When to Change Gear
An area of constant discussion and argument, the subject of when is the optimum point to change up is one again that can help us understand the relationship between gear ratios and the engine, and better understand the drivetrain as a whole. Many people advocate changing gear at the point peak engine power is reached (with many disagreeing in regard to this being bhp or torque), some suggest the red-line, others still maintain it should be the point at which the next gear would reach peak power when you change up
Ford and ex-General Motors powertrain engineer, Ed Lansinger, wrote one of the finest papers I have read on this subject. The paper in question is reproduced below, please note that it was originally written for a Dodge Neon website and also includes a number of additional comments at the bottom.
Torque vs. Power Author Ed Lansinger
First, a clarification: torque is no more real than power. The DOHC puts out 133 ft-lb of ground pounding torque, but I've seen some older Neons that are leaking torque and you have to avoid driving behind them because the torque, once leaked, is slippery. Don't bother picking it up and adding it to your engine as it degrades quickly and will take you out of Stock class. Consider torque and power as concepts used to describe how things interact to produce movement and how "energy" (another concept) is transferred.
Both torque and power can be observed "directly". Think of slowing a freespinning tire with your hand. Feel the tug on your palm and the tension in your arm? That's a measure of torque, the torque the tire experiences as a result of your palm slowing it down. Feel the heat build up from friction? That's a measure of power.
Incidentally, water brake dynamometers get a direct measurement of power by measuring the increase in the temperature of water flowing past a propeller spun by the engine under test. You can solve for torque if you know engine RPM.
Maximum Acceleration vs Torque
I'd like to think that torque is an intuitively easier concept to understand. If that were true, though, then more people would understand the relationship between torque, horsepower, and vehicle acceleration. In reality, none of it is intuitive. If it were, Newton wouldn't be considered the Really Great Guy that he is.
The classic mistake is to conclude that the fastest way down, let's say, a ¼ mile drag strip is to keep the engine RPM at the torque peak (or as close as possible). The technique is usually stated as "shift just after the torque peak", or "shift N RPM above the torque peak so you are N RPM below the torque peak in the next gear when you finish the shift". Unfortunately, *engine* torque does not tell you the full story. What matters is the torque *delivered to the tires*, including the effects of the transmission.
We all know a car does not accelerate as hard in second gear at peak torque RPM as it does in first gear. The transmission amplifies or multiplies the torque coming from the engine by a factor equal to the gear ratio. So to determine how much the car is accelerating at a particular instant, you have to know both the torque output of the engine as well as the gear ratio.
To figure out your shift points knowing only torque, generate tables of transmission output torque vs. RPM for each gear. To get transmission output torque, multiply the engine torque by the gear ratio. You are simply comparing gear to gear, so the final drive ratio can be ignored. You may also need to know the relationship between RPM in one gear and RPM in another gear (which is RPM * (gear2ratio/gear1ratio) at any particular vehicle speed.) Then it's easy to see what shift points to choose to maximize your transmission output torque at all times.
Here's an example for the 1999 Neon DOHC engine with a five-speed manual transmission. Before you flame, understand that I do not have an accurate torque curve for this motor. I'm estimating visually from the curve printed in the 1999 brochure, which is seriously flawed (it makes a lot more sense if the torque curve is shifted to the right 1000 RPM). I get:
Engine Transmission output torque (ft-lb):
RPM Torque (ft-lb)
1st Gear
(3.54)
2nd Gear
(2.13)
3rd Gear
(1.36)
4th Gear
(1.03)
5th Gear
(0.72)
1,000 50 177 107 68 52 36
1,500 65 230 138 88 67 47
2,000 80 283 170 109 82 58
2,500 92 326 196 125 95 66
3,000 104 368 222 141 107 75
3,500 114 404 243 155 117 82
4,000 120 425 256 163 124 86
4,500 125 443 266 170 129 90
5,000 130 460 277 177 134 94
5,500 133 471 283 181 137 96
6,000 130 460 277 177 134 94
6,500 122 432 260 166 126 88
7,000 110 389 234 150 113 79
(note: peak torque is at 5500 RPM, peak horsepower is at 6500 RPM)
Without graphing, there's something immediately apparent: in any gear, at 7000 RPM, the transmission torque output is always higher than at any RPM in the next gear up. What this means is, for this car:
* Shift at the redline, not at the torque peak!
Walk through an example. You're hammering down the track in 1st gear. Engine RPM is 6000, just past the engine's torque peak. Do you shift? Well, if you do, the engine will be pulled down to 3600 RPM, and 2nd gear will send 246 ft-lb of torque to the wheels (actually, to the differential first, which amplifies the torque by a constant factor and sends it to the wheels). Don't you think it would be better to hold it in first gear? Torque is dropping off, but it's still 389 ft-lb at 7000 RPM, right before the 7200 RPM redline. So, for this powertrain, first gear is *always* the best deal for acceleration, at any speed, except that you can't accelerate past the redline. The 1-2 shift at 7200 RPM pulls the engine down to 4400 RPM, where 2nd will deliver 265 ft-lb of torque. Not only did you win by maintaining the high torque of 1st all the way to 7200 RPM, you are now better off in second gear. Same thing goes for the 2-3 shift. 2nd gear output torque at the redline is still greater than 3rd gear output torque at any engine speed, so you wind her out as far as she'll go before you shift to 3rd. Same for the 3-4, same for the 4-5.
But, you ask, isn't your acceleration greatest at the torque peak? Yes, it is! But only within that gear. The next gear down will give you even greater acceleration at the same speed, unless the vehicle speed is too high for that gear.
To use engine torque to understand how your car performs, you MUST include the effects of the transmission.
Maximum Acceleration Vs. Power
OK, so what about power? As has been noted by a previous contributor, Power (hp) = Torque (ft-lb) * RPM / 5252. Note that power is also force * velocity, specifically:
Power (hp) = Force (lb) * Velocity (MPH) / 374
That's net horsepower, which is engine power minus losses like transmission and tire friction. The force is the sum of the longitudinal forces at the contact patches of the two driven tires.
Hmmm... P = F * V ...rearrange to get F = P / V ... that means that you get the maximum force pushing the car if you maximize your *Power* at any given velocity. This gives us another useful rule: * Shift to maximize engine POWER, not engine torque!
This is *exactly* the same as saying "shift to maximize transmission output torque". But it's a little easier to apply. Here's how. Using the torque information above, I get the following power curve:
RPM HP
1000 10
1500 19
2000 30
2500 44
3000 59
3500 76
4000 91
4500 107
5000 124
5500 139 (peak torque)
6000 149
6500 151 (peak power)
7000 147
The tires don't see quite these numbers due to [friction and aerodynamic] losses, but I'm going to assume that the losses are comparable from gear to gear and that the overall shape of the power curve remains the same.
Applying the maximum power rule, we'd like to race down the 1/4 mile with the engine always as close to 6500 RPM as possible. If we had a continuously variable transmission, the lowest E.T. would be achieved by keeping the engine dead on 6500 RPM. 5500 is not the best; at any vehicle speed, the engine would put out more torque but the transmission will have a less advantageous gear ratio, so you get a net loss of force to the tires. Apply P = F * V or P = T * RPM to prove this.
Since the Neon doesn't have a CVT, we have to shift. The shift points are pretty easy to determine. In fact, you don't really need to know anything about the gear ratios of the different gears, which is why power is sometimes easier to understand than torque. I'm going to assume that the DOHC puts out at least 145 horsepower at the redline (7200 RPM). Shifting at the redline in each gear should drag the engine down as follows: shift RPM drop Horsepower change
- ----- ---------- ------------------
1->2 7200->4700 145->114
2->3 7200->4600 145->110
3->4 7200->5500 145->139
4->5 7200->5000 145->124
(I derived this, but all you really need to do is drive the car, shift, and find out where the motor lands) Note - and this is important - the transmission does not amplify power. Power in = power out, minus losses (which are low for a manual transmission). This is predicted by the law of conservation of energy. Is 7200 the correct shift point? It would *not* be the correct shift point if the engine was making more power in the new gear than the old gear. That would mean that you should have shifted earlier. But in this case, the power output at redline is always greater than the power output after the shift. So it's the best performance you can get.
A more rigorous way of doing this is to graph horsepower vs. velocity in each of the gears. If power in one gear drops below the horsepower of the next gear at a particular MPH, then that MPH is where you should shift, otherwise shift at the redline. I leave as an exercise for the reader the following: predicting shift points based on engine torque, RPM, and gear ratio gives the same results as predicting shift points based on power and vehicle velocity.
Exceptions
There are no exceptions; a car running at its (net) power peak can accelerate no harder at that same vehicle speed. There is no better gear to choose, even if another gear would place the engine closer to its torque peak. You'll find that a car running at peak power at a given vehicle speed is delivering the maximum possible torque to the tires (although the engine may not be spinning at its torque peak). This derives immediately from first principles in physics.
However, note the following: - Transmission losses are not shown on engine power curves. The net power curve (power delivered to the ground) may have a different shape or even a different peak RPM as a result. This would result in different shift point. Best results are obtained from a power curve measured by a chassis dynamometer. - The discussion above assumes negligible tire slip. If you exceed the maximum traction available from the tires, then additional power doesn't help. That's why it's sometimes no loss at all to shift early when the tires break loose, and in fact it can be a benefit.
More exceptions: another view (by Maciek S. Kontakt)
Yes, there are exceptions. The Neon engine is not a responsive engine as its band is very narrow. The band is between peak torque and peak power and it is only 1000rpm. This engine is designed with focus on speed and not on acceleration as much. Peak power will tell only how fast you can go because beyond peak power there is almost no acceleration and that is your top speed deteremination on a particular gear.
In addition to that there are very responsive engines like BMW 3 series (not M3) that actually you shift to keep peak torque between points of shift and if you want to accelerate faster you are not supposed to reach peak power (proven on my own BMW of that type). If you have engine with wide band your explanation may not hold true. YOU WILL FIND many points where torque on higher gear would be higher that you were at lower gear only at high rpms. That depends of course how close are gearing ratios put into transmission.
Optimization for speed and optimization for acceleration are very different. It is even not true what is said by many authoritative sources (books written by racers) that you upshift at point where torque value would be lower than on higher gear. It is more complex that that and you have to refer to gain of speed on both gears if you changed rpms (accelerated). That is because torque curve is not flat and it can be differently "sloped" on ascending and descanding parts.
The field (space) under that curve is more relevant to the shift points than values on particular points of the curve. That's pure mathematics and physics which takes... classes at university and does not take track time in a race car. Ask engineers rather than technicians or racers.
By the way, the main principle of physics is: to accelerate there is unbalanced force required (in some places in this world you will not graduated from high school if you at least do not memorize that). Torque represents force. Power is derived from torque and it represents force causing motion. No motion no power. Initial cause of power is force. Power on the combustion engine diagrams past peak torque grows only because rpms grow (power is direct multiplication of torque and rpms). Once torque of engine falls sharply, rpms growth cannot overcome that and power will also fall. Simple as that.
F1 and Indy bolids are build for top speed on long straights. That is why their engine designers struggle for high rpms to achieve high peak power (and power past that point a bit). They accelerate well too but that is not neccesarily primary goal. When there is acceleration required there will be less stress on peak power (read rpms), but on force that is torque curve shape.... given you do not need to accelerate to very high speeds because for example your road/track is full of tight bends rather than straights. Supercharged units have torque almost entirely flat so you again may want to shift at the end of any curve (power or torque), but that's another example justified.
To the Point
Torque and power are (almost) flip sides of the same coin. Increasing the torque of an engine at a particular RPM is the same as increasing the power output at the same RPM. Power is just as useful and relevant in determining vehicle performance as is torque. In some situations it's more useful, because you may not have to play with gear ratios and a calculator to understand what's going on.
A car accelerates hardest with gearing selected to stay as close as possible to the engine *power* peak, subject to the traction capability of the tires. Not all cars should be shifted at the redline for maximum performance. But it's true for many cars. You can determine optimal shift points by graphing horsepower vs. velocity or transmission torque vs. RPM. Engine torque alone will not determine shift points.
Conclusion
The above piece gives us a lot to think about, but I would like to focus on two main points. The first is that no single rule can be applied when it comes to determining a shift point for a given car, you need to look at the power and torque curves (which GT4 does show to us). And you also need to consider how the power and torque is going to be delivered in any given gear in comparison to the next gear. The simplest rule of thumb is that you should only change gear when moving to the higher gear will give you more power and/or torque. The second point is that torque is multiplied by the drive train itself.
To find an approximate figure for torque delivered at the wheels we use the information above as a starting point, in that you multiply the engine torque for the current engine rpm by the gear ratio, you then need to multiply this figure by the final drive ratio.
The resulting figure is the approximate level of torque delivered at the driven wheels; to obtain an approximate figure for each wheel divide by the number of driven wheels. Remember that this is a figure without any drivetrain losses taken into account and will simply be a maximum possible figure.
Lets look at an example using a Nissan 350Z and its first gear ratio of 3.79 and final drive ratio of 3.54.
In first gear at 2,000rpm the torque at the wheels is approx. 3,019lb-ft (225lb-ft * 3.79 * 3.54) or approx. 1,509.5 lb-ft per tyre (3,019 / 2). However at peak torque in 1st gear (4,800rpm) this rises to 3,676 lb-ft or 1,838 lb-ft per tyre. An increase of 657 lb-ft in total, or 328 lb-ft per driven wheel.
This increase in torque, particularly if delivered to the driven wheels quickly may well result in a loss of traction and wheel-spin. The multiplying effect of the gear ratio and final drive is why wheel spin is more likely in lower gears than in higher gears. Now looking at all of this it becomes clear that if we increase the value of a single gear ratio it will produce more torque at the wheels for that gear. And if we did the same for the final drive it would produce more torque at the driven wheels for all gears.
This increase in torque from using a high value will produce more torque at the driven wheels and provide more acceleration, but it also increases the chances of overloading the tyres limit and creating wheel spin. However if we now think back to the section on mph per 1,000rpm, there we found that using higher values for the gear ratios or final drive ratios resulted in a lower overall maximum speed.
This is the balance you have to achieve with gear ratios, the higher the values the better the acceleration, but the lower the overall speed of the car.
Stock Gearbox Vs. Fully Customisable Gearbox
In GT4 it is sometimes advisable to avoid using the Fully Customisable Gearbox with certain cars, particularly those that produce a high level of torque. The standard ratios in the Fully Customisable Gearbox are not the same as the stock gear ratios found in the stock gearbox. In every example where I have compared Stock vs. FC the ratios in the FC box are closer (the values are higher) and in a lot of cases it is not possible to match the stock values. A good example of a car that this causes a problem for is the Ford GT, with peak 500 lb-ft of torque produced at 3,700rpm it can be difficult to control at the best of times, requiring a very gentle touch with the throttle. The standard gearbox ratios are also already quite close, installing the Fully Customisable gearbox only makes matters worse as the ratios are much higher than in the standard gearbox and its not possible to reduce the values to a point near the standard ratios. As a result the Ford GT with a Fully Customisable gearbox is almost impossible to drive on most tyres, but a quick swap back to the standard gearbox resolves most of these power deliver problems.
Remember the Fully Customisable gearbox is not always the best option.
) In the end, it all points back to trial and error.
