Realistic gear ratios - Python calculator now available!

[eran0004]

Update 2015-07-04: The gear ratio calculator is now available as a Python script that you can download and run! All the details in this post.

Spoiler: What is a gear ratio?

What is a gear ratio?

A gear ratio is the ratio of the tooth count between a pair of gears. If gear A has 24 teeth and gear B has 32 teeth, the gear ratio of the pair is 24:32, which can be expressed as the fraction 3/4 and the decimal value 0.75 or 0.750.

Spoiler: How does it work in Gran Turismo?

How does it work in Gran Turismo?

In Gran Turismo, gearbox tuning is done by setting the gear ratios as decimal values. However, for pedants (like me) this means that not all possible values are realistic. For instance, a gear ratio of 1.670 can strictly speaking not be constructed using gears with a tooth count less than 147:88. This is way more teeth than the gears in a gearbox normally have. The smallest tooth count that I've found (so far) is 11 and the greatest is 42.

Spoiler: How do we know which values are realistic and which aren't?

How do we know which values are realistic and which aren't?

Surely, we can't calculate every possible combination of gears between 11 and 42, that would take ages! Well, that's what we have computers for I've made a little calculator that checks the values of all possible combinations and returns a list, sorted in ascending order and with all duplicate values removed.

The charts

Update 2015-06-16: New chart, excluded all values whose greatest common divisor is greater than 1.
The two charts below show all the possible gear ratios greater than or equal to 0.385 for gears with a tooth count between 12 and 49 and whose greatest common divisor is 1. The list is organized in columns by the sum of the tooth count of both gears in the pair (e.g. column t = 40 would include the pairs 29:11 and 23:17, and column t = 60 would include the pairs 23:37 and 31:29).
The greatest common divisor = 1 was added as a criterium because when you design gears you want the wear to be spread out equally between all the teeth (not an issue in GT6, but if you want a realistic tune you should do that).

For maximum realism, select your ratios from columns that are close to each other (t = 50 to t = 55, for instance).

There is also a PDF of these charts attached to this post that you can download and print.

Also below is a list of possible final drive ratios, the smallest pinion tooth count I've found is 6 and the greatest is 22. The smallest ring tooth count I've found is 27 and the greatest 71. This list is not organized in columns, instead it simply lists all the values from the smallest to the biggest. This list is also attached as a PDF file.

​

How to use these charts:

1. Set your gear ratios to the values you'd like to have.
2. Check these charts to see if the values are "possible".
3. If a value is not listed, adjust it to the nearest value that is.

Custom charts:

Alpine A110

If you want a customized chart for a specific car or gearbox, let me know and I'll see what I can do!

 

[Thorin Cain]

Nice work @eran0004 👍 That's a great little tool to have around, might come in quite handy

 

[OdeFinn]

Excellent idea to post this chart!
Totally going to use this.

 

[Bowtie-muscle]

Excellent idea, and excellent work. 👍 I will be trying this out for sure.

Thank you for putting in the effort and the time, great job.

 

[MrGrado]

I know very little about gear boxes. Is it realistic that a gearbox could have any combination of the listed values? I guess what I'm asking is, does a 5 speed gearbox have 5 unique pairs of gears?

 

[ALB123]

I know very little about gear boxes. Is it realistic that a gearbox could have any combination of the listed values? I guess what I'm asking is, does a 5 speed gearbox have 5 unique pairs of gears?

There's probably going to be someone who proves me wrong with cars that have multiple final drives or some kind of fancy transfer gear, but for the most part the answer would be "Yes". Picture a 10 speed bicycles rear tire...those gears are all different sizes because if they were the same size, switching from one to another would result in no change whatsoever. Of course, that bicycle usually has a 2nd front gear sprocket, but that should be ignored for these purposes.

@eran0004 Thank you for providing this handy chart. While I do not do much tuning myself, it will still be nice to have on that strange occasion when I do decide to tune my transmission myself. 👍

 

[MrGrado]

I'm still a little confused. Isn't the top table showing every possible combination of teeth for every gearbox possible?

So if I take 1st gear from a tune of mine: 3.277 and use the nearest available value from the table: 3.273, the value from the table comes from a certain combination of "a cogs" and "b cogs" right? So if I now want to find a realistic value for 2nd gear, I need a value that comes from using a common "a cog"?

 

[ALB123]

I'm still a little confused. Isn't the top table showing every possible combination of teeth for every gearbox possible?

So if I take 1st gear from a tune of mine: 3.277 and use the nearest available value from the table: 3.273, the value from the table comes from a certain combination of "a cogs" and "b cogs" right? So if I now want to find a realistic value for 2nd gear, I need a value that comes from using a common "a cog"?

Technically, you can choose anything you want for a 2nd gear value as long as it's a smaller number than 3.273... Now, I can't promise that you can choose any number you want in GT6 because the game limits what you can choose with a range of values, but in real life you should be able to choose whatever you want. Also, a lot of thought should go into assigning gear ratios.

Just because you can technically choose any gear ratio lower than what you assigned to 1st gear doesn't mean it will be a smart choice. You want to have proper gear spacing which you can visually see in GT6 by those lines shown in the Transmission section of Car Settings. If you have too short of a space, meaning you chose a 2nd gear that is very close numerically to 1st gear, when you're driving and shift out of 1st gear into 2nd gear your RPMs are going to still be sky high and you'll have to shift into 3rd incredibly quickly. Conversely, if you have too big of a gap between 1st and 2nd gears, meaning you chose a 2nd gear ratio value that is quite far from 1st gear. So, when you're driving and shift out of 1st gear into 2nd gear your RPMs are going to drop too much and the car is going to lag considerably and you'll be losing power!

Take a look at how some of your cars gears are currently spaced with the default transmission or the stock gear ratios from the custom transmission. Then it's a matter of testing it out on the race track. I hope I'm explaining this clearly and not just confusing you more.

 

[eran0004]

I know very little about gear boxes. Is it realistic that a gearbox could have any combination of the listed values? I guess what I'm asking is, does a 5 speed gearbox have 5 unique pairs of gears?

I'm still a little confused. Isn't the top table showing every possible combination of teeth for every gearbox possible?

So if I take 1st gear from a tune of mine: 3.277 and use the nearest available value from the table: 3.273, the value from the table comes from a certain combination of "a cogs" and "b cogs" right? So if I now want to find a realistic value for 2nd gear, I need a value that comes from using a common "a cog"?

"A cogs" and "B cogs" and unique for each gear, so you don't need to use a common "A cog".

However, there are some ratios that are rather extreme and perhaps not entirely realistic, like the combination of 40+41. Now, the biggest combined tooth count of a pair that I've seen is 61, so perhaps some kind of treshold needs to be added to the algorithm creating the list so that it ignores combinations with a combined tooth count greater than, say, 65. The same applies to the other end of the spectrum, the smallest combined tooth count of a par that I've seen is 41, so perhaps a minimum treshold of, say, 35, would make sense as well.

Update: Here's a list with these tresholds applied:

 

[OdeFinn]

I know very little about gear boxes. Is it realistic that a gearbox could have any combination of the listed values? I guess what I'm asking is, does a 5 speed gearbox have 5 unique pairs of gears?

There's probably going to be someone who proves me wrong with cars that have multiple final drives or some kind of fancy transfer gear, but for the most part the answer would be "Yes". Picture a 10 speed bicycles rear tire...those gears are all different sizes because if they were the same size, switching from one to another would result in no change whatsoever. Of course, that bicycle usually has a 2nd front gear sprocket, but that should be ignored for these purposes.

@eran0004 Thank you for providing this handy chart. While I do not do much tuning myself, it will still be nice to have on that strange occasion when I do decide to tune my transmission myself. 👍

Actually nope, normally 4th on 5 speed gearbox(5th on 6 speed) is direct connection 1:1 ratio, without any gears between.

Just if wondering what that means.

Edit: before anyone pops sequential transmission here, had to show it too, example uses bike box, but it's similar to car used. There is no direct connection..


Actual movement

 

[eran0004]

OP has been updated with a new chart. It's now organized in columns by tooth count (gear A + gear B)!

For a realistic gearbox, pick values only from nearby columns (within 3-5 columns from each other).

I have also added a link to a PDF (Google Drive) that you can view or print.

 

[eran0004]

Here is a custom chart for the Alpine A110. The real car has a gearbox with combined tooth counts (T) between 59 and 64, so I customized the chart the match that.

Also, when designing gears you want the greatest common divisor (GCD) of the two gears to be 1 (ideally), in order to spread the wear equally between all the teeth. So in this chart I've only included ratios where the GCD is 1.

I also found some good final drive data, and it seems like 5 different options are available for the car. Those are also included in the list, in the right-most column.

​

A PDF is attached as well, if you want to print the list.

 

[eran0004]

I'm working on a user interface for the real gear ratio calculator

Here's a preview of it, still under construction:

Spoiler: First version screenshot

Spoiler: First update

Update: It's coming along nicely
Here's the current look of the main window:

And here is the current look of the gear configuration window that pops up when you click on "Compute":

Update 2: Corrected a small (2px) offset error in the gear visualization canvas and added a velocity scale along the horizontal axis that will scale according to final drive and wheel radius settings.

Threshold sliders added to the setup window:

 

[eran0004]

The realistic gear calculator is ready for use! You can find it attached to this post.

In order to run the script, you need to have Python 3 installed on your computer.
The script is not compatible with Python 2.

You can download Python 3 for free from www.python.org. I'm using 3.4.2, but I just saw that 3.5 is available now as well. I don't think it matters which version you're using as long as it's Python 3.


The zip file: The attached zip file contains the script, the two folders that it's using (don't delete or rename these, or else the calculator will not work) and a readme file. Just place it in a directory of your choise and unzip it there.


Windows: When you have installed Python 3, you can run the script by right-clicking on GearCalculator.py > Open with > Python.exe (you may need to browse for it the first time).

An optional way of running the script is to open it with IDLE, which is an interactive Python interface. Click the Windows start menu and go to All Programs. You will see Python 3.x (whatever version you have) in the menu. Choose IDLE (Python GUI). Once it's open, click File > Open and then browse for GearCalculator.py. Note: This will open the source code, which may be interesting to read, but be careful not to make any changes to it unless you know what you're doing. To run the script, hit F5.

Linux / UNIX / Mac OS/X: The script should be compatible across all the operating systems, but I have only tested it on Windows.


Wheel radius tutorial: The ratio visualizer is using the wheel radius of the car to calculate the speed of the gear ratios. So in order to get a correct speed you obviously need to know the wheel radius of your car. Here is how to calculate it:

1. In GT6, make a free run with the car and save the fastest lap replay.

2. Go to the data logger and load the replay.

3. When the car is on a straight, make a note of the wheel speed (of the powered wheels - on a 4wd car it's probably safest to measure it on the rear wheels), the gear and the rpm (e.g. 155 km/h, 4th gear, 7200 rpm). If the speed is in mph you need to convert it to km/h (multiply by 1.61).

4. Exit the data logger and go to the car settings page. Make a note of the ratio of the final drive and the gear you were in (e.g. final drive: 3.375, gear ratio: 1.490)

5. Get a calculator and calculate the following:

• wheel rpm = rpm / (gear ratio * final drive ratio)
• wheel radius = wheel speed / (wheel rpm * 0.377)

That gives you the radius of the wheel in meters.

That's about it I think. There is a readme file included in the zip that describes the settings used in the calculator. Feel free to ask if you've got any questions or if you spot any bugs!

 

[sinof1337]

I've been meaning to drop a comment for a while now so that its easier to find the thread, but kept forgetting. Awesome work, keep it up!

 

[eran0004]

Here's a gearbox I made for the GT40 Mark I, based on this 5-speed gearbox.
I optimized it for top speed with race exhaust (386 bhp).

Gear tooth count: 11 to 37
T value: 47, tolerance: 1
Threshold: 0.4

Ring tooth count: 30 to 38
Pinion tooth count: 9 to 11
Threshold: 2.0 to 6.0

GCD: Toggled on

Gear ratios (with tooth count):
Gear 1: 3.364 (37/11)
Gear 2: 1.938 (31/16)
Gear 3: 1.350 (27/20)
Gear 4: 1.000 (direct drive)
Gear 5: 0.808 (21/26)
Final drive: 2.818 (31/11)

 

[Gyro1780]

Really nice idea but unless you have the patience (which i don't) it takes far too long.
It only takes me a couple of minutes to set up my transmissions which is best for me as i don't have much free time to play GT6.

 

[eran0004]

Really nice idea but unless you have the patience (which i don't) it takes far too long.
It only takes me a couple of minutes to set up my transmissions which is best for me as i don't have much free time to play GT6.

I guess it depends on how much time you're prepared to spend on making your tunes. Personally I can spend hours just setting up, testing and adjusting the gearbox

Is there any particular thing you think takes too much time?