How to calculate and define a proper differential ratio

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PikPikker
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How to calculate and define a proper differential ratio

#1 Post by PikPikker » 19 Apr 2023 11:25

Hello!

I was busy these days making some transmission mods, and the main problem was making a proper differential ratios for each gearbox... I decided to leave it to players, because this is the main part of custimizing the transmission - and here I'm going to tell you how to choose your differential ratio and apply it to the game. I hope you will find it helpful enough!

First of all, what is a transmission? To put it simple, it is a box of gears (that is why it is also called gearbox) which transfers the rotation from engine to the axle, where it meets the differential, through which the rotation is transferred to the wheels, which makes your car move. But an engine makes too many rounds per minute (RPM), for trucks it can be up to 2500 rpm (and sometimes more). That is why we reduce the RPM twice before transferring it to the wheels. Firstly - at the gearbox, secondly - at the differential. And our goal, as drivers who customize their trucks, is to find our perfect transmission and diferential ratio.

Let's begin with the transmission. It has several gears (there can be 3 gears, 10, 20, 24... any quantity, but for now it does not matter much). Each gear has it's ratio, which shows us how much it reduces the RPM. For example, if the gear ratio is the 10.0, it means that the engine will spin the shaft 10 times, while the final shaft of gearbox is spinned only once. That is why it is 10. Furthemore, if the gear ratio is 1, the both shafts spin at the same time - without reduction. These gears with the ratio of 1 are called "direct gears". They are commonly seen as the last gear of transmission. Also, sometimes there are gears with the ratio lower than 1. For example - 0.7, it means that the transmission shaft spins even faster that the engine (but still reduced at the differential). These gears are called "overdrive gears". And transmission with these gears can be called the same way.

Now we know about gears, let's talk about the "total reduction". This is quite simple but important constant which tells us how many spins make a wheel at a single spin of the engine. For example, if the total reduction is 30, it means the wheel will spin 30 times during a single spin of the engine. This value helps comparing different transmissions with different differentials. It is calculated easily: just multiply your gear ratio by the differential ratio. It is mostly used when comparing first or last gears. For instance, let's try comparing the last gears of the 10 and 13 speeders. The first one has the 1.0 last gear and 2.85 differential ratio, while the second has 0.73 overdrive gear and 3.55 differential ratio. 2.85*1.0 = 2.85 and 3.55*0.73 = 2.59. As we can see, the 13-speeder has lower reduction on the last gear, which means - the truck will reach higher speeds at the same engine RPM.

That's it - the lower the reduction on the last gear, the more speed you will get. But keep in mind - the lower reduction on the first gear means slower launch and acceleration. It can be critical when launching uphill with a heavy load. It tells us that... "a perfect transmission" has a very high reduction of the first gear and very low one on the last.

It leads us to the next thing - overall ratio. It shows us the difference between the first and the last gears of transmission. So, yes, the more it is, the more universal the transmission is. To calculate it, simply divide the first gear ratio by the last gear ratio. The gotten number tells you how many time the first gear is faster. It can be presented as a coefficient or as a percentage (just coefficient*100%). Usually, for modern trucks, 1000% is too little, while 2000% is good enough for any needs.

So, how do we use this information on deciding about the differential ratio? The crucial formula is very simple: the less the ratio - the more speed you get, the higher the ratio - the better launch you get. You only need to find a perfect ratio for your purposes. The heavier your cargoes are - the higher your differential ratio should be. And one more simple formula: the low differential ratios and powerful engines are friends, while the high differential ratios and low power engines are friends too. Also.. a good way to find a perfect ratio is to test different ones. And now you know where you should look for the balance.

Here are some popular differential ratios of modern trucks:

Code: Select all

2.64
2.85
3.08
3.25
3.55
3.70
3.91
4.10
4.30
4.56
If you need ratios for an old truck - the best way is to look for specification sheets or search for clues the creator left for you (sometimes you can find the available ratios in the transmission files of the truck).
Actually, you can use any ratio which comes to your mind, but it would barely be realistic.. but it's always up to you.

Applying the differential ratio into your transmission is quite easy. Open your truck mod archive (if you want to change the SCS files, unpack their archives and re-pack them as a separate mod with applied settings of yours). Go to:

Code: Select all

def/vehicle/truck/(truck name)/transmission
And find the exact transmission you want to change (each transmission has its own differential ratio). Open the file in a text redactor and find a line:

Code: Select all

differential_ratio: 4.10

(it can be any other number, this is just an example)
All you need is to change this number to your wanted differential ratio. Make sure you use dot, not comma.

I guess.. that's all I wanted to tell you. If you still have any question - post it here and I will help as soon as possible. (Also.. did I miss something? Let me know if so)
Thank you for your attention!
wato
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Re: How to calculate and define a proper differential ratio

#2 Post by wato » 21 Apr 2023 08:58

Great explanation, thanks. Cleared up some terms for me.
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Ludo Diabolo
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Re: How to calculate and define a proper differential ratio

#3 Post by Ludo Diabolo » 22 May 2023 10:29

@PikPikker
I have a classic XL freightliner with a DD60 515hp 14L engine and I'm looking to put the most realistic transmission possible ? And with what ratio ? I play in automatic, because not yet received my shifter ;) .
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PikPikker
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Re: How to calculate and define a proper differential ratio

#4 Post by PikPikker » 22 May 2023 10:50

Hello, @LudoModding!

Well, it fully depends on how you are going to use your truck. If it is about heavy hauls (more than 30 tons), I'd recommend Eaton Fuller 13 or 18 speeder, but in such case a sequential shifting would be nice.
However, if you would like to stick with usual cargoes, Allison (6 or 7 speeder) would be a nice choice, especially because you play with auto shifting.
In both cases the 3.55 final ratio seems the best option for you. You can begin with 3.55, and then decide if it gives you the needed top speed, or you should change to 3.25 (higher top speed) or to 3.70 (lower top speed).
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Re: How to calculate and define a proper differential ratio

#5 Post by Ludo Diabolo » 22 May 2023 11:01

Thank you for your answers, the truck will only be used for traditional van and refrigerated transport.
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al_batros
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Re: How to calculate and define a proper differential ratio

#6 Post by al_batros » 10 Jun 2023 14:26

As the differential ratio is related to the target speed, transmission ratio in the gear at target speed, and engine rpms,
I would like to contribute a cut&paste of an Excel sheet I created the other day...
(Actually two, one for ATS, one for ETS2)

ATS:

Code: Select all

# Eaton TX12	0.77	overdrive	rpm	direct
# differential_ratio:	3.34	 # 	1400	2.57
# differential_ratio:	3.22	 # 	1350	2.48
# differential_ratio:	3.10	 # 	1300	2.39 <-- Baseline 1300rpm, 2.39 direct drive = 65mph
# differential_ratio:	2.98	 # 	1250	2.30 # 2.98 = 2.30 / 0.77
# differential_ratio:	2.87	 # 	1200	2.21
# differential_ratio:	2.75	 # 	1150	2.11
# differential_ratio:	2.63	 # 	1100	2.02 <-- 1100 rpm 65mph =2.02 direct drive or 2.63 with 0.77 overdrive
# differential_ratio:	2.51	 # 	1050	1.93
# differential_ratio:	2.39	 # 	1000	1.84
ETS2:

Code: Select all

# ZF 12 TX	0.77	overdrive	rpm	direct
# differential_ratio:	4.05	 # 	1300	3.12
# differential_ratio:	3.90	 # 	1250	3.00
# differential_ratio:	3.74	 # 	1200	2.88
# differential_ratio:	3.58	 # 	1150	2.76
# differential_ratio:	3.43	 # 	1100	2.64 <-- Baseline 1100rpm, 2.64 direct drive = 80km/h
# differential_ratio:	3.27	 # 	1050	2.52
# differential_ratio:	3.12	 # 	1000	2.40
# differential_ratio:	2.96	 # 	 950	2.28
What is this trying to tell us?
(All based on the ATS numbers)
Step 1: direct drive:
- assume you want to drive at a cruise speed of 65mph, have a direct drive transmission in top gear (1.00 ratio)
- what engine speed and differential ratio would you be running?
- when running at 65mph, direct drive, 1300rpm -> differential ratio of 2.39
- this is used as the baseline (actual figures may vary slightly due to difficulty reading it properly from the instrument...)
- If you now want different rpms, say 1100, a matching differential ratio would 2.02.

Step 2: overdrive transmission
- with an overdrive of 0.77 you would divide the direct drive ratio by 0.77
- so again, 1300rpm, 0.77 overdrive, 65mph -> differential ratio 3.10 = 2.39 / 0.77
- or 1100rpm, 0.77 overdrive, 65mph -> differential ratio 2.63

ETS2: similar calculation, but different baseline of 1100rpm=2.64 at 80 km/h

Depending on the level of "reality" you want to run at, you could now either use these calculated ratios - or pick one of those available that are "nearby".

Homework assignment:
Create two excel sheets to match those shown above, where you are able to change the overdrive gear ratio (shown as 0.77 in the tables). :D
Bonus points, if the 65mph or 80 km/h can be changed as well. :ugeek:


"Normalizing" to direct drive
In order to compare transmission and differential ratios, it might be useful to convert their ratios as direct drive ratios.
This allows you to compare a diff ratio of 3.55 on a 13 speed with 0.73 overdrive to a direct drive at 2.28.

Let´s take the SCS stock Freightliner offering as an example:

Code: Select all

Cascadia2019	Top Gear	diff ratio	1:1 diff ratio	rpm @65mph
13		0,73		3,55		2,59 = 0.73*3.55 ~1400rpm
18		0,73		3,25		2,37		 ~1300rpm
dt12da		1,00		2,28		2,28		 ~1240rpm
dt12oa		0,78		2,85		2,22		 ~1200rpm
tx12		0,77		3,45		2,66		 ~1450rpm
Here you can see that the overdrive DT12OA will run at even lower rpms (~1200) than the direct drive DT12 (~1240?).

Also, in conjunction with the Excel Sheet shown above, you now would be able to target the RPMs you are looking for...


Hope this helps,
al_batros
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Snoman
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Re: How to calculate and define a proper differential ratio

#7 Post by Snoman » 03 Jul 2023 00:08

al_batros wrote: 10 Jun 2023 14:26
Homework assignment:
Create two excel sheets to match those shown above, where you are able to change the overdrive gear ratio (shown as 0.77 in the tables). :D
Bonus points, if the 65mph or 80 km/h can be changed as well. :ugeek:
I have created a spreadsheet for myself that does what you are trying to do:

Code: Select all

Paccar	Gear	Ratio	Paccar			Eaton											
Eaton			PO-18F112C			EEO-18F112C											
12 Speed			1850lbft			1850lbft											
AMT	10.00	1.3	2.64	2.80	2.85	2.93	3.07	3.08	3.21	3.25	3.36	3.42	3.55	3.58	3.70	3.73	4.11
55	11	1	1223	1297	1321	1358	1422	1427	1487	1506	1557	1585	1645	1659	1714	1728	1904
55	12	0.77	942	999	1017	1045	1095	1099	1145	1160	1199	1220	1267	1277	1320	1331	1466
65	11	1	1446	1533	1561	1604	1681	1687	1758	1780	1840	1873	1944	1960	2026	2043	2251
65	12	0.77	1113	1181	1202	1235	1294	1299	1353	1370	1417	1442	1497	1509	1560	1573	1733
75	12	0.77	1284	1362	1387	1425	1494	1498	1562	1581	1635	1664	1727	1742	1800	1815	2000
	1500		51.9	48.9	48.1	46.7	44.6	44.5	42.7	42.1	40.8	40.0	38.6	38.3	37.0	36.7	33.3
	1500		67.4	63.6	62.5	60.8	58.0	57.8	55.5	54.8	53.0	52.1	50.2	49.7	48.1	47.7	43.3
As you look at the columns left to right, the constants are speed, mph in this example, gear number and gear ratio.
The top row of the table has all the available differential ratios for this particular gearbox and the axle I am using, in this case 2.64-4.11

Then I enter in the formula to calculate rpm based on speed, gear ratio and differential ratio

Code: Select all

 =SUM(336.1355*diff ratio*axle ratio*speed in mph)/39.9
336.3155 is a constant to convert the result to rpm
39.9 is the tire diameter size for ats. I know the tires in the game list a different tire diameter but I have tested this extensively and this is the most accurate number I have come up with.

After you copy that formula into all the cells in excel, any time you change diff ratio, axle ratio or speed the formula will automatically update with the new rpm.

As a bonus on the bottom 2 rows, I calculated at what speed the truck will shift into the top two gears if set to shift at 1500rpm.

You can do the same for ETS2, but with a different formula to convert to kmh

Code: Select all

=SUM(336.1355*gear ratio*diff ratio*speed in kmh*0.6213711922)/39.5
Again the tire diameter in ETS2 is slightly smaller and doesnt quite match the tire size listed in the game.
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McFly
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Re: How to calculate and define a proper differential ratio

#8 Post by McFly » 01 Jan 2024 13:47

Stupid noob question: I want to either change an existing transmission with a changed final drive or add it as a new, additional transmission for the mack anthem. I have extracted the dlc_mack_anthem.scs, located the transmission file and changed the ratio. But how do I repack it to show up as a mod in game?
I tried repacking it with winrar and changing the file type to .scs (Folder structure within that file: \def\vehicle\truck\mack.anthem\transmission) but it doesnt show up in the mod manager. I've tried looking at different guides for how to do it for 2 days now and neither one helped me so far.

//EDIT: Also tried different folder structures like \dlc_mack_anthem\def\vehicle\truck\mack.anthem\transmission but the mod doenst even show up in the mod manager (so I cant even tell if my mod is working the way I intended)
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PikPikker
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Re: How to calculate and define a proper differential ratio

#9 Post by PikPikker » 01 Jan 2024 14:51

Make sure your archive is in .zip format originally. You do not even need to rename it to .scs then.
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Re: How to calculate and define a proper differential ratio

#10 Post by McFly » 01 Jan 2024 21:13

Wow, no clue why I packed it as .rar
It works now. Thanks a lot!
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