[NVDucati]

Did you simply Google something along the lines of "Helmholtz resonator exhaust formula" or similar?   


It is ugly indeed.   


I'm not sure I understand the wording of this statement.  You're referring to hiding the offensively unattractive exhaust tip inside a larger exhaust cone, I assume.  But what does "it is a final, zero-flow-resistance, smashing against the ground of the sound waves" exactly mean?

Apologies if I'm being obtuse.



Most welcome.  But thank YOU for your comment!

Yeah, your search for a usable, more simple formula will come from sites dealing with factory noise and the muscle car crowd. They get "droning" at specific speeds. They have various formulas that you can scale to. The audio speaker crowd will just drive you crazy and you can pretty much ignore them.
   In a practical sense, the photo of the bike you are working on has a straight shot to the rear. That's handy. You can get some sections of pipe from a place like Cone Engineering and a exhaust pipe expander to form a slip fit. Have a couple of them for experimentation. The Akripovic guys use the same size pipe for their tubes. I had a hard time getting myself to second guess the exhaust gods but I disagree with that approach. The horizontal section of my tube is smaller than the exhaust pipe and the "connector" tubes (perpendicular) are smaller again. My, un-provable, theory is that I get the same "collision factor" as they do but two extra expansion moments. (might not even matter)
It also comes down to space available. You have plenty of space so you might decide to have two resonator tubes, one for 4000RPM and another for 11,000RPM.
    As for the downspout, setting aside some fractional gas friction at the turn, having the exhaust gas (really the sound waves) aimed at the ground breaks them up yet again and the crevices in the pavement act as additional baffles to scatter the sound waves further. Think of it as a flashlight beam reflecting off a carpet. And those same sound waves are also having to survive the air turbulence created locally by your tire. So there you have it. Start welding.

[AzCal Retred]

From @ #8 to @ #11:


https://www.sciencedirect.com/topics/engineering/helmholtz-resonator

[ace.cafe]

Its will be difficult to get enough air mass and diameter in such small resonators to have much effect on anything but higher frequencies.

A fishtail tailpipe is aimed at shaving high frequencies if that is the goal.

[AzCal Retred]

This Zontes R310 single cylinder sport bike seems to have grafted on enough extra pipe, maybe that's about what a functional factory resonator might look like.

So the basic open fishtail mainly takes the "crack" out when spinning the motor up a bit? How does the Brooklands fit in here, it's "sort of" a fishtail, but with perforations and a resonator section.

[ace.cafe]

This Zontes R310 single cylinder sport bike seems to have grafted on enough extra pipe, maybe that's about what a functional factory resonator might look like.

So the basic open fishtail mainly takes the "crack" out when spinning the motor up a bit? How does the Brooklands fit in here, it's "sort of" a fishtail, but with perforations and a resonator section.

The Brooklands silencer has the expansion chamber to trade velocity for pressure, and then the fishtail to tame the high freq's.
If the expansion chamber is at least 15x displacement, the engine sees it as if it were exiting the exhaust into free air.

[Richard230]

The Brooklands silencer has the expansion chamber to trade velocity for pressure, and then the fishtail to tame the high freq's.
If the expansion chamber is at least 15x displacement, the engine sees it as if it were exiting the exhaust into free air.

That is interesting. I always wondered how those Brooklands silencers worked. And now I know. Thanks, Ace.