Bill, how many photons in a (cd s)? How to deal with the proper units such as : candela (cd) as photons/s [generated by the whole source over 4 pi sr] and lumen (lm) as photons/s [as captured by the receiver's solid angle of observation (sr)] It's like giving different *fundamental* (!?) units to different measures of energy contained in food: <http://www.gov.on.ca/OMAFRA/english/livestock/dairy/facts/92-017.htm#general> Energy A nutrient essential for maintenance, growth, production and reproduction. Energy is required in larger amounts than any other nutrient except water, and is often the limiting factor in livestock production. Gross Energy (GE):. The total combustible energy in a feed, determined by measuring the amount of heat produced when a feed sample is completely burnt in a bomb calorimeter Digestible Energy (DE): Energy that is available to the animal by digestion; measured as the difference between gross energy content of a feed and the energy contained in the animal's feces (gross energy minus fecal energy.) Metabolizable Energy (ME): A measure of the useful energy in a feed. It represents that portion of the feed gross energy not lost in the feces, urine and belched gas. Net Energy (NE): The amount of feed energy actually available for animal maintenance and production. It represents the energy fraction in a feed left after fecal, urinary, gas and heat losses are deducted from the gross energy value of a feed. Total Digestible Nutrients (TDN): A term describing the energy value of feedstuffs, comparable to DE in accuracy. TDN over-estimates the energy value of roughages in comparison to grains. Calorie: A measure of energy; usually expressed as kilocalorie (kcal) or megacalorie (Mcal). 1 cal = the amount of energy required to increase the temperature of 1 g of water 1 degree C. Joule: A unit adopted by Systeme International (SI) for expressing energy. The Joule is more commonly used in Europe than in North America (4.184 J = 1 calorie). W. ----- Original Message ----- From: "R. William Gosper" <rwg@tc.spnet.com> To: <math-fun@mailman.xmission.com> Cc: <rowlett@email.unc.edu> Sent: Saturday, November 01, 2003 8:59 AM Subject: [math-fun] units
My unit-conversion challenges prompted me to write a long-planned Macsyma package. (Macsyma comes with a units package that leaves much to be desired and brings much to be undesired.)
"Miles per gallon" has the same units as "per acre".
(c147) uconv(mpg,acre) 12043468800 (d147) ----------- 7 acre
What is the physical significance of this (tiny) area?
The cross-sectional area of the thread of gasoline the car would need to continously sip to keep running.
What's the speed of light in furlongs per fortnight?
(c148) uconv(c,furlongs/fortnight)
2518256647200000 furlongs (d148) ------------------------- 1397 fortnight or approximately (c149) dfloat(%) 1.80261749978525d+12 furlongs (d149) ----------------------------- fortnight
This package introduces absolutely no floating point approximations.
Scrooge McDuck's money bin is said to contain three cubic acres. How much is that in square gallons?
(c150) uconv(3*acres^3,gallons) 2 679899097202688000 gallons (d150) --------------------------- 49
Could that guy who'd walk a mile for a Camel plod a picoparsec for a Pall Mall?
What is a parsec?? The Web is rife with units conversion pages that are mostly rubbish. Exception: http://www.unc.edu/~rowlett/units/index.html . This is a "dictionary" of measurements worthy of Weisstein, but without the cupidity of Wolfram and CRC. It defines parsec as the distance at which an astronomical unit (ua) subtends an arc second, and defines ua as the "average" distance to the sun. This contradicts my recollection of parsec defined in terms of the semimajor axis of Earth's orbit. This would also seem a more logical definition of ua, since, as JMC recently reminded us, planetary periods only depend on the major axis. Also, what is meant by "average"? Down in the noise, but relevant to "theoretical" units conversion, is the question of slant height vs altitude: ua cot arcsec or ua/2 csc arcsec/2?
By the way, (c161) uconv(arcsecond,radian) %pi radian (d161) ---------- 648000 To further show off my package, (c151) uconv(hectare,meter*yard)
12500000 meter yard (d151) ------------------- 1143
a crazy unit of area that was claimed to be used in Japanese cloth trade, due to cutting off metric lengths from bolts woven with the old British loom width. However, Rowlett's definition of "bolt" lists different widths for different fabrics, none of which is a yard.
It's very easy to add new units to the package. E.g., after adding the two lines uput('tropicalyear,'canon=365*'days+5*'hr+48*'min+459747/10000*'sec)$ uput('siderealyear,'canon=365*'days+6*'hr+9*'min+954/100*'sec)$ one can ask (c152) uconv(siderealyear,tropicalyear)
35064610600 tropicalyear (d152) ------------------------ 35063251083
The continued fraction of this coefficient is (c153) cf(numfactor(%)) (d153) [1, 25790, 1, 25, 4, 1, 2, 4, 850] which says the difference is very nearly 1 part in 25791.
uput('mhz,'canon='megahertz)$ uput('rpm,'canon='revolution/'min)$ were all that was needed for (c153) uconv(mhz,rpm) (d153) 60000000 rpm
Prefixes and plurals are treated generically:
(c154) uconv(megamicromumble,millimumbles) (d154) 1000 millimumbles
which is not always the right thing!
(c155) uconv(centipede,millipedes) (d155) 10 millipedes
I'll distribute the package when I get this parsec business straightened out, and add a few hundred more units. Who knows, a dumb little application like this might leverage some Macsyma sales. Except Macsyma isn't for sale.-( --rwg
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