[mortinson]

A question to pick up your technical brains....

My 1991 300 GD was fitted by a previous onwer with a MB-exchange gearbox a couple of years ago, at a cost of some € 3,000. The gearbox is silky smooth and it works perfectly well. The problem is that in my opinion the gearing is either too short or both the rev counter and the speedometer are lying. Let me explain....

The truck is fitted with 235/85R16 tyres, which are substantially taller than the 215R16 ones that it was fitted with when it left the factory. However, I have the original invoice from a VDO Kienzle service showing that they recalibrated the speedo after the newer tyres were fitted (at a cost of DM 360!). Results of the test show that after recalibration when the truck is travelling at 116 Km/h the speedo shows 120 Km/h.

The gearing in fifth gear in any G-Wagen should be as follows:

formula should be: 1,000 x (1/gearbox ratio)x(1/transferbox ratio)*(1/differential ratio)x(60x2xPi)x(radius of the wheel).

In my case:
gearbox ratio is 0,799
transferbox ratio is 1,05
differential ratio (37:7) is 5,286
Pi is 3,05 (rather than 3.1415926 assuming "flattening" of the tyre due to the weight of the truck)
radius of the wheel is (assuming size 235/85R16, width is 235 milimetres, profile is 85% of the width and diameter of the rim is 16 inches [406,4 mm] and given that radius equals half of the diameter of the rim plus one lateral section of the tyre)= 235*85%+406.4/2 = 402,96 mm

So gearing in fifth gear must be:
(1000*(1/0,799)*(1/1,05)*(7/37)*(60*2*3,05)*0,40296)*(1/1000)= 33,26 Km/h (20.67 mph) @ 1.000 rpm.

Now I have noticed on numerous ocassions that at 90 Km/h my rev counter gives 3,000 revs. At a indicated 120 Km/h (actually 116 Km/h) the engine is working hard, clearly over 4,000 revs. If this is the case, I have a gearing roughly 10% shorter that it should be and I am wondering whether I am making a mistake with my calculations or the gearbox currently fitted to my truck is not the GL76/27K-5 as it should be but another one with a shorter fifth gear.

I have the "Einbaupass" of the new gearbox and it is listed as "Getriebe 463 260 03 00/80" with serial number 430 781 and "Lieferschein 484631". I have checked these and they match the numbers in the plate attached to the gearbox so there's no mistake to be made here. Can somebody check these numbers with their (working) EPCs and let me know?

Thanks in advance,

 

[Captain Spalding]

I'm not certain, but I don't think you can mess with Pi.

I'm no math whiz, but something struck me strange about what you wrote here:

mortinson - 2/20/2005 8:18 AM
In my case:
gearbox ratio is 0,799
transferbox ratio is 1,05
differential ratio (37:7) is 5,286
Pi is 3,05 (rather than 3.1415926 assuming "flattening" of the tyre due to the weight of the truck)
radius of the wheel is (assuming size 235/85R16, width is 235 milimetres, profile is 85% of the width and diameter of the rim is 16 inches [406,4 mm] and given that radius equals half of the diameter of the rim plus one lateral section of the tyre)= 235*85%+406.4/2 = 402,96 mm

At the part where you say Pi is 3.05 - that's where you lost me. Whenever I'v done such calculations, Pi is always the same. The way I account for the flatness of the tire is by using an actual measurement from the center of the wheel to the ground as the radius. This allows for the calculation of the virtual circumference of the tire with respect to the flat spot.

 

[mortinson]

RE: I'm not certain, but I don't think you can mess with Pi.

Captain Spalding - 2/21/2005 8:19 PM

I'm no math whiz, but something struck me strange about what you wrote here:

mortinson - 2/20/2005 8:18 AM
In my case:
gearbox ratio is 0,799
transferbox ratio is 1,05
differential ratio (37:7) is 5,286
Pi is 3,05 (rather than 3.1415926 assuming "flattening" of the tyre due to the weight of the truck)
radius of the wheel is (assuming size 235/85R16, width is 235 milimetres, profile is 85% of the width and diameter of the rim is 16 inches [406,4 mm] and given that radius equals half of the diameter of the rim plus one lateral section of the tyre)= 235*85%+406.4/2 = 402,96 mm

At the part where you say Pi is 3.05 - that's where you lost me. Whenever I'v done such calculations, Pi is always the same. The way I account for the flatness of the tire is by using an actual measurement from the center of the wheel to the ground as the radius. This allows for the calculation of the virtual circumference of the tire with respect to the flat spot.

I agree with you... it simply did not occur to me that I could be wrong with regard to the amount of "flatness" of the tyre, which seems to be consistent to that accounted for by the official figures when they quote the max speed in individual gears.

I shall measure the actual radius of the tyre tomorrow... in the meantime, if somebody can check the gearbox number in the EPC I will really appreciate it.

Cheers

 

[DUTCH]

Edited

mortinson - 2/20/2005 3:42 PM

in the meantime, if somebody can check the gearbox number in the EPC I will really appreciate it.

Cheers

That 463.260.03.00 part number is listed as correct for the 300GD.

 

[Captain Spalding]

Did some more thinking, and checking.

mortinson - 2/20/2005 8:18 AM
. . .I am making a mistake with my calculations or the gearbox currently fitted to my truck is not the GL76/27K-5 as it should be but another one with a shorter fifth gear...

I took a look at Harald's transmission data page. Unless I'm mistaken, there isn't a transmission with a shorter top gear than your GL 76/27 K-5 at 0.799.

I think if I had this to sort out for myself, I'd start by finding out what my true speed was in top gear at 1000 RPM. I'd use a GPS. The first thing I would suspect is the recalibrated speedo because you KNOW that's been messed with.

Harald's page:
http://4x4abc.com/G-Class/transmissions/getriebe.html

 

[Roly]

The G should have had 205/82-16 tyres when it left the factory 29.2". The 235/85-16 are 31.7" or 8.5% larger.If the speedo was reset to read 120Km/hr at 116 Km/hr , that's an increase of 3.3%.
The info I have says it should run 19.1 MPH/ 1000 RPM in 5th with 205s, If this is adjusted for the speedo reset that's increased to 19.73 MPH. So at 90 Km/hr 56 MPH you should run at 2840.
I don't think there is anything major wrong, you cn adjust the speedo using the MB supplied part at the connection to the transferbox.

 

[4x4abc]

Jesus,

I put the numbers into my software: I get 4104 rpm @ 116 km/h. Assuming you have BFG tires (Ø 2475 mm) and the depression due to weight is about 10 mm. However, that is with a 5th gear of 1:1 - 0.799:1 in 5th should give you 3279 rpm.
Looks like you have one of the 5-speed Getrag with a 1:1 5th gear. The serial number 430 781 supports that. Looks like a GL 76/27 P5 717.43/44 transmission. You should have a serial number that starts with 439 (GL 76/27 K5 717.439)
http://4x4abc.com/G-Class/trans.html

Get 285/75 R 16 tires (Ø 2545 mm) and your problem is solved (3189 rpm @ 116 km/h)

Harald

 

[79percent]

The best idea is to take a GPS handheld with you. Then you will be really sure. I did it and after all the speedo shows 10% more what I drive. Driving 100Km/h showing on the speedo will end up with 91 on the GPS.

BTW: everything per DC installed correctly.

RGDS
Klaus

 

[kallieir]

Calculations

If I understand you right, I think that you are all making a mistake in the wheel size calculations.
On a 4x4 website here in Iceland some months ago there was a long discussion about if a less tire pressure (more flattening of tire) gives you lower final gearing.
Finally most of the people involved in the discussion agreed, that flattening of the tire did not change final gearing SINCE THE CIRCUMFERENCE OF THE TIRE IS ALWAYS THE SAME. That means that for every revolution of the tire the car always travels the same distance.
The only change of this distance is when the tire STRETCHES when air pressure is high, but that is so little that it does not make a big difference in these calculations.

Also, comparing speedometer and GPS when driving on 38" tires both with 2 psi and 25 psi shows no difference.

Kalli

P.S. Before I read the discussion on the Icelandic site I totally agreed with your calculations.

 

[4x4abc]

RE: Calculations

Kalli,

No, we are not making any mistakes in our calculation.

Sorry, your discussion forum came to the wrong conclusion. Less tire pressure results in more revolutions per given distance. Less tire pressure results in more torque at the contact patch (the gears are not changed but the imaginary lever arm from wheel center to the ground gets shorter - remember mechanical advantage from school?).

The tire in our example has a Ø of 2475 mm (radius 394 mm)
fully inflated (without any depression) the tire will have to rotate 404 times to cover 1000 meters

substantially deflated to show a depression of 25 mm (resulting in a radius of 369 mm = Ø 2318 mm) the tire will have to rotate 431 times to cover 1000 meters

Since the imaginary lever arm (radius) is shortened from 394 to 369 mm the available torque increases by 6.8%
When off-road in low range this will make a major difference. With the vehicle in question combined with the 235/85 tires the overall torque will increase from 5884 Nm to 6282 Nm - that is exactly 100 Nm per wheel more!

Harald

 

[sjtymko]

Harald,

I have a different calculation yet. Did you calculate using a diff ratio of 5.286 as Mortinson noted or a ratio of 4.88? I get about the same as you if I use 4.88 but not if I use 5.286.

Just wondering.

Steve

 

[mortinson]

4x4abc - 2/21/2005 11:51 PM

Jesus,

I put the numbers into my software: I get 4104 rpm @ 116 km/h. Assuming you have BFG tires (Ø 2475 mm) and the depression due to weight is about 10 mm. However, that is with a 5th gear of 1:1 - 0.799:1 in 5th should give you 3279 rpm.
Looks like you have one of the 5-speed Getrag with a 1:1 5th gear. The serial number 430 781 supports that. Looks like a GL 76/27 P5 717.43/44 transmission. You should have a serial number that starts with 439 (GL 76/27 K5 717.439)
http://4x4abc.com/G-Class/trans.html

Get 285/75 R 16 tires (Ø 2545 mm) and your problem is solved (3189 rpm @ 116 km/h)

Harald

Harald,

I don't understand. Isn't the gearbox with the direct 5th (1 to 1) the GL 76/33 K-5 717.436?

I guess that I'll have to crawl underneath the truck to check any other serial number, because all that's in the "serviceheft" is what I wrote in my first post.

But I am quite in agreement with your assessment that my gearbox must have a direct 5th given that it's the only thing that has been changed in the drivetrain.

Cheers,

 

[kallieir]

RE: Calculations

Ok, I see where you are going Harald. This is the exactly the same as I was thinking before.

Lets look into this anoter way. Lets say that the tire has 100 threads. Each thread is 1 inch apart. Given this I can see no way that the tire is travelling more or less than 100 inches per revolution, no matter how compressed or not, as long as the rubber is not stretched when fully inflated.

Kalli

 

[joir]

Harald and Kalli

I have to point one thing out that could cause your different findings.
Harold argues that when the tire is deflated the radius gets smaller and therfore the circumferance. The problem with that argument is that when the tire is deflated it then it is not a circle any more and therefore the "radius" is not usable for calculating the circumferance.
When a tire is deflated all that happens is that it changes shape, it's circumferance is still the same, but you need other math formulas and other measurements to calculate it!

You can all try this out with a string tied as a circle, lay it on a table and make different shapes, regardless of the shapes the string has the same length/circumferance.

Regards from Iceland, Johannes

PS: PI is a constant approx 3.14159

 

[Captain Spalding]

I think Harald's logic regarding the difference in torque between an inflated tire and a deflated one is inescapeable. The lever arm principle certainly comes into play.

As to the effect of a tire's level of inflation on the speedo issue, that seems less obvious. It can be imperically tested though. Most of L.A. is submerged right now, but when things dry out a bit I will conduct the GPS vs. speedo test with tires inflated and deflated and then report back. (Access to local dirt roads is restricted when it rains - to help lessen erosion and road damage.)

 

[kallieir]

Torque

If Harald´s theory of the torque increase is right, I can not agree that this added torque will help when one needs more torque, since it is my experience that when running on low tire pressure, much of engine power goes into "bending" the tire (I cant find the right word for this in english [] )

At least this is true regarding Ground Hawgs and BFG A/T, which are the tires I´m using altough the GH are quite soft tires.

Kalli

P.S. I´m glad that I´m finally making some inputs into this forum after been reading it for two years []

 

[Karl Ingolfsson]

RE: Torque

I like Haralds theory.

He suggests that when using bigger tires it is not necessary to lower gearing to get the same tourqe to the ground... -as long as tire pressure is low enaugh to keep the hub at same height from ground as with the smaller tires...
Since the use of big tires in our part of the world is to run it at very low pressure under demanding conditions... - I would assume that there is no need to lower gearing when bigger tires are mounted...(as long as you ride it at a wery low pressure)

If Haralds assumption is right, -the wheel has to move faster than the tire... Well I have seen that happen -but not for long... [}]

Unfortunately, -we who drive with deformed big tires at low pressure... -we have to lower the gearing when we beef up the tires regardless of what pressure we run.

But just imagine how convinient it would be to get lower gearing when offroading by lowering the tirepressure and when a higher gear is needed on the highway you just pump up!

If the tourqe increase at lower pressure was reallity you would also get "better" mpg at low tirepressure! (but the miles would be far shorter [xx(] )

Haralds theory also supports the assumtion that by lowering the tirepressure you would get better acceleration.

(I admit ignoring friction and heat here)

Unfortunately none of this is true and like other Icelanders I get the same reading between spedometer and GPS what ever tirepressur I use.

But like Kalli said, -there might be a little difference between full pumped tire and overpumped tire, -but I have no experience of the latter

 

[4x4abc]

RE: Torque

Karl,

it is a known fact that you lose about 3.5% of torque for every inch (25.4 mm) of tire size increase over stock.
Lets assume you had stock tires of 29" and moved to 30" tires.
So, in order to retain the same torque at the point where the tire hits the ground you would need to deflate the 31" tire to the point that it shows a 12.7 mm depression.

However, when you move to a 35" tire you would need to deflate so much as to show a 3" depression - and that is not practical.

Harald

 

[Captain Spalding]

RE: Torque

kallieir - 2/21/2005 4:24 PM
P.S. I´m glad that I´m finally making some inputs into this forum after been reading it for two years []

We're glad too. []

 

[4x4abc]

RE: Torque

Now here is the solution for the argument over whether a deflated tire makes less revolutions per 1000 meter or not.

Imagine a military wheel of 33" diameter with an internal runflat device of 31".
Now drive 1000 meters with the tire intact. After that drive 1000 meters with a busted tire. The smaller runflat device will rotate more than the intact tire to cover 1000 meters. Am I right or wrong?

Harald