Let's establish a few facts first, straight from the discipline of contemporary Physics.
No header/exhaust system is ideal for all applications. Depending on their design and purpose, all exhaust/header systems compromise something to achieve something else. Before performing header or other exhaust modifications to increase performance, it is critical to determine what kind of performance you want. Do you want max low RPM power for chugging around town casually like a Harley? Not likely if you ride a BSA! Do you want max mid-range power for ease of passing while cruising down an Interstate highway? Do you want max peak-RPM power for top speed and/or bragging rights? Maybe you just want an exhaust that looks cool. Or do you want the best of all worlds? In the latter case, a well-designed aftermarket exhaust system is where you'll find it.
If you are wowed only by peak HP numbers on a dyno chart, consider the following: For a vehicle to cover "X" distance as quickly as possible, it is not the highest peak power generated by the engine that is most critical. It is the highest average power generated across the distance that typically produces the quickest time. When comparing two power curves on a dynamometer chart (assuming other factors remain constant), the curve containing the greatest average power is the one that will typically cover the distance in the least time. This fact is what makes the nature of the power band important. You don't want to give up powerful mid-range performance just to have the highest peak power numbers--that's only good for bragging rights and will kill your acceleration because most time spent accelerating is in the mid-range, not at peak-power RPM. Actually, we want both (maximum mid-range power and maximum peak power), don't we? I'll answer for you--YES!
In the strictest technical sense, an exhaust system cannot produce more power on its own. The potential power of an engine is determined by the amount of fuel available for combustion. More fuel must be introduced to increase potential power. However, the efficiency of combustion and engine pumping processes is profoundly influenced by the exhaust system. A properly designed exhaust system can reduce engine pumping losses. Therefore, the primary design objective for a high performance exhaust is (or should be) to reduce engine-pumping losses, and by so doing, increase volumetric efficiency. The net result of reduced pumping losses is more power available to move the vehicle. As volumetric efficiency increases, potential fuel mileage also increases because less throttle opening is required to move the vehicle at the same velocity. This is where the old bugaboo of back-pressure rears it's ugly, mythical head. Much controversy and confusion surround the issue of exhaust back-pressure which, in other terms, is a pumping loss. Many performance-minded people (including some "professionals") who are otherwise well-enlightened still cling tenaciously to the old cliché "You need some back-pressure for best performance." WRONG--period > if your definition of "best" performance is "maximum power throughout the power band".
For virtually all high performance purposes: back-pressure in an exhaust system increases engine-pumping losses and thereby decreases maximum engine power. Are we clear about this?
Here is something to chew on: Theoretically, in a normally aspirated state of tune without special fuel or oxygen-rich additives, an engine’s maximum power potential is directly proportional with the volume of air it flows. This means that an engine of 750 cc has the same maximum power potential as an engine of 1000 cc that is if they both flow the same volume of air. In this example, the power band characteristics of the two engines will be quite different but the peak attainable power is essentially the same. In view of this reality, I have amended the old hot rod proverb "There's no substitute for cubic inches" "except there is more efficiency!"
Many "performance" people resist some of these notions but their resistance does not change reality nor the laws of physics.
Are you still awake? Okay, let's establish a few Rules of Thumb.
1- Longer header tubes tend to increase power below the engine’s torque peak and shorter header tubes tend to increase power above the torque peak.
2- Large diameter headers and collectors tend to limit low-range power and increase high range power. Conversely, small diameter headers and collectors tend to increase low-range power and limit high-range power.
3- "Balance" or "equalizer" tubes between the header tubes tend to flatten the torque peak(s) or widen the power band.
4- Stainless headers do not transfer heat to the ambient air as fast as mild steel headers. Keeping more of that heat "inside" the header pipes and aids exhaust flow because the exhaust gas is more energetic and it reduces the amount of heat flowing across the engine (and across you).
The objective of most engine modifications is to maximize air and fuel flow into, and exhaust flow out of the engine. The inflow of an air/fuel mixture is a separate issue, but it is directly influenced by exhaust flow, particularly during valve overlap (when both valves are open for "X" degrees of crankshaft rotation). Gasoline requires oxygen to burn. By volume, dry, ambient air at sea level contains about 21% oxygen, 78% Nitrogen and trace amounts of other gases. Since oxygen is only about 1/5 of air’s volume, an engine must intake 5 times more air than oxygen to get the oxygen it needs to support the combustion of fuel. If we introduce an oxygen-bearing additive such as nitrous oxide, or use an oxygen-bearing fuel such as nitro methane, we can make much more power from the same displacement because both additives bring more oxygen to the combustion chamber to support the combustion of more fuel. If we add a supercharger or turbocharger, we get more power for the same reason and more oxygen is forced into the combustion chamber.
Perhaps the most important aspect of exhaust flow is the issue of flow volume vs. flow velocity. This also happens to apply equally to intake events.
An engine needs the highest flow velocity possible for quick throttle response and torque throughout the low-to-mid range portion of the power band. The same engine also needs the highest flow volume possible throughout the mid-to-high range portion of the power band for maximum performance. This is where a fundamental conflict arises. For "X" amount of exhaust pressure at an exhaust valve, a smaller diameter header tube will provide higher flow velocity than a larger diameter tube. Unfortunately, the laws of physics will not allow that same small diameter tube to flow sufficient volume to realize maximum potential power at higher RPM. If we install a larger diameter tube, we will have enough flow volume for maximum power at mid-to-high RPM, but the flow velocity will decrease and low-to-mid range throttle response and torque will suffer (the "back-pressure" myth probably arises from a misunderstanding of these factors). This is the primary paradox of exhaust flow dynamics and the solution is usually a design compromise that produces an acceptable amount of throttle response, torque and horsepower across the entire power band.
Guess what? There's more. It's called scavenging and it's complicated.
Inertial scavenging and wave scavenging are different phenomenon but both impact exhaust system efficiency and affect one another. Scavenging is simply gas extraction. These two scavenging effects are directly influenced by tube diameter, length, shape and the thermal properties of the tube material (stainless, mild steel, titanium, etc.). When the exhaust valve opens, two things immediately happen. An energy wave, or pulse, is created from the rapidly expanding combustion gases. The wave enters the header tube (or manifold) traveling outward at a nominal speed of 1,300 - 1,700 feet per second (this speed varies depending on engine design, modifications, etc., and is therefore stated as a "nominal" velocity). This wave is pure energy, similar to a shock wave from an explosion. Simultaneous with the energy wave, the spent combustion gases also enter the header tube and travel outward more slowly at 150 - 300 feet per second nominal (maximum power is usually made with gas velocities between 240 and 300 feet per second). Since the energy wave is moving about 5 times faster than the exhaust gases, it will get where it is going faster than the gases. When the outbound energy wave encounters a lower pressure area such as a larger collector pipe, muffler or the ambient atmosphere, a reversion wave (a reversed or mirrored wave) is reflected back toward the exhaust valve with little loss of velocity.
The reversion wave moves back toward the exhaust valve on a collision course with the exiting gases whereupon they pass through one another, with some energy loss and turbulence, and continue in their respective directions. What happens when that reversion wave arrives back at the exhaust valve depends on whether the exhaust valve is still open or closed. This is a critical moment in the exhaust cycle because the reversion wave can be beneficial or detrimental to exhaust flow, depending upon its arrival time at the exhaust valve. If the exhaust valve is closed when the reversion wave arrives, the wave is again reflected toward the exhaust outlet and eventually dissipates its energy in this back and forth motion. If the exhaust valve is open when the wave arrives, its effect upon exhaust gas flow depends on which part of the wave is hitting the open exhaust valve.
A wave is comprised of two alternating and opposing pressures. In one part of the wave cycle, the gas molecules are compressed. In the other part of the wave, the gas molecules are rarefied. Therefore, each wave contains a compression area (node) of higher pressure and a rarefaction area (anti-node) of lower pressure. An exhaust tube of the proper length (for a specific RPM) will place the wave’s anti-node at the exhaust valve at the proper time for it’s lower pressure to help fill the combustion chamber with fresh incoming charge and to further extract spent gases from the chamber via vacuum effect. This is wave scavenging or "wave tuning".
From these cyclical engine events, one can deduce that the beneficial part of a rapidly traveling reversion wave can only be present at an exhaust port during portions of the power band since it's relative arrival time changes with RPM. This makes it difficult to tune an exhaust system to take advantage of reversion waves which is one reason why there are various anti-reversion schemes designed into some header systems and exhaust ports. These anti-reversion devices are designed to weaken and disrupt any detrimental reversion waves (when the wave's higher-pressure node impedes scavenging and intake draw-through). Such anti-reversion schemes include merge collectors, truncated cones/rings built into the primary tube entrance and exhaust port ledges.
Unlike reversion waves that have no mass, exhaust gases do have mass. And since they are in motion, they also have inertia (or "momentum") as they travel outward at their comparatively slow velocity of 150 - 300 fps. When the gases move outward as a gas column through the header tube, a decreasing pressure area is created in the pipe behind them. It may help to think of this lower pressure area as a partial vacuum and one can visualize the vacuous lower pressure "pulling" residual exhaust gases from the combustion chamber and exhaust port. It can also help pull fresh air/fuel charge into the combustion chamber. This is inertial scavenging and it has a major effect upon engine power at low-to-mid range RPM.
If properly timed with RPM and firing order, the low pressure that results from gas inertia can spill-over into other primary tubes, via the collectors, and aid the scavenging of other cylinders in that bank.
There are other factors that further complicate the behavior of exhaust gases. Wave harmonics, wave amplification and wave cancellation effects also play into the scheme of exhaust events. The interaction of all these variables is so abstractly complex that it is difficult to fully grasp. I am not aware of any absolute formulas/algorithms that will produce a perfect exhaust design. Even factory super-computer exhaust designs must undergo dynamometer and track testing to determine the necessary tube adjustments for the desired results.
We all are the benefactors of all this technical information. Be glad that there are bright minds in the world whom sort it out for us.