Home |
Search |
Today's Posts |
#81
![]() |
|||
|
|||
![]()
On Thu, 25 Sep 2003 01:16:33 GMT, Dave Shrader
wrote: Gene Nygaard wrote: [SNIP] Apparently you are claiming that pounds are not units of mass. Where did you learn that? Well, I learned that a Pound is a unit of Force. Well, I learned that a Slug [pound mass] is Pound*acceleration. Well, I learned that mass is pound*sec^2/foot. Where did I learn this? What's my source? Physics 101, University Physics, Sears and Zemansky, Addison-Wesley Publishing, 1956, Chapter 6, page 94. I hope tou don't need another reference? Now, what's your real problem? What are you trying to say? Can you quote it to me, specifically where it says that pounds are not units of mass? I'll bet you just misunderstood what it said. I have the 1970 edition of Sears and Zemansky myself, so I'm betting that if anything, what it actually says is clearer in that older edition than it is in the 1970 edition. Pounds force do exist, of course. What I'm asking you to show me is not that, but rather that pounds are not units of mass. Sears and Zemansky didn't lie about this in 1956. They might have been dishonest and deceptive about it, not concerned enough about the possibility that fools like you would misinterpret what they said or actually encouraging such misinterpretation. But they didn't lie about it. Some textbooks today might actually lie about it (or, alternatively, their authors are too poorly educated to know any better--take your choice). Gene Nygaard Dave, W1MCE Being the skeptic that I am, how can I convince myself that that is true? Is there some textbook, or something from some national standards agency, that would help me verify this? Gene Nygaard Gene Nygaard http://ourworld.compuserve.com/homepages/Gene_Nygaard/ |
#82
![]() |
|||
|
|||
![]()
On Wed, 24 Sep 2003 21:04:11 GMT, Richard Clark
wrote: On Wed, 24 Sep 2003 20:15:51 GMT, Gene Nygaard wrote: A balance, by implicit definition again, consists of comparing two masses under the influence of Gravity. Given it is a bridge, in a sense, the constant of Gravity is discarded from both sides and mass is compared only. It is a convenience of earthly expectations (and a defunct system of measurement) that the scale is marked in pounds. The matter of convenience is in the other direction, stupid; we're willing to substitute cheapness for accuracy in what we want to measure on those unreliable bathroom scales. They aren't any more accurate for measuring force than they are for measuring mass on Earth; haven't you ever weighed yourself on your mother's scale or somewhere else and found it differed from yours at home by several pounds? Do you automatically assume you've gained or lost that much weight. I've nowhere introduced the topic of accuracy. It has nothing to do with your original query. Weight and mass can both be measured to considerable accuracy. It all depends on method and standards. And mass can be measured with much more accuracy than force can, but that is entirely irrelevant to the point I was making. Your claim was that the mass-measuring balances are, for a matter of convenience, marked in units of force called pounds. I say that it is in fact the other way around, that the cheap force-measuring spring scales are marked in units of mass, which is indeed what we want to measure. The kilograms used throughout the world, including most hospitals in the U.S., for human body weight are indeed the proper SI units for this quantity. The pounds used for this purpose are the ones legally defined as 0.45359237 kg. Except, of course, for some science teachers and some physics books written recently by authors so miseducated (not uneducated, but actually mistaught) that they believe pounds are not units of mass. American Society for Testing and Materials, Standard for Metric Practice, E 380-79, ASTM 1979. 3.4.1.2 Considerable confusion exists in the use of the term weight as a quantity to mean either force or mass. In commercial and everyday use, the term weight nearly always means mass; thus, when one speaks of a person's weight, the quantity referred to is mass. . . . Because of the dual use of the term weight as a quantity, this term should be avoided in technical practice except under circumstances in which its meaning is completely clear. When the term is used, it is important to know whether mass or force is intended and to use SI units properly as described in 3.4.1.1, by using kilograms for mass or newtons for force. This ASTM E 380 and a separate ANSI/IEEE Standard have now been combined into a joint standard SI 10. I don't know if it says exactly the same thing; but I am certain it doesn't say anything directly contrary to this. Of course, NIST also tells us the same thing. I'll get to that below. A bathroom scale is not a balance. A balance has a scale (the marks along which the balance weights are moved and the markings upon those same weights). However, you do ask for a reference and acknowledge the NIST as a reputable source (many here ignore this commonplace): http://physics.nist.gov/PhysRefData/...constants.html There is absolutely nothing about pounds on this page. So don't be bull****ting us. That is the whole point. You don't see pounds there for mass do you? I don't see pounds as units of mass because this page just lists units in the International System of Units. Exactly. So why were you offering it as evidence that pounds are not units of mass? Do you think I'm that stupid, that you can pull the wool over my eyes so easily? Guess again. Show me something from NIST saying that pounds are not units of mass. Or from some textbook. That's because pounds are not a unit of mass. They are a unit of weight which is NOT a constant throughout the universe (nor on earth for that matter). Just your say-so? That's the best you can do? I am a trained Metrologist. I have measured mass traceable to the NIST. I have done this in four different Primary and Secondary Standards Labs. I was the head Metrologist of two of them. Wow! This is even better than I dreamed of. A genuine Capital-Letter Metrologist. Of course, it's also pretty sad, as most people will understand if they stick with me for the rest of this message. I'm sure that as a Metrologist, you are well aware of one particular subset of English units, used only in calculations, which is a coherent, gravitational foot-pound-second system in which the derived unit of mass is a slug, equal to 1 lbf·s²/ft. One of several such subsystems, of course. But if you are really a capital-letter Metrologist, and an old fart on top of it (that system with the slugs was never used in physics textbooks before 1940, and even a couple of decades later I learned the system I'm about to describe first, before learning the one with slugs--and you must be at least close to my age, and a genuine expert on weights and measures on top of it all), you'll have a damn hard time convincing me, or anyone else, that you are also not aware of a much older coherent foot-pound-second system of mechanical units, the absolute fps system in which the derived unit of force is the poundal, the force which will accelerate the base unit of mass in this system at a rate of one foot per second squared. Now, fill in the blank, please: The BASE UNIT OF MASS in this oldest English system of mechanical units is the _______________. Hint: it is the "p" in this fps system. BTW, while the gravitational fps system of units enjoyed a brief heyday in science in North America, outside of North America the absolute fps system with poundals remained the system of choice for doing calculations in English units. You probably also know that both of these limited use, coherent systems of units are, like SI, coherent systems of units. That means that in neither of these do we have any pints or gallons of any sort, not U.S. liquid, not U.S. dry, and not imperial. Nor are there any Btu, nor horsepower, in either system. Not only that, but there are no ounces (neither avoirdupois nor troy, nor U.S. nor imperial fluid ounces), no tons (neither long nor short, neither force nor mass), and no miles or inches (and thus no pounds force per square inch either). Of course none of our ordinary measurements are made in the context of any of these specialized systems of mechanical units which serve as calculation aids. The fact that many of the we use are not part of these systems is one bit of evidence of that fact. That fact that nobody ever measures (as opposed to calculating from other measurements) mass in slugs is another. The fact that we can generally choose any of several different systems of units to use in our calculations, with no change in difficulty, is still another piece in the puzzle. Let's look at what the English physicists William Thomson (for whom the SI unit of temperature is named) and Peter Guthrie Tate had to say about this way back in 1879, Treatise on natural philosophy, 1879, reprinted as Principles of mechanics and dynamics, quoted by Jim Carr in Apr 1998 on newsgroups alt.sci.physics, sci.engr, sci.physics. "By taking the gravity of a constant mass for the unit of force it makes the unit of force greater in high than in low latitudes. In reality, standards of weight are masses, not forces. They are employed primarily in commerce for the purpose of measuring out a definite quantity of matter; not an amount of matter which shall be attracted to the earth with a given force." ... description of merchant using spring scale to defraud or be defrauded depending on latitude, etc ... Jim Carr "It is therefore very much simpler and better to take the imperial pound ... as the unit of mass, and to derive from it, according to Newton's definition above, the unit of force." Then you might also know what "weights" means in the English versions of the international bodies charged with keeping our international standards: CGPM General Conference on Weights and Measures CIPM International Committee for Weights and Measures BIPM International Bureau of Weights and Measures In the introduction to their SI brochure (available at http://www.bipm.fr), the BIPM tells us for the first half-century of their existence, their only responsibility was keeping the standards for length and for mass. Take a wild guess which of those two corresponds to "weights" in these names. I can, OTOH, prove that pounds are indeed units of mass. By a reference found at the NIST? I think you would have done that by now if you could. Cocky little *******, aren't you! Just making clear that you accept the fact that doing so would prove you wrong, before I do it. I have already done so, of course, without referring to NIST, with that description of the absolute fps system above. But before we get to wandering around NIST's website, let's do a little primary source research, and find the definition which NIST considers controlling. For that we need to look to NIST's predecessor, the National Bureau of Standards, and to the law of the land. Earlier in the 20th century, Congress had had the sense to delegate the authority to make these definitions to the experts in the field who know what they are doing, and had given the predecessor of NBS this authority. This was officially implemented in 1959 by official regulatory action by NBS, made official with its publication in the Federal Register of 1 July 1959. This redefinition of the pound was done in accordance with an agreement reached among the national standards laboratories of several of the most advanced nations in the world, not back in the Dark Ages but in the middle of the 20th century, two years after Sputnik and the year before the International System of Units was introduced. The old U.S. definition, which had been a slightly different exact fraction of a kilogram for the 66 years before then, was replaced by the new international definition as 1 lb = 0.45359237 kg. You can read the current U.S. law (this Federal Register Notice), as well as a discussion of the earlier U.S. law and of the international agreement, at one of these web sites (same document both places): http://www.ngs.noaa.gov/PUBS_LIB/Fed...doc59-5442.pdf http://gssp.wva.net/html.common/refine.pdf Of course, the same definition is was also adopted in Canada, in the U.K., in South Africa, in Australia, and in New Zealand, the other parties to this international agreement. It is also used all around the world, and was adopted by statute or regulation in some other countries not a party to the original agreement, such as Ireland. Now, let's get to the NIST web site. You obviously didn't follow the links you provided to get to the right place. Start with the one you recommended http://physics.nist.gov/cuu/Units/units.html click on Return to Units Home Page which takes you back up one level to http://physics.nist.gov/cuu/Units/index.html click on Bibliography: Online publications and citations to go to http://physics.nist.gov/cuu/Units/bibliography.html Go down to NIST Special Publication 811 and first of all, order yourself a free printed copy of this document. You need it. Then look at it in the online version, either in .html or in .pdf, whichever you prefer. I'll use the html version to give some links to specific parts of it below; I also have the printed version, and I have the .pdf version right on my computer. I already know what you think of NIST. In another message, you told us that "NIST describes all this at the links offered and they do not equivocate nor banter terms casually. For any Professional Engineer, they carry the force of law as the only authoritative source for definition. " This is NIST's official _Guide for the Use of the International System of Units (SI)_, by Dr. Barry N. Taylor, reviewed and approved by both the director of NIST and by his boss, the Secretary of Commerce. It is cited as an authority not only by many of the national standards agencies around the world, but also by the BIPM itself. First, a word about Dr. Barry N. Taylor. He is not only a professional metrologist with a Ph.D. in physics, but he has also served on both the Consultative Committe on Units which advises the CGPM (still on that, I think), and on the SUNAMCO Commission (Commission on Symbols, Units, Nomenclature, Atomic Masses and Fundamental Constants) of the International Union of Pure and Applied Physics (IUPAP). In other words, for the benefit of anyone else reading this, if Richard Clark is a "Metrologist" then Dr. Barry Taylor must be a "METROLOGIST" because even capitalizing all the letters won't adequately show the difference between the two, especially when it comes to expertise in the particular subfield related to teh definitions of units of measure. First, before we get to the pounds, let's digress a little bit and finish up that loose end I left above. http://physics.nist.gov/Pubs/SP811/sec08.html Thus the SI unit of the quantity weight used in this sense is the kilogram (kg) and the verb "to weigh" means "to determine the mass of" or "to have a mass of". Examples: the child's weight is 23 kg The same is true for pounds, of course. Units of mass in this context, as the term is used in physiology and medicine, and in sports--the reasons we normally weigh ourselves. There's more to the explanation in section 8.3, including a good discussion of the force definition of weight often used in physics and engineering. This section concludes with the excellent advice that whenever the word 'weight' is used, it should be made clear which meaning is intended. Now, let's go to the extensive list of conversion factors found in Appendix B to SP 811. http://physics.nist.gov/Pubs/SP811/appenB8.html#P To convert from to Multiply by pound (avoirdupois) (lb) 23 kilogram (kg) 4.535 924 E-01 pound (troy or apothecary) (lb) kilogram (kg) 3.732 417 E-01 [The 23 is a reference to a footnote in the printed and pdf versions, a note on a separate page in html] http://physics.nist.gov/Pubs/SP811/footnotes.html#f23 23 The exact conversion factor is 4.535 923 7 E-01. All units in Sec. B.8 and Sec. B.9 that contain the pound refer to the avoirdupois pound. This unit, of course, is not defined by this publication. This is just the legal definition made by NBS in 1959. Also, take a look at another section of American Society for Testing and Materials, Standard for Metric Practice, E 380-79, ASTM 1979. 3.4.1.4 The use of the same name for units of force and mass causes confusion. When the non-SI units are used, a distinction should be made between force and mass, for example, lbf to denote force in gravimetric engineering units and lb for mass. As you can see above, this sensible rule is also followed by NIST. It is also followed by NPL, the U.K. national standards laboratory. It is the older unit, the one more often used, and the one more likely to be used by those who care least about the distinction, which gets to use the original, unadorned symbol "lb"; it is the recent *******ization, the less often used unit, and the one more likely to be used by those who care most about the distinction, that must be distinguished by using a different symbol, "lbf" instead. That will prove that you are flat-out wrong in your claim that they are not. Well, I have seen a lot of math tossed over the transom here. But if we are to work by your own standard, cite an NIST reference. Just for practice, consider the troy system of weights. Unlike their avoirdupois cousins, and unlike grams and kilograms, the troy units of weight have never spawned units of force of the same name. They are always units of mass; a troy ounce is exactly 31.1034768 grams, by definition. There is not and never has been any troy pound force or troy ounce force. Hi Gene, Sounds like you proved a pound is not mass. No. You just proved that you are hopelessly ignorant when you get outside your fields and start discussing things such as linguistics, history, or the law. The pages I offered provide a meaningful quote: "The 3d CGPM (1901), in a declaration intended to end the ambiguity in popular usage concerning the word "weight," confirmed that: The kilogram is the unit of mass..." One of the most confusing and impossible to understand resolutions any political body has ever passed. You will note that NIST places no emphasis on this whatsoever. Yes, even then there were evidently enough scientists so utterly confused as to think that the standards they were keeping were standards of force rather than the standards of mass which they always had been. As were the old standards for pounds, naturally. Of course, by that time, we in the United States has already abandoned our independent standards for pounds, and we already defined them as an exact fraction of a kilogram. So where does that lead you? But of course, you are making a big mistake you think that this particular resolution meant that we couldn't use kilograms force. In fact, it was just the opposite--this very same resolution endorsed the use of grams force and kilograms force by adopting a standard acceleration of gravity, which is not a concept of physics but rather of metrology, something which serves no purpose other than defining units of force in terms of units of mass. Kilograms force had never been well-defined units before then. Neither had pounds force, of course--and what's more, even today pounds force don't have an official definition. The de facto standard, never officially adopted by any national or international standards agency, nor by any professional organization, is probably to use the same standard acceleration of gravity which is official for defining grams force and pounds force, namely 980.665 cm/s² in the units used in that 1901 resolution, before mks systems had come into use, at a time when neither slugs nor newtons had ever been used for the units they are now. Now go back to that Bibliography page on NIST and download NIST Special Publication 330, which includes the unofficial English version of this resolution, or at least the salient parts of it. http://physics.nist.gov/cuu/Units/bibliography.html Then pay special attention to the footnote added by NIST, found on page 17 in the document's own pagination (I don't know the page number in the pdf format): [dagger] USA Editor's note: In the USA, ambiguity exists in the use of the term weight as a quantity to mean either force or mass. In science and technology this declaration [CGPM (1901)] is usually followed, with the newton the SI unit of force and thus weight. In commercial and everyday use, weight is often used in the sense of mass for which the SI unit is the kilogram. Any other usage of "weight" in regard to the sensation of the action of Gravity upon an amount of mass is outdated by more than a century of understanding and convention. You said weight is a force. This resolution clearly said that weight is not a force, but merely something "in the nature of a force," whatever the hell that is supposed to mean. But fortunately, in any case, nobody was ever damn fool enough to give the 1901 CGPM any say-so on what "weight" means for the "net weight" of my bag of sugar, or for the troy weight of a bar of gold or platinum. That's outside their authority. That resolution isn't seriously offered as proof of any change in meaning of the word. In fact, I doubt that the 1901 CGPM ever intended to change the meaning of the word--they wrongly thought that they were merely stating existing definitions. "Outdated by more than a century of understanding and convention"? Nonsense. Go back and read that section 8.3 of NIST Special Publication 811 again. That's 1995--hardly a century ago. Need more. Here's 1989, in the still-effective official National Standard of Canada, CAN/CSA-Z234.1-89 Canadian Metric Practice Guide: 5.7.3 Considerable confusion exists in the use of the term "weight." In commercial and everyday use, the term "weight" nearly always means mass. In science and technology, "weight" has primarily meant a force due to gravity. In scientific and technical work, the term "weight" should be replaced by the term "mass" or "force," depending on the application. 5.7.4 The use of the verb "to weigh" meaning "to determine the mass of," e.g., "I weighed this object and determined its mass to be 5 kg," is correct. Note that "nearly always" is much stronger than "primarily"; they even got that part right. Note further the difference usage for the noun forms in 5.7.3 and the verb forms in 5.7.4; for the former, the meaning is context-specific, but for the latter that definition is unqualifiedly called "correct" (which does not, of course, say anything one way or the other about the use of the verb to mean to determine the force due to gravity, which is also correct). Need more. Here's 2003, on the web pages on the National Physical Laboratory (NPL), the official national standards agency of the United Kingdom of Great Britain and Northern Ireland: NPL FAQ http://www.npl.co.uk/force/faqs/forcemassdiffs.html Weight In the trading of goods, weight is taken to mean the same as mass, and is measured in kilograms. Scientifically however, it is normal to state that the weight of a body is the gravitational force acting on it and hence it should be measured in newtons, and this force depends on the local acceleration due to gravity. To add to the confusion, a weight (or weightpiece) is a calibrated mass normally made from a dense metal, and weighing is generally defined as a process for determining the mass of an object. So, unfortunately, weight has three meanings and care should always be taken to appreciate which one is meant in a particular context. Note that they are talking about DIFFERENT MEANINGS of the word "weight." Just as NIST does. Just as ASTM does. Just as the Canadian Standard for Metric Practice does. Just as any good dictionary does. That, of course, is how the word weight entered the English language over 1000 years ago, meaning the quantity measured with a balance. A quantity which you yourself explained so lucidly to be mass, not the force due to gravity. Of course, when those tribesmen in what is now England were looking for a word to use to measure how much stuff they have, when they buy and sell goods, they didn't make any mistake when they invented this word "weight" for that purpose, did they? They couldn't have used "mass" for this quantity instead, unless they had happened to choose those phonemes for the word they invented. Mass didn't have this meaning until more than 750 years later, when some obscure translator translated Newton's major work into English after Newton's death. Or do you think it was a mistake that these heathens didn't figure out the God-given word they were supposed to invent for this purpose? There is no error when we use the very same word, with the very same meaning, for the very same purposes today. We have a prior claim to this word by 3/4 of a millennium over the physicists who recently borrowed it and often use it with a somewhat different meaning. Sometimes we borrow the physicists meaning, sometimes we use the original meaning. But like all the experts tell you, because of these ambiguities, you should just avoid using the term "weight" in a technical context--and if you do use it, make damn sure your meaning is clear. Gene Nygaard http://ourworld.compuserve.com/homepages/Gene_Nygaard/ Gentlemen of the jury, Chicolini here may look like an idiot, and sound like an idiot, but don't let that fool you: He really is an idiot. Groucho Marx |
#83
![]() |
|||
|
|||
![]()
On Thu, 25 Sep 2003 03:41:10 GMT, Gene Nygaard
wrote: Do you think I'm that stupid, that you can pull the wool over my eyes so easily? Hi Gene, As I pointed out earlier, your feelings belong at the end of the line with the rest whose minds I cannot change. 73's Richard Clark, KB7QHC |
#84
![]() |
|||
|
|||
![]()
Gene Nygaard wrote:
Apparently you are claiming that pounds are not units of mass. Where did you learn that? Being the skeptic that I am, how can I convince myself that that is true? Is there some textbook, or something from some national standards agency, that would help me verify this? Gene Nygaard Nice web page you have on the subject, but I suspect it is not quite so cut and dried as you make out. I have a strong recollection (from many years ago) of being taught that pounds where force. Going to google with 'pound mass force' yields some modern university teaching material which says the same. My ancient thermo text uses lbf and lbm throughout to eliminate confusion. There seems to be little doubt that today the pound is defined in terms of the kilogram so is clearly a unit of mass. But usage of the pound seems to be less consistent. Consider pounds per square inch or foot-pounds; in each of these the pound is a unit of force. I expect the definition of pound will be argued for some years to come. Let's just all go metric. The only really confusing measure there seems to be the definition of the litre. ....Keith |
#85
![]() |
|||
|
|||
![]()
Gene, thanks for the compliment in calling the Program Chief Engineer
of the USAF MX [Peacekeeper] Re-Entry System/Re-Entry Vehicle a fool. It says a lot about you. I forgive you. Dave, W1MCE + + + Gene Nygaard wrote: not concerned enough about the possibility that fools like you |
#87
![]() |
|||
|
|||
![]()
On Thu, 25 Sep 2003 12:13:47 GMT, Dave Shrader
wrote: Gene, thanks for the compliment in calling the Program Chief Engineer of the USAF MX [Peacekeeper] Re-Entry System/Re-Entry Vehicle a fool. It says a lot about you. I forgive you. Gee, if I'd known you were so important, I'd really have taken you to task for being too damn stupid to understand what you read in Sears and Zemansky! Gene Nygaard http://ourworld.compuserve.com/homepages/Gene_Nygaard/ |
#88
![]() |
|||
|
|||
![]()
On Thu, 25 Sep 2003 12:13:47 GMT, Dave Shrader
wrote: Gene, thanks for the compliment in calling the Program Chief Engineer of the USAF MX [Peacekeeper] Re-Entry System/Re-Entry Vehicle a fool. It says a lot about you. I forgive you. Dave, W1MCE + + + Gene Nygaard wrote: not concerned enough about the possibility that fools like you Since you aren't honest enough to tell us exactly what Sears and Zemansky said in 1956, I'll tell everyone what they said in 1970. If there are any significant differences, feel free to point them out. This thing is, I know that Sears and Zemansky weren't going to lie about this, because they grew up using poundals, which are by definition the force which will accelerate a MASS of 1 lb at a rate of 1 ft/s². Francis Weston Sears and Mark W. Zemansky, University Physics, Addison-Wesley, 4th ed., 1970. [page 3] 1 pound mass = 1 lbm = 0.45359237 kg [The actual number will, of course, be different in 1956, because the U.S. didn't adopt this definition until 1959 (it had been in use in Canada since 1953, six years before the international redefinition).--GAN] [page 4] We select as a standard body the standard pound, defined in section 1-2 as a certain fraction (approximately 0.454) of a standard kilogram. [page 59] In setting up the mks and cgs systems, we first selected units of mass and acceleration, and defined the unit of force in terms of these. In the British engineering system, we first select a unit of force (1 lb) and a unit of acceleration (1 ft s^-2) and then define the unit of mass as the mass of a body whose acceleration is 1 ft s^-2 when the resultant force on the body is 1 lb. end quote Now, Sears and Zemansky might be incompetent for not allowing for the fact that there are going to be people out there who are too blamed stupid to understand that that adjectival phrase "British engineering" has some meaning, and that it identifies one particular limited subset of the British units. It's perhaps even understandable, because that fact would be quite clear to anyone who, like them, had grown up using poundals in a "British absolute" system of units. However, that doesn't change the fact that you are in fact one of the people who are that stupid. -- Gene Nygaard http://ourworld.compuserve.com/homepages/Gene_Nygaard/ "It's not the things you don't know what gets you into trouble. "It's the things you do know that just ain't so." Will Rogers |
#89
![]() |
|||
|
|||
![]()
On Thu, 25 Sep 2003 12:13:47 GMT, Dave Shrader
wrote: Gene, thanks for the compliment in calling the Program Chief Engineer of the USAF MX [Peacekeeper] Re-Entry System/Re-Entry Vehicle a fool. Is that as good as being chief of the Mars Climate Orbiter program as evidence of competence in the use of units of measure? Gene Nygaard http://ourworld.compuserve.com/homepages/Gene_Nygaard/ |
#90
![]() |
|||
|
|||
![]() |
Reply |
Thread Tools | Search this Thread |
Display Modes | |
|
|
![]() |
||||
Thread | Forum | |||
50 Ohms "Real Resistive" impedance a Misnomer? | Antenna |