Godless Commie

iTrader: (2)

I have decided to replace my gearbox and diff with stronger BMW units before I break anything.
Twin turbo torque gives me nightmares of a broken 5 speed in the middle of nowhere, so I figured I could be proactive and do this project properly, without any roadside drama.

The transmission will be a 6 speed unit, and since gear ratios are wildly different than a Miata box, the diff will be a limited slip Bimmer offering.
I have enough problems with a pretty much useless first gear, and the second goes by too quickly anyway, so keeping the Miata 4.10 with the already shorter 1st and 2nd BMW gears would not be ideal to say the least.

So, I looked at all available diff ratios and settled on a 3.15 diff for my setup. It will not be a straight up junkyard unit, I will have one rebuilt with new clutch packs and everything.
Please keep in mind that my boost comes on very early, like just above idle, and I have quite a bit of torque from 2000 rpm on. Which means, I could use widely spaced, tall gears.

I would like your opinion on my diff ratio choice before I place the order.

Here is my current 5 speed and 4.10 diff:







And, this is the 6 speed with the 3.15 diff:




İf you are interested, please click on the links below to see both setups in action:

Miata 5 speed and 4.10

BMW 6 speed and 3.15

This is a fast DD car. It sees some track duty.
I would also like to be able to reduce my cruise rpm, and I calculate roughly 2750 rpm at 70 mph with the 3.15 diff.

I would very much appreciate your input in my diff selection.
What would your choice be?


Paging @Savington @curly @sixshooter @Joe Perez

technicalninja

You will NOT be able to run 300 KPH.
It will be an aircraft at that point...

The two charts look very similar through the first 4 gears.
It should feel very similar to the Mazda set up...
1st will still be useless and second will "go by quickly" as well.
If you have the torque (and you DO) a numerically lower rear gear than 3.15 for the BMW trans is appropriate.
Do they make them lower?
I'd want one somewhere around 2.9 maybe lower.

SO now you have a Miata that's geared for 200+ MPH (320KPH)
No longer an airplane...
Cruise missile ?

Godless Commie

iTrader: (2)

There are 2.56, and a 2.95 ratios available, too.

You can compare 3.15 and 2.95 ratios here:
click...

portabull

lfx, mv7 transmission (6th is 0.75:1), 3.23 rear end ratio, and 205/50/15 tires my rpm is ~2750 at 80mph. it feels relaxed and has plenty of torque at that rpm.

technicalninja

Here's a quick cheap test.
Your current set up hits just over 100kph in second...
These will be maximum effort 0-100kph tests.
Test using first and second gear then
Test using second gear only.
Which is quicker?
It wouldn't surprise me on your car with your early onset boost might be quicker using second only.
If it is then a first gear that can hit 100kph is what you want...

Quick question, how much torque do you have at 2K?

2.95 is still too high but 2.56 will be too low.
2.95 better than 3.15 in my book

Godless Commie

iTrader: (2)

I stand corrected:

It should be 2.93, not 2.95.

Turbomack

Real chance I’ll be buying the same solution that comes out of this discussion but I’m thinking about the Getrag 260 as well. Had 3 different E30’s the last couple of years and like that box a lot.

der_vierte

2.93 and 3.07 are very common 188K Diffs found in E46 330i and Z4 3.0i cars. You can find them cheap here in Germany. Shipping isn't too bad, as these Diffs fit easily in a mid size box.

I can help out, if you want

Godless Commie

iTrader: (2)

Thank you very much for your kind offer.
I found a BMW specialist here in Istanbul, and he will be rebuilding a dif for me with new gears, clutches and other internal parts. All I need to do is do my homework right and tell him what ratio I want. It will be a "new" unit.
It will cost me around $550 instead of the $200 - 250 for a junkyard diff, but the peace of mind will be well worth it.

Godless Commie

iTrader: (2)

I keep going back and forth between 2.93 and 3.07 at this point.
There is an advantage with the 3.XX ratio. Once set up, it is very easy to change the ratio within the 3.XX gear selection available. (for instance, 3.07 to 3.15, if need be)
Going from 3.XX to 2.XX will require a whole new housing, LSD parts, etc.

Here is the 2.93 results:





And, the 3.07:

der_vierte

2.93 looks more adequate for a daily. Cruising RPM lower, more traction in lower gears, enough power to use long gears, not really any downside going this route, eh?

Godless Commie

iTrader: (2)

I am kinda leaning that way myself.

jonboy

Subbing - I'm thinking of a BMW box as well at some point, and the diff options that the US guys can find in junkyards are not at all common in the UK, so I'm interested to see how and what you end up using

Tran

I'd probably be tempted by the 3.15 diff out of those options.

Sure you can get lower cruise RPM with a taller diff and your particular setup might make good steady state torque at 70mph, but dropping the RPM 8% (3.15 to 2.93) drops the available power for in-gear flexibility 8% straight away, ignoring the fact that transient response (and steady state torque) will likely be lower. Then factor in that if you're cruising at 70mph, you probably drop down to below 60mph at times and wouldn't want to downshift there if cruising.

Also factor in track driving, and you either want a super tall second or short third. Lots of tracks have a (or multiple) <40mph corners. If you have to drop to second gear for that, especially a short second gear, that will cost a fair bit of time on exit, along with traction management issues, and the transient response, (and engine power) would not be good with 3000rpm (or less!) in a tall third gear on exit.

Factor in the fuel savings from dropping the cruise RPM, unless you do a lot of miles at 90mph+, I can't see it being that significant. Then when you figure out the laptime perfomance you'd lose and how much it would cost to get that back...

technicalninja

I respectfully disagree...
After looking at the ratios one thought I had that I decided not to share was...
Running an engine at low vacuum (50+kpa-100kpa) is what ALL the OEMs are doing right now for fuel economy.
They are getting this two ways.
#1 by selectively killing multiple cylinders in six and eight cylinders engines thus requiring a higher throttle opening and a higher vacuum reading. This is done with DOD equipment and sucks the big hooter...
#2 going with what would be a undersized engine for the application and turboing it. This is the current crop of 1.4-1.6L turbo engines that replaced 2.0 to 2.5 l NA engines in a butt load of Honda, Toyota, GM engines. Pretty much everybody has small turbo 4 cylinders now...
In cruise these engines are at a much higher throttle angle with a much higher KPA and get much better fuel economy as they are closer to their maximum efficiency NA. They will wear out quickly IMO...

In Commies case he has a strange turbo set up that makes serious boost where normal "systems" make almost none. He has an excess of torque, this is actually what everyone wants, chasing high HP is a pipe dream, you want the highest AVERAGE torque.

I would bet he has to feather the throttle in the first two gears anyway.

I would want something in the 2.75-2.85 range to make 1st gear a useable gear and to allow full throttle application in 2nd.

This would push the 70mph rpm down to somewhere around 2k rpm.

A 1.8l engine will have a KPA of 55-70 operated at 2k rpm and 40 HP (estimate of cruise hp- I may be way off here). It is seriously "undersized" for this application

Properly tuned he should be able to achieve 25% better fuel economy over a bone stock Miata operating it at 50% less rpm and a much higher throttle angle.

So he will have a Miata geared for 200mph, that can accelerate faster than most supercars, and IF he can stay out of it maybe get 35+ MPG.

This would also produce less pollutants than the stock car.

I just didn't think "Economy" and "Green" are appropriate buttons for what Godless Commie created here...

technicalninja

This is also the reason for my question "how much torque at 2k rpm?".
If he has more than 100lbs/ft at 2 k he will not have to down shift to achieve "reasonable" acceleration at 2k 70mph cruise.
If he has more than 200lbs/ft at 2 k he will need even lower gears...

Tran

I made a car performance spreadsheet a while ago that derives acceleration performance from aero loads, road friction loads, torque curves estimated at the wheels and with the appropriate gear ratios etc. Kind of like a reverse virtual dyno before I'd ever heard of that. The correlation with actual dyno data and a vbox is great.

I'd made the sheet for my NA, so assuming this NB has similar drag and mass etc, it needs 24.0hp (at the wheels, the decimal place is here just for number comparison, I doubt my inputs are accurate to that degree) to maintain a constant 70mph. A 3.15 final drive with 580mm tyre is 2743rpm here, a 2.93 is down at 2551rpm. So a 3.15 needs 46.0 wtq, call it 50.5ftlb @ engine, and for a 2.93, that's 49.4wtq, 54.4ftlb @ engine.

So now we have the difference in operating points, 2743rpm, 50.5ftlb (68.5Nm) vs 2551rpm, 54.4ftlb (73.8Nm).

If we look at a BSFC map of a 1.9L N/A saturn engine I found on the internet (most gasoline engine BSFC maps are a similar shape, just better tech lets it achieve better numbers, so we can estimate the percentage differences around the operating points to follow similar trends. I know this isn't turbocharged but if someone can find a better suited BSFC map, try that)




From the operating points, we move from the 275g/kWh line to roughly 270g/kWh. 2% improvement in engine efficiency and so a 2% improvement fuel economy at that specific cruise speed, so not even 1mpg at a very specific cruise. You won't get an overall 2% fuel improvement because with a shorter FDR, you can always upshift earlier to keep the average RPM closer.

Assuming the engine makes a 5-speed busting 270wTQ from 2000rpm (I would be very impressed if it did, even if it can datalog full boost there), acceleration potential in 6th gear drops from 0.24G to 0.22G (though these numbers are still good!), though in reality i'd expect it to be more like 15% in a pull due to the fact torque will likely be rising with RPM, even at constant boost and then add a fair bit more for transient effect's if looking for the acceleration from a throttle step input.

So basically, barely any better economy (the numbers would be more in favour the higher the cruise speed though) for what would be a noticeable reduction in flexibility, I don't think it's worth it. Think about how much fancier the engine/turbo system would have to be to claw back that 6th gear 70mph acceleration. Just because an OEM does something to achieve their marginal year on year gains, doesn't mean we should. Look at all the Cayman GT4 owners buying shorter FDRs because Porsche had to give them really long FDRs for emissions (fuel economy) legislation.

Tran

If he cruised at 2000rpm, 70mph, this would need a 2.30 FDR and the resulting acceleration would be ~0.02G with 100wtq (or ~0.10G with 200wtq......)

der_vierte

One thing:
He is at 2600rpm at 70mph!

Godless Commie

iTrader: (2)

This should give you an idea...
5th gear pull from just above idle.


Never mind the boost dip at 3K rpm. It's long gone.