A basic understanding of how...
A basic understanding of how to tap into an exhaust system's capability to act as a simple supercharger is instrumental toward generating race-winning power.
Long before having anything to do with V-8s inflicted with undersized carbs or restrictor plates, I built an engine to the highly restrictive European Formula 111 Single Seater rules that existed in the late '60s. The build produced 112 horses at around 9,600 rpm from a pushrod, four-cylinder 60-incher-all through a single orifice of, if I remember correctly, some 22 mm (about 7/8 inch). For its day, that was a competitive output.
I learned a lot from that engine, which by 1972 had, in unrestricted form (130 hp at 9,300 rpm), found its way into my ground-effect road race Ford Anglia. Because the engine proved reliable, it spent more time being refined on the dyno than would have otherwise been the case.
What I learned reinforced the importance of three power-related factors: 1. the need for effectively flowing large quantities of air from the point of induction to the tip of the exhaust; 2. the need to understand what factors affect optimal valve events; 3. the importance of proportioning the exhaust system to utilize the considerable pressure/kinetic energy contained in what is so often erroneously referred to as the spent exhaust charge.
The vertical red lines represent...
The vertical red lines represent the BDC starting point of a cylinder's exhaust stroke, and the number beside it refers to the cylinder number to which it pertains. The crank rotation between 1 and 3 cylinders is 270 degrees. Between 3 and 5 it is 180 degrees, and from 5 to 7 only 90 degrees. From 7 back to 1 is 180 degrees. Note how the pulses shown in green from cylinders 5 and 7 overlap to the extent that they form one longer and larger pulse.
If ever there was a word used out of context, it is spent in this reference. In reality, there is a very substantial amount of potential energy contained within the cylinder at the point the exhaust valve is opened. Unless you already know, the first thought to come to mind here is, Why not hold the exhaust valve closed longer to allow the pressure to act on the piston area longer? On the face of things, this looks like a totally reasonable question. But the bottom line is that unless the cylinder is given enough time to "blow down," the piston will have to expend power to push out the exhaust. In practice, we find that for an effective exhaust stroke (i.e., one that loses the minimum amount of power) the cylinder pressure at BDC needs to be less than about 15 psi above atmospheric. That's a number I could not really quantify until the advent of more readily available rapid response in cylinder pressure measurement a decade or so after the Formula build.
So, how much energy are we talking about here? Assuming a typical induction-limited (say a carb flow of 450 cfm) late-model engine, the amount of gas pressure that is dumped into the exhaust system at 6,000 rpm is equivalent to around 50 hp. But is there potential to harness any of the exhaust energy to do something useful toward making more power? The answer, as you might expect, is most definitely yes.
In the mid '70s, when I went from working predominantly on four-cylinder race engines to V-8s, one thing quickly became clear. Namely, a V-8 with a separate and independent exhaust system for each bank of cylinders is not two four-cylinder engines. In fact, it isn't even close. Why? Because the two-plane crank commonly used means uneven spacing between the firing pulses down each bank. Take a look at Figure 1. This shows the exhaust pulses as seen in the collector.
Just so we are all on the...
Just so we are all on the same page, here are the dimensional factors we are going to deal with.
As you can see, the exhaust pulses experienced by the collector are not at a consistent frequency, nor are they the same size as No. 5 and No. 7 combine to form one big pulse. The implication is that at least the collector is not likely to work in quite the same manner as a similar-appearing header on a four-cylinder engine. If it comes to that, the primaries of cylinders 5 and 7 may also be functionally different. It could be that if these two cylinders each had a short primary that joined into a secondary of a slightly larger diameter that then went on to a conventional collector (to make a 4-3-1 system), we may have something that makes more power. Then again, it may not-I certainly don't have a budget to try all the possibilities here.
So this leaves us with a key question. My screamer F111 used primaries 22 inches long that dumped into a 15-inch-long, 4-degree megaphone secondary. Just how closely to this engine's exhaust system would a V-8 system react? Let's find out if the basic rules for a four-cylinder system still hold true.
Although other factors are involved, a successful exhaust system is mostly about dimensions. The photo below shows the critical dimensions and other factors we are going to consider. The dyno tests involved are from tests done over a number of years, with several different engines hopefully within the most significant horsepower range for the most readers.

Here, three primary diameters...

Here, three primary diameters are tested. The 1 5/8 diameter is shown in blue, the 1 3/4 in green, and the 1 7/8 in red. Going a little too big cut the torque from the test start point at 3,000 rpm all the way to around 5,600 rpm.

These curves show the results...

These curves show the results of 18- (black curves), 29- (green), 32- (red), and 38-inch-long headers (blue). Although the length required is not fussy between 29 and 38 inches, it is obvious that when a conventional 4-into-1 system is involved, V-8s do not like short headers.

These tests show that the...

These tests show that the use of an overly large secondary or collector cuts low-speed output all the way to peak power rpm. A collector that is slightly too small helps low speed while costing a minimal amount elsewhere.