Because the tC exhaust is constructed of stainless steel individual tubes, it is considered a header. Just like the term coilover is misused frequently, header is also misused. FYI, all McPherson strut suspensions are coilover because coilover just means the spring is concentric with the damper. Saying you want coilovers for the tC doesn't make sense, it came that way from the factory. Same with the header issue, It came that way from the factory.
The header's job is to remove exhaust gases from the combustion chamber in a controlled fashion. I think we all agree here. The part needing clarification is the backpressure issue, and the elements of the header design and how they affect the engine's ability to make power.
So, how does the engine make power? A fuel/air mixture is ignited creating a high pressure region directly above a piston which creates a force on the piston dome. If we've done everything right, the piston moves down swiftly and transfers the force to the crank. While the piston is moving downward a couple of things are happening:
1. The volume of the trapped, expanding gas is increasing
2. The heat generated by the mixture burn is being turned into kinetic energy and being absorbed by the engine's components in direct contact with the gas.
These are the two most important thermodynamic effects. So how does the header design affect this process? When the exhaust cam opens the exhaust valve, there is still pressure in the cylinder from the expanding combustion process. This is called blowdown because there is a very strong gas pulse created in the exhaust by the (usually large) pressure differential between the exhaust system and the cylinder. The ability of the exhaust system to create this pressure differential is what discriminates between good and bad.
The ideal exhaust system will provide a very low pressure somewhere in a vacuum range to extract as much of the combustion effluents as possible. If we really get it right, we'll actually be able to use this process to pull fresh intake into the cylinder at overlap (the time when the exhaust valve and intake valves are open at the same time) because we have developed a very large pressure differential between the intake manifold and the exhaust. If we get it wrong (well, maybe not wrong, but that's a different discussion), we get natural EGR (exhaust gas recirculation) because the inert exhaust gases left in the cylinder will dampen the combustion process in the next cycle.
Now to the hard question, why do people believe backpressure is necessary? Because they've read in some magazine that an oversized exhaust can negatively affect performance from a loss of backpressure. Nothing could be more inaccurately stated. As Tchi mentioned, an overly large exhaust affects exhaust velocity. One of the fundamental exhaust concepts is the exhaust is a series of pulses, not a continuous stream. Those pulses can be engineered to control exhaust pressure through the exhaust system, and pressure control for blowdown is critical to performance.
BTW, I define performance as thermal efficiency, not maximum measured power. Generally improved thermal efficiency leads to more measured power, but not always.
So our header gives us the opportunity to manage when and where high and low pressure areas exist at any given point in time. It also gives us the opportunity to optimize when blowdown occurs. If the exhaust is "restrictive" because it is designed to optimize low rpm torque, blowdown is slower to permit the pressure on the piston to remain longer. If it is "freeflowing" it is optimized to get the exhaust gases out of the cylinder as quickly as possible consistent with creating a low pressure region in the cylinder at overlap. Neither is right or wrong, they are just different for different applications. The header features most important to this part of the process are diameter and length of primary tube. Larger diameters tend to favor high rpm torque, longer primary tubes tend to favor low rpm torque. The header designer has to strike a balance between low and high rpm operation with the primary tube diameter and length.
The other thing a header does is allows the designer to use the exhaust pulses of other cylinders to affect the cylinder actually having an exhaust event. By combining primary tubes with complementary pulses, it is possible to further control the location and size of high and low pressure regions. This is sometimes called extraction. The idea is to use the exhaust pulse from another cylinder to "pull" the exhaust from the next. This is part of the theory behind 4 - 2 - 1 headers for 4 cylinder engines. By merging the complementary (360 degree apart firing events) cylinders in pairs before merging them into the final collector, the header provides better "scavenging." Scavenging is a term used to simply describe creating a very low pressure region in the combustion chamber at the right time and thereby ensuring the most complete extraction of inert exhaust gas.
Break time, this post is getting too long. I'll finish later.
The other thing going on with extraction is again, controlling when and where the pressure zones exist. In our ideal model, we have our lowest pressure zone at the exhaust valve seat when the intake starts to open. This encourages the fresh fuel/air mixture to move into the cylinder and jump starts the intake process. When you are really on top of your engine's tuning and you know where in the rpm range it is most important to make power, you can use this to get better than 100% volumetric efficiency, meaning you get more air than if you filled the cylinder at ambient pressure. It's a sort of supercharging effect all tuners like to find because it makes a smaller engine breathe like a larger one.
I touched briefly on EGR. Something important to our tC engine is Toyota uses VVTi to create EGR effects without having an EGR system as most cars do. This seriously complicates the trade-offs the header designer will have to make for the tC and any other car using this engine managment system. Without having a clear understanding of what VVTi doe to perform EGR, a different header may have some very undesirable effects while still delivering a better peak power number.
If any of you have tuned EFI systems, you know it is really easy to get an engine to run with EFI, and it's pretty straight-forward to get WOT to work well. It is far from easy to get good driveability under a wide range of operating conditions. It is extremely difficult to make a change to a system as carefully integrated as a modern engine with variable cam timing and drive-by-wire throttle without upsetting the reliability of the engine to perform under a wide range of operating conditions. Tchi has a perfect example, he drives up and down a 5000' climb on a regular basis. That's a HUGE difference in operating conditions for an engine.
With this in mind, don't expect to install a header and/or aftermarket exhaust and have the same basic reliability with more power. Designing the parts is far from simple, and few, if any, of the aftermarket parts sources can perform testing to equal the manufacturers. Expect there will be problems, and you will be basically unsupported by Toyota (unless the mods say TRD on them). An engine is a symphony of parts. It is very easy to make the symphony nothing but noise with just a few imprudent changes.
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