PHYSICS to correct a poor previous (no gain) Muffler Mod in a OEM muffler.

[one.man.band]

formulas and more formulas.

for Husq 340e.

Temp, need accurate EGT temp. Used 730F which equals 387.778C. The 730 came from timberwolf's test 3 loaded/buried the bar in the wood condition.

for stock unmodded OEM muffler

velocity of sound was corrected for temp: v = 331.4+ (0.6 x T) =331.4 + (0.6 x 387.77) = 564.0667 m/s

using hemholtz equation: res. freq. = (corrected speed of sound)/2pi x sqrt(A/(V x L))
where:
v sound = 564.0667 m/s
A= area exit hole = 0.915224 cc
V= volume muffler = 368.71 cc
L= exit hole length = 0.1 cm (This muffler does not have a stinger pipe, so 0.1cm = 1mm).

therefore:
answer= 1414.399 Hz

then covert motor RPM to frequency:
1 RPM = 0.01666667 HZ
so, 9500RPM = 158.333 Hz

initial freq = 158.333 Hz
2nd harmonic = 158.333 Hz x 2 = 316.66 (and so on)
3rd harmonic = 474.99 Hz
4th = 633.32 Hz
5th = 791.65 Hz
6th = 949.98 Hz
7th = 1108.31 Hz
8th = 1266.64 Hz
9th = 1424.97 Hz

4 even order harmonics, and 5 odd order harmonics were necessary. the lower harmonicss are stronger in amplitude the the higher harmonics. picture the effect of plucking a guitar string. volume fades out over time. both even and odd harmonics are need for calculation, to account for the effect of a muffler volume having two ends open during filling period and 1 end closed when piston is blocking the exhaust port.

muffler volume: measured then computed to be 368.71cc
motor displacement: 40.8cc

368.71/40.8 = 9.04 piston strokes to fill muff to capacity.

the number of harmonics (in this case 9) were chosen to approximate the # of piston strokes necesary to fill the muffler with gas, there is no question that the 10th stroke will have to expel gases.

the muffler needs to be able to produce the first through 9th harmonic which is 1424.97 Hz.
the OEM muffler is 1414.399 Hz and is adequate in doing so. frequencies for 9500RPM through 12500RPM can easily be reproduced as long as they are below the threshold of 1414.399 Hz. any frequencies on 10K RPM to 12.5K RPM trendline on the graph, would not 'hit' as hard because they are diminished in strength on would be 10th order harmonics or more.

my theory to improve upon this is to tune the frequency of the muffler to a certain RPM. for this box muffler to hit the hardest, it would need to hit harder at lower frequencies. tuning it for 158.333 Hz would in theory hit more of the stronger lower #'d order or harmonics, and still reproduce the higher order harmonics.

as i mentioned in post #14 ways to tune for specific frequencies. change the variables to meet the end freq you want.

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as for why i chose to use the hemholtz equation and frequencies:

ask NASA why they chose to use them as well.

see pages #9 and #10

reference:
NASA Technical Translation
Soundproofing and Filling In of Engines
By: J. Rauch
NASA-TT-F14063

As i mentioned before, many factors also contibute to this that i did not calculate. Pressure being one of them.
those who can do calculus, as those formula's need for solving, can be my guest to get those #'s.

OMB

 

[homelitejim]

As a firewood guy I do not see the benefit of calculating the proper harmonic frequency to determine what size drill bit I need to get me a hundred or so more rpm to undue what the EPA has put upon us. If I read the thread right I could put some vacuum tubes on the tank and wire them through the muffler to the coil and while I am cutting firewood I could listen to a Japanese radio station. Why are we over thinking this? I am sure Stihl and Husqvarna have rooms full of nerds working this out.

 

[troutfisher]

Holy Crap. I thought I was just poking a hole in the muffler to let more exhaust out.

 

[one.man.band]

agree. for a stock saw turning stock max RPM, there is not a need to monkey with the muffler exit opening(s). if you have a baffled and/or cat equipped saw, there are restrictions within the muffler. whether someone wants to deal with those, for whatever reason, it also is of no concern to me.

however, some folks like to change things. searching for power gains. normally this leads to more RPM and higher max RPM. for those folks, it may make a difference.

 

[sachsmo]

you are way over thinking this.

Air in air out, some things are best left super simple.

 

[edisto]

I'm a little confused, but curious.

What are you trying to reflect back, positive or negative waves?

Upon leaving the port and entering the exhaust, a negative wave will be produced, so presumably what you are interested in are positive waves. I would guess the biggest problem in reflecting anything back are the size and shape of the muffler. There is no way to properly reflect anything back from the end of a box to a hole in a box, and there is not enough distance to get the timing right.

 

[one.man.band]

I'm a little confused, but curious.

What are you trying to reflect back, positive or negative waves?

Upon leaving the port and entering the exhaust, a negative wave will be produced, so presumably what you are interested in are positive waves. I would guess the biggest problem in reflecting anything back are the size and shape of the muffler. There is no way to properly reflect anything back from the end of a box to a hole in a box, and there is not enough distance to get the timing right.

both.

+ wave reaching the muffler exit hole opening turns (-). not beneficial but, this can't be helped or changed as far as i know. this effect is present on all exhaust systems.

+ wave stays positive as it reflects from muffler wall to stuff more of the fuel mix back in.

disagree with portion of your last sentence about reflection.

"a flat plate could do the same job (*as a reflective cone), but the wave duration would be so short that this would only occur over a very narrow RPM range".

-Bell
page 78

*added be me only to put this statement in context to the subject, for those who don't have the book.

distance.
the distance to reflect the wave back is set by the muffler back wall. it is what it is.

timing.
trying to improve on this, is what this thread is all about. even though it is a very small wave duration (ala Bell), it expands into a muffler whose volume is 9.04 times greater than the single 40.8cc exhaust pulse. a damping effect occurs, by the 8 previous exhaust gas pulses still inside from the previous strokes.

 

[RAMROD48]

And while all this was going on, some kid just opened a christmas present...

It was the toy chainsaw from Stihl...and you know what? he was happier than you all will ever be no matter what power band you hit or temp wave you acheive...

Oh the simple joys of being a child and not caring how the wheel got to be round...

 

[one.man.band]

congratulations!

my kids were up at 1:30, 3:30, and 5:30am. opened gifts @ 6am.

happy merry christmas

 

[troutfisher]

I'm trying to understand the end goal here. Are you trying to create a header type efftect pulling exhaust out? Maybe a tuned pipe effect re-stuffing the cylinder? Just eliminating harmonics? I don't get it

 

[sachsmo]

Engineering 101,

If you can't befuddle 'em with brilliance-----Baffle em with Bullchit.



Apologies to OMB,

And Merry Christmas to all!

 

[weimedog]

Just wonder if there is a point of diminishing returns.....all the calculations...then money and time spent trying to out think two proven concepts; First is the engineered stock design, and the second is the big hole, big noise back yard muffler mods done by quite a few that probably don't add a whole lot of performance but are a lot of fun.. ( BTW my hill billy engineered 3/4 in diameter tube brazed into the top clutch side corner of a hogged out muffler can seems to work really well in the noise & fun department on 272 and 372 class Husqvarna's, they even seem to help in the throttle response & power department as a side benefit! ):msp_w00t:

Merry Christmas!

 

[one.man.band]

I'm trying to understand the end goal here. Are you trying to create a header type efftect pulling exhaust out? Maybe a tuned pipe effect re-stuffing the cylinder? Just eliminating harmonics? I don't get it

goals:

to tune the muffler: by correctly sizing the exit hole. correctly sizing a 'stinger' pipe length. (if a stinger is needed). and keeping the rest of the muffler as it came from the factory.

 

[one.man.band]

Engineering 101,

If you can't befuddle 'em with brilliance-----Baffle em with Bullchit.



Apologies to OMB,

And Merry Christmas to all!

back at ya

 

[one.man.band]

rep button used up sorry sach

 

[troutfisher]

goals:

to tune the muffler: by correctly sizing the exit hole. correctly sizing a 'stinger' pipe length. (if a stinger is needed). and keeping the rest of the muffler as it came from the factory.

A couple used mufflers, a log and a stopwatch is what I would use. I use electrical conduit for muffler outlet pipes, in different sizes for different saws.

 

[sunfish]

Ya know, a Muff Mod is the easiest and cheapest way to get gains. We tried to help you in your other thread when you did yours, but you wanted to do it your way. Nothing wrong with that, but most here have done this stuff and found out what works and what doesn't. :msp_wink:

 

[weimedog]

A couple used mufflers, a log and a stopwatch is what I would use. I use electrical conduit for muffler outlet pipes, in different sizes for different saws.

Bingo..along with how much time are you willing to spend...I'm still doing exactly that right down to the electrical conduit! It's a long evolutionary process and part of the on going fun of this hobby. AND don't forget adding lots of the following to make certain you have a practical solution....love those front exit mods that work at GTG's but just get stuffed in the woods.
View attachment 213286
View attachment 213281
View attachment 213284
View attachment 213285

 

[J.W Younger]

I like the avatar, that ole boy had to be one of the greatest in blowin smoke.

 

[sachsmo]

There was a fellow named Earnhardt, that could "see" the draft.

Suppose there are some that can see the "flow".




Some things just work, some don't.

If you keep at it long enough, you will find a bone or two.