I have a degree in mechanical engineering which may be part of the reason the shorter explanation works well for me.
With respect to gearing, what is really going on is you have to get into and stay into the rpm range where peak hp is developed to maximize acceleration. It is correct to think of the gearing as multiplying torque but what we really care about for acceleration is the hp. If you shift early, the hp available is less so you accelerate more slowly. If you shift around red line, you are typically spending most of your time near peak hp so you accelerate more quickly. A really high numerical advantage at the start gets you into peak power very quickly. Tight gear to gear spacing keeps the fall off less when you shift gears.
A manual transmission is in some ways helpful to acceleration so a lot of the time the manufacturer will compensate with the gearing. A 128i manual is faster than a 128i automatic. But in a 135 they are essentially identical. At least in 2009, the 135i automatic has more gearing advantage at the start to make up for the lower efficiency of the torque converter automatic. With the DTC the losses of the torque converter are eliminated so the automatic may be quicker if it still has a gearing advantage. Shifts of an automatic are quicker but torque converter automatics are somewhat inefficient due to the need to transfer power through the torque converter.
Last edited by JimD1; 12-07-2012 at 12:56 PM.