znod

I didn't go to that much trouble. I just used the table that cobradav posted in #21 here. I have all the same things caclulated very accurately for two different in-spec tire sizes for the 545i/550i autos (i.e., Steptronics). Regardless of which in-spec tire size is assumed things come about pretty much the same.

Here are some of the calcs I made for my car running 275 X 30-19's.

There are 814 revs per mile given 275 / 30-19
At 60 mph one would do a mile a minute, or 814 tire revs per minute.
If the effective rear-end is 1:1, then a mile a minute would take 814 engine RPM.
If the effective rear-end is 2.3322:1 (as below for 6th gear), then 60 MPH would take 2.3322(814)] = 1,898.4108 RPM
Given the above, it the car could turn 6,500, then its top speed would be 60(6,500 / 1,898.4108) = 205.43498804

Thus, given the effective rear-end ratios below, and assuming that a 545i gets to 6,500 when shifting::
Top speed in 1st gear would be 205.43498804(2.3322 / 14.0946) = 33.99283975
Top speed in 2nd gear would be 205.43498804(2.3322 / 7.9092) = 60.57698365
Top speed in 3rd gear would be 205.43498804(2.3322 / 5.1376) = 93.2566722
Top speed in 4th gear would be 205.43498804(2.3322 / 3.8532) = 124.3422296
Top speed in 5th gear would be 205.4398804(2.3322 / 2.9406) = 162.935078
Therotical top speed in 6th gear would be, as shown above, = 205.43498804

545i Effective Rear-End Ratios:

1st gear--4.17 X 3.38 = 14.0946
2nd gear--2.34 X 3.38 = 7.9092
3rd gear--1.52 X 3.38 = 5.1376
4th gear--1.14 X 3.38 = 3.8532
5th gear--.87 X 3.38 = 2.9406
6th gear--.69 X 3.38 = 2.3322

The effective rear-end ratio in 5th for a manual/SMG would be about the same: 2.93 X 1 = 2.93

I like to use the manufactuer's tire revs per mile values rather than tire diameters in my calculations since rolling diameter differs from actual diameters. I think the manufacturers tend to actually determine tire revs per mile under rolling conditions, but I am not sure (nor am I sure how fast they roll ). But, either measure will work well enough, and, as said, I am not sure what the manufacturers actully do. But, I have noted discrepancies in the diameters they give and their revs per mile values.

But, regardless, to see one of the comparisons for in-spec tires, here are calculations I made for grogan545i's car. As implied, there is not much difference for in-spec tires.

There are 807 revs per mile given 225 / 50-17 rear tires.
At 60 mph one would do a mile a minute, or 807 tire revs per minute.
If the effective rear-end is 1:1, then a mile a minute would take 807 engine RPM.
If the effective rear-end is 2.3322:1 (as below for 6th gear), then 60 MPH would take 2.3322(807)] = 1,882.0854 RPM
Given the above, it the car could turn 6,500, then its top speed would be 60(6,500 / 1,882.0854) = 207.216952

Thus, given the effective rear-end ratios below and assuming that a 545i actually gets to 6,500 when shifting:

Top speed in 1st gear would be 207.216952(2.3322 / 14.0946) = 34.28769707
Top speed in 2nd gear would be 207.216952(2.3322 / 7.9092) = 61.10243456
Top speed in 3rd gear would be 207.216952(2.3322 / 5.1376) = 94.06559005

The difference for the two cars is that my car has a slightly lower rear-end ratio because of its slightly smaller diameter rear tires. My rear-end ratio is, in effect, 3.41 = 3.38(814/807).

The difference in the top speeds we posted earlier occurs because of differences in the implicit tire revs per mile you used (815.73 = 814(163.8378/162.935)(2.93/2.94) and the value implicit in cobradav's table--about 838 = 814(168.3/162.935)(2.93/2.94)--which definitely looks high. Note that the tire rev values we use explicitly/implicitly, 814 versus 815.73, are very close; thus, your calculations and mine, given above, are virtually the same given proper adjustment (e.g., 163.8378 versus 163.8221 = 162.935(2.93/2.94)(3.41/3.38). How's that for both of our pin-point accuracies?

Thus, as you say, your calculations, IMO, are more accurate than those implied by cobradav's table and those I gave originally. Your calculations also show that the in-spec 18" sport-package tires yield results that are highly consistent with those I calculated above for grogan545i's car and for my car. to your calculations.

vegastrashed

IMHO, this mod is so worthwhile! Probably will be my first performance mod. Will need to look around for differentials other than Dinan's, but if it's the best one available then so be it for $2K.

pennetta

The above statement is true too. Actually, some cars can go faster in 5th rather than 6th gear, I know the previous generation Mustang was one, because of wind resistance and where in the rev band you are at a given speed. Many car's 6th gear is for gas mileage and is geared numerically very low, so the engine can never hit redine in top gear because it can't overcome the wind at speeds nearing top speed.

UUronL

Thanks for the clarification. Duh, you're using the automatic final drive ratio. I thought that since this was a thread about a manual/SMG only mod, that we'd be talking about that ratio...

znod

Your are very welcome. But, no, the duh is to me. My original values were for manual/SMG cars--as derived from cobradavs table. I think that the difference in your calculations and the values I gave originally occur because of the differing implicit tire circumferences you and cobradav used (see above--you posted while I was editing--hate it when that happens). When I made my last post, I had forgotten that we were talking manuals/SMGs. I am going to go back and fix what I said. Double duh to me. Fortunately, the effective gear ratios for Steps and manuals/SMG's are about the same. So, except for a minor error, what I said above holds. Triple duh. Thanks for a great coversation.

choi000

Can anyone confirm that Dinan's 3.45 Differential is a limited-slip differential? I was told that Dinan's Differential is not a limited slip but the stock differential from a 645ci automatic. I also did some probing and koalamotorsport sells differentials with various diffferent ratios (3.15, 3.38, 3.46, 3.64 or 3.91) for the E60 and their price is $1550 shipped with the same warranty as that of Dinan. However, if you want a limited slip differential, Koala Motorsport can make one starting at $3450 depending on the ratio. If Dinan's 3.45 diff is a limited-slip, then I'm all over it, if not then I'd have to seriously consider going with koala motorsport and get the choice to choose how aggressive I want my diff to be.

Anyone know how much it would typically cost to do the install on a differential?

znod

IMO, the Dinan is not an LSD. At least the Dinan site does not say it is an LSD. Dinan gives a 41 labor units for installing the differential. As I recall, there are 6 (maybe 8) labor units per hour. So, that means about 7 hours. I don't remember the Dinan labor rate, but it may work out to be about $70 per hour. So, that means about $420 or so to install the Dinan differential.

From Dinan:

Part #:
Price:

D773-0600
$1999.00
Labor Units: 41.0
Required Products: BMW Differential Fluid
Special Notes: Differential comes without rear cover. Installer must swap with diff from car and add BMW Synthetic fluid. Comes with cover gasket.

choi000

That's too bad. I was hoping Dinan's diff would be an LSD, but that would've been too good to be true. So I guess I am gonna consider my other options, i.e. Koala Motorsport's Quaife LSD or the non-liimited-slip diff but with a more aggressive gear ratios; which is cheaper and comes with a cover.

znod

I am interested in your comment about being told that the Dinan is from the 6er vert. That would make sense and, AIR, the vert diff is 3.45. But, if so, I am wondering why Dinan only installs it in SMGs/manuals. After all, some extremist like me might put one in a 545i even if I did pick up only about 2% more rear-wheel torque. Well, ok, that would be dumb; I take it back. Also, if true, then there is no reason the 545i/550i 3.38 diff couldn't be intsalled in a 545i/550i SMG or manual--an also interesting possibility.

choi000

Znod,
I think you could put in the 3.38 diff from the 545i auto into the 545i SMG/manual. I know Koala Motorsports offer the 3.38 as an option and I wouldn't be surprised if it came from the 545i auto. I also talked to Dinan and confirmed that the diff is not a limited slip, however it is equivalent to almost 60hp. Quite a lot for swapping the diffs. Here's an email that I received from Dinan about my inquiries:

"Hi Jon,
We have just released the differential for your car, and it is a huge change. By the numbers, it is the equivalent of gaining almost 60-hp! There is no limited-slip added, just a ratio change. Our retail price is $1999, and you will be charged just over 4 hours of labor. It takes Dinan about 2-3 weeks to build the part.

Thank you,
Eric Bateman"