120V from both legs



I replied "Freudian slip, imo.", and you didn't follow up. One generally reaps what one sows. I see your modus operandi so: Rather than admit an error, you first throw out a barrage of generally accurate but unrelated equations, etc as distraction. When that is ignored, you then take the insult route.

The Thiele-Small parameters from the 1961-1972 era tied together the former work of Raliegh, Morse, Olson, Beranek, Kinsler, and others. This was over 30 years ago, and they are the standard reference works. Yet you have not apprised yourself of them, and continue to espouse your ignorance. This in spite of their common usage and ready access. Had you done so, you would know that using only E^2/Re as the applied electrical power to a loudspeaker gives the correct electrical to acoustic efficiency. This is made clear from Smalls eq.2 along with eq.31, otherwise from the basic efficiency expression power out/power in and Beraneks and Morses work. Had you been open-minded rather than obstinate in your ignorance, you might have learned something. Accordingly, you give the impression of an internet grandstander.
So where to now? I realize that my knowledge is limited, that I shall never live long enough to learn even 0.01 % of the knowledge available in the world today. This grieves me, but does serve to remind me to be more open-minded. The downside is that when I encounter someone of your apparent ability, but who is close-minded, it dissapoints me. I came here with hopes of finding intelligent and open-minded discussion, but then nothing gained-nothing lost, I suppose.
BTW, I said "since you would find other peoples mistakes amusing, is that why you're here, to amuse yourself with the mistake of some poor soul less informed than yourself?" That you did not respond perhaps explains the situation.
-----------
I'll note here your last error (likely a wasted effort), where you said your equation was correct and I was the one in error:
You stated " U= (BlE/Re)/(Zm +(Bl^2)/Re) "
Beranek gives velocity in his eq.7.1 as
. Bl E U = -------------------- (Rg+Re) (Rm+jXm)
which in your form above is
BLE/(Rg+Re) U = ------------------ (Rm+jXm)
where U=velocity, BLE/(Rg+Re)=force, (Rm+jXm)=mech impedance Zm
you have ignored Rg, which is OK as modern-day amplifiers have negligible source resistance Rg. However, Beranek defines resistance Rm in the next eq.7.2 as
Rm = (Bl)^2/(Rg+Re) + Rms + 2 Rmr
This means (Bl)^2/(Rg+Re) is already *included* in mechanical impedance Zm, so you cannot add it to Zm again. Hooting about phasors as you did doesn't cut it. Phase enters the picture in adding Rm and jXm, not in the addition of resistances. This is sophomoric at best, or conniving at worst. Only you know, and I no longer give a crap.
Northstar snipped-for-privacy@hotmail.com drop the high card to reply
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says...

former
loudspeaker
learned
grandstander. ------------ I thought that I had answered you before. I wish that I did have Small's work and his Eq2 and Eq31 which you have mentioned without either quoting them or indicating the region of applicability. I note that when I had Kinsler, you jumped to Beranek as a reference and when I got Beranek, you jumped to someone else. I really doubt that Kinsler and Beranek have any fundamental circuit model or analysis difference from Small or Morse. I also note that the Beranek version is the 1986 revision and the Kinsler was revised sometime in the 90's. It may be that Small, in your references, is dealing with operation near the minimum impedance point. If so, you omitted this factor. In that case then the input impedance will be roughly approximate to Re +(Bl^2)/Zmech.-at that particular frequency but not in general.
As to the use of E^2/Re in the efficiency calculation. Please note that , as you have admitted, the input power is less than E^2.Re If you want actual efficiency, you would have to use the ratio of (acoustic power out/actual input power). This is obviously NOT the PAE, and, in fact, is higher than the PAE. The PAE, as I previously said, is a convenient measure-allowing quick calculation of relative efficiency at different frequencies by ony calculating the power by Eq. 7.15. This is a turn the crank process which is a hell of a lot easier than solving for the input power as well as output power at any given frequency. -------------->

------- I came with the same objective. The fact that I disagree with you on basic circuit principles seems to be a problem. The fact that your basic understanding of the principles is less than you think is also a problem. Have you ever had a formal AC circuits course? It appears that you are self taught and nothing is wrong with that except that you have had nobody to point out and clear up misconceptions which then become engrained. You have made conceptual mistakes that any sophomore student would soon have explained and corrected. I hark upon circuit analysis because that is all that has been involved so far in the models. Please do not take this as a comment on your intelligence or ability. It is not a comment on your ability to put together a damned good speaker system. It is a comment on an area of knowledge where your understanding is weak. You want to be open minded- part of this is questioning yourself. You are having a problem with someone who is not a speaker expert nor pretends to be, is questioning you- not on speakers per se but on interpretation of the models and equations that we have been dealing with. I happen to have a strong circuits and machines background which is the basis of my disagreement. Part of the problem may be that I do not necessarily use exactly the same terminology asd Beranek uses (Partly because his terminology is relatively clumsy- not his core expertise). -------------------

--------- I responded. Did you not read it? ---------

Zm,
you
------------- I wonder why you put Eq. B i a different form than A? Actually it is correct but for comparison , B can be written as . Bl E

which is the same form as you used for A. The difference, which I explained before, is that I used Zm as the actual mechanical impedance ( Berenak in Eq 7.1 to 7.3 does not name it as mechanical impedance or anything else- his Rm and Xm are simply shorthand notation which is common practice to keep equations easier to follow. Nothing more.) His Rm does include (Bl^2)/Re. My Rm doesn't, as I explained more than once, and on the basis of the development from scratch. As a result [(Bl^2)/Re +Rm] is the same as Beraneks Rm. I could have used Beraneks notation but I started with E=ZeI +BlU F=BLI =ZmU where Ze =Re +j0 ignoring inductance and source resistance Zm the mechanical and acoustic impedance=(Rms+2Rmr) +j[(wMmd +2Xms-1/wCms] Thus I have my (Bl^2)/Re + Zm =[ (Bl^2)/Re +Rms +2Rmr ] +j[(wMmd +2Xms-1/wCms] which agrees with Beranek's Zm . There is no difference. The addition is done correctly. (Think: Ze =Re=Re +j0) I kept the (Bl^2)/Re term separate only to emphasise that it is electrical in origin, not mechanical. Beranek's Fig. 7.4 emphasises this. There is no difference between what I say and what Beranek or Kinsler say. We are working by the same rules of analysis and get the same results even if somewhat different terminology is used along the way. Surely you can, given the definitions for my Rm and Xm, relate them to Beranek's results- it isn't difficult. The "error" is not mine.
At least I try to do my work independently from basics and check as far as I can against other references available- taking into account changes in notation. It appears that you simply plug into a formula without understanding what is behind it and then try to defend it on faulty reasoning or false arguments. Pity. I think you are capable of more.
--
Don Kelly
snipped-for-privacy@peeshaw.ca
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------------------
No point in addressing your further dialogue below, since you still don't understand the velocity equation, and in fact still blame the inability on me. Instead, I'll post prove again.
You stated " U= (BlE/Re)/(Zm +(Bl^2)/Re) "
Beranek gives velocity in his eq.7.1 as
. Bl E U = -------------------- (Rg+Re) (Rm+jXm)
which in your form above is
BLE/(Rg+Re) U = ------------------ (Rm+jXm)
where U=velocity, BLE/(Rg+Re)=force, (Rm+jXm)=mech impedance Zm
you have ignored Rg, which is OK as modern-day amplifiers have negligible source resistance Rg. However, Beranek defines resistance Rm in the next eq.7.2 as
Rm = (Bl)^2/(Rg+Re) + Rms + 2 Rmr
This means (Bl)^2/(Rg+Re) is already *included* in mechanical impedance Zm, so you cannot add it to Zm again. Hooting about phasors as you did doesn't cut it. Phase enters the picture in adding Rm and jXm, not in the addition of resistances.
As Beranek shows, (Bl)^2/(Rg+Re), or (Bl^2)/Re with source impedance = zero, must be included *in* Rm to obtain the correct mechanical impedance.
Northstar
-----------------------------------------------------------

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Noting a few of your remarks of late:

So what does impoliteness and disparagement get you? Read on to find out. I gave you ample time to find your error, but instead of finding and correcting it you really believe the error is mine. Therefore it is obvious you don't even know you made an error, and that you are the one whose understanding is weak. Plus... you arse off too much. Too bad.
Now to your error, and it is fundamental, not trivial. Starting by recapping what I tried to help you with (to no avail):
You stated " U= (BlE/Re)/(Zm +(Bl^2)/Re) "
Beranek gives velocity U in his eq.7.1 as
. Bl E U = -------------------- (Rg+Re) (Rm+jXm) rearranging in the form you used above gives
BLE/(Rg+Re) U = ------------------ (Rm+jXm)
where U=velocity, BLE/(Rg+Re)=force, (Rm+jXm)=mech impedance Zm
you have ignored Rg, which is OK as modern-day amplifiers have negligible source resistance Rg. However, Beranek defines resistance Rm in his next eq.7.2 as
Rm = (Bl)^2/(Rg+Re) + Rms + 2 Rmr
This means (Bl)^2/(Rg+Re) is already *included* in mechanical impedance Zm, so you cannot add it to Zm again.
End of recap, now simplifying for your benefit:
-----
At mechanical resonance the reactance Xm is effectively zero, so the Xm term drops out of the equation, leaving Zm to be just the resistance (Rm+jXm)= Rm. Now, you stated, with reference to Beraneks equation
" His Rm does include (Bl^2)/Re. My Rm doesn't "
Fine, you are adding resistances and your equation is valid at mechanical resonance, where your equation gives the same velocity as Beraneks eq. 7.1 *at resonance*. Clear enough?
Now above resonance the load is partly reactive and reactance Xm does *not* drop out of the impedance term (Rm+jXm). So above resonance and restating *your* equation above
U= (BlE/Re)/(Zm +(Bl^2)/Re)
noting Zm *with reactance present* must be (Rm+jXm), staying with *your* equation, and substituting (Rm+jXm) for your Zm
U= (BlE/Re)/(Rm+jXm)+(Bl^2)/Re)
Now impedance (Rm+jXm) has an angle as well as a magnitude, and therefore it is a vector, while (Bl^2)/Re) is resistive per Beraneks equations, as well as per Small, and also as you used it, and you cannot add the two arithmetically. This gives the wrong velocity at *other than resonance*, whereas Beraneks eq. 7.1 is valid at *any frequency*. This is not a trivial error, it is a major error in fundamental principle. Pity, did you say?
BTW, I did a rather thorough search, and nowhere did you say your velocity equation applied only at resonance, so there is no wiggle room there.
Finally, you stated " some knowledge of phasors would be useful "... True, and we both have some of that knowledge, but knowing how to apply that knowledge in the area we discussed is also useful. Perhaps even more important is to have a non-arsing off approach, but I suppose that may be a built-in trait. Too bad.
Northstar
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degrees = is 2+j2 then A+B =(2+2) +j(0+2) =4+j2= 4.47 @ 26.6 degrees
For a graphical check: Draw a horizontal line of length 2. Put an arrowhead on the right end From the end draw a line of length 2.83 at an angle of 45 degrees upwards and to the right. Put an arrowhead on the end. You have now two vectors. Now draw third vector from the beginning of the first one to the far end of the second vector . This is the vector sum. Measure its length and the angle. . Compare with the numbers above. Please try it.
SO: Ze =Re +Rg +jwLe and, in the situation where Rg and wLe can be ignored (0) then Ze =Re +j0 Now (Bl^2)/Ze then becomes (Bl^2)/Re -j0 as a phasor Adding this to Zm=Rm +jXm leads to (Bl^2)/Ze +Zm = [(Bl^2)/Re -j0] +[Rm+jXm]= [(Bl^2)/Re +Rm] +j[0+JXm] which is [(Bl^2)/Re +Rm] +jXm as I said.
I am saying exactly what Beranek has said. I also repeatedly stated where my Zm differs from his. You are free, and more than welcome to attack what I have said above but please be able to present a strong and valid reasoning. There is no point in just saying that I am wrong- point out where and why you think I am wrong - as you just have- thank you. I will always look again and either show where I disagree with you or admit error.

------------ I certainly don't want to wiggle as it is correct at any frequency. -----------

----------- NO. You have a very rudimentary knowledge of phasors. I have a knowledge of phasors and circuit analysis that has been established, first through multiple circuits courses at undergraduate and graduate levels and also through almost daily use over the past 50 years. This is not boasting but a statement of fact. Practical knowledge of speakers and their construction is your forte- I only built one- a bass reflex enclosure - about 1955 and used a cookbook design at that. However, what we have been talking about so far has been nothing more than a circuit model of a speaker and that is where I have an edge. My first questioning of you was due to statements that you made which did not fit either the model or the physics involved. The rest has followed- some arsing off shared by both of us. Frustration over what could be settled in half an hour or so over a beer.
--
Don Kelly
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says...

for
lack
------------
--------- I am not accusing you of lying. I note that you referred to Beranek using pf where he didn't. I also referred to situations where you have incorrectly interpreted what has been said- as you have done below in your reply. I do not keep a list of your errors but here is an example "Siskind even notes rotor power input (RPI) at start-up simply as (E^2/R^2)*R, which is of course E^2/R. "
He does not say that - it is your interpretation and distortion of what he did say which you later quoted correctly
"Sorry, you are wrong, it is true for an AC machine. Siskind is referring to an *AC motor* in his book "Electrical Machines" vol. 2, (eq. 80), where he states:
RPI = (Ebr^2 / Rr^2 * Xbr^2) * Rr
RPI = rotor power input Ebr = voltage applied to blocked rotor Xbr = reactance with blocked rotor Rr = Rotor resistance"
This is NOT what you originally quoted. Nor does it mean the same. I explained why. There are other things as well but it is not worth while searching them out -------------

models.
------------ ">> For net force, phase must be considered at other than mechanical

I said

----------- To which you responded:
"YES. You gave no phasor info. My correction was appropriate"
--
This came after I re-re- explained that the terms E,I, F,U and Z that I have
used were all phasor quantities. As such they include both magnitude and
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Even though you claim I'm the one in error, I would not continue this, except for your false accusation that most people would construe as calling someone a liar. Therefore you are not going to bluff your way through with a smokescreen, such that your mistake is buried in the ensuing cascade of non-pertinent equations and espousing. You gave the velocity equation as U= (BlE/Re)/(Zm +(Bl^2)/Re). Mechanical impedance is given as Zm=Rm+jXm. This is not debatable, see Beranek eq. 7.36 and Kinsler eq. 1.28. Zm is a vector, (Bl^2)/Re) is resistance, again not debatable. You cannot add the two arithmetically, which you clearly do.
There is a method called try it and see, that will prove who is correct without further argument. I shall now assign typical magnitudes to the terms in Beraneks eq.7.1
E = 2.0 Bl = 8.0 Rg = 0 Re = 6.0 Rms = 1.5 2Rmr = 1.2 Xm = 35.0
Solve for velocity U using Beraneks eq. 7.1, then do the same using your equation U= (BlE/Re)/(Zm +(Bl^2)/Re). If you claim the same result, then prove it by posting your math work showing such. That's it. Either your equation gives the same result or not. If you cannot do this in a straightforward manner, you have proved your own self wrong.

No proof, just implications I lied. One is tempted to namecall, but I'll just say - there you go again... Too bad.

Jesus Christ man, are you daffy, grasping at straws, or what? This refers to the electrical side and we were ignoring coil reactance, giving Siskinds equation #80 as you note above
RPI = (Ebr^2 / Rr^2) * Rr
RPI = Ebr^2 / Rr
Equating Siskinds and our terms:
Ebr = E, and is constant blocked coil or not Rr = Re, and is constant RPI = power in
giving
Power in = E^2/Re
Which is what I originally said, and as given in your quote of what I said above.
Enough of this crap, just do the math at the top of the post. TIA.
Northstar
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Magnitude =(16/6)/root (13.37^2 +35^2) =0.0712 phase angle= (-) arctan 35/13.37= (-)69.1 degrees You can look up why the sign is negative.
Now using my terms:
Zmk =1.5+1.2+j 35= 2.7 + j35 (NOTE: NOT the Zm of Beranek as it doesn't include the Bl^2/Re term)
(Bl^2)/Re .67 (or 10.67+j0 which is the same thing* )
Then
8*2/6 16 16 U = --------------------------- = --------------------- = -------------- [(10.67+j0) +(2.7 + j35) ] (6) [(10.67+2.7) + j (0+35)] (6)(13.37+ j35)
=0.0712 @ -69.1 degrees
Identical. So what's the problem?
*Please note that any scalar can be represented as a vector but the reverse is not true. Vector or phasor arithmetic includes scalar arithmetic as a subset so it is perfectly valid to use phasor arithmetic with scalars (but it is inconvenient and to do so). Normally I wouldn't carry the j0 term along but did so for emphasis.
I gave you an example to try for yourself - evidently you haven't, nor have you even gone to another reference to see how to add vectors or phasors. Why? Don't trust me (as if you did) but look at how it is done. Is that too much to ask? You want to learn but this desire seems to break down when you run into something contrary to pre-conceived notions -so much so that you don't check out the possibility that the pre-conceived notions might possibly be in error. Why? --------------

------ What you interpreted Siskind as saying and what HE actually said are still two different things. What he said is not what you implied that he said. That is my point. Do you get it?
You said that "Siskind even notes rotor power input (RPI) at start-up simply as

This is definitely NOT what he said. You did NOT indicate that, in the case of reactance being negligable, this is what it would be (which is definitely not the case for an induction motor which is the subject of Siskind's equation) but left it as "Siskind says ....."
This is not the only time that you have indicated "xxx says..." when what you are saying is an "interpreted" version hiding as an original quote. That IS crap.
If you wish to quote an author - do it exactly - THEN do your interpretation. Otherwise it is intellectual dishonesty. I don't think it is deliberate lying on your part but has the same effect.
(In this case, your interpretation is about as much use as Siskind's RPI which, out of context, is meaningless (I don't even know why he bothers as doesn't appear to be useful as is) and, given the differences between an induction motor and a speaker, cannot be logically extended to a speaker - an induction motor is more complex electrically and magnetically)
In any case, where Re is the ONLY circuit element involved Pin =E^2/Re is quite correct. No problem there and no need to distort what Siskind actually said. If Re is in series with another resistance or a reactance- then Pin =E^2/Re is incorrect unless E is the voltage across Re alone. Hence in a speaker E^2/Re is the power in, ONLY if there is no coil inductance and there there is no mechanical load (that is blocked coil). In other situations, it is not true and only provides an upper limit to the input power. This has been discussed before so a misquote of Siskind is really not providing any new information.
If you want to think objectively- fine. If not- that's your prerogative and not worth further discussion.
--
Don Kelly
snipped-for-privacy@peeshaw.ca
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This is absolutely UNTRUE. See Google, where I noted on 12 Nov, 2004, that coil inductance was assumed negligible:
http://www.google.com/groups?as_epq=inductance%20of%20the%20coil%20is%20neglec ted&safe=images&ie=ISO-8859-1&as_ugroup=alt.engineering.electrical&as_uauthors =northstar&lr=&hl=en
" IOW the inductance of the coil is neglected for low frequencies per the above, and since that is what is almost universally done, it is what I have done, and shall continue to do. Siskind even notes rotor power input (RPI) at start-up simply as (E^2/R^2)*R, which is of course E^2/R. "
You have a problem dealing with the truth, otherwise are ignorant in relating inductance to reactance. Which is it?
----------
You said" " I note that you referred to Beranek using pf where he didn't."
When ask for proof, you could not do so. You have a problem backing up what you say.
-----------
You said: " I did nothing wrong in adding the impedance Rm and the resistive element Rm. "
Impedance is NOT Rm. You have a problem with the most elementary basics of electronics.
-----------
You said:

You added so: " Zm +(Bl^2)/Re) "
Zm IS a vector, (Bl^2)/Re) IS a scalor. You have a problem with vectors.
-----------
You said"
" why don't you simply learn how to add vectors? "
You have a problem with projection.
---------
You said: " I have no intention of being polite "
You have a problem with the most basic courtesy.
----------- -----------

Your equation is a jumble. Likely deliberate, otherwise you have a problem with the stating of a simple equation. Your equation does NOT equal 0.0712 as written. Otherwise UNJUMBLE it and prove it does, or you are wrong. And it is NOT that difficult to make the equations readable here.
So again, would you please just unjumble your equation and stop wasting our time? TIA
Northstar email snipped-for-privacy@hotmail.com remove the high card to reply
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When I open the post in a separate window and apply a 'fixed' text size to view it, it (Don's equation) is quite readable. Perhaps you need to try a different news reader.
Don starts with a numerator term of '8*2/6' and a denominator term that is the sum of two vectors. The first vector is (10.67 + j0) and the second vector is (2.7 + j35). Adding these two vectors yields [(10.67+2.7) + j(0+35)]. Taking the '/6' term from the numerator to the denominator, he then has just 16 (the results of 8*2) in the numerator term and (6)(13.37+j35) in the denominator.
The 'scalar' 10.67 is a purely resistive element? So to convert this to an impedance vector is trivial, just add j0 as Don did (purely resistive elements have zero reactance). Then adding the vector (10.67+j0) to the vector (13.37+j35) is accomplished by adding the two real terms and adding the two imaginary terms. Don shows this as [(10.67+2.7) + j(0+35)] (13.37+j35).
This *does* work out to magnitude 0.0171174 @ -69.1 degrees, just exactly as he said and like the first form.
daestrom
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daestrom@NO_SPAM_HEREtwcny.rr.com says...

Thank you for clarifying the jumble, and I assume 0.0171174 is a typo, and you meant velocity magnitude as 0.0712 rounded.
First, the original objection I expressed to Dons velocity equation, which he *originally* gave on Nov. 13, 04 as
U= (BlE/Re)/(Zm +(Bl^2)/Re)
Zm as we had used it and as Beranek gives it is Zm=Rm+jXm, where Beranek defines the total mechanical resistance term Rm as
Rm = (Bl)^2/(Re+Rg)+Rms+2Rmr.
Now when Don originally gave the equation and when I originally objected, he had not stated that he had omitted (Bl)^2/Re from Rm and thereby from Zm. Note he has now renamed his impedance term as Zmk. The Zm term in his equation then was the actual total impedance including (Bl)^2/(Re+Rg), and he cannot then add (Bl)^2/(Re+Rg) back to impedance Zm, as it is already included in Zm.
Then if you redo your math above with Dons original equation as stated, i.e. with a single vector term of impedance Zm=Rm+jXm, and where (Bl)^2/(Re+Rg) is included in Rm, plus the resistive term (Bl)^2/(Re+Rg) in the denominator you will get an erroneous result giving velocity as too high in magnitude.
As to adding a vector and scalor per se, note again that Don originally gave mechanical impedance as (Zm +(Bl^2)/Re), which if Zm contains (Bl)^2/(Re+Rg), and noting Don did not say (Bl)^2/(Re+Rg) was excluded, then Zm is a true impedance and a vector, whereas (Bl)^2/(Re+Rg) is resistive and therefore a scalor, and his equation does not include j.
Does this clarify the matter?
Northstar
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arctan
doesn't
problem
0.0712
And
to
a
is
an
adding
as
Zm. ------------- . Somehow you have developed a fixation such that you misinterpreted what I said on Nov. 13
"The equations that you refer to are initially established from phasor relationships. Note that he establishes the fundamental equations for the model in ch3 and these are in phasor terms. These are the same equations that I am using. " This was followed by
"To say that E=ReI +BlU gives I =(E-BlU)/Re and then note that I =F/(Bl) =ZmU/(Bl) to get ZmU/(Bl) =E/Re -BlU/Re and from this get U= (BlE/Re)/(Zm +(Bl^2)/Re) will be correct for phasor quantities E,I, Zm and U. It will not be correct if only magnitudes are used."
The implication there is that the Zm that I was using is the Zm +Zl of Eq.3.60 - It is the actual mechanical impedance plus the acoustic impedance referred to the mechanical side. It is NOT, and never was the Zm that Beranek used in Eq.7.1. Later, I repeatedly explained to you that the Zm that I used was different than that used by Beranek.. This apparently did not get through. ----------------------

-------------- No- Again, you misinterpret: Please note that I said: "OK but I will use Zmb for Beranek's "Zm" and Zmk for my "Zm" in the hope that the difference will be plain to you." I did this as you, even after many repeated explanations, simply ignored what I had said and ranted away on the basis of your (deliberate) misconceptions. I had hoped that the different subscript would make it clear. You are twisting in the wind. ----------------

---------- Hwever, when you do the math with the Zm that I used, (now Zmk) or with the Zm that Beranek used (or Zmb) the result is the same. -----------------

---------- No I did not give mechanical impedance as Zm +(Bl^2)/Re and you bloody well know it.
Note also that (Bl)^2/(Re+Rg) =(Bl)^2/(Re+Rg)+j0 There is no difference as j0 =0+j0=0-j0 =0 and adding zero doesn't change anything. ----------------- As for Siskind: You wrote: "I did NOT modify Siskinds equation 80. That is not my style. I do not play around with equations trying to "win" or "trap" someone as you appear to do. His equation is EXACTLY as I gave it originally with the stipulation that inductance is ignored, WHICH I NOTED IN THE SAME POST AS I GAVE THE EQUATION, as quoted above"
You wrote:Siskind even notes rotor power input (RPI) at start-up simply as (E^2/R^2)*R, which is of course E^2/R. "
This is NOT what he said as indicated by your later quote of what he actually said. You said that the inductance could be ignored and THEN brought in Siskind as "support." As I said before, bring in your reference and then give the result in the case of inductance being negligable. Sorry, the implication that Siskind "notes" that RPI is E^2/R is there but in the actual context of Eq. 80, it is simply not true. Siskind never considers the case of negligable reactance as it simply doesn't occur in the induction motor. To imply that he did is wrong. This is what you have done. It is along the lines of what you claim that I said- what is actually said is made into what you want to be said. Is this deliberate? I don't know but at this stage, I don't give a damn. Also please note that I have given the steps in any derivations of equations and have tried to be sure that all quantities are specified as I have used them. It appears that this is "playing around" to you. I erroneously gave you too much credit for the ability to think.
This conversation is closed.
--
Don Kelly
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No, this is NOT TRUE. On Nov. 13, Per Google, you said:
" U= (BlE/Re)/(Zm +(Bl^2)/Re) "
And in your post IMMEDIATELY PRECEEDING per Google, you defined Zm as
" Zm =Rm +jXm =|Zm| @ zm where |Zm|= root(Rm^2 +Xm^2) "
You definition was EXACTLY THE SAME as Beranek equations 7.1 and 7.36, proving you change history rather than admit an error. Too bad.

Yes, you said that - 15 DAYS LATER, on Nov 28, 04 per Google, in another attempt to change history.

Deliberate misconceptions? Per the above, this is proof of your projection.

You wish.

Now here is the crux of the matter. Although per yourself, you are a whiz at phasors, as is Captain Kirk :) , sorry but you are a miserable failure at putting them in practica in the area we discussed. You gave mechanical impedance as Zm +(Bl^2)/Re, and apparently don't even know it, otherwise you are purposely being disingenuous. Your equation again:
" U= (BlE/Re)/(Zm +(Bl^2)/Re) "
Since velocity = applied force / mechanical impedance, you DID give mechanical impedance as Zm +(Bl^2)/Re. Enough said, except you really should be more prudent in equating my math to sophomoric level. Remarks like that can come back to bite you on the arse.

Unless you cannot comprehend the sequence of my statements in that post, this is a deliberate attempt to imply that I lied, because I said in the SAME post ***PRIOR*** to giving Siskinds equation
" the inductance of the coil is neglected for low frequencies per the above, and since that is what is almost universally done, it is what I have done, and shall continue to do. (in fact Small states input power as E^2/Re, with the coil inductance neglected). "
This was clearly with reference to a speaker motor, not an induction motor. There was NO implication that Siskind considers the case of negligable reactance in an induction motor. Having bobbled your velocity equation, then instead of admitting your mistake, you resorted to personal insult. Too bad.

Your choice.
Northstar
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remove the urine to answer
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PS Lest you become elated :), note all in the equation after [(Bl^2)/Re] is one parameter, i.e. the impedance as you defined it without (Bl^2)/Re. As such, perhaps better stated enclosed as { ---- }
Zm = [(Bl^2)/Re] + { [ Rms +2Rmr ] +j[(wMmd+2Xms)-(1/wCms)] } = 55.88
Same for the following similiar equation using vector addition:
Zm = [(Bl^2)/Re] + { [ Rms +2Rmr ] +j[(wMmd+2Xms)-(1/wCms)] } = 42.38
Northstar
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hope
you
your
and
actual
shorthand
explained
+2Xms-1/wCms]
----------- Since you did not bother to give the frequency, I had to reconstruct. It appears that with the magnitudes that you gave for Beranek's Zm , then Xm8.71 This agrees with the magnitude of 38.78 that you give for Zm'
I get, from Berenak's expression Zm .5+j38.71B.34 @ angle 63.27 degrees
Now Zm' =2.4+j38.71 8.78 @ angle 86.45 degrees
Adding (Bl^2)/Re to Zm' gives 17.1 +(2.4+j38.71) .5 +j38.71 8.78 @ angle 86.45 degrees So (Bl^2)/Re +Zm' = Berenak's Zm in both magnitude and phase.
You set the trap but caught yourself.
It appears that you took root[(17.1^2)+38.78^2)] B.38 and called it vector addition
This is NOT how you add vectors. Where did you get the idea that it was?
Please do as I suggested, and go back and learn how to do it. Add the real components: add the reactive components- then you can use Pythagorus' theorem to find the magnitude. I once asked you to do an example graphically and check it.
--
Don Kelly
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I have taken the liberty to clip all but the technical part you respomded to, and we can discuss the Siskind bit or whatever later if you wish. I used a non-updated set of specs, and the specs should not have included 2Xms. Since the driver was not measured in a vacuum during the mass measurement, the mass of the air load Ma was included in Mmd, and thereby the mass reactance 2Xms (Beraneks Xmr). As the cone moves back and forth, it brings the air load along with it, the air load being stuck to the cone, as it were. Adding 2Xms=5.92 to (w Mmd) throws Zm way off. My apology. Same for leaving out the frequency, but it is simply f78/2 pi = 203.4 Hz. The driver is an 8 inch woofer, operating in a 1 cubic foot sealed box, no stuffing.
So... Shall we start over? I shall solve each equation exactly as before, but with correct total mass reactance, and my comments (as left unclipped above) are unchanged. All your criticism should be unaffected, but the magnitudes will be accurate and valid as a true representation of the driver. So please re-state your criticism, using the correct specs, which I shall now list. Again, my apology and TIA.
--------------------------------------- ---------------------------------------
Bl = 11.01 Re = 7.09 Rms = 1.57 2Rmr = 0.83 w = 1,278 f = 203.4 Mmd = 0.0281 (includes mass of the air load, such that *total* mass reactance wMmd+2Xms = wMmd = 35.91 Cms = 0.000250 E = 1.41 Rg = 0
Directly above you give this equation, saying it agrees with Beraneks Zm:
" =[ (Bl^2)/Re +Rms +2Rmr ] +j[(wMmd+2Xms-1/wCms] which agrees with Beranek's Zm. "
Then with Beraneks Zm, (which you give correctly, BTW), the correct Zm is
Zm = [ (Bl^2)/Re +Rms +2Rmr ] +j[(wMmd+2Xms)-(1/wCms)] = 38.14
Now... you say above: " His Rm does include (Bl^2)/Re. My Rm doesn't " OK, lets do it *your* way, leaving (Bl)^2/Re out of Rm, and call the result Zm'
Zm' = [ Rms +2Rmr ] +j[(wMmd+2Xms)-(1/wCms)] = 43.34 = 32.87
Now you say above " Thus I have my (Bl^2)/Re + Zm =[ (Bl^2)/Re +Rms +2Rmr ] +j[(wMmd+2Xms-1/wCms] which agrees with Beranek's Zm . There is no difference. "
Lets solve for your (Bl^2)/Re + Zm' where Zm' is Beraneks equation with (Bl^2)/Re left out of Rm, as you say you did
Zm = [(Bl^2)/Re] + [ Rms +2Rmr ] +j[(wMmd+2Xms)-(1/wCms)] = 49.97
Thusly, adding magnitudes, you are too high.
or using vector addition
Zm = [(Bl^2)/Re] + [ Rms +2Rmr ] +j[(wMmd+2Xms)-(1/wCms)] = 37.05
and you are too low.
Northstar
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