If you're considering changing the final drive ratio in your BMW, the cheapest approach is to simply replace your existing final drive ratio with one of Dan's @ DiffsOnline. But there are also options to replace your differential at the same time. I'll explain those options below.
Our current differential is a type of torque-sensing limited slip differential that uses an internal pump to shift the torque from one wheel to another when needed. It can supposedly adjust from 0% to 100% lock up, depending on the needs. Dan has found that there's a lot of "slop" in our differentials, and they are especially unpredictable when cornering under deceleration, or cornering under braking. To fix the deficiencies in our existing limited slip differential, Dan offers a variety of solutions using a standard clutch packed Salisbury differential.
The original Salisbury differntial uses a series of clutches to apply pressure to a set of gears which control the amount of lock up. This is known as a static lock-up because it is fixed at a certain percentage. Dan offers a standard Salisbury differential, along is much better Salisbury differentials with variable lock plates.
Here's what Dan had to say to compare the differentials:
The m3 right now has the m variable unit in it. It is a pump differential and does not have ramps. All dynamic lock is controlled by the pump inside. This unit in my opinion has excessive slop inside and is prone to clunking after being subjected to aggressive/abusive driving. By changing to the traditional 2 disc, 3 disc, or 3 disc setup with different ramps, the differential will have preload in it and the dynamic locking will be controlled by pins and ramps. This setup is much more positive and has not one drawback in the m3s.
The factory m variable unit requires one wheel to lose traction before it adds lockup. Going with the Salisbury style carrier instead of the pump diff ensures you always have traction. The M Variable is a great differential for most people, but in spirited/performance driving situations the Salisbury style lasts longer. The easiest way to make the Salisbury unit its best is to add the 30/90 variable ramps. This will enable the differential to have altered locking characteristics similar to the MVariable unit found in your e90m3 differential. The M Variable diff is able to vary lock from 0-100% (according to BMW), which means that when you are off throttle it will have no lockup. This doesn’t allow the limited slip to be able to pull the differential back in line and be predictable.
See a more technical description of these differentials is found in this article.
Chosing the right ratio:
If you change to a numerically higher final drive ratio, you will accelerate faster but have a lower (theoretical) top speed. In reality, it's possible to have a higher top speed because the gears change your speed compared to your motor's power. Therefore it's possible to have a theoretically lower top speed, but experience an actual higher top speed because you're at a stronger part of your motor's power band. In choosing a numerically higher ratio, you would want to select one that will not cause an extra shift on 0-60 or 1/4 mile races -- but instead would "max out" near the end of the 1/4 mile drag race.
If you change to a numerically lower final drive ratio, you will experience slower acceleration, but theoretically have a higher top speed. This most likely will never be the case as we will never hit our maximum theoretical speed. You will get slightly better gas mileage however. One reason to choose a lower gear ratio, is to avoid one shift during 0-60 races or 1/4 races.
For forced induction applications, I do not recommend choosing a numerically higher final drive. I would recommend either keeping the original, or going numerically lower. With the extra power of the supercharger, accelerating faster will not be an issue. Therefore, you won't need a numerically higher final drive. Instead, I recommend selecting numerically lower, thereby increasing your top speed. When enough power is added (such as stroker + supercharger), then going much lower (such as 3:85 to 3.15) will actually yield the best performance results. Going this much lower will actually increase 0-60, 1/4 mile, 60-130, standing mile, and flying mile results. Since there is so much extra power, the lower final drive makes it possible to achieve each of these performance goals with one less shift -- thereby saving approximately 0.75 seconds from each time.
For my Mojave Mile / Texas Mile set up, I changed my BMW 3.85 final drive -- all the way down to a 3.15 -- the same ratio found in the DCT transmission.
See this article and spreadsheet for the effects of differential final drive ratios on our M3's. If you want to take the analysis even further, then I would recommend purchasing "CarTest2000." CT2000 is a physics-based car performance modeler. I've found it to be very accurate for modeling my performance tests. CT2000 allows you to input your actual dyno charts and then model different gear and final drive scenarios.
Dan will offer BMW M3 owners the following options:
Option-1: Replace our final drive ratio using our current differential.
Option-2: Replace our final drive ratio + 2-clutch 40% static lock Salisbury differential.
Option-3: Replace our final drive ratio + 3-clutch 50% static lock Salisbury differential.
Option-4: Replace our final drive ratio + 30-90% variable lock differential.