Let's say there's a 6-Gear manual transmission car, whose 6th gear equals 2000 rpm at 100 km/h (~60 mph).
How can one theoretically add a 7th gear that can maintain the same speed at 1400 rpm in order to enhance fuel economy?
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This is something that used to be quite common - in the '60s and '70s, people would add an electronic (or manual) overdrive to the back of the 4-speed gearbox to give an extra gear (usually two, as it would operate in both 3rd and 4th, although on many cars the difference between overdrive-3rd and direct-4th was very little).
It's unlikely to be possible on many, if any, modern cars however, for several reasons:
Most modern cars are front-wheel-drive, so there's no output shaft on the gearbox, with the drive going directly into the differential (although some early 5-speed FWD boxes were simply the previous 4-speed with an extra bit bolted to the side to have the same effect)
There's no extra space in a modern engine bay to add the extra components.
The electronics integral to modern car engines would get very confused
It wouldn't be worth it anyway, as modern gearboxes are designed to more closely reflect the characteristics of the engine, so the top gear will be set to have the engine at optimum RPM at a typical cruising speed - that's much easier to do with 6 gears than it used to be with only 4. The use of overdrives I mention above largely coincided with the proliferation of motorways and other faster roads, so allowed the higher cruising speeds necessary for those roads.
As @SteveMatthews points out in the comments, it depends on the make/model of the car. To answer your question outright, though, you cannot just "add" another gear. A transmission in most cases are built as they are built. You wouldn't be able to just "add" in another gear, because there's not space to put it in there. They aren't designed to have more gears.
There might be several ways of working around it, though. If the vehicle is rear wheel drive, there's the option to add a product called the Gear Vendors under/overdrive. This attaches to the output of the existing transmission, which, when activated, can give an underdrive (like the low gear in a 4wd transfer case) to provide more torque or it can also give an overdrive, which compounds the output of the transmission to do exactly what you're suggesting. (NOTE: I have no affiliation with this product.)
Another way to partially accomplish this is by putting taller tires on the vehicle. The taller the tire, the more distance is traveled per revolution of the tire. This means at a given speed, your RPMs would be lower. Mind you, for this option, you are limited by the amount of space in the wheel well and by the available torque of the engine.
There may be another option of actually changing out the transmission itself. This is highly dependent upon the manufacturer of the vehicle and what they've created which might fit into your vehicle. Just note, most transmission's final drives sit about the same, depending upon the engine. This means, even if a different transmission has more gears, your engine would still be spinning about the same to achieve the same speed. If you have funds available, you could possibly retrofit another transmission into your vehicle, but the cost/labor/time involved would make this a non-starter for most people. It would be easier/cheaper/better to just purchase a different vehicle which gets better fuel mileage.
TL;DR: If you really must, try changing gear ratios. But what you actually want is a new car with automatic gearbox.
A 6 gear car must be a pretty modern one (15 years old or newer). Which means the car is very finely tuned and calibrated to work as a whole and is thoroughly controlled by electronics, which is more of a trouble than upgrading a pure mechanical car. You have basically one option only (you'd have one more if you wanted to upgrade from 5 gears to 6) which will most likely confuse your car, render it road illegal (subject to locale), void any warranties, make your car behave erratically under circumstances, lead to premature wear of the drivetrain and may even cause your car stop fulfilling ever more stringent exhaust regulations. That said, it sounds interesting, let's do it!
Your only workable option is to change gear ratios. You can't another gear, the upgrade will be prohibitively expensive (not only updating the gearbox housing, lever guides, linkage system and drivetrain control system, you'd have a big trouble working the stick to the seventh gear all the time, and once you lend your car to an uninitiated driver, the consequences of ensuing confusion may be fatal).
That may actually be pretty straightforward (changing the ratios, not killing your passengers!), because modern cars (European platform based ones I know tiny bit about) have standardized gearboxes for many model and engine combinations, where the only difference are the gear ratios. So you should only need to acquire a gearbox or two with the ratios you'd like, swap the cogwheels, synchronizing rings and their accessories, perhaps machine a new shaft or two, and you are good to go.
Depending on make and model, ESP and other governing systems may get confused by the relationship of engine power, engine revs and actual speed being way off, and you'd need either to disable the offending and offended systems (more probably they will disengage themselves automatically and light up a check bulb) or do a bit of tweaking in the ECU (drivetrain control unit). Modern cars tend to make it difficult, but the older your six speeder is, the easier it should be for a qualified geek to update the ECU to new values.
(On a side note, I used to think about optimizing the manual transmission in my car for a long time, so thank you for putting the idea here to get it properly answered!)
The proper solution
Most European car makers offer geared automatic gearboxes with dry or wet clutches. Perhaps you've read or heard of automatic gearboxes being inefficient, but that goes only for the traditional hydrodynamic ones. In a modern European gearbox, say Volkswagen DSG, you get 8 gear and a pair of dry clutches. The 'automatic' means that there is a robot doing the cluch and shift work for you, actually pretty nicely and comfortably. The added two (you buy one and get one free!) gears are what you are after, without compromising on efficiency (apart from the missing stick, the system is same as your manual one). The car will do all the shifting for you in a highly optimized manner, further enhancing your fuel economy and ecology.
There are a number of responses on here that mention that it's infeasible to add a 7th gear to improve fuel economy, but none of them seem to actually answer the theoretical question of adding this extra gear to a manual transmission! So let's investigate this.
First you'll need to make sure that there's enough space in your transmission to fit a 7th gear (and the gear selector!). If there isn't, then you'll need to modify the transmission housing to accommodate. If the modified transmission interferes with something else in the engine bay or transmission tunnel, then you'll have to modify that to fit the new transmission. Finally, you'll have to extend the gear shafts in the transmission so that they're still properly attached to the transmission housing (hint: this probably means you'll have to machine your own gear shafts).
Then, you'll have to add the new 7th gear. Or more specifically, if you want your 7th gear to drive at 1400 RPM at a speed where 6th gear would be at 2000 RPM, then you'll need a pair of gears which has a ratio of the number of teeth that is 0.7 times that of your 6th gear ratio. So if you had a 6th gear ratio of 0.5, then you'll need new gears that have a ratio of something like 0.35. Depending on the design of your transmission, these gears might go on the counter-shaft and the output shaft. Or, you might not have a output shaft at all (sometimes the counter-shaft directly connects to the differential), so then it would just go on the input and counter shafts. But that detail probably doesn't matter because most likely...
You'll need a new gear selector fork. And selector collar, and probably synchro too. These will be placed next to the 7th gear that will be free-spinning. Oh, by the way, the corresponding 7th gear that meshes with the aforementioned one should be splined to whichever shaft it goes on. So if want your input shaft gear to be free-spinning, then the selector collar and synchro will go next to it to connect it to the input shaft, and the counter-shaft gear will be fixed to its shaft. If you're lucky, you can reuse your reverse gear selector fork and collar, which might save you some work on the next step.
That next step is to modify the gear selector linkage on the transmission, as well as on the gear stick that you'll be using in the car. Basically, you'll have to make it so that when you move the gear stick to the side, it lets you control your new 7th gear selector fork, and then when you move the gear stick forward or backward, it moves the selector fork and engages the selector collar to your 7th gear. The way this works differs with the design of the car, but it's pretty easy to understand once you have a look at how it selects the other gears, like in this example.
Once you've done all that, you'll finally have a working 7th gear in your car! But chances are, as others have mentioned you'll probably have to reprogram or adjust your ECU to accept the new gear. Again, this will differ depending on your car... in the worst case you might have to invest in a standalone ECU that will take an arbitrary number of gears! Or, you might not have to do anything at all...
But that's not the end of it, you'll need to make sure that your car is actually more fuel efficient with the new gear ratio at 100 km/h (otherwise you'll have done all the work for nothing)! The factor that determines this is your engine's brake specific fuel consumption (or BSFC for short). In fact, we even have a question on this site dedicated to explaining what that is. If it turns out your engine is less efficient at 1400 RPM, then you'll have to re-tune the whole thing to make it work. This could mean redesigning the intake for low-speed air, adjusting the cam profiles or timing, or even changing the bore to stroke ratio of your engine (which usually just means lengthening the stroke). But, I'll let you make a new question for that if it comes down to it.
And that's the basic gist of it. Not surprisingly, as the other answers have suggested, it's pretty complicated, even though manual transmissions are usually the easiest to work on. But, if you ever do decide to take on this task, make sure you let us know! I'm sure it'll be a very interesting (and perhaps slightly pointless) project! I'll also be adding links to this post to expand on relevant topics when time permits (it's taken me long enough to write this up as it is). For now, if you have no idea what any of this means, this article on HowStuffWorks explains pretty much all of it.
Theoretically the idea can work (essentially this is what the 7th gear in the Porsche 991 is for) and if you could find a 7-speed gearbox with the desired ratios that fit your car you could swap them and replace the selection linkage, shifter etc to match.
However, back in the real world.. the aforementioned 991 and the Corvette Z06 are the only cars I know of with a 7-speed manual box and the chances of that fitting into anything else are slim at best. And even if it does fit it's not going to be cheap - thousands upon thousands of dollars.
So your chances of actually saving any money through improved economy are negligible - and your chances of doing so versus trading in for a more efficient car are basically non-existent.
As to why 7-speed 'boxes specifically are so rare, well that's a little more complicated - the concept of a cruising or "overdrive" gear for economy purposes is not new and many 5/6 speed gearboxes over the years have done just that. In fact it's highly likely that your car does that already!
Specifically talking about adding a 7th gear though - well aside from the obvious factors of increased complexity, weight and cost there are issues elsewhere. 7 gears doesn't make for an easy to use H-pattern selector, and people have grumbled about this very issue in the Porsche.
Additionally there is the engine's efficiency to worry about - an internal combustion engine is always operating at it's most efficient at peak torque - which is not the same as the most fuel efficiency in the car! However they are related - particularly in petrol engines efficiency of the engine drops off massively with lower RPM and past a certain point the inefficiency in the use of the fuel by the engine will overtake the economy gains from the lower RPM.
Short Answer: Adding a 7th to a 6 spd trans is not how you want to tackle the problem. It would extremely expensive and require a lot of fabrication. It sounds easy but its not.
However, you can achieve your goals through a different methods.
1) Swap to a different 6 spd transmission. Many automakers use the same drivetrains in various cars with minor differences. One of these differences is usually the gearing in the transmission. Volkswagen does this with the GTI/Beetle/Jetta GLI. GTI has the most aggressive gearing (lowest mpg), where as the GLI and Beetle have different gearing, aimed more towards mpg (and so that they don't compete with the performance of the GTI). One could simply swap the GTI trans out for the GLI or Beetle Trans.
You can also look into older generations of the same car. Sometimes the transmissions are compatible and will offer different gearing
2) You could swap out the gears or the tallest for improved fuel economy. This could be done with VW GTI/GLI/Beetle example I gave above. Would yield the same results.
3) Taller tires would be the easiest way to reduce the rpms at highways speeds. However, you would slightly raise your car as well, which is counterproductive when mpg is our goal.
There are also many other ways to improve your mpg, such as Low Rolling Resistance Tires (LRR), lightweight wheels, aerodynamic mods, keeping up with maintenance, etc
There is nothing wrong with want some extra mpgs out of current car. I suggest you check ecomodder where these topics are discussed in depth.
Instead of adding more gears, have you considered stretching the gearing by using slighty larger wheels/tyres?
This would move the top gear to slightly lower RPM at the same road speed, but will make all the gears a little taller so it will be easier to stall in first gear when moving off.
This will also affect your reverse gear in the same way.
Another point - if your spare wheel is full sized then it will be subtly smaller than the four on the car. If you have a space saver it will be a lot smaller, resulting in weirder handling and tyre wear.
If you tow a bit, this might not be a good idea. The car will be slightly taller too, slightly increasing body roll in corners.
Also, your speedo and odometer will now under-read by a few percent. This can be fixed with a replacement driver on the speedo cable, which is scaled for your wheels.
Finally your location may require recertifying the vehicle for a tyre size change. Your insurance company will need to be informed of the change too.
If your goal (as stated) is to lower engine RPM at a given speed in top gear, then there are several ways to do that without adding an extra gear shiftable to the transmission.
The simplest way would be to simply use larger tires, possibly on a larger wheel. Another answer that suggests this was downvoted but it really is a cheap, effective method. However, you really are looking at a few percent increase at best unless you radically alter the wheel well or raise the vehicle. Note that this method will affect your speedometer and odometer calibration.
Given a rear-wheel drive vehicle, a more invasive method would be to change the differential gear ratio. On Ford cars especially, this is an easy swap. Many competition-oriented Fords do the opposite: they swap in a lower-geared differential. Like the tire swap, this method will affect your speedometer and odometer calibration.
Going up the complexity ladder, if your transmission has a locking torque converter available, perhaps for a different model, you could try to source that. It's a long shot, but some vehicles, i.e. the Crown Victory Police Package, offered locking differentials whereas the same engine/transmission combo in the Grand Marque did not. This would not require recalibrating the speedo and odometers.
Lastly, if you are willing to rebuild the transmission, then you could ask the builder if a taller top gear is available. If the tranny was used for many models and many model years, then it is certainly possible. This method would also not require recalibrating the speedometer and odometers.
I've done this on more than one occasion.
This is a gear with a ratio of typically 2.73:1 through 5.00:1. It is located in either
You aren't going to get a 30% ratio bump this way. But you won't have any trouble getting around a 10% bump, and I have serious doubts that you would want more. The people* who designed your car are not morons.
I've always driven more simple cars, so the rear end swaps I've done have always involved lugging a live rear axle through a junkyard after determining its ratio by spinning a wheel.
This one is a little trickier because it involves lots and lots of really geeky research, especially if the car is post-1996. Also, this only works because it's a manual; automatics are very tightly integrated with the powertrain computer and would be a staggering challenge.
You need to search for a transmission that has all the features your car needs to physically fit - the engine - the frame - the halfshafts - the electrical controls needed by the OBD system, starter interlock, reverse switch, etc.
This requires a craft of skill that isn't necessarily anything like run-of-the-mill hotrodding. Pretty much, you will be locked into one vendor, and it will just be a matter of figuring out which junkyard pick has the transmission you need.
Getting the electricals right is critical, both so the car works (reverse lights come on), and so it'll pass smog in the 12 states and not blow SES ligts. It's important not to just "put up with" the SES light being on 24x7, you want the SES light cleared so it can warn you about a new, genuine problem.
This is an obsolete method and only works on RWD cars, so I will just touch on it.
Really. Smog legal and all. Broadly, you are allowed to put any engine in your car where service class is yours or better (car engine in truck, ok) and engine year >= car year.
Realistically in this day and age with OBDII and smog, that involves changing the entire powertrain, cutting at the fuel line, halfshaft, battery terminals and radiator hoses. I've done this too across wildly different model lines, and it's a PitA/ labor of love (you couldn't possibly pay someone to do this exceptionally tedious and research-driven work). Even though I did not touch the powertrain package at all, there were still like 20 circuits that "came through the firewall" and every one had to be engineered to match the vehicle.
Back when the Ford Festiva/Aspire was a thing, it was common for Miata owners to swap in the Festiva engine (or simply the 2V heads) for a significant bump in fuel economy, at the expense of power, of course. Hotrodders who thought a Festiva was a good place to start a performance build were all too happy to take those 4V heads off them. In that case the transmissions were electrically compatible, so the harness stayed with the engine.
Done competently, an engine change is smog legal in California. (In the Miata/Festiva case, both directions, heck, you can out a 'Vette LS1 in a Festiva and pass smog. Really, smog quotas are by year, not vehicle weight.)
* they're in Detroit. Really. All the world's makers have engineering departments in the Detroit suburbs, including makers who don't even build for the North American market. Both for the talent pool and the prototyping capability, and all the world's suppliers also have offices there. It's the Davos of cars.