer was revving closer to its power band, and both cars had similar acceleration to the top speed of approximately 135 mph. In drag racing, the Ricer would have lost the race, but on a racetrack, the difference could be quite minor. Therefore, it can be said that a vehicle which is subject to widely varying speeds must have a very wide power band to be competitive, while a vehicle operating in a narrow range of speeds does not.
Shift Points
When the Ricer and Redneck were racing, they were shifting gears at their engine's redlines. In many real-life cases, shifting gears earlier may be advantageous for acceleration. An engine with a power curve that begins to "fall off" at very high RPM should be shifted earlier, if doing so would bring the engine to an RPM where it is making more power. Gear shift points should always be chosen in such a way that the engine is putting out the highest average power to the wheels.
In the race between the Ricer and Redneck, both cars were fitted with a three-speed, wide-ratio transmission. A high-revving engine with a narrow power band would benefit greatly from a transmission with closer ratios, and additional gears so that the engine can be revved much more closely to its power peak as the vehicle's speed changes. For a more detailed analysis of the effects of transmissions on vehicle performance, refer to the transmissions article.
Driveability
Driveability is a subjective term used to describe the ability to "access" an engine's power. A naturally-aspirated engine with a wide power band will have very good driveability; putting the pedal to the floor at any speed in any gear should yield reasonable acceleration. On the other hand, a car with a narrow power band would not be considered as "driveable". Passing cars while cruising on the highway often requires dropping a gear to bring the engine's revs up to access the power. This is one of the reasons that luxury cars often come with large, naturally-aspirated or supercharged engines, while small, turbocharged engines are not as common and often found in more "focused" sportscars where outstanding driveability is not expected or required.
Engines are sometimes described as being "torquey". This is slang for having good driveability, a wide power band, or a lot of power at low RPM.
Streetability is another term which is often used to describe engines with the aforementioned characteristics, along with good road manners, such as a smooth idle and the ability to start in very cold temperatures.
High Torque Engines versus High Revving Engines
The torque that an engine can produce is somewhat related to the displacement of the engine. Larger displacement engines are likely to be much bigger and heavier, making them unsuitable for certain types of vehicles. This is why many small race cars have engines with small displacement, high-revving, and sometimes equipped with forced induction to produce high horsepower. Also, race cars are often given limits on displacement, which means their only chance at producing a lot of power is to rev very high or use forced induction. A large engine may be able to produce power more reliably than a smaller one, but not necessarily. There are plenty of big, gutless engines that don't last.
Heavy vehicles are almost always equipped with large displacement engines because they require more low-RPM power to accelerate from rest (and very low speeds). As the weight of a vehicle goes up, the ability to accelerate from rest becomes increasingly significant.
Conclusion
In order to quickly accelerate a vehicle, the engine must be able to make a large force at the speed that the vehicle is traveling. The amount of power determines the force that the engine can create at a given speed, whether it is a very low speed or a very high speed. It does not matter if the engine makes power by revving high or making a lot of torque, because drivetrain gearing can be used to adjust the torque and revs proportionally.
“ Peak power sells cars. High average power wins races. ”
A vehicle's peak torque and power figures can only give a general idea of performance. The best way to make a good comparison between vehicles is to go racing!
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- 1,835
- New york
- IvIaster__Shake_
Nice job here, @Otaliema , and thanks for the shoutout. Lots of detailed information here, well phrased & structured, and other good sources that makes a gearhead like me smile. The game has a very skewed view of realistic physics; making my guide, if you can really call something as simple as what I did a true guide, limited to the game engine and how it determines power and acceleration in correlation to the power chart. Something as simple as the 5252 RPM horsepower & torque intersection wasn't something PD apparently considered, and therefore is quite wrong in a lot of vehicles.
If my PS3 would cooperate with GT6 without crashing, I would be back online test & tuning with some of the info on here. 👍
If my PS3 would cooperate with GT6 without crashing, I would be back online test & tuning with some of the info on here. 👍
- 5,489
- mid west USA
- Otaliema
Not a problem sir. Sorry to hear your game is having fits. Hopeful it's just the game and not what happened to me a few months back and the PS3 tanked out.
Boot your machine into safe mode and rebuild the database/file structure. Just back up your saves first.
Gen1-3 PS3 fat/slims to boot to safe mode: from a powered down state press and hold the power button until it does three fast beeps after two short beeps.
Have a sub cable handy in safe mode wireless is unreliable.
- 1,835
- New york
- IvIaster__Shake_
Considering GT6 is really the only game I have issues with as well as spending most of my time on the PS4 now, I think I'll just stay retired. It's not worth the effort of rebuilding the database and redownloading 100 gigs(I have lots of digitals) worth of games & patches for a slim chance it'll work. I have the old fat 80 gig version, and it's served me well for over 8 years now. Good luck with the guide and racing.
- 5,489
- mid west USA
- Otaliema
Totally understand that. It could be your game disk too. I wish well on the PS4. @shaunm80 rav's about Drive club, if your play might look him up 👍Considering GT6 is really the only game I have issues with as well as spending most of my time on the PS4 now, I think I'll just stay retired. It's not worth the effort of rebuilding the database and redownloading 100 gigs(I have lots of digitals) worth of games & patches for a slim chance it'll work. I have the old fat 80 gig version, and it's served me well for over 8 years now. Good luck with the guide and racing.
- 5,489
- mid west USA
- Otaliema
@Lionheart2113 @OdeFinn and myself are working on some mathematics for tire grip and rotational tire speed to allow for some serious fine tuning of transmissions. TBH this is a lot of new math formulas for me so it's taking me about to get it sorted out and than simplflied so it's not a bunch of discombobulated letters and Greek symbols 👍
Dotini
(Banned)
- 15,742
- Seattle
- CR80_Shifty
This is my first visit to your tuning guide, and I have to say I'm impressed, and how I appreciate all this information, much of which I have yet to closely study. Thank you!
I have a question with respect to automatic transmission builds. I have noticed that mostly they don't select 1st gear except for pulling away from a pit stop or other standing start; in other words, they don't usually engage 1st for ~45 mph hairpins, so you don't get the full benefit of all (5 or 6) gears. Is there a method of building to ensure the automatic transmission will select first gear in low speed corners?
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- 5,489
- mid west USA
- Otaliema
Your most welcome 👍
Yes you can force a AT build to go into 1st gear by setting it as long as it will go and then adjusting second gear shorter until second gears speed is low enough that the game decides first gear is better. I'd look at the Race style builds for this to keep the torque down to help with wheel spin. Also don't forget that moving the top speed slider to higher speeds will give you higher speeds in first gear making it easier to get the car into first.
You can also use the top speed style build and just lengthen first gear until it's speed is high enough that the car shirts into it.
Rotary Junkie
Premium
- 9,810
- Canton, MI
- RJs_RX-7
Final drive is bad mmkay. No, but seriously, setting your gearbox up to have the same overall ratios (as in Gear X * Final) with the minimum FD possible is worth a not-inconsiderable amount of straight-line performance. Most noticeable with FR or AWD layouts. The gap is somewhere on the order of .050sec through 1/4 mile, doesn't seem huge until you realize it's a small percentage gain at all times you're accelerating. Can easily mean a tenth or two around any given track.
Just a little note. I'd also argue that in the vast majority of cases you're best off with as close of ratios as possible, but what do I know, I'm retired.
Just a little note. I'd also argue that in the vast majority of cases you're best off with as close of ratios as possible, but what do I know, I'm retired.
- 6,293
- Canada
Great write ups guys 👍
To really complete this guide, I think more needs to be discussed regarding driveability, and how this relates to going fast.
The two main situations I can think of is corner entry, and corner exit.
On corner entry, the gear you are currently in will effect how sharply you can turn into a corner. The lower the gear, the sharper the turn in. A properly timed downshift can really aid the turn in...but if you downshift into a gear which is set too slow, you will upset the balance of the car.
Conversely, on corner exit, it can sometime be beneficial to short shift up a gear to be able to put down full throttle earlier. If your gears are too far apart, short shifting is not an option as you will bog down.
Another thing to consider is where on the track you will be shifting. Shifting upsets the balance of the car, especially at high speed. it may be beneficial to set your transmission in a way which prevents you from needing to shift at awkward moments. Same thing with a straight away. You don't want to be hitting the rev limiter a second before reaching the braking point. Yes, you could up shift, but that's an extra up and downshift that would not be necessary if the trans was set to not require the up shift in the first place.
Another topic which I think could use discussion is how to set a transmission for a tune which uses the power limiter, or uses a low or mid RPM Turbo (eg. R33 or R34). This involves locating where peak power occurs, making this your upshift point, and then working backwards from there to set the RPM drop as you upshift.
I built a Wangan Spec R33 using the mid turbo (which produces more HP and more torque than the high, just over a narrower range, and not at peak rpm). I'm not in front of the game atm, but if I remember, I think my upshift point is around 6000rpm. I have the drop set for about 1500rpm for gears 1-3, and about 1000rpm for gears 4-6.
I use long gears combined with a very long final gear to achieve the spacing. In the tuning menue, I can only see up to 4th gear. 5 and 6 are off the screen. I've used the same transmission, with a shorter final gear, and minor adjustments for circuit racing and preferred it over a traditional setup.
This setup really allows me to take full advantage of the insane torque the motor makes in the lower revs, and still utilize the peak power.
Also, if you want to get really into it, most race transmissions do not have even spacing between the gears. 1st is set up to optimize starts, and is not used for anything else (exceptions like the hairpin at Monaco). The jump from 1 to 2 can often be quite large, but then going from 2-3, 3-4, 4-5, etc is very very close.
Lastly, the idea of not using every gear. On a small track like Tsukuba, in almost any car with more than 200ish HP, you really don't need 6 gears. You really only have to focus on optimizing gears 2 through 5, as excessive shifting down to 1, or up to 6, just leads to more time off throttle and hence a slower lap.
To really complete this guide, I think more needs to be discussed regarding driveability, and how this relates to going fast.
The two main situations I can think of is corner entry, and corner exit.
On corner entry, the gear you are currently in will effect how sharply you can turn into a corner. The lower the gear, the sharper the turn in. A properly timed downshift can really aid the turn in...but if you downshift into a gear which is set too slow, you will upset the balance of the car.
Conversely, on corner exit, it can sometime be beneficial to short shift up a gear to be able to put down full throttle earlier. If your gears are too far apart, short shifting is not an option as you will bog down.
Another thing to consider is where on the track you will be shifting. Shifting upsets the balance of the car, especially at high speed. it may be beneficial to set your transmission in a way which prevents you from needing to shift at awkward moments. Same thing with a straight away. You don't want to be hitting the rev limiter a second before reaching the braking point. Yes, you could up shift, but that's an extra up and downshift that would not be necessary if the trans was set to not require the up shift in the first place.
Another topic which I think could use discussion is how to set a transmission for a tune which uses the power limiter, or uses a low or mid RPM Turbo (eg. R33 or R34). This involves locating where peak power occurs, making this your upshift point, and then working backwards from there to set the RPM drop as you upshift.
I built a Wangan Spec R33 using the mid turbo (which produces more HP and more torque than the high, just over a narrower range, and not at peak rpm). I'm not in front of the game atm, but if I remember, I think my upshift point is around 6000rpm. I have the drop set for about 1500rpm for gears 1-3, and about 1000rpm for gears 4-6.
I use long gears combined with a very long final gear to achieve the spacing. In the tuning menue, I can only see up to 4th gear. 5 and 6 are off the screen. I've used the same transmission, with a shorter final gear, and minor adjustments for circuit racing and preferred it over a traditional setup.
This setup really allows me to take full advantage of the insane torque the motor makes in the lower revs, and still utilize the peak power.
Also, if you want to get really into it, most race transmissions do not have even spacing between the gears. 1st is set up to optimize starts, and is not used for anything else (exceptions like the hairpin at Monaco). The jump from 1 to 2 can often be quite large, but then going from 2-3, 3-4, 4-5, etc is very very close.
Lastly, the idea of not using every gear. On a small track like Tsukuba, in almost any car with more than 200ish HP, you really don't need 6 gears. You really only have to focus on optimizing gears 2 through 5, as excessive shifting down to 1, or up to 6, just leads to more time off throttle and hence a slower lap.
- 5,489
- mid west USA
- Otaliema
I agree completely but as @twitcher pointed out, too tight or non opimized gears in a non-drag racing situation can lead to an upset car. hence the variations in top speed set and placements of the IFG. As in enduro race you want long gears to use as little fuel as possible and still deliver power to the track effectively.Final drive is bad mmkay. No, but seriously, setting your gearbox up to have the same overall ratios (as in Gear X * Final) with the minimum FD possible is worth a not-inconsiderable amount of straight-line performance. Most noticeable with FR or AWD layouts. The gap is somewhere on the order of .050sec through 1/4 mile, doesn't seem huge until you realize it's a small percentage gain at all times you're accelerating. Can easily mean a tenth or two around any given track.
Just a little note. I'd also argue that in the vast majority of cases you're best off with as close of ratios as possible, but what do I know, I'm retired.
Agreed, whist I don't cover that in detail it is touched on in the TT transmissions.
As for using or not using all the gears on a track in a car that is entirely up to the tuner, based on the car and track. I've made transmissions for cars that use 5/6 gears on lower powered car in a short track that drive the aliens around here nuts but they can't make it better. I've made 3 speed trannys on that by all reason shouldn't work but gave the best lap times on long tracks.
Every car has different needs for the track it's on for a TT style transmission. If you're building a racing set up you need to set up in a way that will let you just change the final to fit the track for your style that way you can just set it and go when online and don't have to make one from scratch every time.
- 6,293
- Canada
Or you can get ultra serious and buy multiple copies of the same car so you can have custom tunes for specific tracks.
But yes in general, for online racing, you want to find a happy middle ground and just use the final gear to adjust to the track.
The only times I went really nuts with making custom trans this for specific tracks was when I was racing in leagues (and therefore knew upcoming tracks), or for unique tracks like Nürb, La Sarthe, etc.
- 5,489
- mid west USA
- Otaliema
Yeah that's just too crazy
car for each track you drive....Maybe for the die hard hard core. But you could get away with one car for three tracks. Just besure you put the right parts on But yeah some tracks like Nurb, Sarth, Spa need their own transmissions, they are too picky to run really good with a general transmission. But you can get away with a general transmission for online with 90% of the tracks in the game.
- 6,293
- Canada
Long story short, we need more settings sheets.....waaaaaaaay more settings sheets!Yeah that's just too crazy
But yeah some tracks like Nurb, Sarth, Spa need their own transmissions, they are too picky to run really good with a general transmission. But you can get away with a general transmission for online with 90% of the tracks in the game.
- 2,643
- Finland
- OdeFinn
This fights against cornering ability, acceleration and overall handling.
Longer (smaller number) final gear is, more car is prone to understeer during cornering, and more open LSD you have to have installed, more open LSD and less power delivered to ground when exiting corner.
Reason for parachute locks (brake side higher than acceleration) is "wrong" gearing (gear+ final gear), handling error fixed by abnormal locking methods, long final doesn't use/give engine brake thru on wheels so sharp and you have to exaggerate it by using really high brake side lock. On acceleration long final rises wheel spin too quickly relatively versus rpm and you have to ease that with low locking rate. (Data logger will show how those parachute locked cars Drivetrain wheels spins separated speeds during acceleration, wasting power what could be used on differently made setup)
So good point to mention handling vs. Gearing.
Good general gearing work from Tsukuba to Nordschleife, if it's not relaying on "parachute" lock, on most cars, exceptions can be.
That "demo" gearbox for FD3S using defaults of car is good example for Tsukuba to Nordschleife.
Agreed!
Rotary Junkie
Premium
- 9,810
- Canton, MI
- RJs_RX-7
Smaller final = lower driveline RPM = lower driveline inertia = sharper activation of the differential, is this where you're going?
Strange that with all the things not simulated, ignored, or hit with a blanket statement of "this is how every car behaves", driveline (not just engine/flywheel) inertia is simulated. Instead of, you know, at least having some form of rudimentary suspension model for any given suspension type as opposed to the current everything has perfect camber curves and no bump steer and no toe change and all this regardless of situation.
Strange that with all the things not simulated, ignored, or hit with a blanket statement of "this is how every car behaves", driveline (not just engine/flywheel) inertia is simulated. Instead of, you know, at least having some form of rudimentary suspension model for any given suspension type as opposed to the current everything has perfect camber curves and no bump steer and no toe change and all this regardless of situation.
- 2,643
- Finland
- OdeFinn
Not what I said (write), if you want to change LSD activation reaction time, then you have easy parts to use, clutch for softer behavior of LSD, due slipping on there, can make LSD locking stiffer if more plates used on clutch, keeps driveline rpm closer 1:1.
For quicker reactions use carbon propeller shaft, opens/locks differential quicker due smaller weight, normal drive shaft keeps lock locked longer and tires rolling longer because of inertia.
Final gear has it own effects(gearing overall), lot to do with car engine torque value when using engine brake and what happens to each side tire traction, and how you have to manipulate that traction with LSD. Also during acceleration as you know.
People have to think Drivetrain both ways, it can be 3:1 when acceleration is going, but when braking its 1:3.
- 5,489
- mid west USA
- Otaliema
What the final drive affects is the number of RPM's the engine makes to one RPM of the Drive shaft. It's literally a equal ratio. 2.500 = 2.5 engine RPM to one 1 RPM of the drive shaft. That's why smaller Finals accelerate harder and faster than Higher but have a lower top speed. In reference to the guide. The higher final the less work the engine does per RPM but takes more RPM to get the same work done so it can pull at higher speeds, giving a higher top speed but slower acceleration.
So it does have an affect on the LSD in that the smaller Final number generates more torque then a higher final does so it will activate the LSD Intial faster. But it will not affect the actual torque required for activation.
So it does have an affect on the LSD in that the smaller Final number generates more torque then a higher final does so it will activate the LSD Intial faster. But it will not affect the actual torque required for activation.
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Rotary Junkie
Premium
- 9,810
- Canton, MI
- RJs_RX-7
My initial post was at least somewhat clear on this...
The only ratio that matters in terms of effective gear ratio is the overall (i.e gear * final), and that the lower you can set the final while maintaining the same overall ratios in each gear, the vehicle will accelerate noticeably quicker in side-by-side testing.
Example, take two gearboxes, I'll pull the numbers out of thin air but you'll get the point.
Gearbox #1:
[2.320/1.690/1.290/1.000/.850/.725], final 5.000 (first 4 are accurate close-ratio Ford Toploader ratios if anyone wants to make a historically accurate Cougar/GT350/Mach 1 racecar, for some reason in GT5/6 they come with GM close-ratio Muncie ratios... Although they all would've had the wide-ratio Toploader instead)
Gearbox #2:
[4.640/3.380/2.580/2.000/1.700/1.450], final 2.500.
The ratios are identical, they should act the same. Certainly vehicle speed at any given RPM in whatever gear is identical. Thing is, the lower final accelerates harder every single time. I've tested this in every GT game since GT4, there has never been a change in that.
Power flow:
Engine + transmission input
Transmission output + prop shaft + differential pinion gear
Differential ring gear + differential unit + axles + tires
Engine at 5000rpm, 1st gear. Transmission output speed @ 2.320 = ~2155rpm. Final @ 5.000, wheel speed @ ~431rpm. 4.640/2.500 combo ends up at ~1077rpm driveshaft speed and ~431rpm wheel speed. End result is the same and the actual torque level acting upon the differential is exactly the same, only difference is that the driveshaft has less inertia due to spinning slower.
If this changes handling, it is due to exactly what I said, as well as what you say the CF driveshaft does (they have the same net effect, although the final drive change reduces internal transmission speed and therefore inertia as well).
As for the braking/decel lock and "changes" to the gear ratio, you're not quite thinking right. Engine braking is still amplified by gear ratio, as it is a reverse force applied at the crankshaft. Forces applied to the crankshaft from the tires DO operate at an inverted ratio, but a braking force is only applied to the engine while either left-foot braking or decelerating harder than the engine's rotational inertia would allow. Either of these situations would actually apply the accel-side ramp of the differential rather than the decel side.
- 1,485
- Hampshire
- Lionheart2113
👍
Below is an example of basically the scenario you just described but on a Scirocco. This first is a 50% Initial Final flip, which means I have to have a smaller End Final number (yellow box in center) to get the same Top Speed (137/138mph blue box) as the second scenario that is a 100% Initial Final flip that has a larger End Final number to achieve the same Top Speed (137/138mph).
50% Intial Final Flip
100% Initial Final Flip
In theory they should act the same but in the limited testing that I have done so far I have noticed a small difference. It seems that cars with a flat HP curve (usually caused by reducing the power limiter) thrive better on a 50% Initial Final flip and cars that have a nice steady rise throughout the graph do better with a 100% Initial Final flip. That is with the same gear ratios/percentages.
Track used, placebo, or what I'm unsure. Only being able to test an automatic transmission might also have something to do with it.
Rotary Junkie
Premium
- 9,810
- Canton, MI
- RJs_RX-7
*snip*
In theory they should act the same but in the limited testing that I have done so far I have noticed a small difference. It seems that cars with a flat HP curve (usually caused by reducing the power limiter) thrive better on a 50% Initial Final flip and cars that have a nice steady rise throughout the graph do better with a 100% Initial Final flip. That is with the same gear ratios/percentages.
Track used, placebo, or what I'm unsure. Only being able to test an automatic transmission might also have something to do with it.
Actually, a heavily power-limited vehicle would be the most obvious way to test this. Since the power curve winds up completely flat, as long as you're in the flat range wheel torque at a given road speed is identical. Ex: 200hp @ 2000rpm is (200x5252)/2000=525.2 ft-lb, 200hp @ 4000rpm = 262.6 ft-lb, so with twice the gear ratio you have the same wheel torque. Shouldn't matter how far you rev it, right?
Well, no. Flywheel inertia is the single biggest savings possible. The higher you rev it, even though you have the exact same amount of wheel torque available, the harder you have to fight to accelerate the flywheel (and driveline). This results in a car that pulls harder when shifted as early as possible without falling below the flat range. Thing is, because of this, a "flat" powerband is the easiest way to spot out driveline inertia as well, particularly if using automatic and being stuck at the top end of the rev range where total inertia is greatest. Set up the gearbox at max final, round the numbers to something that can be doubled (I'd suggest going somewhat wide with the autoset/max speed slider for this test), set it up again with double the individual ratios and minimum final. Hit SSRX, run both in auto and just record first sector times flooring it from the initial rolling start. In auto your results will be 100% repeatable for any given setup. Can also be used for determining how much more downforce is actually hurting you on straights.
The peakier cars still benefit but it's more exaggerated here, and there may be some benefit to a shorter final due to dulling response some. FWD/MR benefit the least, AWD benefits the most. There is some truth to OdeFinn's statements of FD changing required LSD settings, but it's also something that if driven and tuned around will result in a quicker car. It's free horsepower.
Edit: Just realized SSRX's first actual checkpoint is at the 5K mark, uphill. No bueno. Could've sworn it was at 1K previously. All I know is I miss speed test.
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