Firstly, you should know why we want to change the exhaust to a high performance setup.. Every vehicle of any make/model that rolls off of the production line has an ill equipped air intake and exhaust system. Restrictions are put in place on both of those systems to limit the amount of noise a consumer will hear. I suppose auto manufacturers have to appeal to a very broad audience as far as buyers, so they make the vehicle as quiet as can be.. The problems with that is: IT REDUCES YOUR VEHICLES POWER AND GAS MILEAGE!
A simple understanding of VOLUMETRIC EFFICIENCY (VE) can help you understand why you can get better power and/or fuel economy by helping your engine breathe better. Volumetric efficiency is basically a ratio (or percentage) of what amount of fuel/air is being drawn into your engine as compared to the actual capacity that is possible. Think about breathing through a straw. Sure you can do it just fine while your sitting down on the couch vegging out, but if you decide to go jogging then its just not going to work out so great is it?
When we eliminate the restrictions on the air intake system, we allow the engine to BREATHE much easier. We do this by putting a high flow performance air intake system on the vehicle. The amount of air that it will draw in naturally will be increased because there are no more intake resonators (restrictions used to quiet suction noise) or restriction stock paper air filters for the air to try to get through. By having more air entering easier than it used to you will not have to apply as much throttle to get up to speed. This is where your mileage can increase. Now when you want to have some fun and mash that pedal to the floor - you will have much more air available to create more power which is just plain fun. Gas mileage does not really increase when you drive like this though :(
Alright. Now, the engine can breathe in easier. Next order of business: HELP THE ENGINE EXHALE. The design of factory exhaust systems is horrible for the most part. All sorts of restrictions built in to keep that SUCK-PUSH-BANG-BLOW quiet. Mufflers are usually the most restrictive part of a stock exhaust system. The exhaust gasses basically have to maneuver its way through a series of walls, chambers, louvers, baffles, and other maze-like flippety-doo's.. This needs to be fixed!
**A note on catalytic converters: Many people are under the mistaken impression that the converter is the 'bad-guy' that is restricting your power and want to remove it. DON'T! Converters on almost all late-model vehicles are designed with HIGH-FLOW catalyst biscuits. They offer just the right amount of back-pressure needed to maintain some bottom range torque, yet flow free enough to not hinder performance at the higher RPM range. Do your research and if you find that your converter is of a bad design then do the smart thing and upgrade - Not remove! I won't even get into EPA mandated laws and fines and violations etc...
There are lots of other factors that help with the power/mileage aspect of VE such as exhaust scavenging and valve overlap, but if you want to learn more you should do some surfing.