Really? And where did I say that? Because that's a barefaced lie, isn't it.
In the interests of fact, to give two examples, assuming the above values, an 8ohm coil and an Sd of 220cm^2, then B*L would be around 268. With an Sd of 500cm^2 it would be 610 [nearly]. These are not synonyms for 'infinite' (such as a Qt of zero would be).
No.
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Bollocks. But you'll need to up your game if you wish to cause offence. People in these parts don't have a princess-thin skin. 😉
Nope. Mms is the total powertrain + air load mass. The profile of the coil, especially for such a large driver is neither here nor there as far as that goes & a change in material e.g. from copper to CCAW will almost certainly have a greater impact on the overall mass. The profile change in theory results in an asymmetric load applied to the diaphram, altering the generation of the concentric wave and distributing it over a wider frequency range, albeit a rather complex way of doing so from the perspective of implementation.
Acceleration is proportional to the current in the coil: Γ = Mms / (B*L*i) in SI units (meters per second per second per ampere, the latter being the significant part). To put it another way, it's just a way of of expressing conversion efficiency. It's a relatively efficient driver for its dimensions because it's designed to be, i.e. fairly low mass, fairly high motor power. You don't require an elliptical coil for that.
you did not say it, you build it in your construct. Qes=0.000...,, since Qes=2*pi*Fo*Md*Rc/(BL)^2 to have Qes zero either mass and /or Rc shoud be zero (since Fo is 40 and is different from zero) or BL should be infinite. From another side Fo=1/(2*pi*sqrt(Cms*Md)=40 the mass cannot be zero, neither Cms (otherwise F0=0, i.e there is no resonance) so the only conclusion in your construct is that Rc is zero or BL is infinite. I suppose you not talking about zero Rc, so BL must be infinite.
apparently you do, otherwise you cannot reduce the mass without compromising the quality of the driver
well, if you believe a perfect sound transducer should have resonance there is fundamental gap between us , that makes this discussion impossible... we all know i hope that the resonance is the beginning of the end, there left of it the spl rolls of 12db per octave (if i remember correctly). Resonance also causes phase shift. Impedance change. one of the characteristics of perfect driver is infinite frequency response (from zero to infinity), another is instant impulse response, and so on, perfect transient function, i.e absolute copy of the imput signal, zero flat phase shift. i will stop here this discussion with you, as your perfect is different from mine.
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Your construct, not mine. 😉
Are you sure? If you re-read, you will see I very clearly classed Qes = 0.001 since the equations have singularity at a 0 value (i.e. they cease to be functional, or actually have meaning). So, using the example values I gave
Fs = 40Hz
Qes = 0.001
Qms = 5.0
Qts = 0.001 [nearly]
And setting Sd & Re to 220cm^2 and 8ohms respectively, we calculate
Mms = 35.87g
B*L = 268.91T/M
Rms = 1.8 kg/s [nearly]
Res = 40,000Ω[nearly]
Ces = 0.0005uF [nearly]
Lces = 31831mH
Fhm = 80KHz
Γ= 7487 m/s^2
Neither Re nor Mms appear to be zero. And back-calculating Qes = (2pi*Fs*Mms*Re)/(B*L^2) = 0.000999951, rounding to the three decimal place giving the stated Qes = 0.001. QED.
You appear to be implying an Fs of 0Hz [infinitely low], which has multiple issues. As a concept a drive unit that has flat axial and power responses from 0Hz to infinitely high (which by definition also means a flat phase response, infinitely fast settling time / zero ringing etc.) which also possesses zero HD, IMD etc., is the 'ideal'. It starts to fall down however when applying real-world concepts to it like Fs. Fs describes a system resonance (so can't even conceptually exist if set as 0). And if you then also insist on an inifinitely high level of electromechanical damping in addition to an Fs of 0Hz, you have a further conceptual contradition, since to achieve that you would logically expect to run into the necessity of other factors like compliance rapidly changing if you hold dimensions & mass static.
According to whom, and in what universally accepted, closed form ways?
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indeed, i do , and i stick my statement, a perfect sound transducer would have no resonance , which means a damping of zero! here is why. no resonance means infinite compliance and/or zero mass, (I never said it is practically doable, all i am saying this the ultimate goal, i.e the direction to go). as Fs = 1/(2*Pi*sqrt(Cms*Mms)=0, since Qe=2*Pi*Fs*Mms*Rc/(BL^2) = 0 (for Fs=0) and Qm = Fs/(f1-f2), where f1 and f2 are measured at -3db is also zero so the Qts=is also zero? as 0*0/(0+0) = 0. you also dont need to know any formula, just to know that resonance and damping are related and only exist where there is mass and coil (stiffness).
You don't see a contradiction in terms between infinite compliance & infinite damping then? 😉
As I say, I doubt anyone would disagree with the concept / philosophy of a massless transducer with a totally flat frequency / amplitude response from infinitely long to infinitely short wavelengths, with zero distortion of any kind, being a fantasy ideal. That's fine, no worries there. But like a lot of things, the fantasy / idealisation starts to go pear-shaped if you then try to apply actual engineering terms like Fs to it, since Fs is defines a resonance (that's its entire meaning), and if you don't have a resonance, it (as in Fs) doesn't exist. It vanishes down that philosophical black hole. The equations, as I've said, have singularity at 0 value, i.e. they don't work & cease to have any meaning -they require a value to function.
As I say, I doubt anyone would disagree with the concept / philosophy of a massless transducer with a totally flat frequency / amplitude response from infinitely long to infinitely short wavelengths, with zero distortion of any kind, being a fantasy ideal. That's fine, no worries there. But like a lot of things, the fantasy / idealisation starts to go pear-shaped if you then try to apply actual engineering terms like Fs to it, since Fs is defines a resonance (that's its entire meaning), and if you don't have a resonance, it (as in Fs) doesn't exist. It vanishes down that philosophical black hole. The equations, as I've said, have singularity at 0 value, i.e. they don't work & cease to have any meaning -they require a value to function.
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i don't see contradiction. Undamped natural frequency w= sqrt(s/m), where s is the stiffness (in our case s = 1/Cms) and m is the moving mass. since 1 over infinity is zero, there is no spring, so there is nothing to damp as damping ratio generally speaking is a mathematical tool that shows the influence of the damping constant on the transient response of an MSD system (mass, spring, damper). If spring is missing there is no MSD system and w=0. where do you see contradiction? with regard to fantasy thank you for your complement. the first step to achieving greatness is defining it and this is not called fantasy, its setting your goals. the rest is a question of innovations and technology. one good example is RAAL, they have achieved near zero mass and near infinite acceleration and the result is next level closer to perfection. you have to hear to believe it.
This is getting increasingly whimsical (and irrelevant to the thread). For a start 1/∞ is not actually zero. It's undefined since infinity is not a number. It's often described as ≡ to zero, but that isn't strictly the case.
You still seem to be trying to make an argument from a black-hole. Fs is by definition resonance, and conceptually has no meaning if set to zero. You are also requiring infinite compliance to achieve infinite output at a non-existent frequency, and an infinite level of damping at the same non-existent frequency. These equations have no functional meaning without value.
I've heard (and measured) RAAL tweeters. Remaining in the real world, they are quality ribbon designs (not elliptical coil drive units from Scan Speak), with their own balance of advantages and compromises, and they do not have 'near infinite levels of acceleration'. Based on the published values for the 140-15D, Γ = 23181.81m/s^2, which is a goodly way from 'near-infinite'.
Do you have anything relevant to contribute regarding the Scan Ellipticor drive units?
You still seem to be trying to make an argument from a black-hole. Fs is by definition resonance, and conceptually has no meaning if set to zero. You are also requiring infinite compliance to achieve infinite output at a non-existent frequency, and an infinite level of damping at the same non-existent frequency. These equations have no functional meaning without value.
I've heard (and measured) RAAL tweeters. Remaining in the real world, they are quality ribbon designs (not elliptical coil drive units from Scan Speak), with their own balance of advantages and compromises, and they do not have 'near infinite levels of acceleration'. Based on the published values for the 140-15D, Γ = 23181.81m/s^2, which is a goodly way from 'near-infinite'.
Do you have anything relevant to contribute regarding the Scan Ellipticor drive units?
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Anyone seen measurements of BMS drivers?
I’ve seen only a few; but not all that impressive
https://www.justdiyit.com/comparatif-15-pouces-pro/
I’ve seen only a few; but not all that impressive
https://www.justdiyit.com/comparatif-15-pouces-pro/