I agree with "kPa" that "we need to forget pounds exist..."; "we" being the entire USA!!!
While that end-objective remains (continues in progress) , we observe that the numerical exercise of f = m a, for lbm and lbf clearly demonstrates the unambiguous superiority of SI. However, the reality is, with regrets, that pounds-mass (lbm) are firmly entrenched in US Commerce and they are not easily discarded (i.e. replaced by grams and kilograms), even in some offices within NIST; and pounds-force are not easily discarded even in some activities of NASA or by some NASA contractors (e.g. by Lockheed-Martin and by the Boeing Company), even when and where earth-gravity is irrelevant , nor easily discarded in contracts financed by the US Department of Transportation, as the recent history of highway construction proves! John Steele deserves commendation for his thorough analysis (below) of the numerical exercise of f = m a. On my own cell-phone calculator, I get the product (of lbm and 9.80666) as equal to 4.448221615 with loss of the remaining digits (2605). On my TI-30XA calculator I get the same product, with loss of the remainder, (2605). I do not yet know if double-precision software is installed in my MacMini computer (at the next level up). At the University of Illinois, I often used double-precision arithmetic, but the precision of "arbitrary accuracy" that John mentions was unknown to me. Although it is true that the level of accuracy of the proposed new definition of the kilogram does not even reach an accuracy of 14 significant digits, this study of high-precision calculations does have value in promoting SI! Eugene Mechtly ________________________________ From: Kilopascal [kilopas...@cox.net] Sent: Saturday, May 11, 2013 8:49 AM To: U.S. Metric Association Subject: [USMA:52759] RE: Numerical Verification of lbf and lbm with 9.80665 in Newton\'s Second Law Why do we really care about how many digits there are in pounds force or mass? How is this going to help us metricate? If this is important to someone, isn't there a math forum that this can be taken too? As far as I'm concerned, we need to forget pounds exist and have them removed as legal units. Let them become befuddled and confusing. The more harm they will bring to those that use them the faster they will disappear. [USMA:52759] RE: Numerical Verification of lbf and lbm with 9.80665 in Newton's Second Law<http://www.mail-archive.com/search?l=usma@colostate.edu&q=subject:%22%5BUSMA%3A52759%5D+RE%3A+Numerical+Verification+of+lbf+and+lbm+with+9.80665+in+Newton%27s+Second+Law%22> John M. Steele<http://www.mail-archive.com/search?l=usma@colostate.edu&q=from:%22John+M.+Steele%22> Sat, 11 May 2013 06:05:43 -0700<http://www.mail-archive.com/search?l=usma@colostate.edu&q=date:20130511> I verified that the calculator in Windows accessories gives the correct result. I like a program called Calendar Magic which does date manipulation but later versions contain several other calculators. It has a stack-oriented (RPN) double precision scientific calculator which gives the correct result. Finally, it has a "big number" calculator which does basic calculations to arbitrary accuracy. Since the 14 digit answer (13 decimal) is approaching the limit of double precision, I also verified it gives the correct result. Finally, going back to basic properties, the product of numbers with 5 and 8 decimal digits can have no more than 13 decimal digits, and multiplying the last two digits allows determination that the final digit of the result is 5. I will leave confirmation of Excel and the numerous other calculator apps to others. The Big Number printout is pasted below: *** Big Numbers Calculator *** x = 9.80665 y = 0.45359237 x * y = 4.4482216152605 Digits in result = 14 Time taken in seconds = 0.0 File produced on May 11, 2013 ________________________________ 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
