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. 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.
When done properly, progressive shifting often results in quicker acceleration because diesel engines produce the most torque in lower rpm ranges. Additionally, this technique reduces wear on the transmission because synchronizers only need to compensate for relatively small differences in rotational speed between different components in the gearbox.
As defined by KE =1/2 mv^2, acceleration is the process of gaining kinetic energy, so 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.
Shifting at peak torque doesn't 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.