We are getting overly deep into a minor point, not worth it. However, in my view poundals and slugs are not "real" units, they are inventions to fix the coherence problems in F = ma, and not the native units in which anything is measured. Some people (mostly aerospace) instead invent a unit of acceleration in gravities to fix the coherence problem and use lbf and lbm. I am also not advocating ANY of the three ways, but I view them all as about equally invalid. The approaches all involve two real units, and an invented unit for purposes of coherence whether (poundals, pounds-mass, ft/s²), (pounds-force, slugs, ft/s²), or (pounds-force, pounds-mass, gravities). They all involve slipping a factor of approx. 32.17 into the equation and it can be slipped into any of the three variables by unit invention.
The important point is that all are inferior to (newtons, kilograms, meters per second squared) ________________________________ From: "mechtly, eugene a" <mech...@illinois.edu> To: U.S. Metric Association <usma@colostate.edu> Sent: Sun, May 12, 2013 12:18:16 AM Subject: [USMA:52761] RE: Numerical Verification of lbf and lbm with 9.80665 in Newton's Second Law John, I don't understand your second paragraph. I never advocated "inventing" or even using any "gravitational" units; not the pound-force (lbf), and certainly not the kilogram or ton (t) defined as 1000 kg, and treated as a unit of force. And as to rocket engineering, I have in hand a copy of Von Braun's "Das Marsprojekt" (published in 1952). On Page 10, he begins a list of numerical parameters (for each of the three propulsion stages. Some excerpts, for the first stage are: Schub (thrust) "12 800 t" Treibstoffgewicht (propellant weight) "4 800 t" Treibstoffverbrauch (rate of propellant use) "55,81 t/sec" Duesenenddruck (pressure at end of nozzle) "0,7 kg/cm^2" As you can see, these are an abuse of units of mass (kg and t), and an atrocious mix of mass and force ? (also t) units in a "gravitational" non-system of units, non-system by 1960 SI Standards of coherence, but that was 1952. Just as the pound can not coherently be both mass and force at the same time in f = m a; neither can the kg and t. To the credit of Von Braun and his immigrant engineers from Germany, they quickly endorsed SI shortly after 1960 when they became aware of the "definition" of SI by the CGPM. Eugene Mechtly ________________________________ From: John M. Steele [jmsteele9...@sbcglobal.net] Sent: Saturday, May 11, 2013 6:15 AM To: mechtly, eugene a; U.S. Metric Association Subject: Re: [USMA:52757] RE: Numerical Verification of lbf and lbm with 9.80665 in Newton's Second Law We agree on all the BIG stuff: *Aviation/aerospace should get with the program and go SI (as should all of the US that hasn't already done so) *Even the kilogram-force can't redeem a gravity-based system and is long deprecated. An earth-gravity based system is particularly ill-suited to an organization whose specific mission is to leave earth's gravity behind (at least surface level gravity). I think the only (minor) point on which we may disagree is whether inventing a unit called the gravity (shortens to g or gee) is (a) no worse, (b) even worse than inventing units like slugs or poundals to fix F = ma. All three are bad but I don't see much gradation; they all fudge and get into obscure units that make any discussion seem as difficult as rocket science. Since some people use it, it deserves to tabulated as the third bad way to fix F = ma; that is not a recommendation. (I learned the slug in high school and thought it was the only way. I never heard of poundals until I got into weights & measures discussions and thought the gee was just to help people "appreciate" the force.) As I said before, since I learned about the newton, I have practiced slugicide. ________________________________ From: "mechtly, eugene a" <mech...@illinois.edu> To: U.S. Metric Association <usma@colostate.edu> Cc: "mechtly, eugene a" <mech...@illinois.edu> Sent: Fri, May 10, 2013 9:49:55 PM Subject: [USMA:52757] RE: Numerical Verification of lbf and lbm with 9.80665 in Newton's Second Law John (Steele), Thanks for pointing out that: 1. the exact product of lbm and 9.80665 = (exactly) lbf (by definition of lbf) which is cited numerically on Page 53 of NIST SP 811 (2008 Edition) as Footnote 23, and that 2. computers capable of double-precision calculations can do the arithmetic directly without fracturing, and that 3. units *outside* SI (such as lbm and lbf) are often *defined* as exact multiples of an SI unit with a number of significant digits used for definition which is much larger than the number actually necessary to be retained after appropriate rounding, for most applications, and that 4. YES, it is best practice to store the exact definitions in memory to as many digits as storage fields permit, before calculations, and to do all appropriate rounding *after* calculations are done with the excess number of digits. On all these four points at least John and I are in complete agreement! I hope some readers will actually test the arithmetic of f = m a, and not merely accept the NIST product number (m a) without confirmation either by a double-precision calculation or by a single precision fractured calculation. I am curious to know haw many readers have actually or plan to work through the multiplication? Doing so will increase your appreciation of the gravity-free advantage of of SI! Eugene Mechtly ________________________________ From: John M. Steele [jmsteele9...@sbcglobal.net] Sent: Friday, May 10, 2013 5:22 PM To: mechtly, eugene a; U.S. Metric Association Cc: mechtly, eugene a Subject: Re: [USMA:52755] Numerical Verification of lbf and lbm with 9.80665 in Newton's Second Law Well, 1) I didn't realize we were having a contest 2) The exact figure already appears as footnote 23 in Appendix B of NIST SP811 3) There are many calculator apps for PCs that use double precision floating point and can do the multiplication directly and explicitly (as can Excel) While it is more digits than would ever be needed, I do think it is useful to have "exact" values (or at least the full precision of the math processor) in computerized conversion routines. It makes little sense to store the "wrong" value when you can store the "right" value as a compiler constant. ________________________________ From: "mechtly, eugene a" <mech...@illinois.edu> To: U.S. Metric Association <usma@colostate.edu> Cc: "mechtly, eugene a" <mech...@illinois.edu> Sent: Fri, May 10, 2013 6:08:13 PM Subject: [USMA:52755] Numerical Verification of lbf and lbm with 9.80665 in Newton's Second Law Why has no person yet volunteered a confirmation of the exact arithmetic of lbf and lbm in f = m x 9.80665? Do the exact numerical values simply have two many necessary digits to be multiplied exactly by most of us? Hint: Use (a + b) x (c + d) where the numbers ( ) with "too many digits" are expressed as sums, and each part of each sum is initially expressed in exponential form. Then, this exercise becomes tractable on many inexpensive digital calculators. Who will be the first to confirm the exact fit of lbf and lbm (as *defined* numerically) with Newton's Second Law? Or, would most of you simply prefer to trash all that is non-SI? (a perfectly respectable attitude) Eugene Mechtly
