Lets do step #1, selecting the primary tube size. This is no simple task, so I'm going to provide a bunch of info, and then take my best guess based on what I'm trying to design into the header. This design target is low to mid range power, 2000-3000 rpm is generally the range I'm targeting.
My info from Ed says that for the horsepower each cylinder produces (math is 55 engine horsepower / 3 cylinders = 18.3 horsepower per cylinder or tube) I should use 1.25" OD tubing. However, I'm on the very low end of the range of power for 1.25" tubing size, so its safe to say I could downsize that. Unfortunately, 1.25" tubing is the lowest on his chart, so that leaves some guessing up to me. This is also for a higher rpm producing header. I care little about that, I want more torque in the mid and low range. So, I'm going to downsize my tube.
Another source of sizing exhaust tube size is found here:
How To Calculate Muffler Size and Exhaust Pipe Diameter - Exhaust Videos | Exhaust Videos
This chart is for exhaust piping in general, but we can use it for our header design. Again, his chart only goes down to 1.5" tube. However, I extended his chart down to 0.5" tube using his calculations in an excel document. The key when looking at this chart is each square inch of tube area gives ~115 CFM of flow.
According to this chart, I should be looking at 0.75" 16ga tubing.
So, wait a minute! These two estimates are very different. Why is that? I believe the two designers are targetting two different flow velocities. This is the speed of the exhaust gas inside the exhaust tube. Too fast of a flow velocity and you get excessive back pressure which causes the engine to have to push harder to get the exhaust gas out. Too low a flow velocity and you don't get good scavenging effect, your exhaust gas cools and then becomes more dense and more mass to push out the exhaust tube, and a few other things. Our goal is to balance these two.
To find the flow velocity of your engine and tube size, you'll need to do two calculations.
1) Find your flow rate for each cylinder. This is roughly equal to 2.2 CFM per engine horsepower (per exhaustvideos). Now divide by the number of cylinders.
2) Find your velocity.
Velocity calculator here. Directions: solve for velocity, put your CFM in from the above calculation and your tube inner diameter in the other field.
Most articles say to target ~250 feet per second (FPS) for peak torque. Using Ed's sizing, our flow rate is around 200 FPS. Using the exhaustvideos calculation, its around 275 FPS. But, these are values at max rpm and wide open throttle (WOT). The thing is, for a fuel economy header, we're again tuning for a lower rpm, roughly half of peak rpm. This translates into roughly half the flow, and thus half the flow velocity. So, I could probably go with 5/8" OD 16ga tubing and call it good.
(Yes, my name is Timothy
)
This seems ridiculously small, but if I measure the exhaust tube on my 1981 Honda CM400 which has a 42 horsepower 2 cylinder engine, the outlet's inner diameter is 9/16" (there are two exhaust tubes), so I don't think I'm too far off.
Sadly, I haven't been able to find any information that says "don't exceed this velocity", or "after X FPS you start getting Y psi of back pressure". So, I can't really design to that factor.
Now, when searching for actual parts for the header, I was only actually able to find 3/4" OD 16ga mandrel bent 304 stainless tube. This gives me 320 FPS at max power output (5700 rpm). So I should have ~250 FPS around 4450 rpm. That is pretty high for me, but since I haven't been able to find smaller tube it'll have to be good enough, and its certainly smaller than the stock setup. So, that is pretty much that... 3/4" 16 gauge stainless it is.
Also, please keep in mind that these are very rough calculations. This is by no means a super specific guide. Real header builders calculate tons more stuff like valve diameter, cam lift and duration, bore and stroke, and lots more stuff. This is by comparison very rough.