one.man.band
ArboristSite Guru
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.
---------------------------------------------------------------------------------------------------------------------
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
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.
---------------------------------------------------------------------------------------------------------------------
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
