Dinan 3.62 Diff question

[stylinexpat]

Originally Posted by swamp2

It is better in precisely 25 of 42 of these metrics and almost universally better less than 120 mph. In general the 3.62 is "better" for WOT runs at lower speeds that would make the 3.62 "better" in some sense for you.

On my E46 330 I had a 2.93 and went to a 3.46 (about the same % change as 3.15 to 3.62) and was very happy with it. It made a pretty big difference and couldn't complain about it. Here is an example of that supercharged 330 I had with the 3.62 LSD in it:

in 4th gear from 100-120 it would do it in about 5 sec. or so. I had 5th and 6th left of course and it used pull all the way to redline in 6th

[mixja]

Originally Posted by swamp2

Guys, there has been a lot of debate about differentials. In short a higer FD ratio does produce more wheel torque and more wheel power however, the trade off is less time accelerating in each gear (i.e. you have to go to 2nd which is much lower acceleration than 1st while the car with the stock diff is still pulling hard to a higher speed before the 1-2 shift, similarly across all gears). There has also been a lot of debate (mostly in the past) about physics based simulation for determining a vehicles performance. In short simulation is pretty well accepted and has been shown to be quite accurate across a large range of vehicles. I finally decided to run some sims of the M3 (M-DCT) with the stock FD (3.15) vs. a 3.45 and 3.62. This is actually one of the best cases to simulate since it essentially washes out any baseline effects, the only changes to each set up is the FD ratio and therefore even though you might see some inaccuracy on an individual run the RELATIVE results between these results and any apples to apples real world test should be excellent.

In short the 3.45 FD has little to no effect (except at very high speeds) but the 3.62 has a combination of positive effects with few downsides. #1 is stock, #2 is 3.45 and #3 is 3.62. I think this goes against much of the guesses and common wisdom on the topic. Personally, I trust simulation as much or even more than test. Tests often get obfuscated with many non controlled/controllable factors leading to a non apples to apples scenario.

I'm not quite sure the figures are right for 60-130MPH...

For example, in 5th gear, the 3.62 is making ~130MPH at redline in 5th gear, so the 3.62 will either have no gear change or one gear change right near the end of the run, whilst the other cars are always in 5th gear...You can't tell me that the 3.62 with 5% more in-gear torque than the 3.45 is going to run 60-130MPH slower...

Using my own spreadsheet that I made to model this, 60-130MPH starting in 2nd gives the closest results (basically the 3.45 and 3.62 are dead even and the 3.15 is a few hundredths of a second behind)...the cars are also never more than a metre apart...

Starting in 3rd gear or higher, the 3.45 and 3.62 always win with the winning margin getting higher and higher as you increase the starting gear, purely because the 3.45 and 3.62 get too much of a lead in the starting gear...

[Lemans_Blue_M]

I have a few questions about the numbers posted earlier myself...

Not sure how a diff ratio that has almost 10% SHORTER gearing (3.45), has virtually no improvement in 1st and 2nd gear acceleration over the stock gear ratio (3.15) ?

There should be evidence of improved acceleration from the stock diff ratio numbers. (due to higher torque multiplication)

But for some unexplained reason, that doesn't show up in the numbers.

These results appear to defy the laws of physics...

[swamp2]

Originally Posted by mixja

I'm not quite sure the figures are right for 60-130MPH...

For example, in 5th gear, the 3.62 is making ~130MPH at redline in 5th gear, so the 3.62 will either have no gear change or one gear change right near the end of the run, whilst the other cars are always in 5th gear...You can't tell me that the 3.62 with 5% more in-gear torque than the 3.45 is going to run 60-130MPH slower...

Using my own spreadsheet that I made to model this, 60-130MPH starting in 2nd gives the closest results (basically the 3.45 and 3.62 are dead even and the 3.15 is a few hundredths of a second behind)...the cars are also never more than a metre apart...

Starting in 3rd gear or higher, the 3.45 and 3.62 always win with the winning margin getting higher and higher as you increase the starting gear, purely because the 3.45 and 3.62 get too much of a lead in the starting gear...

I think I know a little bit about your spreadsheet. It might do an OK/first pass job but is does it include the following effects:

-Aerodynamic effects?
-Tire losses and growth?
-Drivetrain inertia and losses?
-Shift times

The first three of these are rpm/speed dependent!

Note with my software CarTest you can also allow or not allow shifts for the times from speed x to speed y. When you limit the results to no shifts allowed you can definitely see the trends across the ratios, much more as you might expect based on "ignoring" the importance of time in each gear.

[swamp2]

Originally Posted by Lemans_Blue_M

I have a few questions about the numbers posted earlier myself...

Not sure how a diff ratio that has almost 10% SHORTER gearing (3.45), has virtually no improvement in 1st and 2nd gear acceleration over the stock gear ratio (3.15) ?

There should be evidence of improved acceleration from the stock diff ratio numbers. (due to higher torque multiplication)

But for some unexplained reason, that doesn't show up in the numbers.

These results appear to defy the laws of physics...

This one is fairly simple. There is no defying physics, you've just missed some of it. Acceleration in first at WOT especially from a standing stop is largely traction limited. Also don't forget the fundamentals, you get to hold 1st longer with a lower FD ratio. Between the lowest and highest ratios considered here it amounts to holding 1st gear for about 0.5 seconds longer. That is significant since the average acceleration in 2nd is reduced by about 50%.

[stylinexpat]

Best thing to do is to put two to a test right next to each other to put an end to this..

[swamp2]

Originally Posted by stylinexpat

Best thing to do is to put two to a test right next to each other to put an end to this..

There are problems associated with testing as well. Most folks tend to overlook these things. Ideally you want to isolate a single variable such as FD ratio. However, all of these (and other) factors will obfuscate a perfect apples to apples test (in no particular order):

-Driver skill
-Tires, brand and wear level
-Wheel sizes and weights
-Degree to which cars is broken in
-Natural power variations among cars
-Car weight, including options, driver, "luggage" and fluids
-Lack of proper statistics (multiple runs)

As you can see getting perfect and legitimate test results, especially when cars are more or less apart by a "drivers race" is difficult and in reality not often accomplished. With simulation you have nearly a perfect apples to apples "test" with truly one single variable changing.

[Lemans_Blue_M]

Originally Posted by swamp2

This one is fairly simple. There is no defying physics, you've just missed some of it. Acceleration in first at WOT especially from a standing stop is largely traction limited. Also don't forget the fundamentals, you get to hold 1st longer with a lower FD ratio. Between the lowest and highest ratios considered here it amounts to holding 1st gear for about 0.5 seconds longer. That is significant since the average acceleration in 2nd is reduced by about 50%.

The 0-50mph and 0-60mph numbers make no sense.

The is no way you are going to shorten the ring and pinion gearing by nearly 10% and show 0% improvement in elapsed time. That does defy the laws of physics.

And if the grip is largely 'traction limited' as you put it...then the 3.62 would suffer from this even more due it's shorter gear ratio. (promoting even more wheel spin at low speeds)

So it still doesn't add up. The 3.45 shows no low end improvement whatsoever in the time-to-speed comparison, which means some of the "assumptions" the program is using must be flawed or incorrect.

Take off the engineering hat and think about it for a second. A shorter gear ratio will yield a slightly faster time 0-50, and this is absent from your calculations. (no difference)

That's mechanically impossible, since you haven't even shifted into second gear at that point...

Second gear also shows virtually no improvement over thw 3.15 stock gear ratio either. Your math is wrong.

[turbo8765]

Originally Posted by stylinexpat

Best thing to do is to put two to a test right next to each other to put an end to this..

Agreed, and the 3.62 will win. It's only a matter of time...

[swamp2]

Originally Posted by Lemans_Blue_M

The 0-50mph and 0-60mph numbers make no sense.

The is no way you are going to shorten the ring and pinion gearing by nearly 10% and show 0% improvement in elapsed time. That does defy the laws of physics.

And if the grip is largely 'traction limited' as you put it...then the 3.62 would suffer from this even more due it's shorter gear ratio. (promoting even more wheel spin at low speeds)

So it still doesn't add up. The 3.45 shows no low end improvement whatsoever in the time-to-speed comparison, which means some of the "assumptions" the program is using must be flawed or incorrect.

Take off the engineering hat and think about it for a second. A shorter gear ratio will yield a slightly faster time 0-50, and this is absent from your calculations. (no difference)

That's mechanically impossible, since you haven't even shifted into second gear at that point...

Second gear also shows virtually no improvement over thw 3.15 stock gear ratio either. Your math is wrong.

Well, I disagree, so do the simulations an so does the basic physics. What part of traction limited and less time in gear with a larger gear ratio did you miss? If you really want to examine FD ratio effects ONLY. Look as times for runs from speed x to speed y where speed x is greater than or equal to 30 mph (no wheel spin) and gear shifts are not allowed. Under these circumstances you can clearly see the FD ratio effects and they line right up with higher ratio = faster time (as per your simplified point of view). But as we all know to get from most speeds to most other speeds shifting is required and that complicates your simplistic point of view. If you really want to see the no shift results I can post them for you.

Also, 50 mph is 2nd gear in all cars, 6MT, M-DCT (3.15, 3.45, 3.62). The range of speeds at the 1-2 shifts for all four cars is 37-43 mph. Thus even without any traction effects you still have the time in gear effects to 50. Don't forget the average acceleration in 2nd gear is reduced by about 1/2 compared to 1st gear. It is a big "penalty" you get for being in 2nd and being in second earlier.

So it is not "my math" is it "THE math and "THE" physics and it is a bit more complex that you think. There is no such thing as a free lunch with the FD ratio. If it were so simple everyone would run an infinite (or at least really huge FD ratio). Do you know what would happen then to acceleration performance?

[Lemans_Blue_M]

Originally Posted by swamp2

Well, I disagree, so do the simulations an so does the basic physics. What part of traction limited and less time in gear with a larger gear ratio did you miss? If you really want to examine FD ratio effects ONLY. Look as times for runs from speed x to speed y where speed x is greater than or equal to 30 mph (no wheel spin) and gear shifts are not allowed. Under these circumstances you can clearly see the FD ratio effects and they line right up with higher ratio = faster time (as per your simplified point of view). But as we all know to get from most speeds to most other speeds shifting is required and that complicates your simplistic point of view. If you really want to see the no shift results I can post them for you.

Also, 50 mph is 2nd gear in all cars, 6MT, M-DCT (3.15, 3.45, 3.62). The range of speeds at the 1-2 shifts for all four cars is 37-43 mph. Thus even without any traction effects you still have the time in gear effects to 50. Don't forget the average acceleration in 2nd gear is reduced by about 1/2 compared to 1st gear. It is a big "penalty" you get for being in 2nd and being in second earlier.

So it is not "my math" is it "THE math and "THE" physics and it is a bit more complex that you think. There is no such thing as a free lunch with the FD ratio. If it were so simple everyone would run an infinite (or at least really huge FD ratio). Do you know what would happen then to acceleration performance?

You have still not answered my question...

Why does your software not assign a net gain for the shorter 3.45 gearing (0.00 improvement) YET, it does reward the even shorter 3.62 gearing very generously in the acceleration time gained portion of your results?

In second gear, there is no advantage derived by the 3.45 gearing...even though it has a nearly 10% torque multiplication advantage over stock.

And don't give me the shifting 'excuse' with the DCT cars either. The DCT ECU can shift that tranny faster than you can blink. (and more efficiently to boot with the dual-clutch setup)

The 3.62 has a shorter amount of time to shift than the 3.45, so please stop telling me how great your canned software program is...and just answer this basic fundamental question please...

BTW: It IS your math since you interjected your own interpretations in to the program by using personal assumptions to calculate these numbers.

So the results will follow the logic based on those interpretations...

[mixja]

Originally Posted by stylinexpat

Best thing to do is to put two to a test right next to each other to put an end to this..

I'd pick the 3.45 would actually beat the rest down the 1/4 mile.

Reasons being:

1. Traction control will be an issue at launch, particularly for 3.62
2. Making precise gear changes in 1st , maybe 2nd on the 3.62 is going to be hard. Traction on the 1st to 2nd gear change on the 3.62 will be an issue on stock tires.
3. 3.62 is changing to 4th @ 106MPH whilst 3.45 is changing to 4th @ 112MPH

[mixja]

Originally Posted by swamp2

I think I know a little bit about your spreadsheet. It might do an OK/first pass job but is does it include the following effects:

-Aerodynamic effects?
-Tire losses and growth?
-Drivetrain inertia and losses?
-Shift times

The first three of these are rpm/speed dependent!

Note with my software CarTest you can also allow or not allow shifts for the times from speed x to speed y. When you limit the results to no shifts allowed you can definitely see the trends across the ratios, much more as you might expect based on "ignoring" the importance of time in each gear.

Granted I'm sure the car simulation software is far more accurate than my home grown effort, but it does incorporate drag, rolling resistance and shift times. Nothing in there for tire losses or drivetrain inertia - I'm using www.rri.se figures for torque delivered to wheels...

One other thing to also note is that a car that is slightly faster for a given speed range is not necessarily ahead in terms of distance travelled. Distance travelled is the most meaningful measurement - can your software graph distance traveled over time?

[stylinexpat]

Originally Posted by mixja

Granted I'm sure the car simulation software is far more accurate than my home grown effort, but it does incorporate drag, rolling resistance and shift times. Nothing in there for tire losses or drivetrain inertia - I'm using www.rri.se figures for torque delivered to wheels...

One other thing to also note is that a car that is slightly faster for a given speed range is not necessarily ahead in terms of distance travelled. Distance travelled is the most meaningful measurement - can your software graph distance traveled over time?

Interesting.. I would like to know this too.

[swamp2]

Originally Posted by Lemans_Blue_M

You have still not answered my question...

Well you do seem to be continually ignoring a good portion of the problem.

Originally Posted by Lemans_Blue_M

Why does your software not assign a net gain for the shorter 3.45 gearing (0.00 improvement) YET, it does reward the even shorter 3.62 gearing very generously in the acceleration time gained portion of your results?

You can see some advantage in 0-speed X times for the 3.45, it just does not have a universal advantage. Advantages in both time to speed and time to distance come and go and vary smoothly but then get instantaneous or step like changes at shift points. It is more of a dynamic orchestra than a simple case of A is always > B. Now that being said, simulation is not perfect. There certainly can be small errors at single data points and even occassional flipped results compared to a real world apples to apples test (when the predicted differences are very smal). Again if you want to see results that make more intuitive sense (intuitive but missing the very important time in gear point), you can look at speed x to speed y times, NOT allowing shifts AND when above 30 mph. These results line right up in order with the values of the FD ratios. I can post these if you like but have not posted them yet, since I thought of them as fairly trivial.

Originally Posted by Lemans_Blue_M

In second gear, there is no advantage derived by the 3.45 gearing...even though it has a nearly 10% torque multiplication advantage over stock.

See above. I did not post 2nd gear only, no shift results. 3.45 does outperform stock under such circumstances.

Originally Posted by Lemans_Blue_M

And don't give me the shifting 'excuse' with the DCT cars either. The DCT ECU can shift that tranny faster than you can blink. (and more efficiently to boot with the dual-clutch setup)

DCT is irrelevant here since all tests are DCT vs. DCT. I have of course updated default software options for these vehicles to reflect the fact that DCT shifts much faster than MT. Of course this software is also ideal to explore the DCT vs. 6MT case as well, another area which I have done a great deal of work.

Originally Posted by Lemans_Blue_M

The 3.62 has a shorter amount of time to shift than the 3.45, so please stop telling me how great your canned software program is...and just answer this basic fundamental question please...

BTW: It IS your math since you interjected your own interpretations in to the program by using personal assumptions to calculate these numbers.

So the results will follow the logic based on those interpretations...

Not sure what you mean here. Shift times are identical across all simulations. This is not a "canned" software program. Well it can be used that way but as with any such similar physics based performance simulation tools the primary inputs that must be correct and losses, shift times and aerodynamic information. All of these values have been very well vetted with prior simulation efforts. Do you have a problem with the 1/4 mi times or any other well known performance numbers we have seen in real life vs. these simulations?

Last but not least it would be great if you yourself can be more concrete. Please provide some ACTUAL numerical calculations/estimates/guesses, anything to counter the ones I have provided. It is easy to find fault and criticize without being precise. This is obviously a leading question as it is a foregone conclusion that you do not have such capability.

Being a physicist/mathematician and engineer in prior lives I was initially quite skeptical of the capability of CarTest to provide accurate simulations. Those old discussions are actually documented here on the forum. However, in working with a huge range of cars and cases I have come to appreciate its complexity, depth and accuracy. It is perfect, no, but again to make true "apples to apples" comparisons such as this is it an invaluable tool to provide insight and to settle debates.

[swamp2]

Originally Posted by mixja

I'd pick the 3.45 would actually beat the rest down the 1/4 mile.

Reasons being:

1. Traction control will be an issue at launch, particularly for 3.62
2. Making precise gear changes in 1st , maybe 2nd on the 3.62 is going to be hard. Traction on the 1st to 2nd gear change on the 3.62 will be an issue on stock tires.
3. 3.62 is changing to 4th @ 106MPH whilst 3.45 is changing to 4th @ 112MPH

-Traction is an issue with any of these FDs
-I did take the case of DCT just for example purposes, however, I doubt MT would upset the results too much. Of course in software all shifts are identical, MT or DCT.
-3.62 and 3.45 cars are in 5th at the 1/4 mi end, stock 3.15 is in 4th. However, the former two have been in gear for some time after the last shift, mitigating the small hit from the shift.

I'd be willing to bet on the 3.62 for the best ET in the 1/4, again DCT only.

Originally Posted by mixja

One other thing to also note is that a car that is slightly faster for a given speed range is not necessarily ahead in terms of distance travelled. Distance travelled is the most meaningful measurement - can your software graph distance traveled over time?

Good point. Who is physically ahead in a head to head race is most important. CarTest does produce all of the following graphs, distance, speed and acceleration vs. time and speed vs. distance. Unfortunately, the trace widths in the plots, combined with a large total time covered makes seeing subtle details on cars with close performance nearly impossible to actually see. You can only really see the differences for relatively short times. In this case all variants are so close you really see a single trace. Did you want to see something in particular, I can try to show it or tweak it to enable it to be seen?

[dcstep]

The OP didn't say he's a racer of any type and he mainly drives in the city. He's looking for a performance gain that he can feel without too many sacrifices. Forget your friggin' charts and spreadsheets, he needs the 3.45, not the 3.62.

I went from the 3.85 to a 4.10 in my 6MT, which is about a 6.5% change in final drive ratio. That change gives me much improved mid-gear acceleration and makes the car really squirt. For street and autocross, which is what I do, that's ideal. It almost makes 1st gear useless.

Going to a 3.62 is a 15% change!! That will truly make 1st gear worthless except for jumping of the line in an 1/8th mile drag. It's already been shown to be too short for 1/4-mile drag. Why you'd want for city driving is beyond me. I suspect that whomever suggested that has never driven one. Oh, realize that you get exactly a 15% decline is gas mileage.

The 3.45 FD is almost a 10% change, which is a lot. Apparently the DCT adjusts easily to it.

Dave

[eeeboy]

I drive around the city 98% of the time and my mpg went from 9.5 to 10.7 after the 3.62. the reason is because I don't have to STOMP and redline the car like I used to, in order to get a rush, also with the 3.62, I never hit 8300rpm much because there is no need. Also, when on the freeway cruising at 50, when youfloor it the car takes off like MADDDDD. Oh yeah 1st gear useless? 1st gear redline and you are hitting about 40mph ...useless??? I thought stock 1st gear was useless because it felt like my 328i loaner

[swamp2]

Originally Posted by dcstep

The OP didn't say he's a racer of any type and he mainly drives in the city. He's looking for a performance gain that he can feel without too many sacrifices. Forget your friggin' charts and spreadsheets, he needs the 3.45, not the 3.62.

It is a good point - he did not say he wanted to race. Nonetheless I still say your conclusion is pretty subjective. You will be able to feel both pretty well. With a DCT in city driving you would most likely be in D modes so there is not too much cause for concern about too much shifting required.

By the way - I would hate to see what a modern sporty car like an M3 would turn out like without spreadsheets, charts and an enormous plethora of very advanced simulation software

[dcstep]

Originally Posted by swamp2

...
By the way - I would hate to see what a modern sporty car like an M3 would turn out like without spreadsheets, charts and an enormous plethora of very advanced simulation software

Point taken.

Still, for most of us, the mid-gear feel (and performance) is the reason we go for this mod, not 900 to 8600 rpm performance.

Done in moderation, this is one mod that makes a ton of sense, because BMW was constrained greatly by fleet mileage goals, where we can tune our cars to our own preference.

Dave

[TOOMANYCARS]

While the table tells us the story between the 3 ratios, but a dyno graph comparison of all 3 diff equipped cars would give us a clearer picture.

[mixja]

Here's my own comparison I did in CarTest 2000 - they seem to contradict swamp2's results somewhat...

Cars are:

1. M3 DCT Coupe Stock FD
2. M3 DCT Coupe 3.45 FD
3. M3 DCT Coupe 3.62 FD
4. M3 DCT Coupe Stock FD with +5% power

The results show that changing the FD does not make the car any faster overall. Over a given speed range, it very much depends on the specific speed range as to which car will be faster.

For example - the stock FD is faster 0-150km/h and 0-200km/h, but slower 0-180km/h...

One thing that is clear - adding 5% power definitely makes the car faster over and above what any change in Final Drive ration can do...



The other interesting point to note is that the higher FD cars only really have an advantage off the line (i.e. standing start). Here is a comparison between each of the four cars referenced above for a rolling start @ 30km/h in 1st gear...

Notice that with the car with 5% more power aside, the stock DCT is ahead in terms of distance of the higher FD cars, except for 0-20m...