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Unit Conversions and Gc? Please resolve this conflict!
1a. Let's say you have a formula that is supposed to yield a force. Using SI units, density (kg/ft^3) is one term plugged into a formula...and, along with the other units, the units reduce to kgm/s^2. You say "Ahha! That's a Newton, so I don't need to convert kg to Newtons. So, did you just get lucky that Gc is not needed? Yet, your conscience tells you 1kgmass = 1kgforce <> 1 N, so do you only apply Gc at the end when the units don't work out right?
1b. Then, you run the same exercise in English units and wind up with units of lbft/s^2. You know that's a weird set of English unit so you divide by Gc which (a) does yield the converted answer from (1a) above, BUT (b) the units reduce to being unitless! What's up? That dang Gc thing always messes me up...every dang time. Last edited by Jinx; 11302008 at 09:22 AM. 




I don't get you.
Are you saying that kg/ft^3 is an SI unit? When you say "1kgmass = 1kgforce <> 1 N", what does the "<>" mean? Obviously not "less than greater than", so do you mean "is interchangeable with" or are you representing conversions back and forth? Is the argument that "<>" takes just the "kgforce" or the statement "1 kgmass = 1 kgforce"? I don't like using kilograms to describe forces and am not sure what the conventions are, but would guess that by "kgforce" we mean the weight of a kg mass, which would not be 1 N but rather about 10 N. Sorry, but what is "Gc"? Is it the gravitational constant multiplied by some c? Is it just the gravitational constant, specifically the one relating mass and force in Earth's gravity field? I think it is best to do everything in SI units, and the first operation in using anything that is not already in SI is to convert it there. If you want to use English units too, use slugs. There is too much going on here, but without the formula you're dealing with, for me to figure out what is up. Can you post it? 




Since there are no replies just yet....It has been a long time since I've studied physics but it sounds like you have a pretty basic question. However, I'm trying to figure out just what your question is. Let me see if we can clarify it so that I or someone more knowledgeable can answer it.
1a. Using SI units, density (kg/ft^3) Well, ft are not SI units so you've got me there. If you have volume in ft you need to convert to m^{3} first (maybe you do it further down the road, but you should do those conversions first). ...the units reduce to kgm/s^2. You say "Ahha! That's a Newton, so I don't need to convert kg to Newtons. Well, yes, those units are Newtons, but...a kg in SI is a unit of mass, not force. You can't convert mass to force, unless you want to assume the force of Earth's gravity at a point on the surface... So, did you just get lucky that Gc is not needed? Yet, your conscience tells you 1kgmass = 1kgforce <> 1 N, so do you only apply Gc at the end when the units don't work out right? ...which would be g (the force of gravity at sea level, equal to 9.80665 m/s^{2}), although you're discussing Gcdo you mean the gravitational constant, usually just G (I'm very rusty on that one, though). And again, there is no such thing as 1 kg of force. By 1b I am completely lost. You start with an expression that is supposed to yield a force, and it does. So not sure why you are uncomfortable with that. If you had an expression that yielded mass, and you wanted to find out the force of gravity on that mass, then you would use g. It would also help immensely if you explained just what it is you're trying to figure out in realworld terms before jumping down into units and equations. 






I expect it's to do with the issues mentioned under "Use of pound as a unit of force" in the wikipedia article on Pound force.
Apart from that I've nothing to add, except to repeat that there's no such unit as kgforce, and I wish they'd teach that to the people who translate Discovery programs into Norwegian. 




This is due to the difference in the definition of N and lbf:
1 N == force required to accelerate 1 kg to 1 m s^2 == 1 kg m s^2 1 lbf == force exerted on 1 lbm due to gravity on Earth == 32.174... lbm ft s^2 Suppose you come up with the quantity 42 kg m s^2 after your calculations. You need the answer in N. Since 1 N == 1 kg m s^2, 42 kg m s^2 * 1 (N)/(kg m s^2) == 42 N. However, suppose you need to convert 42 lbm ft s^2 to lbf. 1 lbf == 32.174... lbm ft s^2. Therefore, 42 lbm ft s^2 * (1 lbf / 32.174... lbm ft s^2) == 1.3054 lbf. Hope this helps. 




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That was/is a reasonably common nonSI unit although it is evil. 




Gc is an abomination used by engineers who insist on doing things like using completely different units that happen to have the same name. If you're working in a sane unit system, such as SI, then it's easy to know when to use Gc, because the answer is "never". If you're doing a calculation in SI that's supposed to yield a force, and your answer has any units other than Newtons, then either your formula is wrong, or you made a mistake in your calculations.
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>1kgmass = 1kgforce <> 1 N
CookingWithGas, good idea, maybe it "means not equal". It's tarnished, though, by the obvious inequality that preceeds it, written as an equality. Chronos, about the abomination "Gc"  is it supposed to mean something? What? Better, is it supposed to mean two subtly different and inconvertable things at once? Or, maybe, it's supposed to mean "moment", which is an engineering phrase meaning "don't ask" or "no meaning assigned" or "everybody now argue over what to say"? Jinx, did you just make the whole thing up from random phrases so you could laugh at our attempts? 






I'm glad to see I wasn't the only person baffled by the OP.
And for Chronos, what exactly is this Gc of which you write? I accept your position that it's a kludge, but what's it (supposedly) do? ETA: Napier's latest wasn't here when I loaded this page, so I wasn't trying to pile on. Last edited by LSLGuy; 11302008 at 03:09 PM. 




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I found an example of Gc online. Abomination indeed. But first, to the OP...
Jinx: I would highly encourage you to throw Gc out of your life entirely. Here's what you should be doing for something like F=ma, regardless of the units. Ex 1: m=3 kg, a=9.8 m/s^{2}. Finding F... F=(3 kg)*(9.8 m/s^{2})But, a newton is defined as kg m / s^{2}, so we're there: F=29.4 NEx 2: m=3 kg, a=32.2 ft/s^{2}. Finding F... F=(3 kg)*(32 ft/s^{2})Now we've got a weird combo unit for our answer. The solution: multiply or divide by 1. In particular, you can multiply or divide by any ratio of the form A/B as long as A and B are equal (since A/B would thus be 1). Here, we note that 1 m = 3.281 ftThus, 1 = (1 m/3.281 ft)Multiplying by 1: F=96.6 kg ft / s^{2} * (1)The "ft" in the numerator cancels the "ft" in the denominator. Notice that I'm viewing the units as actual factors multiplied into the expression, not as separate pieces off to the side. F=(96.6/3.281) kg m / s^{2}We again have kg m / s^{2}, which we can replace with the equivalent N: F=29.4 NWe get the same answer, even though in the first case someone decided to report the acceleration in ft/s^{2}. One final example: Ex 3: m=6.6 lb, a=32.2 ft/s^{2}. Finding F... F=(6.6 lb)*(32 ft/s^{2})Here we will need to multiply by 1 twice if we want to get to N. Our two "ones": 1 = (1 m/3.281 ft)Multiplying by 1: F=212.5 lb ft / s^{2} * (1 m / 3.281 ft) * (1 kg / 2.20 lb)The "ft"s cancel and the "lb"s cancel, leaving F=(212.5/3.281/2.20) kg m / s^{2}The beautiful thing about this approach is that it can detect many common errors. That is, if you plug in a number for acceleration that is not an acceleration (say, a velocity), you'll never be able to convert it to newtons. The Gc thing is just taking appropriate multiplybyone factors for various input unit choices and putting them in a table. But, as the saying goes, teach a man to fish and he eats for a lifetime. The Gc tables will limit what you can calculate comfortably. Regrading Gc: What I've found online differs slightly from Chronos's description. ISTM that Gc is used more generally for unit conversions, with a different value for different expected input units. Thus F=ma/G_{c}, and if you will be working with mass in pounds and acceleration in ft/s^{2} and you want force in N, you'd look up G_{c}=7.22. (It pains me not to give that number units.) I didn't dig too deep, though, because in either case, I'm going to back away slowly and pretend like no one is being taught this. 




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The crux of the misunderstanding is that the fundamental units of SI are mass, length, and time; the fundamental units of the imperial system are force, length, and time. All the units for dynamic situations can be derived from these three fundamental units, but the imperial system makes it a pain in the ass. 




I See The Light!
1. Dang! I had a MAJOR blooper in the OP...sorry! The start of the OP should have read "kg/m^3"! Sorry all!
2. Yes, it is an accurate statement put in math shorthand that 1 kgmass = 1 kgforce <> 1 Newton. An expression can have more than one equal sign, ya know. (Like, a= b =c.) In my case, one is simply an inequality, that's all. 3. Chronos, Santo Rugger, and Pasta offer some good advice. Yes, Gc is because engineers have bastardized the units for us. Perhaps the root of the problem stems from trying to Americanize the metric system? I mean, cans of soup express weight in kg. No such animal! It's like a unicorn of science. (Whew! Good thing the unit "slugs" need not appear on a can of soup!) So, someone created the rule that 1 kgmass = 1 kgforce...removing the need for Newtons. (But, they went on to say 1 lbforce = 1 lbmass! Criminal!) About Gc, though: Chronos claims "you pretend Gc is dimensionless...". I wasn't taught it like that. I was taught Gc had the same units as gravity. Often, you see G/Gc tossed into an equation which reduces to "1". This just adds to the confusion over its purpose. (What the heck is the point of G/Gc, anyway?). 4a. Santo Rugger offers good advice on a subtle point. The basic English units are FORCE, distance, and time; however, science is more concerned with mass most likely. Hence, you divide the English result by gravity. This will help me keep things straight. 4b. Last, 4a explains the last part of my OP...if we assume Gc is dimensionless as Chronos suggests. [I hate to say it, but I really got f'd by profs who didn't give a damn about teaching.] Thanks all for the group effort! 






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Only BASICderived ones. A wider variety of commonlyused languages (the ones not called BASIC or Basic) use !=.
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My advice to the OP: Use different units for mass and force. kg should always be mass, so that 1 kg m/s^{2} = 1 N. If for some god awful reason someone is giving you a force in kgforce units, just immediately rewrite this in Newtons. (1 kgforce = 9.8 kg m/s^{2} = 9.8 N)
If you are dealing with both poundmass and poundforce, I would denote them differently, say lbm vs. lbf. That way, at least you know whether a given number written on your paper corresponds to a mass or a force. Where Gc comes in is when someone specifies a mass by telling you the force that mass feels at standard gravity. So, if I say a mass of one pound, you can view this as 1 lbm = 0.45 kg (in which case you don't include Gc at all), or equivalently you can view it as 1 lbm = 1 lbf / Gc = 1 lbf / (32 ft/s^{2}) If you want to express the acceleration in m/s^{2} 1 lbm = 1 lbf / Gc = 1 lbf / (9.8 m/s^{2}) If you want to express the force in terms of Newtons, use 1 lbm = 1 lbf / Gc = 4.45 N / Gc = 4.45 N / 32 ft/s^{2} = 1 N / [(32/4.45) ft/s^{2}] = 1 lbf / Gc(new) Here we changed the value of Gc to absorb the conversion factor. Of course, if we already know the individual conversion factors there's no need to absorb them all into a single factor. We can just apply any conversions one at a time, and I think that's the less error prone way to go. The only reason to put them all in a single factor is so you can just look them all up at once, but as Pasta points out it's easier to check your work if you convert your units explicitly instead of just looking up one factor that changes them all at once. Using just one big conversion factor also makes it seem like you need Gc to change your units. But you don't. You can always just multiply by the equivalent of 1, like Pasta said. The reason you have Gc with units of acceleration is because you converted from a mass unit to a force unit. There was no need to pull those other numerical factors into Gc except to let you look up the combined conversion factor in a book. Note in the above examples you always want to make sure you're only converting force to force, mass to mass, etc. Which is why you don't want to use the same symbol for force units and mass units. Last edited by tim314; 12012008 at 09:12 AM. 




U.S. engineer here...
The whole concept of g_{c} arises because in the USCS (U.S. Customary System), both force and mass are expressed in pounds. (The USCS does not use slugs as a unit of mass, as was done in the imperial system from which it arose.) The poundmass (lbm) is defined as that mass that exerts a force of 1 pound (lbf) at the standard value of gravity at the Earth's surface (g = 32.174 ft/s^{2}). (Note that g_{c} is a universal conversion factor that should not be confused with the local acceleration of gravity g, which may vary from the standard value of 32.174 ft/s^{2}.) Therefore, the poundforce (lbf) is that force which accelerates one poundmass (lbm) at 32.174 ft/s^{2}. Thus, 1 lbf = 32.174 lbmft/s^{2}. The expression 32.174 lbmft/(lbfs^{2}) is designated as g_{c} and is used to resolve expressions involving both mass and force expressed as pounds. For instance, in writing Newton’s second law, the equation would be written as F = ma/g_{c}, where F is in lbf, m in lbm, and a is in ft/s^{2}. I agree with Chronos that the concept of g_{c} is indeed an abomination, particularly with more complex calculations involving viscosity, etc. Many times I have found it easier to convert all of my units to SI, do my calculations, and convert the answer back to USCS. Other times I find myself working in a mixture of USCS and SI units. When working out calculations, it is even more critical for U.S. engineers to always write out the units, or you are sure to screw up the calcs. Last edited by robby; 12012008 at 09:21 AM. 






Suddenly, the whole "Mars lander crashed because we were using different units" makes more sense.
Which brings me to my question... why on earth are you still using imperial for engineering? As you say, you convert into SI to perform the calculations anyway, and it's not like the hoi polloi need to know what units you're working in. Is it really harder to pour concrete in meters? I'm sure China does metric like the rest of the world. So why stay in imperial? 




Agree. Perhaps a better way to say this is that the only place I have ever seen "<>" is in a programming language (Excel also uses it).





The fact of the matter is that there is a unit of mass in the Imperial system
called the slug. I remember this from physics in high school. From Wikipedia: The slug is an English unit of mass. It is a mass that accelerates by 1 ft/s² when a force of one poundforce (lbf) is exerted on it. Therefore a slug has a mass of 32.17405 poundmass or 14.5939 kg.[1] Using pounds as mass is pure crap. 




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Also, while engineers at least learn the SI system in their general science classes, many technicians and construction workers are not at all familiar with it. This goes back to the general abandonment of converting the U.S. to the metric system. (That is, with the noted exception of the hard sciences, such as chemistry and physics, which are universally taught and worked in using SI units.) In addition, all of the tools and instruments (everything from calipers to survey equipment) are in USCS units. Not to mention standard details, drawings, and specifications. Finally, as I noted above, we don't use imperial units. We use a system that is derived from the imperial system, but differs in many ways. P.S. Also, I said that I often convert units to SI for easier calculations. This is uncommon, I think. Perhaps because I used to teach chemistry and physics, I'm very familiar and comfortable with the SI system, and appreciate its advantages. Last edited by robby; 12012008 at 10:16 AM. 




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I agree that the unit of poundmass (lbm) is completely screwed upbut I didn't invent it, either, so I take no responsibility for it. I do recall the day that the units of poundmass, poundforce, and g_{c} were first introduced in one of my engineering design classes. I remember being absolutely floored by how stupid and confusing it all was. Voicing this to the instructor simply resulted in the instructor noting that this was the industry standard. Finally, as an aside, I'll note that from a conceptual point of view, while using the pound as a unit of mass is indeed stupid, it's just as stupid for metric spring scales to be calibrated in units of mass (such as kilograms) instead of newtons. People all over the world routinely confuse force and mass units. 






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I have. I was taught to use slugs in most physics and engineering classes, and use slugs preferentially myself. When I taught classes, I taught using both slugs and poundsmass (as well as SI units). Most of the folks I work with know perfectly well what a slug is, although most also voice a preference for doing calculations in SI units, for reasons that are obvious.





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While I certainly know what a slug is, I have never used the unit. For engineering purposes, I have used only poundsmass and SI units. When I taught physics, I only used SI units. None of the physics textbooks that I have seen over the last decade have used anything other than SI units. I've never heard of the slug as being any more than a historical curiosity. FWIW, the unit is not even mentioned in the supplied reference book for the NCEES Fundamentals of Engineering (FE) exam. Last edited by robby; 12012008 at 01:35 PM. 




FWIW, I used slugs extensively in both fluid dynamics and fluid design. I finished my undergrad about three years ago.





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To convince myself that I'm not misremembering things, I just pulled out my copy of Unit Operations of Chemical Engineering, 4/e, by McCabe, Smith, and Harriott, published in 1985. This book was the text I used as an undergrad for fluid mechanics (among other topics). Slugs are not even mentioned in the text. There is an introduction to the SI system, as well as what the author calls the FPS (footpoundsecond) Engineering system. In this section, the author discusses the necessity of defining g_{c}, called the "Newton'slaw proportionality factor for the gravitational force unit." However, that being said, I've also got an introductory book on fluid mechanics (published in 1999) that I picked up in grad school that only uses the SI system, and what the author calls the "British Gravitational" (BG) system of units. The text goes on to state that the book will not use g_{c} because it is unnecessary in the SI or BG systems. So I guess the upshot is that it depends on the textbook and the instructors as to whether slugs are still used. However, I'll note again that the unit is not mentioned in the supplied reference book for the NCEES Fundamentals of Engineering (FE) exam. Only SI units and poundsmass are used. 






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However, my old dynamics, fluid mechanics, and design books all use slugs preferentially. So, as you say, it probably depends on the preferences of textbook wrriters, and the preferences of the professors who choose the textbooks. 




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g_{c} is in units of (ftlbm)/(lbfs^{2}). Quote:
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Looking up factors on a table (especially ones that don't have units) seems a sure fire way to miss your errors. 




I'm not familiar with a Gc table; I learned it the way Irishman described; specifically, I remember it in the context of "showing all work" when writing out conversions for homework. In my work, I frequently see F=ma carried out where F is just in lbs.; however, there's often a Gc (no units or other notation, just the "Gc") written in the equation.
I also remember encountering slugs as a unit in homework problems. I graduated in December 2006, in case anyone is wondering. 




This is interesting. I'm an engineering student in Canada, and we are learning both the SI system and what I assume is the foodpoundsecond system robby mentions, with slugs tossed in occasionally when the questions were worded that way to begin with. I have never heard of Gc. All of my profs have been very good about stressing the importance of showing unit conversions, so I guess things just get taken care of by doing the math properly in the first place!





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There's also the ever popular ~= or the old keypunch symbol that looks like a hypen with a tail hanging down from the right end. That symbol followed by = was not equals in PL/I. IIRC there are a few older oddballs (SNOBOL anyone?)which use = as not equals as well. 






I don't remember much discussion or consternation over footpounds, slugs, and the like in my fluid mechanics class. Given, though, that I took it almost 10 years ago, I can't say I remember much of anything from fluid mechanics.
I'm really curious if my students are learning all SI or have to deal with this too. Most of them are currently also taking fluid mechanics. I think I'll ask around tomorrow, but I have the sneaking suspicion that they'll look at me like I have three heads. (They do that enough as it is!) Based on how upset they were when I used gallons in class the other day, I'm thinking they actually haven't had much exposure to engineering in nonSI units. Come on, guys, how else are we gonna do calculations related to the fuel economy of US cars? 




I just realized it may be due in large part to the fact that my fluid and thermal design instructors used to work in the oil fields. Those petroleum guys mix units as much as explosives guys (cal/g? WTF?).





What's so odd about calories per gram? They're neither of them SI, but they're both metric, and given that a calorie is defined in terms of the heat capacity of a gram of water, that seems like a perfectly sensible unit to me, in the right context at least.





Pascal uses it, too, but there's a chance they all got it from BASIC: The first version of BASIC was created in 1964, years before both Pascal and SQL.
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We could go back to the old FORTRAN conventions and use .NEQ. for this purpose. Last edited by Derleth; 12022008 at 01:42 AM. 






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Force = mass times acceleration. If instead of telling you the mass, I tell you the object's weight under standard gravity, then you need g_{c} to convert from weight to mass. Last edited by tim314; 12022008 at 02:27 AM. 




I've never, ever used calories as a unit for anything in a calculation other than when predicting detonation energy. Pretty much all the intermediate calculations are done in calories, which are then compared to TNT (which is defined as having 1,000 calories per gram) to give the equivalence. It seems so odd to me because I've never used it for anything else.





>The crux of the misunderstanding is that the fundamental units of SI are mass, length, and time; the fundamental units of the imperial system are force, length, and time.
I don't think this is the crux. Which units are fundamental and which ones are derived are of interest in the field of metrology, but people applying the technology of measurement don't need to know. >Suddenly, the whole "Mars lander crashed because we were using different units" makes more sense. >Which brings me to my question... why on earth are you still using imperial for engineering? Oh, God, yes, this is a nightmare. The reason we still use imperial or English or US Customary units is that most of the engineering components used in industry are sold in these sizes, and many physical value references are in these units, and most measurement devices measure with these units. The USA spends an enormous, enormous sum every year carrying all this horrible baggage along, for what seems to those of us doing the carrying absolutely no reason at all. Almost every single thing I figure out, my first step is betting on whether it will be more efficient to convert to SI at the start and then back at the end, or more efficient to try to use the imperial units without making any mistakes. And, if you think it's awkward when calculating forces, just wait till you try heat transfer coefficients! 




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If the reason I gave isn't the crux, then what is? 




It's the crux in so far as the familiar, commonly used unit is force instead of mass. You could treat the foot, slug, and second as the fundamental units: There's nothing about the unit system which forces you to call one thing or another "fundamental". Compare the SI electrical units, where officially it's the amp that's fundamental and a coulomb is one ampsecond, but where in practice everyone treats it the other way around.
The problem, though, is that slugs are so rarely used, while pounds are ubitquitous. In SI, a quantity of something is typically expressed in kilograms, mass units, while in the American system, such a quantity is typically expressed in pounds, force units. It's even further complicated by the fact that there's at least three different treatments of pounds in the US system(s). You can treat pounds as the force unit and slugs as the mass unit, or you can use pounds as the mass unit and poundals as the force unit, or you can use pounds as the mass and force unit, and throw Gc willynilly into all the formulae. 






In high school (including advanced physics), I was taught there are the SI and English units. We used slugs all the time for English. At some point, I recall a discussion on how can a scale meaure weight in kg, and not Newtons? This really confused me. This led into the concept of kgmass (kgm) and its evil twin, the kgforce (kgf). Luckily, knowing 1 kgf = 1kgm makes it simple to sidestep the whole issue. It's like it was dummieddown for the public who couldn't be bothered to understand Newtons. This discussion led into a mention of poundmass (lbm) and poundforce (lbm)...which I just accepted as being analogous to the kgm and kgf.
I never heard of the USCS set of units in high school. In college, I recall a mention of USCS units in a drafting class (c.1985just before CAD came out fullforce), but it didn't mean much. It sure looked like English units to me! Someone should have stressed the subtle differences, but no one did. As I recall, it was in Thermo where we had to solve problems in both SI and English and this started to become problematic. Here, we were taught about "gc" in a sloppy way perhaps by those who lacked a firm understanding themselves! Also, our English units problems were always in lbf and lbm. No mention of "slugs". The book was even deemed a SIEnglish version (as it could come as one or the other or both). Last, in all my years (other than that drafting class), no one ever bothered to differentiate between English and USCS...and I always wondered why we never spoke of "slugs" anymore. Personally, I thought the whole lbm and lbf business was because someone was bothered by calling a unit of measure a "slug"! 




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Don't get me wrong...I prefer SI units in principle. I find them easier to work with and less prone to causing me to make mistakes. But I use British units more because they're customary in the fluid dynamics world. Like it or not, airplanes fly at somanythousand feet, weigh somany pounds, and their engines provide somany pounds of thrust. When all the numbers you're given are in Imperial units, it only makes sense to stick with that system. Otherwise you spend all your time converting units back and forth and end up crashing your space probe. Even worse is that the CFD weenies I have to interact with love to use "snails", which is equal to 12 slugs (that way, 1 lb = 1 snail * 1 in/s^{2}). Next time they give me a mass flow rate in snails/s, I'll be sure to slug them. Or pound them. 




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>I disagree. Note that basically the entire discussion has been the difference between pound mass, pound force, the use of slugs, etc. Since mass is not a fundamental unit in the imperial system, you must do some conversion that's not done in the SI system.
The crux of this discussion is the use of force versus mass, and the further confusion of creating new units that represent the masses associated with various forces or the forces associated with various masses. You can measure mass and force in the Imperial and SI systems. If you want not to use slugs, then there is an inconsistency in the Imperial system to keep track of. However, the issue of which units are fundamental in any system is an entirely different thing, and it is not of interest or use to people wrestling with the problems in this thread. The organizations like NIST that take responsibility for defining and improving measurement standards have a difficult job reconciling the results of various fascinating experiments in a way that is forwardthinking and yet deals effectively with history too. A year or two ago there was a fascinating article in Scientific American about an attempt to make very precise spheres of crystalline silicon, so that the number of atoms in the sphere could be very accurately calculated (maybe to 7 digits, IIRC). These spheres would then become mass standards, replacing the archaic platinumiridium alloy master cylinder stored in France, and the several copies of it that normally live in other countries. Those cylinders have to be painstakingly moved together and compared every so often. Worse, the master appears to be gaining weight relative to all the copies. This is the issue of which units are fundamental. This is what makes the issue interesting and important. There was a fascinating review article in Physics Today perhaps 5 years ago or so about the latest regression analysis of various experimental results relating the various fundamental and derived units. You can also get some idea of this topic browsing the NIST website. But, in discussions like the OP, it is enough to go looking up (on the NIST website if you are obsessed or in the CRC handbook or anyplace else if you aren't) the conversion factors between units. You never have to know which ones were the fundamental ones. 