Progressive shifting is a technique for changing gears commonly practiced by drivers of semi-trailer trucks. It is meant to reduce fuel consumption — something very important for drivers who travel several hundred miles each day.
Progressive shifting is accomplished by changing gears upward as early as possible when accelerating, while staying within the torque range. Each shift will go a little higher into the RPM, until the vehicle is in its top gear at cruising speed. After each shift is completed, the engine and transmission should be operating at or near the lowest rpm speeds recommended by the manufacturers of those parts.
As defined by KE =1/2 mv^2, acceleration is the process of gaining kinetic energy, so the greater the power delivered, the quicker it gains kinetic energy.
The best average acceleration in a truck with a Caterpillar C15 engine is achieved by going all the way up to 1950RPM, then shifting to a gear that will put the engine at 1500RPM, so that the truck is receiving as close as possible to maximum power throughout the entire time it is accelerating. This, however, is not progressive shifting, and has increased fuel consumption and wear on the motor.
Shifting at peak torque does not provide the maximum acceleration as even the engine maybe making the maximum torque, with each up shift, the mechanical advantage of the transmission is reduced.