san
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Performance Differentials
Some people refer to it as "Torque Multiplication"... we simply call it added acceleration!The principle behind this is simple. It's easier for the engine to turn the rear wheels if the gearing is "low". Low gearing is actually a numerically higher ratio than "high" or "tall" gearing.Why are there different differential ratios?Different amounts of torque and horsepower in different engines make the need for different gear ratios necessary. When an engine has a lot of torque, it generally means that it has a low maximum RPM, therefore, to attain reasonable highway speeds, you need a "tall" differential. When RPM levels are higher, diff ratios can be made lower to give faster acceleration. BMW does not chose differential ratios arbitrarily, they are chosen for a specific compromise of acceleration and cruising comfort.
Why chose a different ratio?You and BMW may have a different idea of how your car should perform. Lowering your ratio will give you better acceleration, but at a loss of theoretical top speed, and a higher cruising RPM.What is theoretical top speed?Theoretical top speed is the mathematical calculation of maximum engine RPM, divided by the top gear ratio of the transmission, divided by the differential ratio, which gives the number of wheel rotations per minute. When you take the circumference of the wheel and divide it into a mile, you can determine the minutes taken to cover a mile, or, the miles per hour the vehicle will travel.Here's an example using some typical numbers. Assuming a maximum engine speed of 7000 RPM, a top gear ratio 0.83:1, a differential ratio 3.15:1 and a wheel circumference of 80 inches, we find that at your maximum RPM:If we have...7,000 / 0.83 = 8,434 driveshaft revolutions per minute8,434 / 3.15 = 2,677 wheel revolutions per minute...and...Inches in one mile = 63,36063,360 / 80 = 792 wheel revolutions per mile...we can calculate...2,677 / 792 = 3.38 miles per minute...or in miles per hour...3.38 x 60 = 202.8 mphIf you do the calculations, you'll see that most vehicles are incapable of reaching their theoretical top speed. In some cases this is due to factory-installed electronic vehicle speed limiters, but just as often, the engine simly cannot overcome the vehicle's aerodynamics.How much am I losing by going to a lower differential ratio?Again, you can do the math. Take your current gear ratio, and subtract it from the new ratio. Divide the difference by the original ratio and multiply the result by 100. This will give you your percentage change. Let's look at another example...If your current differential ratio is 3.15, and your desired ratio 3.46:3.46 - 3.15 = 0.310.31 / 3.15 = 0.0980.098 x 100 = 9.80 (or 9.8%)Your difference is 9.8%. Now, you can take your current RPM at any given speed and add 9.8% to see your new engine speed. If you are currently turning 3000RPM at 70mph with a 3.15:1 differential, you will be turning 3294RPM with a 3.46:1 differential.The major gain here is getting the engine into it's peak power band at a 10% lower lower road speed, which translates to faster acceleration.
