Been sick with influenza, pretty much stuck in bed for eight days, so been researching and attempting to design a BLH subwoofer. Having done so much research, looking at and reading so many pages, I am forgetting where information has come from. Being I have a Macintosh without VMWare and don't want to take time and space for a one time need, doing the calculations by hand; I love mathematics so it is fun. At this point, I am trying to calculate the volume using:
V = 2,9*At*R, where R is the distance where throat area has doubled.
At=(2pi*Fs*Qts*Vas)/c
I found this paper: https://www.passdiy.com/pdf/KleinHorn.pdf. It gives the formula:
Area at x (which I will simplify to Ax)=At*e^(4π*x/λ).
I graduated High School almost 27 years ago, so took me too much time to find how to bring down the exponent, spent an hour solving for x, however, the value is clearly not right. Can someone please help?
My solution for x is as follows:
Ax=At*e^(4π*x/λ).
Divide by At, giving:
Ax/At=e^(4π*x/λ)
According to this: https://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut45_expeq.htm, we are to take the natural log.
ln(Ax/At)=ln(e)*(4π*x/λ)
But this: https://mathinsight.org/logarithm_basics says to take the log.
Neither resolves the conflict.
Since ln(e) = 1, provides more beautiful and elegant formula, so use that until know which is correct, giving:
ln(Ax/At)=4π*x/λ
Times by λ gives:
4πx=(ln(Ax/At))λ
Divide by 4π:
x=((ln(Ax/At))*λ)/4π
Since R is the distance x where Ax = 2*At, therefore:
R=((ln(2))*λ)/4π
Therefore
V = 2,9*At((ln(2))*λ)/4π)
Let us use a Faital Pro 12FH500.
At=(2π*Fs*Qts*Vas)/c
=(2(3,14159265359)*45cm*0,0873)/343
=0,07196353784m^2
=719,635378cm^2
Then assume a tune of λ=40Hz, so the wavelength is 858,04cm.
Therefore
V = 2,9*719,635378((ln(2))*858,04)/4π)
V = 98771,9515445cm which is clearly incorrect.
So then where did I mess up, please?
Anyone happen to know the formula for calculating volume?
Thanks in advance! 🙂
PS This is an example of my obsessive personality, I should have been in bed over three and a half hours ago... 🙄
V = 2,9*At*R, where R is the distance where throat area has doubled.
At=(2pi*Fs*Qts*Vas)/c
I found this paper: https://www.passdiy.com/pdf/KleinHorn.pdf. It gives the formula:
Area at x (which I will simplify to Ax)=At*e^(4π*x/λ).
I graduated High School almost 27 years ago, so took me too much time to find how to bring down the exponent, spent an hour solving for x, however, the value is clearly not right. Can someone please help?
My solution for x is as follows:
Ax=At*e^(4π*x/λ).
Divide by At, giving:
Ax/At=e^(4π*x/λ)
According to this: https://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut45_expeq.htm, we are to take the natural log.
ln(Ax/At)=ln(e)*(4π*x/λ)
But this: https://mathinsight.org/logarithm_basics says to take the log.
Neither resolves the conflict.
Since ln(e) = 1, provides more beautiful and elegant formula, so use that until know which is correct, giving:
ln(Ax/At)=4π*x/λ
Times by λ gives:
4πx=(ln(Ax/At))λ
Divide by 4π:
x=((ln(Ax/At))*λ)/4π
Since R is the distance x where Ax = 2*At, therefore:
R=((ln(2))*λ)/4π
Therefore
V = 2,9*At((ln(2))*λ)/4π)
Let us use a Faital Pro 12FH500.
At=(2π*Fs*Qts*Vas)/c
=(2(3,14159265359)*45cm*0,0873)/343
=0,07196353784m^2
=719,635378cm^2
Then assume a tune of λ=40Hz, so the wavelength is 858,04cm.
Therefore
V = 2,9*719,635378((ln(2))*858,04)/4π)
V = 98771,9515445cm which is clearly incorrect.
So then where did I mess up, please?
Anyone happen to know the formula for calculating volume?
Thanks in advance! 🙂
PS This is an example of my obsessive personality, I should have been in bed over three and a half hours ago... 🙄
A = V / (2.9R) is an old W.E. / Altec formula for coupling chamber volume where
A = Throat CSA in in^2
V = Coupling chamber volume (Vb) in in^3
R = Length of horn in which CSA doubles
Citing Badmaieff et al, then calculating for R we have the formula
(A2/A1) = e^kx = 2
Where
A2 = CSA at distance x
A1 = Throat CSA
e = 2.718 (base of Naparian [natural] logarithms)
k = Flare constant
For the desired LF cutoff Fc,
K = (4 Pi Fc) / C
Where C is the local SoS
So using e^kx = 2, and therefore a Naparian log. value of 0.693 [nearly], then assuming a local SoS of 13680 in/sec. and an Fc of 40Hz, we have (rounding to the nearest sensible value)
K = (4 Pi 40)/C = 0.037 and
X [aka R] = 0.693 / 0.037 = 18.73in
A = Throat CSA in in^2
V = Coupling chamber volume (Vb) in in^3
R = Length of horn in which CSA doubles
Citing Badmaieff et al, then calculating for R we have the formula
(A2/A1) = e^kx = 2
Where
A2 = CSA at distance x
A1 = Throat CSA
e = 2.718 (base of Naparian [natural] logarithms)
k = Flare constant
For the desired LF cutoff Fc,
K = (4 Pi Fc) / C
Where C is the local SoS
So using e^kx = 2, and therefore a Naparian log. value of 0.693 [nearly], then assuming a local SoS of 13680 in/sec. and an Fc of 40Hz, we have (rounding to the nearest sensible value)
K = (4 Pi 40)/C = 0.037 and
X [aka R] = 0.693 / 0.037 = 18.73in
Scott, thank you! 🙂
Just shows not everything on the internet is correct.
So the calculations have to be done in British units only? If so, find that interesting, don't recall that happening before. That just means having to convert the speaker manufacture's specifications; at least don't have to convert them back.
I appreciate the explanation of the W.E./Altec formula and e, I left them out not considering others might not know. Also appreciate knowing the names of the formulas.
What is meant by old? No longer the preferred or best formula?
Just shows not everything on the internet is correct.
So the calculations have to be done in British units only? If so, find that interesting, don't recall that happening before. That just means having to convert the speaker manufacture's specifications; at least don't have to convert them back.
I appreciate the explanation of the W.E./Altec formula and e, I left them out not considering others might not know. Also appreciate knowing the names of the formulas.
What is meant by old? No longer the preferred or best formula?
No, it just happened to be done in Imperial, which was the default at the time, so you can use metric equivalents if you prefer (providing you key off consistent values 😉 )
'Old' purely in the sense that it was developed in the 1940s -possibly earlier. Since the baseline physics hasn't changed, it's still valid. There are other formulas / notions scattered about all over the place of course; one point to keep in mind is that if you compromise your horn significantly, the effectiveness of the acoustic low pass provided by formulas like this may decrease.
'Old' purely in the sense that it was developed in the 1940s -possibly earlier. Since the baseline physics hasn't changed, it's still valid. There are other formulas / notions scattered about all over the place of course; one point to keep in mind is that if you compromise your horn significantly, the effectiveness of the acoustic low pass provided by formulas like this may decrease.
Since I can work in either, have you seen a preference or use of one more than the other?
What is acoustic low pass?
Maybe I need to back up?
The Grundig speakers are a poor match for the Technics SU-Z600 (bought about eight months ago used), too much power at 70 watts. Plus, only rated to go down to 70Hz. I enjoy a variety of music, particularly love organ music and rock from the 1950s through 1970s. Additionally, I have infrasonic hearing (may be because of being Autistic) and now that I am in a position (or so I hope), desire to build a system which can achieve this while having clarity and neutrality (not overly warm and especially not too bright, which is painful).
I am 36 and single, so have the distinct advantage of not burdened with wife appeal in my decisions. If a female does decide to create a team with me and can bring folks over, then will compromise and set up a music room. Meaning, if the BiB calculator recommends a 72"/1,84m tall speakers for the best sound, then that is what I will do. However, living in an apartment, I am slightly limited by size (there is an example of my dry humor...); do have 10'-1"/3m ceilings though. When researching folded horns, it has left me with an impression they are a compromise and folding degrades the sound whereas a BiB having only one fold does not noticeably and/or significantly impact the sound. Correct?
My understanding is vinyl's frequency range only goes down to 20Hz, therefore is there a point to having a tuning frequency below 40Hz, assuming a range of three octaves from the horn? Or does a BiB horn have a wider frequency response?
What is acoustic low pass?
Maybe I need to back up?
The Grundig speakers are a poor match for the Technics SU-Z600 (bought about eight months ago used), too much power at 70 watts. Plus, only rated to go down to 70Hz. I enjoy a variety of music, particularly love organ music and rock from the 1950s through 1970s. Additionally, I have infrasonic hearing (may be because of being Autistic) and now that I am in a position (or so I hope), desire to build a system which can achieve this while having clarity and neutrality (not overly warm and especially not too bright, which is painful).
I am 36 and single, so have the distinct advantage of not burdened with wife appeal in my decisions. If a female does decide to create a team with me and can bring folks over, then will compromise and set up a music room. Meaning, if the BiB calculator recommends a 72"/1,84m tall speakers for the best sound, then that is what I will do. However, living in an apartment, I am slightly limited by size (there is an example of my dry humor...); do have 10'-1"/3m ceilings though. When researching folded horns, it has left me with an impression they are a compromise and folding degrades the sound whereas a BiB having only one fold does not noticeably and/or significantly impact the sound. Correct?
My understanding is vinyl's frequency range only goes down to 20Hz, therefore is there a point to having a tuning frequency below 40Hz, assuming a range of three octaves from the horn? Or does a BiB horn have a wider frequency response?
Well, I'm 44, was only ever taught metric, but I think in Imperial. That's just me though; I use both, but given the choice, I prefer the latter. Personal preference and the fact that I'm a naval / maritime historian, so a lot of what I work with outside audio tends to be in Imperial anyway.
Acoustic low pass is more or less what it sounds like -it's a low-pass (i.e. rolls off the response above x frequency); it just does it acoustically rather than electrically. Think mechanical crossover and you're there. That's the purpose of a filter chamber in a back-loaded horn.
A lot (not all, there are exceptions) of vinyl struggles to get much lower than 40Hz or so, and when it does, they often have to mono the LF range to stop the stylus jumping out of the groove on mild dynamic peaks. But all other things being equal, which they rarely (if ever) are, the more LF extension you have the better -especially with vented enclosures which unload < tuning. Depends on your own taste & circumstances as much as anything though, so there isn't strictly a single answer to that. Re folding, for bass horns, it shouldn't be a problem in a well-designed system & in many cases is beneficial since the wavelengths you're focussed on are too long to be significantly affected, while the unwanted higher frequencies (shorter wavelengths) tend to get disrupted. In most of my designs the folding scheme is designed & sized as a functional part of the acoustic low-pass. The BIB is a very simple pipe-horn, but a surprisingly effective (and often relatively compact) one, which scores on ease of build & LF extension in particular.
Acoustic low pass is more or less what it sounds like -it's a low-pass (i.e. rolls off the response above x frequency); it just does it acoustically rather than electrically. Think mechanical crossover and you're there. That's the purpose of a filter chamber in a back-loaded horn.
A lot (not all, there are exceptions) of vinyl struggles to get much lower than 40Hz or so, and when it does, they often have to mono the LF range to stop the stylus jumping out of the groove on mild dynamic peaks. But all other things being equal, which they rarely (if ever) are, the more LF extension you have the better -especially with vented enclosures which unload < tuning. Depends on your own taste & circumstances as much as anything though, so there isn't strictly a single answer to that. Re folding, for bass horns, it shouldn't be a problem in a well-designed system & in many cases is beneficial since the wavelengths you're focussed on are too long to be significantly affected, while the unwanted higher frequencies (shorter wavelengths) tend to get disrupted. In most of my designs the folding scheme is designed & sized as a functional part of the acoustic low-pass. The BIB is a very simple pipe-horn, but a surprisingly effective (and often relatively compact) one, which scores on ease of build & LF extension in particular.
A good basic coverage of all the old school math, i used it to do a number of horns. http://p10hifi.net/planet10/TLS/downloads/Dinsdale-Horns-3parts.pdf
But a good modeler used by someone who knows what they are doing will better deal with the detail, as the math is typically for a stright horn and we typically fold up bass horns to make them more space efficient. The folds do introduce differences in the response.
dave
But a good modeler used by someone who knows what they are doing will better deal with the detail, as the math is typically for a stright horn and we typically fold up bass horns to make them more space efficient. The folds do introduce differences in the response.
dave
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Dave, weird didn't get notified of your helpful post.
Well, I knowing nothing about modeling so clearly not a good modeler, so are you suggesting I ask someone to model for me?
Well, I knowing nothing about modeling so clearly not a good modeler, so are you suggesting I ask someone to model for me?
Well, I did. Chuck didn't ask directly that I recall, yet, got help, and I have not, sure wish knew what I did wrong. Best guess is needs to be totally separate, trying that. Worse case, have to buy a keyboard and teach myself.
Right, TTBOMK based on the original Altec 515B 30 Hz woofer horn.
Thank you.
TTBOMK?
In the end, it is thanks to the generosity of this forum that I was provided an easier and superior sound solution to back horn design: BIB.
TTBOMK?
In the end, it is thanks to the generosity of this forum that I was provided an easier and superior sound solution to back horn design: BIB.
Since the chamber is part of a BP4 driver's design it goes back to before ~1920 and while I've never researched it may date in concept to Edison's 1877 phonograph or at least ~1912 with the invention of the microphone and its inventor's spin-off, the 555W horn driver in 1926.
The BIB needs all the room loading it can get, so folding in half we're dealing with a ~20 ft acoustical pathlength = ~1128.583/4/20 = ~14 Hz Fc, so if you have an upstairs neighbor, then you really are limited to very low listening levels. If you make it much shorter, better to unfold it to ~28 Hz or mount in upside down for floor loading. Again, a very flexible design. Paraphrasing Forest Gump, 'Simple is as simple does'. 😉
Last time! Speaker cabs only load to the driver's upper mass corner, so octave spread is based on the driver's Qts'; its total BW is governed by the driver's inductance, so if wanting more HF out of it requires a Zobel filter.
Story time with Adriel. 😛
So I used to have a mid 1980s Panasonic all in one with a separate CD player, was bio "mother's" and when helping move me out of on campus housing, she threw it out. Anyway, I would play organ music LPs with the bass up and at very high levels, I loved feeling the music and sure Dad did too (I never played oldies that loud). Speaking of Dad, he was a tight laced and devout Christian, women should be fully clothed in public. One night about eight, done with homework and want to relax. It was a quadplex and the woman down stairs, in her thin nightgown, knocked and Dad made it first. Man, he turned pale and didn't say anything, shut the door when she was done telling how she had been vibrated awake. 🤣 Who knew tiny, inexpensive, bookshelf speakers could? 😆
As to my current situation, I am blessed, they are individual houses, only the one bedrooms share one common wall (I am blessed with a two bedroom so have a work room). Though, do have a good point, I will turn it on, walk outside, shut the door, and stand between the houses, I want to be a nice neighbor.
Oops, sorry I upset you.
So the horn handles to 336Hz and then just the front facing? Okay.
I would then think best to keep the vocals out of the horn, correct?
So I used to have a mid 1980s Panasonic all in one with a separate CD player, was bio "mother's" and when helping move me out of on campus housing, she threw it out. Anyway, I would play organ music LPs with the bass up and at very high levels, I loved feeling the music and sure Dad did too (I never played oldies that loud). Speaking of Dad, he was a tight laced and devout Christian, women should be fully clothed in public. One night about eight, done with homework and want to relax. It was a quadplex and the woman down stairs, in her thin nightgown, knocked and Dad made it first. Man, he turned pale and didn't say anything, shut the door when she was done telling how she had been vibrated awake. 🤣 Who knew tiny, inexpensive, bookshelf speakers could? 😆
As to my current situation, I am blessed, they are individual houses, only the one bedrooms share one common wall (I am blessed with a two bedroom so have a work room). Though, do have a good point, I will turn it on, walk outside, shut the door, and stand between the houses, I want to be a nice neighbor.
Oops, sorry I upset you.
So the horn handles to 336Hz and then just the front facing? Okay.
I would then think best to keep the vocals out of the horn, correct?