A Simple Example
Everything explained thus far can be illustrated with an example. My 1982 Chevy Caprice has a three speed automatic transmission, with 2.52:1, 1.52:1, and 1.00:1 gear ratios. The rear axle gear ratio is 2.41:1, and the tire diameter is 27 inches. At 80mph, the wheels are turning at approximately 1000RPM, so I can choose to be in either second or third gear at that speed without over revving the engine. The engine has 170hp at 3700RPM, and 270ft-lb at 2400RPM. Using the horsepower formula, we can see that at 3700RPM, I have 245ft-lb of torque, and at 2400RPM, I have 123hp.
Below is a diagram that demonstrates the effects of changing from 3rd gear to 2nd at 80mph in my Chevy Caprice.
The force at the wheels went up when the engine's power went up, even though the torque at the engine went down.
It can clearly be seen that the decision to drop a gear had a positive effect on the car's ability to accelerate. Even though I had less flywheel torque to play with, the increase in power allowed me to get more force onto the pavement by trading engine speed for torque using second gear in my transmission. The wheel RPM did not change because I'm still doing 80mph. With the wheel speed held constant and the power increased, the wheel torque must therefore increase too. The added torque at the wheels means that I will now have a better acceleration force when I floor it.
-This applies only IF you haven't went beyond the mechanical limits of the previous gear. Ie you can't downshift from 6th to 1st at 80mph becuase your engine would be way above redline!
-This shows why the Si is able to be such a quick little car IF you play within the gear ranges. And explains why a high torque engine is easy and less demanding to drive just mash on the pedal. Where as the Si could require 2 or more downshifted gears. Nothing wrong with either one - personal choice.