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05092013, 12:38 PM #1Member
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Helmholtz Resonator (1/4 length resonator)
Looked into this on my break today, seems that it could help those with drone. I made a quick matlab function to solve this for you. For instance if you are experiencing drone at 2500 rpm's, and the temperature at the point in which you wish to place the resonator is 350 degrees f. Then that would require a resonation chamber that is 34 inches long.
Here is the script:
function [L] = helmholtz_DMA (temp,rpm,cyl)
%Helmholtz resonator function
%5/9/2013
%INPUT:
%temp=degrees ferinheight
%cyl= number of cylinders%rpm= rpm in which drone occurs
%OUTPUT:
%L= length of 1/4 length resonator chamber
pulse=cyl/2;
F=rpm*pulse*(1/60);
T=(temp32)/1.8;
V=331.3+.6*T;
L1=(V/F)/4;
L=L1*39.370;end
ans = 34.4330
Published with MATLABŪ R2012b

05092013, 12:51 PM #2
Don't you need to figure out the cross sectional area of the neck and the volume of the chamber as well?

05092013, 01:21 PM #3Member
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Good point. Although I am not sure it would matter. Most of the cases I have researched, where it has been used on mustang/g35/350z platforms, have continued the same size exhaust piping for the chamber. Now I have seen uses where the exhaust will merge from the exhaust size piping into a large cylindrical chamber that is substantially shorter then the chamber length I have calculated. I am not sure how that transition would effect the harmonics. I am open to suggestions if you have any experience with wave motion.
For clarification of my first post, we are attempting to cancel out the frequency of the wave in which we observe "drone". Which can be related to a section of rpm's. To do this this a resonator will replicate the frequency, canceling it out.

05092013, 01:45 PM #4
Active Autowerke does this with their M3 signature exhaust which I believe is modeled on the factory M3 exhaust:
http://store.activeautowerke.com/act...xhaustp5.aspx
This may also be helpful:
http://en.wikipedia.org/wiki/Helmholtz_resonance
I would solve for the volume of the chamber, using the length and cross sectional area of the neck as inputs.

05092013, 01:50 PM #5
This is just tuning, same principle as adding a port to a loudspeaker. To do it properly you would need volume/diameter/etc. There *is* going to be some effective length/volume factor based on the exhaust not being a straight section which will change stuff a bit. Could probably get close arm chairing it.

05092013, 03:03 PM #6Member
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What you are doing essentially is making a secondary path for the acoustic portion of the exhaust that ends up being 180 degrees out of phase with the primary path, at a fixed frequency (where you have the droning problem). SO that when reintroduced to the main stream they cancel out. A Helmhotz resonator just puts that all together in one can, but you could do much the same by branching off and rejoining down stream L/2 (helmholtz path length is L/4 + L/4 using same entry exit port). These work really well when there is no other major harmonic or RPM with a lot of energy in it.

05092013, 03:13 PM #7Member
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05102013, 01:32 AM #8Member
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05102013, 08:03 AM #9
Aren't the ART pipes for the Nissan NA engines to maximize exhaust scavenging? Or are they simply test pipes that don't sound like test pipes because of the Helmholtz resonator?

05102013, 09:44 AM #10Member
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05102013, 09:45 AM #11Member
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05102013, 07:47 PM #12Member
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They work the similar in both cars. Lower noise, similar hp, more low down tq than either test pipes or HFCs. Also supposed to eliminate, or reduce, rasp and drone. Like I said, very interested in how this works out for the N54.

05102013, 09:57 PM #13
Maybe it's interesting to mention that a 1/4 wavelength resonator is something different than a Helmholz resonator. The helmholz resonator is tuned by it's (air)mass in the resonator to the (air)mass in the chamber (that would be the rest of the exhaust).
Just to prevent the mixup of different physical phenomenaE85 Z4 3.0i  ESS TS2+  Quaife ATB LSD  Custom Brembo BBK front/rear  Schrick cams  Schmiedmann headers/cats  Powerflex/strongflex/PSB PU bushings  Vibratechnics engine mounts  H&R anti rollbars

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05122013, 01:09 PM #15Member
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Very interesting. I will be looking into the math of a helmoltz in greater detail this week. I am hoping that I could write a simple matlab function to solve this at the rpm in which people observe drone. Then they could fabricate the correct size resonator
Thanks for the clarification. It seems that a lot of people are using the 1/4 length resonators with success. I think that the math from my origional post is pretty close for this type of resonator.
For the helmholtz, I will need to take a few days and get the physics down.
Should not be hard to fabricate once you have the specific measurements.

05122013, 03:02 PM #16Member
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05122013, 07:19 PM #17Timeout
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If someone made a cat delete but welded vbands on and made a helmholtz testpipe that you could swap in and out for emissions, that would be great for track and dyno days.

05132013, 11:39 AM #18Member
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Okay, did a few more computations.
My first post should the correct equations for a 1/4 length resonator.
Now a helmholtz, I believe after doing some researching and a little bit of algebra, this should do it.
The first equation is the origional equation for a helmholtz.
The second equation is the equation for the volume of the canister (Vo).
The third equation is equation one solved for Vo.
So.
Solving the third equation for these variables:
v= velocity of the air = 331.3+.6*(temp of exhaust gas at given point)
A= Area of neck = pi*r^2 ; where r= stock exhaust pipe size (2.5"==.0635m)
L= length of neck (I decided give it an arbitrary number constant) = 6" == .1524m
F= frequency in which drone is observed = rpm"observed" * 3/60
Therefore, set the solution from above equation = the second equation:
where ,
r= the radius of the helmholtz chamber (I gave this a constant of 4"==.1016m)
So then you just need to solve for l, which would give you the length of your chamber for a given frequency assuming that the chamber has a 4" radius, the radius of the stock exhaust is 2.5" and the length of the neck will be equal to 6".
That should do it.

05132013, 02:38 PM #19Member
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What would be cool for R&D purposes is something you could vary the volume (or length) of to tune it more precisely after road tests. Like for the resonator version a sliding section or even just a plug on one end you fill up with something & clamp a cap over.

05132013, 04:03 PM #20Member
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05132013, 04:24 PM #21Member
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05152013, 07:45 AM #22Member
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05152013, 10:30 AM #23Member
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Nice discussion here:
http://en.wikipedia.org/wiki/Helmholtz_resonance
I had not thought about it, but the analogy they mention is it is exactly like blowing air across the top of an open empty bottle or jug.
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