Why a shorter rear gear will accelerate the car quicker
You know that a shorter gear will provide more acceleration than a taller gear, but at the expense of lower top speed with the shorter gear. But how does it do it?
It's a matter of applying power pulses from the motor (or work) to the tire.
An 8 cylinder motor will have 4 power pulses for each 360 degree revolution of the crankshaft. It doesn't have 8 like you might think, because it's a 4-cycle motor. With any given cylinder in your motor, it takes about 180 degrees to pull in the fresh fuel/air mixture, 180 degrees to compress the mixture, 180 degrees to push down on the piston and transfer work to the crankshaft and 180 degrees to push the burned mixture out of the cylinder. 4 times 180 degrees equals 720 degrees to complete a cycle, or 2 complete 360 degree revolutions of the crankshaft. So, for each 1 revolution of the crankshaft, only 4 of the 8 cylinders in your motor will have fired to produce work.
I don't want to confuse you, but I have to explain it that way in order for you to do some calculations on your own. We'll use a 2.73 and a 3.73 rear gear for this explanation.
Now, let's pick any given rpm of the motor, we'll use 3,000 rpm's. The crankshaft is turning 3,000 rpm's, so 3,000 times 4 will equal 12,000 power pulses that the motor is producing in 1 minute.
Now, divide the 3,000 rpm's the motor is producing by the gear ratio 2.73 and you find that the tire is turning 1,099 rpm's. If we assume a 88" circumference tire (28" tire diameter times 3.14159), then the tire is traveling 96,712 inches at the given 3,000 motor rpm's with a 2.73 gear. (88 times 1,099). If it's getting 12,000 power pulses per minute at that motor speed, then dividing 96,712 by 12,000, the tire is getting a power pulse each 8.059 inches of its circumference or a total of 10.9 power pulses for each 1 revolution of the tire.
Using the 3.73 gear (shorter), the tire is turning 804 rpm's under the same conditions (3,000 divided by 3.73) and rolling 70,752 inches (88 times 804). Getting the same 12,000 power pulses, divide 70,752 by 12,000 and find that the tire is getting a power pulse each 5.896 inches of its circumference or a total of 14.9 power pulses for each 1 revolution of the tire.
Now you can see, with the shorter gear, more work is being applied to the tire with each revolution of the tire. More work equals quicker acceleration.
For the same crankshaft speed, the taller gear (2.73:1) will allow the car to go faster, but not get there as quickly. The shorter gear (3.73:1) will allow a slower top speed, but will get there in a hurry.
In addition to more power pulses, the numerically lower gear will multiply the torque in a direct ratio to the the amount of gear change. Take an engine that produces 400 ft/lbs torque with no gear reduction. With a 3.00 rear gear ratio, it will out put 3 times the torque at the wheel. If the same 400 ft/lb engine has 4.00 gears behind it, the torque will increase 4 times producing 1600 ft/lbs of torque. The downside is the reduction in wheel speed, now at 75% the original speed for the same engine rpm's. EXAMPLE: A motor turning 5,000 rpm's with a 3.00 gear and 88" circumference tire has a terminal speed of 138.88 mph. A motor turning 5,000 rpm's with a 4.00 gear and 88" circumference tire has a terminal speed of 104.16 mph, a reduction in terminal speed of 25%.