Black & Tan 332iT

[Bry5on]

How come welding a very rigid piece of metal in the middle of large, uninterrupted pieces of the exhaust can't achieve the same effect? I'm not a physics or mechanical major, but i thought doing so would change the length of the vibrating piece and therefore the resonant frequency. IE. A 1ft piece resonates at 1hz but two 0.5ft pieces will resonate at 2hz.


This was my original idea to kill my headache inducing drone at 2500-2800rpm on my M3, but I ended up buying a stock section 2 (still to be installed)

You can certainly add another resonating part to the exhaust, like welding a tuning fork on which would add new resonant frequencies but not necessarily remove or materially affect any existing ones. This mechanical resonance is a bit different than acoustic resonance but they’re very related in concept (wave propagation vs mechanical stiffness). You can tune out acoustic resonances by adding pipes of certain length (quarter wave length) to effectively cancel out certain frequencies, like the damper is doing for mechanical resonance. To kill an acoustic resonance you’d need to understand the frequency of the sound that’s loud, rather than just the speed of the motor, even though they’re related.

You’ll also note that the modern M cars have exhausts without dampers but they do not resonate (in these frequency ranges). This is because the pipes are far apart from each other, so they are stiff like an I beam. Our exhausts are flimsy because the pipes are so close together for the whole length. The stiffer the ‘beam’, the higher the natural frequency. Ideally it’s so high that the first mode is higher than the engine’s operating rpm.

Think of how much easier a 2x4 or 2x6 bends along its thin edge than its thick edge

[YoitsTmac]

Oh wow you're right! I'd mistakenly thought that both auto and manual tied to the transmission. Yes, this would definitely make a difference! The natural frequencies would be slightly shifted higher for the manual in this case, something like ~2100 and ~5800 rpm instead of 1900 and 5400, if I had to guess. This is due to having a shorter suspended length (to the factor of 1/L^2).

How come welding a very rigid piece of metal in the middle of large, uninterrupted pieces of the exhaust can't achieve the same effect? I'm not a physics or mechanical major, but i thought doing so would change the length of the vibrating piece and therefore the resonant frequency. IE. A 1ft piece resonates at 1hz but two 0.5ft pieces will resonate at 2hz.


This was my original idea to kill my headache inducing drone at 2500-2800rpm on my M3, but I ended up buying a stock section 2 (still to be installed)

[Bry5on]

Could it be because the MT connects to the transmission where the auto just connects to itself up in that area?

Oh wow you're right! I'd mistakenly thought that both auto and manual tied to the transmission. Yes, this would definitely make a difference! The natural frequencies would be slightly shifted higher for the manual in this case, something like ~2100 and ~5800 rpm instead of 1900 and 5400, if I had to guess. This is due to having a shorter suspended length (to the factor of 1/L^2).

[George Hill]

Could it be because the MT connects to the transmission where the auto just connects to itself up in that area?

[Bry5on]

While we're talking about exhaust resonance, for the fellow nerds out there:

A non-m e46 actually has two dampers if it's an automatic and one damper if it's a manual. So an auto e46 should feel smoother throughout the rev band than a manual because the exhaust system is otherwise identical (weight, size, shape, supports). The automatic has both #4 (at muffler) and #12 (at resonator) dampers in this image, where the manual only has #12.



Here's the nerd part: The muffler damper is tuned to 32Hz and the resonator damper is tuned to 60Hz. In an earlier thread we discussed first, second, third, etc frequency resonant modes/natural frequencies. A rough approximation for the second and third modes is 2* and 3* the first natural frequency due to the mass being concentrated at the end of the exhaust. Recall this image (it's technically slightly incorrect, but you get the idea) and note that the largest oscillations for the first and third mode are at the END of the vibrating member, while the second mode oscillates at the MIDDLE of the vibrating member:



So here we can see the the non-m e46 has a first resonant mode around 32Hz, a second mode around 60Hz and a third mode around 90Hz. This corresponds to 1920rpm, 3600rpm and 5400rpm respectively.

So why the difference between manual and automatic? Likely that the vibrations higher in the rev range around 5400rpm make the engine feel more sporty, and the manual car is the sporty version, so they left the damper out that would have otherwise arrested the first and third mode. The automatic has dampers that should be arresting all primary natural frequencies of the exhaust that are excited by the rotation and firing of the engine. This is one of the major things that makes the automatic cars so buttery smooth.

Thanks for reading, hope this was as interesting for you as it was for me.

[0-60motorsports]

I think they've been out of production for 15+yrs

Oh wow. They really look like art.

[George Hill]

Nice! are they still making those headers?

I think they've been out of production for 15+yrs

[0-60motorsports]

The only reason I initially S54 swapped my wagon was because I had a set of Kromer Kraft headers. They were old and tired but sounded amazing. They needed some repair and were pulled in favor of a "temporary" euro setup. I think that was 4yrs? ago, lol. My spring goal is to get them back on and I'm probably going to make a muffler to quiet everything down as I can't really buy anything I like at least that I can find.

Going from E36 to ZHP, I think there's room on the table to make more power and be similar sound level even if you are guessing at some parts of the design. IIRC we saw a ZHP left 15whp on the table vs a Stromung conversion muffler, Dinan or BMW Performance mufflers (E36 was even more than that).

Nice! are they still making those headers?

[Bry5on]

What is a shear plate?

That aluminum plate that ties the subframe to the frame rails. Which reminds me, I also want to design a flat sheet to close that M3 plate out and stiffen it up like the non-m plate

[George Hill]

I guess one of us needs to scan an s54 without headers installed with the shear plate....

What is a shear plate?

[Bry5on]

Unfortunately it makes no torque lol. HTE couldn't get it to make any power up top but I have some graphs from similar setups make a ton of HP up top (Epic Tune) so I'm not sure what the problem was. The consensus seems to be the 2-1 merge kills the torque but makes the noise so I'm conflicted haha. I was thinking about making a second 2-1 merge that is either bigger or to carry it out longer.

I think this kit is for an E36 and I've made it work in the E46 chassis. I don't know how different it is from his E46 kit (or if there is a difference at all), but it would be hard to package in an E46. This one is going to require a custom A/C line (and I had to cut the metal partition).

I guess one of us needs to scan an s54 without headers installed with the shear plate...

Modeling equal length headers shouldn't be very tough and there are a few online suppliers that do custom mandrel bent tubing nowadays. Should be a lot easier now than it was back in the 2000s and 2010s.

[George Hill]

"Was that a flame? Oh, yeah, well of course there's an exhaust pipe coming from the side skirt."

That 6-to-1 looks so good... tempting.

Haha, ya its ridiculous but so much fun. I'm trying to tame it down without losing its character though. And its splitting hairs but its actually a 6 - 2 - 1

wow that sounds buttery smooth, almost more like an s38 than an s54. Always preferred the s38 exhaust note. I like it!

Unfortunately it makes no torque lol. HTE couldn't get it to make any power up top but I have some graphs from similar setups make a ton of HP up top (Epic Tune) so I'm not sure what the problem was. The consensus seems to be the 2-1 merge kills the torque but makes the noise so I'm conflicted haha. I was thinking about making a second 2-1 merge that is either bigger or to carry it out longer.

I think this kit is for an E36 and I've made it work in the E46 chassis. I don't know how different it is from his E46 kit (or if there is a difference at all), but it would be hard to package in an E46. This one is going to require a custom A/C line (and I had to cut the metal partition).

[Bry5on]

https://www.youtube.com/watch?v=mLs6hziC6is

So lazy with the 6MT and 3.15 diff, lol

https://www.youtube.com/watch?v=s6XZn8W12wk

wow that sounds buttery smooth, almost more like an s38 than an s54. Always preferred the s38 exhaust note. I like it!

[bmwfnatic]

Ok - very cool...

"Was that a flame? Oh, yeah, well of course there's an exhaust pipe coming from the side skirt."

That 6-to-1 looks so good... tempting.

David

One would think you have enough headers by now

[davidinnyc]

https://www.youtube.com/watch?v=mLs6hziC6is

So lazy with the 6MT and 3.15 diff, lol

https://www.youtube.com/watch?v=s6XZn8W12wk

Ok - very cool...

"Was that a flame? Oh, yeah, well of course there's an exhaust pipe coming from the side skirt."

That 6-to-1 looks so good... tempting.

David