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# "BL^2/RE": how is this the 'force factor" in a driver?

I've seen this "BL^2/RE" as a measure of a driver's 'force factor' mentioned a few times. Can anyone state what that means in a plain way? I get what BL is and I kind of get what RE is, but I don't see how together they determine the 'force factor' of a driver.

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Quote:
Originally Posted by shadyJ

I've seen this "BL^2/RE" as a measure of a driver's 'force factor' mentioned a few times. Can anyone state what that means in a plain way? I get what BL is and I kind of get what RE is, but I don't see how together they determine the 'force factor' of a driver.

I'll take a stab at this ...

Magnetic field strength (lines of flux), cutting thru a given cross sectional area of the VC, across the coil's DC resistance ... which in turn determines the current.

Somewhat akin to; V/R=I
Let me see if I got this right....B is the strength of the magnetic gap that the voice coil rides up inside of, and L is the actual amount of wire that is wound up on the actual coil, right? I know that the B is multiplied by L to get the BL product. The higher the BL product, the more control a drivers voice coil will have, right?

RE is simply the DC resistance of the coil. Right?

I am unsure what the purpose is of taking the BL to the second power then divided by the RE? Is it to determine the current capabilities?
This paper that the old Lambda Acoustics site had up explains the force factor quite well. I haven't had time to transfer it to my site but you can see it here

http://web.archive.org/web/20010810141852/lambdacoustics.com/library/whitepapers/bl_mms.htm

Because current is a critical aspect of the force factor, the Re is the determining factor in the amount of current applied.
Hey John, your two links absolutely nailed it, they were very informative and answered my question exactly how I had hoped, thank you very much!
Sorry shadyJ, when you said "plainly" I went as plain as I could, focusing on the resultant current.

I presumed you had seen the other work/Wiggins paper.
i disagree with wiggins.

woofer speed is not just a function of frequency, but also of amplitude. not sure why that obvious fact has been missed the last seven thousand times that the wooferspeed paper has been referenced. maybe our crystals were out of alignment.

a lighter cone will move more for a given amount of power, so it actually is "faster" holding all other things equal except for moving mass.
Quote:
Originally Posted by shadyJ

I've seen this "BL^2/RE" as a measure of a driver's 'force factor' mentioned a few times. Can anyone state what that means in a plain way? I get what BL is and I kind of get what RE is, but I don't see how together they determine the 'force factor' of a driver.

Standard references seem to say something else.

BL^2/RE is called "damping factor" in a goodly number of references including those by Klipple, Eargle, and Vanderkooy.

Force Factor is usually given as BL

Google these terms and you will see what I mean.
bl^2/re is motor strength.

it is a measure of how much physical force the motor applies for a given amount of electronic force (voltage).

resistance is in the denominator because no matter how much electronic force that you apply, if the resistance is infinite, there will be no current and there will be no physical force applied. if the resistance is zero (superconductor), then even a tiny voltage will cause an infinite flow of current which will create and infinitely strong physical force (this is the idea behind superconducting magnetic linear accelerator, aka rail gun).

B and L are in the numerator because no matter how much electronic force that you apply, if the magnetic field (the B) is zero or if there is no wire in the magnetic field (the L), there will be no physical force applied.
Quote:
Originally Posted by LTD02

...woofer speed is not just a function of frequency, but also of amplitude. not sure why that obvious fact has been missed the last seven thousand times that the wooferspeed paper has been referenced.

Because they don't mean literally speed/verlocity, they mean transient response, which is still not quite right; the real issue is Q//damping.
Quote:
Originally Posted by noah katz

Because they don't mean literally speed/verlocity, they mean transient response, which is still not quite right; the real issue is Q//damping.

I think I get what you mean, but can you explain this distinction between speed/velocity and transient response a bit more? Is there a more direct determinant of transient response than BL^2/Re?
Quote:
Originally Posted by shadyJ

Is there a more direct determinant of transient response than BL^2/Re?

This is an interesting issue.

There's different aspects of transient response. However, again,... as simple as possible, if you're defining transient response as a cone at rest, and what determines how quickly it'll respond to track a rising waveform of a given freq, the determining factors are how much current is available thru a value of inductance opposing that current.

So a monumentally capable high current amplifier, and a low inductance motor

After that point there's other elements, but I believe that's the beginning determinant.

I'd be interested to read J Janowitz' comments, as he's much better versed in the additional components involved.
"So a monumentally capable high current amplifier, and a low inductance motor
After that point there's other elements, but I believe that's the beginning determinant."

that's the argument in the paper, but when for practical purposes what folks are calling transient response / fast bass / good punch / whatever...holding all other things equal is uncompressed high spl and the easiest path there is through high sensitivity.

if you start with a horn loaded driver with 105db 1w1m sensitivity and compare it with an 80db 1w1m direct radiator at 100hz, the former is going to have a transient response / fast bass / good punch / whatever that will absolutely kill the latter.

these things are all inter-related though, so picking out one dimension doesn't get you there. i'm sure if you put a large enough inductor on the horn, you could find a way to kill its transients response.
Quote:
Originally Posted by LTD02

that's the argument in the paper, but when for practical purposes what folks are calling transient response / fast bass / good punch / whatever...holding all other things equal is uncompressed high spl and the easiest path there is through high sensitivity.

if you start with a horn loaded driver with 105db 1w1m sensitivity and compare it with an 80db 1w1m direct radiator at 100hz, the former is going to have a transient response / fast bass / good punch / whatever that will absolutely kill the latter.

these things are all inter-related though, so picking out one dimension doesn't get you there. i'm sure if you put a large enough inductor on the horn, you could find a way to kill its transients response.

I can't disagree with any of what you're saying. Similarly, I often strongly suggest that eliminating the smearing effects of SBIR, in addition to properly executed time alignment of the bottom end to the associated spectral cues higher in freq add a level of coherency that when played at ample SPL, in a well damped/properly bass trapped environment, one can achieve all the subjective transient response one could ever desire.

I presumed from the OP we were examining the subject in a more specific and simple manner;

"what is force factor in a plain way" ...
Magnetic field strength (lines of flux), cutting thru a given cross sectional area of the VC, across the coil's DC resistance ... which in turn determines the current.

"Is there a more direct determinant of transient response than BL^2/Re?"
the determining factors are how much current is available thru a value of inductance opposing that current.
Quote:
Originally Posted by shadyJ

I think I get what you mean, but can you explain this distinction between speed/velocity and transient response a bit more? Is there a more direct determinant of transient response than BL^2/Re?

I believe we're talking about bass, so the box tuning and room modes could both have much greater effects on perceived bass quickness than BL^2/Re.

To expand on what I said earlier, what makes bass sound slow is not how fast it starts, but how fast it stops; ringing after the signal is gone is what makes it sloppy.

As a point of interest, years ago I did FEA (finite element analysis) of a mass/spring damper system analagous to a driver and found that higher Q (less damping) actually makes the bass start faster; damping is "sticky" and slows the cone's initial response.
Quote:
Originally Posted by noah katz

so the box tuning and room modes could both have much greater effects on perceived bass quickness than BL^2/Re.

Can't speak to alignment/tuning, but sure, the room (typical HT size) absolutely owns how we experience bass, perceived bass quickness, etc. You mentioned modal influences, but LF decay is equally or possibly more influential wrt the experience.

Quote:
Originally Posted by noah katz

To expand on what I said earlier, what makes bass sound slow is not how fast it starts, but how fast it stops; ringing after the signal is gone is what makes it sloppy.

In addition to, as you said, the cone ringing, but the energy ringing ... or LF decay in room, as I mentioned above. My bass trap experiments, both empirical and anecdotal, would suggest this is huge. Note to note delineation, and perceived speed/tightness are the area where the gains are experienced.

Quote:
Originally Posted by noah katz

As a point of interest, years ago I did FEA (finite element analysis) of a mass/spring damper system analagous to a driver and found that higher Q (less damping) actually makes the bass start faster; damping is "sticky" and slows the cone's initial response.

Very cool Noah, not surprising, but very cool for sure. Any effort to assure the box doesn't negatively impact a driver's ability to track the signal is a worthy one.

As an enthusiast with both an IB, and multiple small sealed owner, I constantly go back and forth listening to the characteristics of each subwoofer type, and the sum of both. There's distinctive differences, I've made countless measurements, but I'm most interested in the subjective character of each. It's not easy wading through the all the variables, making suitably valid determinations for my own consumption.

I hadn't thought of the term "less sticky", but yeah, the less sticky IB possesses a good sound. I'm not done, but I have shared many of my subjective findings/opinion here and there. Theoretically, the IB has the advantage as the superior approach for subwoofing. Sure, it takes many more multiple drivers than other approaches, the placement limitations are well recognized as well. But whether it's an open baffle like Linkwitz favors, or an IB, any approach that doesn't impact the driver's ability to accurately track the signal, is a step in the right direction. Fortunately, the wavelengths are so long we don't have to worry about driver to driver integration. So we can employ as many drivers as necessary to achieve our SPL goals.

Also, with the low drive currents associated with the IB alignment, help keep force factor non-linearities low, flux modulation low, resulting in less significant harmonic distortion. Drive levels for IB drivers can easily be 1/10th of their sealed brethren. Less compression, magnetic or thermal ... all steps in a positive direction.

Noah, I'd enjoy any links etc to the work you referred to.

Thanks
Quote:
Originally Posted by FOH

You mentioned modal influences, but LF decay is equally or possibly more influential wrt the experience.

Right, I meant (slow) LF decay caused by high box Q and/or room modes.

Re IB, they do indeed have all of the benefits you mention, but there is one downside - the spring linearity is entirely dependent on the suspension and doesn't benefit from the linearizing effect of an air spring.
Quote:
Originally Posted by FOH

Noah, I'd enjoy any links etc to the work you referred to.

The FEA was one of my first posts on the old Basslist, dunno if that can be found or not.

But a much better/more comprehensive job was done here by Illka

Unfortunately Illka links to his sims are dead, but there are some graphs in the thread.

I started the same topic here http://www.audioasylum.com/forums/hug/messages/102291.html

I trust you'll find those threads rather interesting.
Quote:
Originally Posted by noah katz

Re IB, they do indeed have all of the benefits you mention, but there is one downside - the spring linearity is entirely dependent on the suspension and doesn't benefit from the linearizing effect of an air spring.

Good point, well, one can't have their cake and eat it too! If you remove the influence the box imparts on the driver, you gotta take the bad with the good.
Quote:
Originally Posted by noah katz

I trust you'll find those threads rather interesting.

Wow, good stuff. Got thru the audioasylum discussion, I set aside the other for a future read.

I dig AVS, interacting with others with similar interests, but it's a shame that oftentimes the lowest common denominator bar doesn't seem to move. So many strong contributors over a good period of time, yet often the same issues are kicked around and around, without the advancement needed. Yeah, there's exceptions, and I'm thankful for that, ... but I yearn for in depth science linked to the subjective experience, more well vetted best practices, shared by all, elevating the pastime even further. We're going in the right direction, but not at the speed I'd like to see. Perhaps we're just at that point in the curve ...

Thanks for the links, solid stuff, as always.
Thanks, I thought you'd like those

Re same issues repeating, not everyone has read everything or necessarily have the requisite background to understand it, and even then people won't always agree, interpreting the same data differently.
"I dig AVS, interacting with others with similar interests, but it's a shame that oftentimes the lowest common denominator bar doesn't seem to move. So many strong contributors over a good period of time, yet often the same issues are kicked around and around, without the advancement needed. Yeah, there's exceptions, and I'm thankful for that, ... but I yearn for in depth science linked to the subjective experience, more well vetted best practices, shared by all, elevating the pastime even further. We're going in the right direction, but not at the speed I'd like to see. Perhaps we're just at that point in the curve ..."

so create a website with the information that people can use to educate themselves. then whenever somebody asks an lcd question, you can just point them to your website. problem solved.
Quote:
Originally Posted by noah katz

I believe we're talking about bass, so the box tuning and room modes could both have much greater effects on perceived bass quickness than BL^2/Re.

To expand on what I said earlier, what makes bass sound slow is not how fast it starts, but how fast it stops; ringing after the signal is gone is what makes it sloppy.

As a point of interest, years ago I did FEA (finite element analysis) of a mass/spring damper system analagous to a driver and found that higher Q (less damping) actually makes the bass start faster; damping is "sticky" and slows the cone's initial response.

In addition to environmentally induced decay time, the frequency response also adds to the perception of "quick" vs "slow".

It should be obvious to anyone interested in the subject that a single cycle at 10 Hz takes 4 times as long to complete as a single cycle at 40 Hz. Given the same start time, lower frequency will last longer. It doesn't matter how long each burst of those to example frequencies might be, the 10 Hz burst will take longer to stop = sound slower.

Wiggins on motor strength:
Quote:
Originally Posted by DanWiggins;480515
How high do you want to go? I've played around with some designs and have pushed BLs into the 50+ range... Not too useful, though. Qes ends up through the floor, so you get no bass extension.

Lots of PA drivers have BLs in the 20-30 N/A range, but none really create "bass". Loud above 50 Hz? Sure. Usable output below 40 Hz? Nope.

You can have a really high BL and raise the Qes to a usable level (in terms of low end extension) by adding a lot of mass to the driver. Of course, this lowers the efficiency of the driver a lot, and you might as well start with a lower moving mass and lower BL - same results, and a LOT lower cost.

The reason you don't see a lot of high BL designs in audio applications is because there's really never a need for it. Unless you're looking for a 15" driver with a lower end limit of 100 Hz or so, BLs above 25 N/A or so are, IMHO, a waste. And for true subwoofers, BLs above 20 N/A are detrimental to performance.

Now, if you're talking about some electrodynamic voice coil driven actuators, well, BLs can reach into the 80s or 90s, but those are for some esoteric applications where the motor is used for non-audio applications. Like shaker tables, pneumatic air valves, etc.

Dan Wiggins

Transient response is frequency response. When talking about subwoofers in HT systems, they are all subject to a LPF. It's the LPF that determines the transient response of the sub, with no exceptions. So, if a better transient response is the goal, a better integration with, and transient response from the satellite speakers is the target.
Quote:
Originally Posted by John_E_Janowitz

This is also good to read

http://www.diy-audio.narod.ru/litr/WooferSpeed.pdf

Quote:
Originally Posted by LTD02

i disagree with wiggins.

Me too. Why does this paper keep coming up. It's biased by what Dan was selling, and it doesn't prove anything. So, adding an inductor to a woofer changes the impulse response. Ya, so I can show you 100+ measurements of that exact change. So what if I add a very big inductor and a tweeter in series, and the impulse response goes up? Does that mean the woofer speed just went up? NO!!! Because the IR yields the frequency reponse, which an inductor changes. That paper needs to go away.
Quote:
Originally Posted by bossobass

It's the LPF that determines the transient response of the sub, with no exceptions.

It would be more accurate to say that it contributes to it; i.e. a sub's box tuning is the main factor in bass transient response is with an 80 Hz LP, as it's likely an octave or two lower (or three around these parts).
it would also be accurate to say that 'transient response' is not actually what most people who are not familiar with the jargon are trying to describe when they use the term. this is the source of most of the confusion related to the topic imho.
Isn't sound fun that way?
Quote:
Originally Posted by LTD02

"So a monumentally capable high current amplifier, and a low inductance motor
After that point there's other elements, but I believe that's the beginning determinant."

that's the argument in the paper, but when for practical purposes what folks are calling transient response / fast bass / good punch / whatever...holding all other things equal is uncompressed high spl and the easiest path there is through high sensitivity.

if you start with a horn loaded driver with 105db 1w1m sensitivity and compare it with an 80db 1w1m direct radiator at 100hz, the former is going to have a transient response / fast bass / good punch / whatever that will absolutely kill the latter.

these things are all inter-related though, so picking out one dimension doesn't get you there. i'm sure if you put a large enough inductor on the horn, you could find a way to kill its transients response.

Haha, funny you mention that. All the calculations/math point to that, but the human ear/brain is a very strange entity and proved otherwise. We performed double blind listening tests back in the 80's at the Canadian NRC with experienced listeners and just that criteria (not just the bass but the entire audio spectrum). The results were unanimously in favour of the low sensitivity product. Listeners found them to be more dynamic, accurate and less fatiguing.
Quote:
Originally Posted by tuxedocivic

Me too. Why does this paper keep coming up. It's biased by what Dan was selling, and it doesn't prove anything. So, adding an inductor to a woofer changes the impulse response. Ya, so I can show you 100+ measurements of that exact change. So what if I add a very big inductor and a tweeter in series, and the impulse response goes up? Does that mean the woofer speed just went up? NO!!! Because the IR yields the frequency reponse, which an inductor changes. That paper needs to go away.

It served him well.
Quote:
Originally Posted by mrogowski

Haha, funny you mention that. All the calculations/math point to that, but the human ear/brain is a very strange entity and proved otherwise. We performed double blind listening tests back in the 80's at the Canadian NRC with experienced listeners and just that criteria (not just the bass but the entire audio spectrum). The results were unanimously in favour of the low sensitivity product. Listeners found them to be more dynamic, accurate and less fatiguing.

Is there a paper or something on this?
Quote:
Originally Posted by noah katz

It would be more accurate to say that it contributes to it; i.e. a sub's box tuning is the main factor in bass transient response is with an 80 Hz LP, as it's likely an octave or two lower (or three around these parts).

Agreed.
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