zIFBoards - Free Forum Hosting
Create your own social network with a free forum.

Learn More · Register Now
Welcome to Dozensonline. We hope you enjoy your visit.
You're currently viewing our forum as a guest. This means you are limited to certain areas of the board and there are some features you can't use. If you join our community, you'll be able to access member-only sections, and use many member-only features such as customizing your profile, and sending personal messages. Registration is simple, fast, and completely free. (You will be asked to confirm your email address before we sign you on.)
Join our community!
If you're already a member please log in to your account to access all of our features:

Name:   Password:


Pages: (19) [1] 2 3 ... Last » ( Go to first unread post )

 The Primel Metrology, What if we start with the hexciaday?
Kodegadulo
Posted: Jun 23 2012, 09:12 PM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



EDIT: This system has evolved over the years. See the Primel Metrology Wiki for the most up-to-date description.

The Primel Metrology

or: What if we start with the hexciaday?

Note: This post has been revised based on possibilities explored in later discussions in this thread. But you can find a snapshot of a previous version of this post here.

This thread will serve as a reboot of my investigation into the potential of the "Primel" metrology. The goal of this effort is to see whether a viable system of measurement can be constructed using many of the same principles that Tom Pendlebury embodied in his TGM metrology, but starting with a somewhat different set of initial conditions. The chief principles I want to preserve in Primel are:

(1) 1:1 correspondence between related physical quantities and the eschewing of extraneous scale factors; and

(2) basing the system on fundamental realities of common human experience of life on Earth, including the mean solar day, acceleration due to Earth's gravity, the density of water, and so forth, but not necessarily including (nor necessarily precluding) universal constants such as the speed of light or the fine structure constant.

The chief point of divergence from TGM is to start with a smaller base unit of time, namely the hexciaday (h↓Dy), which is 10-6z days, rather than TGM's pentciasemiday (p↓2\Dy) which is 6×10-6z days long.

This was initially motivated, in part, by the perception that some of TGM's units are "too large", particularly the Volm, the unit of volume, and the Maz, the unit of mass. However, I believe that issue can be mitigated somewhat by using a combination of multiplier and power prefixes from Systematic Dozenal Nomenclature to identify "human-sized" scalings of the base units, and then coining colloquial names for those as auxiliary units (e.g. Pendlebury's "tumblol" for the trinabiciaVolm (t•b↓Vm), a close approximation of the U.S. or Imperial pint, and the "pounz" for the trinabiciaMaz (t•b↓Mz), a close approximation of the Avoirdupois pound). We are likely to find this technique useful to mitigate perceived problems with the sizings in the Primel metrology as well.

So rather than viewing Primel as a "cure" for problems in TGM, I'd like to approach this as an exercise in vindicating the basic principles of TGM, and a chance to get some fresh insights into how rational systems of measurement can be constructed.

First, a couple of conventions: To name its base units, Primel will make use of Quantitels, "anonymous" names for units derived (relatively) directly from the terms for the quantities they measure, by appending a common "-el" ending, standing for "element of", by analogy with a "pixel" being an "element of" a picture or image. "Primel" serves as not only a label for the entire metrology, but also as the disambiguating adjective which can be prefixed onto Quantitels to distinguish Primel units from other systems that also use Quantitel nomenclature, as well as from the use of Quantitels to speak generically about units of measure. However, rather than repeating this adjective ubiquitously, Primel Quantitels will be prefixed with a prime character ( ′ ), which can either be pronounced "Primel", "prime", or not at all, whichever proves most convenient depending on the circumstances.

As of z|11E9/04/15, I've decided to adopt the convention I spelled out in the Radix Bracketing thread: Surround every number with square brackets and prefix with a letter indicating the base; otherwise use the same notation conventions from decimal in all bases.

As of 11EE/09/1Ez, I've revised this post to follow the convention spelled out in The Duodecimal Bulletin, Volume 52z, Number 1, Whole Number X2z, in the article "Base Annotation Schemes": Every dozenal number will be annotated with a subscript "z", every decimal number with a subscript "d", e.g. 100z = 144d.

The rest of this post will serve as an executive summary of the results of this investigation, so it will be edited from time to time to add results as they are accrued; but such changes will be announced in follow-up posts.

Primel Base Units

The following table lists all the base units of the Primel system derived to date. This just lists the base unit for each physical quantity, for reference and definition purposes, without considering scalings and colloquialisms. See later subsections of this post (TBD) for more detailed treatments of each physical quantity tailored to the most convenient human-sized usages.

Subscripts indicate base: d = decimal, z = dozenal. Greyed-out digits are provided for completeness but were computed and should be taken with a grain of salt.

MECHANICS
Physical Quantity Primel Unit Abbrev Derivation TGM Equivalent SI Equivalents Customary Equivalents
Time ′timel ′Tmℓ hexciaday2 unciaTim 28.93518d milliseconds =
42z triciaseconds =
1.7361d thirds (1/60d second)
Acceleration = Gravity ′accelerel = ′gravitel ′Acℓ = ′Gvℓ SI standard gravity ~ Gee 9.79651584d meters/second2 (exact) 32.1408d feet/second2 (exact)
Velocity = Speed ′velocitel = ′speedel ′Veℓ = ′Spdℓ ′accelerel × ′timel ~ 2 unciaVlos 0.283464d meters/second (exact) =
1.02047d kilometers/hour (exact)
0.93d feet/second (exact) =
0.63409d miles/hour (exact) =
0.551009935205184d knots
Length ′lengthel
= ′widthel
= ′heightel
= ′depthel
= etc.
′Lnℓ
= ′Wdℓ
= ′Htℓ
= ′Dpℓ
= etc.
′velocitel × ′timel ~ 4 biciaGrafut 8.202083d millimeters (exact) 0.322916d inches (exact) =
31/96d inch (exact)
Area ′squarel ′Sqℓ ′lengthel2 ~ 1.4z triciaSurf 67.2741710069445d square millimeters 0.10427517361d square inches (exact)
(31/96)2d square inches (exact)
Volume ′volumel ′Voℓ ′lengthel3 ~ 5.4z pentciaVolm 0.551788356779876d milliliters 0.0186582026740114d fl. oz =
0.111949140334977d tsp (~1/9)
Density ′densitel ′Dsℓ SI maximal density of water 1 Denz 999.972d kilograms/meter3 8.345d pounds/gallon
Mass ′massel ′Msℓ ′densitel × ′volumel ~ 5.4z pentciaMaz 0.551772906705886d grams 0.0194632375111434d ounces =
8.51516641112524d grains
Force = Weight ′forcel = ′weightel ′Fcℓ = ′Wtℓ ′massel × ′accelerel ~5.4z pentciaMag 5.40545202062705d milliNewtons =
540.545202062705d dynes
Pressure = Stress ′pressurel = ′stressel ′Psℓ = ′Stsℓ ′forcel / ′squarel ~4z biciaPrem 80.3495894444997d pascal =
0.602671482871005d torr
0.0237272237350789d inHg =
0.0116537227022589d psi
′atmosphere ′Atmℓ 890z ′pressurel
(890z = 2Ez × 30z = 22·32·5·7])
~ Atmoz 101,240.4827d pascal =
759.366068417466d torr
 
29.8963019061995d inHg =
14.6836906048462d PSI =
0.999165879102587d std. atm.
Tension ′tensionel ′Tsℓ ′forcel / ′lengthel ~1.4z triciaTenz 0.659034028422907d N/m
Work = Energy ′workel = ′energiel ′Wkℓ = ′Ngℓ ′forcel × ′lengthel ~1.94d hexciaWerg 44.3359679275181d microJoules =
443.359679275181d ergs
Power ′powerel ′Pwℓ ′workel / ′timel ~X.8z hexciaPov 1.53225105157503d milliWatts =
15.3225105157503d kiloergs/second
"Specificity"
(Amount per Mass)
′specifel ′Spℓ 1 / ′massel ~23,000z / Maz 1812.33980111502d / kilogram =
1.81233980111502d / gram
51.3789136790559d / ounce =
822.062618864894d / pound
HEAT/THERMODYNAMICS
Physical Quantity Primel Unit Abbrev Derivation TGM Equivalent SI Equivalents Customary Equivalents
Temperature ′temperaturel ′Tpℓ (see Note 1) 4 biciaCalg 0.397598253275109d quadciakelvin 0.715676855895196d quadciarankine
′quadquatemperaturel =
′stadegree
q↑′Tpℓ =
′Ϛ°
104z ′temperaturels 4 bigrees 0.397598253275109d kelvin 0.715676855895196d rankine
"Thermacity"
(Thermal Capacity) =
Entropy
′thermacitel
′entropel
′Θcℓ =
′Npℓ
′workel / ′temperaturel ~5.4z pentciaCalkap 2.31226023598472d J/K
"Specithermacity"
(Specific Thermal Capacity) =
Specific Entropy
′specithermacitel
′specifentropel
′SpΘcℓ =
′SpNpℓ
′specifel × ′thermacitel =
′specifel × ′entropel
~ 1 Calsp 4190.60125621071d J/K/kg
ELECTRO-MAGNETISM
Physical Quantity Primel Unit Abbrev Derivation TGM Equivalent SI Equivalents Customary Equivalents
Current ′currentel ′Crℓ (see Note 2)   0.329570169592234d ampere
Charge ′chargel ′Chℓ ′currentel × ′timel   9.53617388866417d millicoulomb
Electrical Potential ′potentiel ′Ptℓ ′powerel / ′currentel   4.6492407169946d millivolt
Resistance =
Reactance =
Impedance
′resistel =
′reactel =
′impedel
′Rsℓ =
′Rcℓ =
′Ipℓ
′potentiel / ′currentel   14.1069828096d milliohm
Conductance =
Susceptance =
Admittance
′conductel=
′susceptel=
′admittel
′Cdℓ =
′Scℓ =
′Amℓ
  70.8868801711083d siemens E+01
Capacitance ′capacitel ′Cpℓ ′chargel / ′potentiel   2.05112500495105d farads
Magneto-Motive Force ′magnetel ′Mgℓ ′currentel × turn   0.329570169592234d ampere-turns
Magnetic Gradient ′magnegradiel ′Mgrℓ ′magnetel / ′lengthel   40.181275439236d ampere-turn / meter
Magnetic Flux ′fluxel ′Fxℓ ′potentiel × ′timel   0.134526641116742d milliweber
Magnetic Flux Density ′fluxdensitel ′FxDsℓ ′fluxel / ′squarel   1.99967742601919d tesla
Permeability ′permeabel ′Pmbℓ ′fluxdensitel/ ′magnegradiel   0.497664d milli-weber-meter/ampere-turn
Inductance ′inductel ′Idℓ ′resitel × ′timel   0.40818816d milli-henry
Charge Density ′chargedensitel ′ChDsℓ ′chargel / ′squarel   1.41750894079093d megacoulomb / square meter
Potential Gradient ′potengradiel ′Pgrℓ ′potentiel / ′lengthel   56.6836561889105d volt / meter
Permittivity ′permittel ′Pmtℓ ′chargedensitel / ′potengradiel   25,007.3660750954d coulomb / volt-meter
CHEMISTRY
Physical Quantity Primel Unit Abbrev Derivation TGM Equivalent SI Equivalents Customary Equivalents
Amount of Substance ′substancel ′Sbℓ (See Note 3) ~5.4 pentciaMolzz 0.551772906705886d mole
Number Concentration ′concentratel ′Ccℓ 1 / ′volumel (of solution) 1812.28905560059d / liter
Number "Solventage" ′solventel ′Svℓ 1 / ′massel (of solvent) 1812.33980111502d / kilogram
Substance Concentration ′substancentratel ′SbCcℓ ′substancel × ′concentratel ~Molv 999.927d molar
Substance "Solventage" ′substansolventel ′SbSvℓ ′substancel × ′solventel ~Molm 1000.0d molal

Note 1: The ′temperaturel is approximately the change in temperature induced in 1 ′massel of water when 1 ′workel of heat is applied to it. The canonical value is rounded up so that a whole number (250d = 18Xz) of ′quadquatemperaturels fit between the freezing and boiling points of water under standard atmospheric pressure.

Note 2: The ′currentel is the amount of current flowing through a pair of wires one ′lengthel apart, sufficient to produce a magnetic force between them of one ′pentciaforcel per ′lengthel of wire (defining Ampere's magnetic force constant as kA = 0.6×10-5z ′Wkℓ/′Crℓ2).

Note: Even as late as 11EE/09/1Ez, the whole electromagnetic subsystem is very much up in the air. The above reflects an earlier approach based on Ampere's Law, following a pattern similar to what Pendlebury did for TGM. But I am also considering an approach suggested by Gingerbill, jrus, Wendy Krieger, and others where the ′resistel is set to the vacuum impedance. See Primel Metrology Wiki

Note 3: The ′substancel is an amount of a given substance with the same number of particles as there are in 10z ′massels of pure Carbon isotope 10z.

(The name of each physical quantity above will (eventually) be a link to a follow-up post which goes into detail about its associated Primel units.)

Top
Treisaran
Posted: Jun 24 2012, 11:59 AM


Dozens Disciple


Group: Members
Posts: 1,221
Member No.: 630
Joined: 14-February 12



QUOTE (Kodegadulo)
I still do not favor the semicolon ( ; ) or Humphrey point as a dozenal radix point, because it too easily registers as punctuation rather than as a base marker.


I don't think this is a problem when used as a radix point, only when used as a base marker akin to your former use of a subscript after the number. I've seen hideous examples of two consecutive semicolons, the one being a base marker and the other a punctuation semicolon, but the Humphrey point when used inside numbers as a separator between the integer and the fractional part doesn't suffer from this problem. Note also that the punctuation semicolon is followed by a space, while the semicolon as radix point isn't.

QUOTE
As for decimal numbers, I now want to avoid using a center dot (\(\cdot\)) as a combination decimal radix point/decimal marker, because it's just too useful as a multiplication operator.


I concur, though I'd actually prefer × (U+00D7) as a multiplication symbol but for the fact that there are not one but two X-like symbols to clash with: not just the algebraic x (I remember switching to · once I started pre-high school algebra) but also the X a lot of us, including me, use for ten out of necessity.

QUOTE
I don't want to use the period ( . ) as a decimal marker on integers, because it too easily registers as a full sentence stop rather than as a base marker.


Again, I think this isn't an actual problem. The punctuation full stop, like the semicolon and the comma (which latter the Continental Europeans use as a decimal 'point'), is followed by a space, while the radix separator isn't. It's a far cry from the use of punctuation marks in names, like 'Yahoo!', in the middle of a sentence which is really in conflict with punctuation usage.

Even my use of an asterisk for marking dozenal numbers, though it could be improved upon, doesn't conflict with the punctuation asterisk, because it comes before the number while the punctuation asterisk comes after the text. One good sign of a true clash between usages is that it's blatant, it sticks out, it becomes one of the pet peeves people talk about at the pub. smile.gif
Top
Kodegadulo
Posted: Jun 24 2012, 02:14 PM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



QUOTE (Treisaran @ Jun 24 2012, 11:59 AM)
... comments about radix marking ...

Let's redirect this side-discussion to here.
Top
Kodegadulo
Posted: Jun 24 2012, 07:52 PM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



Edits to the original post:
  • In the base units table, I added a Symbol column with proposed abbreviations for the units.
  • I also added a note about how to get Greasemonkey and MathJax to render all these TeX insertions.
  • Started the Time Units section (added table).
Top
Kodegadulo
Posted: Jun 25 2012, 05:39 PM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



Edits to original post:
  • Eliminated TeX inserts; reverted to normal forum syntax/HTML, but encoded as UTF-8.
Top
Kodegadulo
Posted: Jun 26 2012, 09:44 PM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



Primel Time Units

Note: If you read this post, realize that it's obsolete. I've supplanted it with this later post, where I've changed the colloquialisms for the units. I'm keeping this one around for historical reasons to avoid confusion, rather than editing it.

The mean solar day is a fundamental reality of Primel, just as it is for TGM. However, Primel will use a round dozenal power of the day, the hexciaday, as its base unit of time, the ′timel. This contrasts with TGM, which first divides the day in half, and then takes the pentcia of the semiday as its base time unit, the Tim. As a consquence, the ′timel is equivalent to one-sixth of a Tim. This makes the ′timel a very fleeting moment of time, just beyond human perception. (I have proposed calling it, colloquially, a "′twinkling".) Nevertheless, it is a useful quantity for precision scientific and engineering purposes, and its scale will have interesting effects on the rest of the Primel metrology.

On the other hand, the unqual powers of the ′timel, starting with the unqua′timel, do fall within the human scale. The table below shows a range of dozenal powers of the ′timel, from ennqua down to enncia. The ′timel itself is highlighted in blue, and the "human scale" powers up to the full day are shown in green. Each of these is equivalent to an uncial power of the day, and these equivalents can be used as synonyms. One useful feature to note at the top of the scale is that higher powers of the ′timel correspond to whole powers of the day, so there is a seamless transition from large-scale measures of time based on the day and smaller-scale measures of time.

Primel Unit Symbol Derivation
(and Synonym)
Colloquialism TGM Equivalent SI Equivalents Customary Equivalents
ennqua′timel e′Tmℓ = 9′Tmℓ triquaday 2 octquaTim z|1000 days
octqua′timel o′Tmℓ = 8′Tmℓ biquaday 2 septquaTim z|100 days
septqua′timel s′Tmℓ = 7′Tmℓ unquaday 2 hexquaTim z|10 days
hexqua′timel h′Tmℓ = 6′Tmℓ day 2 pentquaTim z|20 hours = z|42,000 seconds
pentqua′timel p′Tmℓ = 5′Tmℓ unciaday ′featurelength =
′sitting
2 quadquaTim 1 "duor" = 1 bihour = 2 hours = z|4200 seconds
quadqua′timel q′Tmℓ = 4′Tmℓ biciaday ′segment 2 triquaTim 1 "temin" = 1 decaminute = d|10 minutes = z|420 seconds
triqua′timel t′Tmℓ = 3′Tmℓ triciaday ′minute =
′trice
2 biquaTim d|50 seconds = z|42 seconds
biqua′timel b′Tmℓ = 2′Tmℓ quadciaday ′verse =
′breath
2 unquaTim d|4.16 seconds = z|4.2 seconds
unqua′timel u′Tmℓ = 1′Tmℓ pentciaday ′syllable =
′beat
2 Tim d|347.2 milliseconds =
z|420 triciaseconds =
d|20.83 thirds (d|1/60 seconds)
′timel ′Tmℓ hexciaday ′twinkling 2 unciaTim d|28.93518 milliseconds =
z|42 triciaseconds =
d|1.7361 thirds (d|1/60 seconds)
uncia′timel u′Tmℓ = 1′Tmℓ septciaday 2 biciaTim d|2.4113 milliseconds =
z|4.2 triciaseconds
bicia′timel b′Tmℓ = 2′Tmℓ octciaday 2 triciaTim d|200.94 microseconds =
z|420 hexciaseconds
tricia′timel t′Tmℓ = 3′Tmℓ ennciaday 2 quadciaTim d|16.745 microseconds =
z|42 hexciaseconds
quadcia′timel q′Tmℓ = 4′Tmℓ decciaday 2 pentciaTim d|1.3954 microseconds =
z|4.2 hexciaseconds
pentcia′timel p′Tmℓ = 5′Tmℓ levciaday 2 hexciaTim d|116.28 nanoseconds =
z|420 ennciaseconds
hexcia′timel h′Tmℓ = 6′Tmℓ unnilciaday 2 septciaTim d|9.6903 nanoseconds =
z|42 ennciaseconds
septcia′timel s′Tmℓ = 7′Tmℓ ununciaday 2 octciaTim d|807.53 picoseconds =
z|4.2 ennciaseconds
octcia′timel o′Tmℓ = 8′Tmℓ unbiciaday 2 ennciaTim d|67.294 picoseconds =
z|420 unnilciaseconds
enncia′timel e′Tmℓ = 9′Tmℓ untriciaday 2 decciaTim d|5.6078 picoseconds =
z|42 unnilciaseconds

The unqua′timel is equal to 2 Tims or about a third of a second. It is equivalent to a beat of a metronome in the presto range. Counting unqua′timels in threes approximates the tempo of a Viennese waltz.

A gross of unqua′timels constitutes a triqua′timel. The triqua′timel is noteworthy in that it is also the triciaday, making it exactly intermediary between the ′timel and the day on the exponential scale. Calling it a "′trice" therefore makes for a nice play on words. Alternatively, at d|50 seconds it is very close to a conventional minute, so giving it the colloquial name "′minute" would be quite reasonable.

A dozen (z|10) ′minutes is equivalent to ten (d|10) conventional minutes, which might be called a "′segment". A gross (z|100) ′minutes is equivalent to a long hundred (d|120) conventional minutes, which is the same as 2 hours, an uncia of a day. Using an SDN prefix, we might call this a "bihour", but perhaps a less derivative expression would relate it to the fact that it is about the duration of a typical sit-down entertainment performance, such as a feature-length motion picture, or a musical concert, or a theatrical play.

Although the TGM time units are not whole dozenal powers of the ′timel, they are all a simple multiple of one, so we could certainly incorporate them into Primel as auxiliary units:

Auxiliary Unit Colloquialism Primel Equivalent SI Equivalents Customary Equivalents
semiday clock 6 pentqua′timels z|10 hours = z|21,000 seconds
unciasemiday hour 6 quadqua′timels 1 hour = z|60 ′minutes = d|60 minutes = z|2100 seconds
biciasemiday block 6 triqua′timels 1 pentaminute = 5 minutes = 6 ′minutes = z|210 seconds
triciasemiday semi′minute =
semi′trice
6 biqua′timels d|25 seconds = z|21 seconds
quadciasemiday 6 unqua′timels d|2.083 seconds = z|2.1 seconds
pentciasemiday Tim 6 ′timels d|173.61 milliseconds =
z|210 triciaseconds

Here are a few additional auxiliary units that are all interesting multiples of some dozenal power of the ′timel:

Auxiliary Unit Colloquialism Primel Equivalent SI Equivalents Customary Equivalents
septaday week septa-hexqua′timel 1 week = 7 days
biweek = unbinaday fortnight unbina-hexqua′timel z|12 days = d|14 days = 2 weeks
bihexaday short Gregorian month bihexa-hexqua′timel z|26 days = d|30 days
biseptaday long Gregorian month bisepta-hexqua′timel z|27 days = d|31 days
bihexpentaday Gregorian year bihexpenta-hexqua′timel z|265 days = d|365 days
bihexhexaday Gregorian leap year bihexhexa-hexqua′timel z|266 days = d|366 days
quadraweek = biquadraday short Perennial-Calendar month biquadra-hexqua′timel z|24 days = d|28 days = 4 weeks
pentaweek = bilevaday long Perennial-Calendar month bileva-hexqua′timel z|2E days = d|35 days = 5 weeks
ununiweek = septseptaday regular Perennial-Calendar quarter septsepta-hexqua′timel z|77 days = d|91 days = z|11 weeks = d|13 weeks = 3 months
unbinaweek = octbinaday leaping Perennial-Calendar quarter octbina-hexqua′timel z|82 days = d|98 days = z|12 weeks = d|14 weeks = 3 months + leap week
quadquadraweek = bihexquadraday Perennial-Calendar year bihexquadra-hexqua′timel z|44 weeks = d|52 weeks = z|264 days = d|364 days
quadpentaweek = bihexlevaday Perennial-Calendar leap year bihexleva-hexqua′timel z|45 weeks = d|53 weeks = z|26E days = d|371 days

(A Perennial Calendar can be constructed where every year and month starts on the same day of the week, where every year and month contains a whole number of weeks, and where a leap year adds a leap week onto the last month of the year, rather than a leap day in February. The pattern of leap years would be quite different, of course. When such a calendar is interpreted in dozenal, there's a nice sort of correspondence between how each month is either z|24 or z|2E days and how each year is either z|264 or z|26E days; or equivalently, how each month is either 4 or 5 weeks and how each year is either z|44 or z|45 weeks.)

z[

WkJanuary
MTWTFSS
0101020304050607
0208090X0E101112
0313141516171819
041X1E2021222324
0525262728292X2E
WkFebruary
MTWTFSS
0601020304050607
0708090X0E101112
0813141516171819
091X1E2021222324
WkMarch
MTWTFSS
0X01020304050607
0E08090X0E101112
1013141516171819
111X1E2021222324
WkApril
MTWTFSS
1201020304050607
1308090X0E101112
1413141516171819
151X1E2021222324
1625262728292X2E
WkMay
MTWTFSS
1701020304050607
1808090X0E101112
1913141516171819
1X1X1E2021222324
WkJune
MTWTFSS
1E01020304050607
2008090X0E101112
2113141516171819
221X1E2021222324
WkJuly
MTWTFSS
2301020304050607
2408090X0E101112
2513141516171819
261X1E2021222324
2725262728292X2E
WkAugust
MTWTFSS
2801020304050607
2908090X0E101112
2X13141516171819
2E1X1E2021222324
WkSeptember
MTWTFSS
3001020304050607
3108090X0E101112
3213141516171819
331X1E2021222324
WkOctober
MTWTFSS
3401020304050607
3508090X0E101112
3613141516171819
371X1E2021222324
3825262728292X2E
WkNovember
MTWTFSS
3901020304050607
3X08090X0E101112
3E13141516171819
401X1E2021222324
WkDecember
MTWTFSS
4101020304050607
4208090X0E101112
4313141516171819
441X1E2021222324
Leap Week
4525262728292X2E
]z
Top
Kodegadulo
Posted: Jun 27 2012, 02:36 AM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



Primel Acceleration/Gravity Units

The acceleration due to the gravity of the Earth is the next reality of the Primel system, as it is for TGM. Primel standardizes its ′accelerel (identical with its ′gravitel) on the SI value for \(g_0\), the normal or standard gravity. SI specifies this value as exactly d|9.80665 meters/second2. This makes it very precise by definition without requiring precision of measurement, and it is, by definition, within the range of acceptable values for Earth's gravity. So I don't feel there is any need to look for some other basis for defining a gravity value, such as the polar diameter of Earth. Being able to relate the Primel ′gravitel directly to SI's gravitel would seem advantageous. However, this means the Primel ′gravitel is only a close approximation for the TGM gravitel (the Gee), and consequently all other Primel units derived from it will be only approximations to the corresponding amounts of TGM units.

Table 1 lists the gravities expected at various latitudes, as calculated using this formula. The attached image shows a plot of these values.

Tables 2 and 3 list actual measured gravities at various major cities around the world. Table 2 lists the cities in alphabetical order. Table 3 sorts them from lowest to hightest surface gravity.

Table 4 shows a comparison of the surface gravities for the various bodies in the solar system.

Table 1
LatitudeCalculated Gravity
Turnlets
[z]
Customary
[d]
  SI Accelerels  
[d]
′Gravitels
[z]
Deviation
from mean
[z]
00%⊙00° 00′9.780326 m/s20.EE7441 ′Gvℓ -0.477E%
01%⊙02° 30′9.780425 m/s20.EE7467 ′Gvℓ -0.4755%
02%⊙05° 00′9.780718 m/s20.EE7520 ′Gvℓ -0.46X0%
03%⊙07° 30′9.781206 m/s20.EE7625 ′Gvℓ -0.4597%
04%⊙10° 00′9.781883 m/s20.EE7777 ′Gvℓ -0.4445%
05%⊙12° 30′9.782745 m/s20.EE7956 ′Gvℓ -0.4266%
06%⊙15° 00′9.783786 m/s20.EE7E7X ′Gvℓ -0.4042%
07%⊙17° 30′9.784997 m/s20.EE8227 ′Gvℓ -0.3995%
08%⊙20° 00′9.786369 m/s20.EE8515 ′Gvℓ -0.36X7%
09%⊙22° 30′9.787892 m/s20.EE8841 ′Gvℓ -0.337E%
0X%⊙25° 00′9.789555 m/s20.EE8EX3 ′Gvℓ -0.3019%
0E%⊙27° 30′9.791345 m/s20.EE9378 ′Gvℓ -0.2844%
10%⊙30° 00′9.793248 m/s20.EE977E ′Gvℓ -0.2441%
11%⊙32° 30′9.795251 m/s20.EE9EX9 ′Gvℓ -0.2013%
12%⊙35° 00′9.797337 m/s20.EEX438 ′Gvℓ -0.1784%
13%⊙37° 30′9.799491 m/s20.EEX8X4 ′Gvℓ -0.1318%
14%⊙40° 00′9.801698 m/s20.EEE164 ′Gvℓ -0.0X58%
15%⊙42° 30′9.803939 m/s20.EEE633 ′Gvℓ -0.0589%
16%⊙45° 00′9.806199 m/s20.EEEE07 ′Gvℓ -0.00E5%
17%⊙47° 30′9.808459 m/s21.00039E ′Gvℓ +0.039E%
18%⊙50° 00′9.810703 m/s21.00086X ′Gvℓ +0.086X%
19%⊙52° 30′9.812914 m/s21.00112E ′Gvℓ +0.112E%
1X%⊙55° 00′9.815074 m/s21.001599 ′Gvℓ +0.1599%
1E%⊙57° 29′9.817167 m/s21.001X2E ′Gvℓ +0.1X2E%
20%⊙60° 00′9.819178 m/s21.00225E ′Gvℓ +0.225E%
21%⊙62° 30′9.821090 m/s21.002665 ′Gvℓ +0.2665%
22%⊙65° 00′9.822890 m/s21.002X41 ′Gvℓ +0.2X41%
23%⊙67° 30′9.824562 m/s21.0031X6 ′Gvℓ +0.31X6%
24%⊙70° 00′9.826096 m/s21.003515 ′Gvℓ +0.3515%
25%⊙72° 30′9.827478 m/s21.003806 ′Gvℓ +0.3806%
26%⊙75° 00′9.828698 m/s21.003X75 ′Gvℓ +0.3X75%
27%⊙77° 30′9.829746 m/s21.0040X1 ′Gvℓ +0.40X1%
28%⊙80° 00′9.830615 m/s21.004281 ′Gvℓ +0.4281%
29%⊙82° 30′9.831298 m/s21.004415 ′Gvℓ +0.4415%
2X%⊙85° 00′9.831790 m/s21.00451E ′Gvℓ +0.451E%
2E%⊙87° 30′9.832087 m/s21.004595 ′Gvℓ +0.4595%
30%⊙90° 00′9.832186 m/s21.0045EE ′Gvℓ +0.45EE%

Table 2 Table 3
Alphabetically
CitySI Accelerels
[d]
′Gravitels
[z]
Amsterdam9.817 m/s21.001X ′Gvℓ
Anchorage9.826 m/s21.0035 ′Gvℓ
Athens9.800 m/s20.EEXX ′Gvℓ
Auckland9.799 m/s20.EEX8 ′Gvℓ
Bangkok9.780 m/s20.EE74 ′Gvℓ
Brussels9.815 m/s21.0016 ′Gvℓ
Buenos Aires9.797 m/s20.EEX4 ′Gvℓ
Calcutta9.785 m/s20.EE82 ′Gvℓ
Cape Town9.796 m/s20.EEX1 ′Gvℓ
Chicago9.804 m/s20.EEE6 ′Gvℓ
Copenhagen9.821 m/s21.0026 ′Gvℓ
Denver9.798 m/s20.EEX6 ′Gvℓ
Frankfurt9.814 m/s21.0014 ′Gvℓ
Havana9.786 m/s20.EE84 ′Gvℓ
Helsinki9.825 m/s21.0033 ′Gvℓ
Hong Kong9.785 m/s20.EE82 ′Gvℓ
Istanbul9.808 m/s21.0003 ′Gvℓ
Jakarta9.777 m/s20.EE69 ′Gvℓ
Kuala Lumpur9.776 m/s20.EE67 ′Gvℓ
Kuwait9.792 m/s20.EE95 ′Gvℓ
Lisbon9.801 m/s20.EEE0 ′Gvℓ
London9.816 m/s21.0018 ′Gvℓ
Los Angeles9.796 m/s20.EEX1 ′Gvℓ
Madrid9.800 m/s20.EEXX ′Gvℓ
Manila9.780 m/s20.EE74 ′Gvℓ
Mexico City9.776 m/s20.EE67 ′Gvℓ
Montréal9.809 m/s21.0005 ′Gvℓ
New York City9.802 m/s20.EEE2 ′Gvℓ
Nicosia9.797 m/s20.EEX4 ′Gvℓ
Oslo9.825 m/s21.0033 ′Gvℓ
Ottawa9.806 m/s20.EEEE ′Gvℓ
Paris9.809 m/s21.0005 ′Gvℓ
Rio de Janeiro9.788 m/s20.EE89 ′Gvℓ
Rome9.803 m/s20.EEE4 ′Gvℓ
Seattle9.811 m/s21.0009 ′Gvℓ
Singapore9.776 m/s20.EE67 ′Gvℓ
Skopje9.804 m/s20.EEE6 ′Gvℓ
Stockholm9.818 m/s21.0020 ′Gvℓ
Sydney9.797 m/s20.EEX4 ′Gvℓ
Taipei9.790 m/s20.EE91 ′Gvℓ
Tokyo9.798 m/s20.EEX6 ′Gvℓ
Vancouver9.809 m/s21.0005 ′Gvℓ
Washington, D.C.9.801 m/s20.EEE0 ′Gvℓ
Wellington9.803 m/s20.EEE4 ′Gvℓ
Zurich9.807 m/s21.0001 ′Gvℓ
Lightest to Heaviest Gravity
CitySI Accelerels
[d]
′Gravitels
[z]
Kuala Lumpur9.776 m/s20.EE67 ′Gvℓ
Mexico City9.776 m/s20.EE67 ′Gvℓ
Singapore9.776 m/s20.EE67 ′Gvℓ
Jakarta9.777 m/s20.EE69 ′Gvℓ
Bangkok9.780 m/s20.EE74 ′Gvℓ
Manila9.780 m/s20.EE74 ′Gvℓ
Calcutta9.785 m/s20.EE82 ′Gvℓ
Hong Kong9.785 m/s20.EE82 ′Gvℓ
Havana9.786 m/s20.EE84 ′Gvℓ
Rio de Janeiro9.788 m/s20.EE89 ′Gvℓ
Taipei9.790 m/s20.EE91 ′Gvℓ
Kuwait9.792 m/s20.EE95 ′Gvℓ
Cape Town9.796 m/s20.EEX1 ′Gvℓ
Los Angeles9.796 m/s20.EEX1 ′Gvℓ
Buenos Aires9.797 m/s20.EEX4 ′Gvℓ
Nicosia9.797 m/s20.EEX4 ′Gvℓ
Sydney9.797 m/s20.EEX4 ′Gvℓ
Denver9.798 m/s20.EEX6 ′Gvℓ
Tokyo9.798 m/s20.EEX6 ′Gvℓ
Auckland9.799 m/s20.EEX8 ′Gvℓ
Athens9.800 m/s20.EEXX ′Gvℓ
Madrid9.800 m/s20.EEXX ′Gvℓ
Lisbon9.801 m/s20.EEE0 ′Gvℓ
Washington, D.C.9.801 m/s20.EEE0 ′Gvℓ
New York City9.802 m/s20.EEE2 ′Gvℓ
Rome9.803 m/s20.EEE4 ′Gvℓ
Wellington9.803 m/s20.EEE4 ′Gvℓ
Chicago9.804 m/s20.EEE6 ′Gvℓ
Skopje9.804 m/s20.EEE6 ′Gvℓ
Ottawa9.806 m/s20.EEEE ′Gvℓ
Zurich9.807 m/s21.0001 ′Gvℓ
Istanbul9.808 m/s21.0003 ′Gvℓ
Montréal9.809 m/s21.0005 ′Gvℓ
Paris9.809 m/s21.0005 ′Gvℓ
Vancouver9.809 m/s21.0005 ′Gvℓ
Seattle9.811 m/s21.0009 ′Gvℓ
Frankfurt9.814 m/s21.0014 ′Gvℓ
Brussels9.815 m/s21.0016 ′Gvℓ
London9.816 m/s21.0018 ′Gvℓ
Amsterdam9.817 m/s21.001X ′Gvℓ
Stockholm9.818 m/s21.0020 ′Gvℓ
Copenhagen9.821 m/s21.0026 ′Gvℓ
Helsinki9.825 m/s21.0033 ′Gvℓ
Oslo9.825 m/s21.0033 ′Gvℓ
Anchorage9.826 m/s21.0035 ′Gvℓ

Table 4
Body Gravities
[z] [d]
Sun23.XX ′Gvℓ27.90 g
Jupiter2.782 ′Gvℓ2.640 g
Neptune1.194 ′Gvℓ1.148 g
Saturn1.180 ′Gvℓ1.139 g
Earth1.000 ′Gvℓ1.000 g
Uranus0.E007 ′Gvℓ0.9170 g
Venus0.XX09 ′Gvℓ0.9032 g
Mars0.4811 ′Gvℓ0.3895 g
Mercury0.4635 ′Gvℓ0.3770 g
Io0.2226 ′Gvℓ0.182 g
Moon 0.1E91 ′Gvℓ0.1655 g
Ganymede0.18E7 ′Gvℓ0.145 g
Titan0.17X6 ′Gvℓ0.138 g
Europa0.1737 ′Gvℓ0.134 g
Callisto0.1619 ′Gvℓ0.126 g
Eris0.0E88 ′Gvℓ0.0814 g
Triton0.0E46 ′Gvℓ0.079 g
Pluto0.08E4 ′Gvℓ0.0621 g
Titania 0.0575 ′Gvℓ0.039 g
Oberon0.0506 ′Gvℓ0.035 g

Additional material:

There are interesting discussions about gravity, and the ′gravitel, in these threads.

Attached Image (Click thumbnail to expand)
Attached Image

Top
Kodegadulo
Posted: Jun 27 2012, 04:11 AM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



Primel Velocity/Speed Units

The Primel base unit for velocity or speed, the ′velocitel or ′speedel, is derived by taking the product of the ′accelerel and the ′timel. This represents the amount of speed a falling object picks up in the first jiff (z|42 triciaseconds) of its descent. Remarkably, this yields a speed that is very close to one customary foot per second, and very close indeed to one kilometer per hour! The table below shows the unqual powers of the ′velocitel, up to and including the Einsteinian limit \(c_0\), the speed of light.

Primel Unit Symbol TGM Equivalent SI Equivalents Customary Equivalents
′velocitel ′Veℓ ~ 2 unciaVlos d|28.376 centimeters/second =
d|1.0215 kilometers/hour
d|0.93096 feet/second =
d|0.63475 miles/hour =
d|0.5516 knots
′unquavelocitel ′UVeℓ ~ 2 Vlos d|3.405 meters/second =
d|12.258 kilometers/hour
d|11.17 feet/second =
d|7.617 miles/hour
′biquavelocitel ′BVeℓ ~ 2 unquaVlos d|40.86 meters/second =
d|147.10 kilometers/hour
d|134.06 feet/second =
d|91.40 miles/hour
′triquavelocitel ′TVeℓ ~ 2 biquaVlos d|490.3 meters/second =
d|1765.2 kilometers/hour
d|1608.7 feet/second =
d|1096.8 miles/hour
′quadquavelocitel ′QVeℓ ~ 2 triquaVlos d|5.884 kilometers/second d|3.656 miles/second
′pentquavelocitel ′PVeℓ ~ 2 quadquaVlos d|70.608 kilometers/second d|43.87 miles/second
′hexquavelocitel ′HVeℓ ~ 2 pentquaVlos d|847.3 kilometers/second d|526.5 miles/second
′septquavelocitel ′SVeℓ ~ 2 hexquaVlos d|10,167.5 kilometers/second d|6,317.8 miles/second
′octquavelocitel ′OVeℓ ~ 2 septquaVlos d|122,010.4 kilometers/second d|75,813.8 miles/second
lightspeed z|2.559X6621X4 ′OVeℓ
z|255,9X6,621.X4 ′Veℓ
d|299,792.485 kilometers/second d|186,282.414 miles/second

Here's a comparison of the kind of speeds you'd find on an automobile's speedometer dial. Although as dozenalists we'd prefer to use dozenal numbers with Primel units, I present the decimal values along with the dozenal values, in order to highlight the close correspondence between speeds expressed in ′speedels and speeds expressed in KPH|

Primel Unit SI Equivalent Customary Equivalent
Dozenal Decimal
z|10 ′Veℓ d|12 ′Veℓ d|12.258 kph d|7.7809 mph
z|20 ′Veℓ d|24 ′Veℓ d|24.5166 kph d|15.5619 mph
z|30 ′Veℓ d|36 ′Veℓ d|36.7749 kph d|23.3428 mph
z|40 ′Veℓ d|48 ′Veℓ d|49.0333 kph d|31.1237 mph
z|50 ′Veℓ d|60 ′Veℓ d|61.2916 kph d|38.9046 mph
z|60 ′Veℓ d|72 ′Veℓ d|73.5499 kph d|46.6856 mph
z|70 ′Veℓ d|84 ′Veℓ d|85.8082 kph d|54.4665 mph
z|80 ′Veℓ d|96 ′Veℓ d|98.0665 kph d|62.2474 mph
z|90 ′Veℓ d|108 ′Veℓ d|110.3248 kph d|70.0283 mph
z|X0 ′Veℓ d|120 ′Veℓ d|122.5831 kph d|77.8093 mph
z|E0 ′Veℓ d|132 ′Veℓ d|134.8414 kph d|85.5902 mph
z|100 ′Veℓ d|144 ′Veℓ d|147.0782 kph d|93.3711 mph

There's also a nice correspondence between z|20 ′Veℓ and approximately d|15 mph. You often see speed limit signs in the U.S. in increments of d|15 mph| d|15 mph, d|30 mph, d|45 mph. Note that z|70 ′Veℓ is very close to d|55 mph which is common as the metropolitan highway limit. d|65 mph is common as the cross-country highway limit, and d|80 ′Veℓ approaches it, though not very well; however some states, especially rural ones, have reinstated d|70 mph as a limit, and z|90 ′Veℓ approximates that very closely.

Top
Kodegadulo
Posted: Jun 27 2012, 09:07 PM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



Added a depiction of a Perennial Calendar in the post about Time Units.
Top
Kodegadulo
Posted: Jun 30 2012, 06:46 PM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



CAVEAT: This post reflects an earlier point in the evolution of Primel, when I was using the SI gravity of 9.80665z m/s2 rather than the gravity which achieves ′ell-length = 46.5d inches. I was also using a prefix form of base annotation, whereas I prefer subscript annotations now. I was also abbreviating the power-prefixes with uppercase vs. lowercase (e.g. unqua = U, uncia = u) whereas I prefer using special symbols now (e.g. unqua = u↑ , uncia = u↓ ). And of course, I have deprecated the ′kernel in favor of the ′morsel. (No more barleycorns, except as a footnote!) See Primel Metrology Wiki for more up-to-date information.

Primel Length Units

The Primel base unit for length, the ′lengthel, is derived by taking the product of the ′speedel and the ′timel. This represents the distance traveled in z|42 triciaseconds by an object moving at very close to 1 kilometer per hour. The resulting length is a bit smaller than an SI centimeter: about 8 millimeters or z|5/14 of a customary inch.

For those accustomed to base units of length being at the scale of the customary foot or the SI meter, this may appear at first glance to be a rather small unit to serve as the basis for a system of measure. However, note that historically the centimeter itself actually served in such a role, as a foundation for the CGS (centimeter-gram-second) system, before that was supplanted by the MKS (meter-kilogram-second) system, now known as SI. The centimeter was, and still is, eminently serviceable as a unit of measure, and we shall see that the ′lengthel is at least as serviceable. In fact, when its dozenal powers are considered along with it, they turn out to constitute a very useful suite of length units.

Here are the unqual powers of the ′lengthel:

Primel Unit Symbol Colloquialism TGM Equivalent SI Equivalents Customary Equivalents
′unnilcialengthel ′unLnℓ   ~ 4 unbiciaGrafut d|0.92086985 femtometers
′levcialengthel ′ℓLnℓ   ~ 4 ununciaGrafut d|11.0504 femtometers
′deccialengthel ′dLnℓ   ~ 4 unnilciaGrafut d|132.605 femtometers
′enncialengthel ′eLnℓ   ~ 4 levciaGrafut d|1.59126 picometers
′octcialengthel ′oLnℓ   ~ 4 decciaGrafut d|19.0952 picometers
′septcialengthel ′sLnℓ   ~ 4 ennciaGrafut d|229.142 picometers
′hexcialengthel ′hLnℓ   ~ 4 octciaGrafut d|2.7497 nanometers
′pentcialengthel ′pLnℓ   ~ 4 ennciaGrafut d|32.9964 nanometers
′quadcialengthel ′qLnℓ   ~ 4 hexciaGrafut d|395.957 nanometers
′tricialengthel ′tLnℓ   ~ 4 pentciaGrafut d|4.75149 microns
′bicialengthel ′bLnℓ   ~ 4 quadciaGrafut d|57.0178 microns
′uncialengthel ′uLnℓ ′point ~ 4 triciaGrafut d|684.214 microns d|0.862 32nds-inch =
d|1.9395 point
′lengthel ′Lnℓ ′spacing
′kernel
~ 4 biciaGrafut d|8.2106 millimeters d|0.3232 inches =
d|0.96975 barleycorns =
d|5.172 sixteenths-inch
′unqualengthel ′ULnℓ ′hand ~ 4 unciaGrafut d|0.98527 decimeters d|3.8790 inches =
d|0.969752 hands
′biqualengthel ′BLnℓ ′ell ~ 4 Grafut d|1.18232 meters d|46.5481 inches =
d|3.8790 feet =
d|1.0344 ell
′triqualengthel ′TLnℓ ′chain ~ 4 unquaGrafut d|14.1879 meters d|46.548 feet =
d|0.70527 chain
′quadqualengthel ′QLnℓ ′stadium ~ 4 biquaGrafut d|170.25 meters d|558.58 feet=
d|0.8463 furlongs =
d|0.96516 stadia (Olympic)
′pentqualengthel ′PLnℓ ′trekel ~ 4 triquaGrafut d|2.04305 kilometers d|1.26949 miles =
d|1.10318 nautical miles
′hexqualengthel ′HLnℓ ′march ~ 4 quadquaGrafut d|24.5166 kilometers d|15.2339 miles =
d|13.2382 nautical miles
′septqualengthel ′SLnℓ ′unquamarch ~ 4 pentquaGrafut d|294.1995 kilometers d|182.8071 miles =
d|158.8580 nautical miles
′octqualengthel ′OLnℓ ′biquamarch ~ 4 hexquaGrafut d|3530.394 kilometers d|2193.685 miles =
d|1906.296 nautical miles
′ennqualengthel ′ELnℓ ′triquamarch ~ 4 septquaGrafut d|42,364.7 kilometers d|26,324.2 miles =
d|22,875.6 nautical miles
d|1.0571 earth circumferences
′decqualengthel ′DLnℓ ′quadquamarch ~ 4 octquaGrafut d|508,376.7 kilometers d|315,890.7 miles
′levqualengthel ′LLnℓ ′pentquamarch ~ 4 ennquaGrafut d|6,100,520.8 kilometers d|3,790,687.9 miles
′unnilqualengthel ′UNLnℓ ′hexquamarch ~ 4 decquaGrafut d|73,206,240 kilometers =
d|0.48935 A.U.
d|45,488,255 miles
′ununqualengthel ′UULnℓ ′septquamarch ~ 4 levquaGrafut d|878,474,000 kilometers =
d|5.8722 A.U.
d|545,859,058 miles
′unbiqualengthel ′UBLnℓ ′octquamarch ~ 4 unnilquaGrafut d|10,541,699,998 kilometers =
d|70.4669 A.U.
d|6,550,308,696 miles
′untriqualengthel ′UTLnℓ ′ennquamarch ~ 4 ununquaGrafut d|126,500,399,972 kilometers =
d|845.603 A.U.
d|78,603,704,349 miles
′unquadqualengthel ′UQLnℓ ′decquamarch ~ 4 unbiquaGrafut d|1,518,004,799,668 kilometers =
d|10,147.2 A.U. =
d|0.16045 light years
d|943,244,452,191 miles
′unpentqualengthel ′UPLnℓ ′levquamarch ~ 4 untriquaGrafut d|18,216,057,596,019 kilometers =
d|121,767 A.U. =
d|1.9254 light years
d|11,318,933,426,302 miles

The ′lengthel is a very close approximation of the line spacing of standard ruled paper, being almost exactly intermediate between the spacing of wide-ruled/legal-ruled paper (z|E/28 inch) and medium-ruled/college-ruled paper (z|9/28 inch). This would suggest ′spacing as an apt colloquialism for this unit. One result of this is that if notebook paper were ruled with ′lengthel-spaced lines, then quoting the number of lines per page would express the page's size in ′spacings. (Not counting header space at the top of the page, of course.) Another consequence is that existing standard ruled paper makes a fairly good approximation of a Primel ruler, which you can use to get a feel for how everyday objects would be measured.

[Note: I am deprecating the previous colloquialism, "′line", for the ′lengthel. The name "′line" should be reserved for the ′unciathumb, an approximation for the customary line, which is one twelfth of an inch.]

The ′lengthel is for instance about the width of standard 8 mm film, such as was used for the Zapruder film, or Super 8 mm film as was featured in the Spielberg movie Super 8. (However, I would not suggest giving it the colloquial name "zapruder" or "spielberg"!) smile.gif

The ′unqualengthel, a dozen ′spacings, approximates the traditional 4-inch "hand" measure, and so can be called a ′hand. This is also remarkably close to a decimeter. This correspondence will prove important later when we derive volume and mass units. It is an interesting coincidence that (decimal) d|10 centimeters, the basis for the liter and the kilogram, is almost exactly equal to (dozenal) z|10 ′spacings, which will be the basis for the ′triquavolumel and the ′triquamassel.

The ′biqualengthel, a dozen ′hands, makes a somewhat longish, but still quite serviceable, "meter" or "yard", and can play the same role as these units. Actually, it better approximates the English d|45-inch "ell" measure, so giving it the colloquial name ′ell is very appropriate. In fact, if we pronounc this "prime-ell", then it becomes a pun on the name of the whole system of measure! smile.gif

As an example, let's take a page from the old adage "mankind is the measure of all things". Here's a comparison of average heights in the US in SI, Conventional, and Primel units:

Average Height, United States (z|11XE-11E2 C.E.)
DemographicSI UnitsConventionalPrimel
Males age z|18-25d|1.789 md[5 ft 10.5 in]z|162 ′kernelsz|16.2 ′handsz|1.62 ′ells
Females age z|18-25d|1.648 md[5 ft 5 in]z|149 ′spacingsz|14.9 ′handsz|1.49 ′ells

Which of these units is the best scale for measuring human proportions? Are kernels the best since they let you express human heights to three digits as whole numbers without fractions, or are ′ells better since they let you deal with smaller numbers, though with more fractional digits? Some of this is a matter of taste. Luckily, there are units for each of these scales, so we can try them all out for size and defer making a decision about this until later.

The ′triqualengthel, a dozen ′ells, is about d|14 meters or d|47 feet. This is about d|71% of a traditional English chain. Although this is a rather loose fit, we could perhaps co-opt this name and give this unit the colloquialism ′chain. This might be a useful unit for architectural or civil engineering measurements.

The ′quadqualengthel, a biqua (z|100) of ′ells, is about d|170 meters, or d|559 feet. This is about d|85% of a traditional English furlong, or d|97% of an ancient Greek stadium (Olympic). The colloquialism ′stadium wouldn't be out of the question. This might be a good unit of measurement for land surveying or measuring city blocks.

The ′pentqualengthel, a triqua (z|1000) of ′ells, is almost exactly 2 kilometers. This explains why the ′velocitel is almost exactly 1 kilometer per hour: Since an unciaday is a ′pentquatimel, traveling a ′pentqualengthel in that time is equivalent to 2 kilometers in 2 hours = 1 kph. This distance also fairly approximates the statute and nautical miles; it is a somewhat bigger brother of both, but not radically so. Hence, it makes a fine unit for measuring geographic and travel distances. It could be given the colloquialism ′triquaell, but with a little word-erosion this could be reduced to ′trekel, which would convey the sense of measuring travel distances.

The ′hexqualengthel, a dozen ′trekels, is around two dozen kilometers or fifteen miles. This is about a day's march for an army on the move. An entire day moving at 1 ′velocitel covers this distance. A real army would of course make better time when actually marching, however they would no necessarily march around the clock; accounting for sleep and logistics, the pace would average out to this. Therefore, calling this distance a ′march makes for an apt colloquialism.

Here are some possible auxiliary units using multipliers on the unqual powers to approximate other traditional units. However, these seem more trouble than they're worth, because the colloquialized unqual powers already seem useful and intuitive enough:

Auxiliary Unit Symbol Colloquialism TGM Equivalent SI Equivalents Customary Equivalents
′trilengthel ′3Lnℓ ′thumb =
′trikernel
~ 1 unciaGrafut d|2.46317 centimeters d|0.96975 inches
′ennealengthel ′9Lnℓ ′palm =
′trithumb
~ 3 unciaGrafut d|7.38951 centimeters d|2.90926 inches
′bitrinalengthel ′23Lnℓ ′span =
′tripalm =
′enneathumb =
′bitrinakernel
~ 9 unciaGrafut d|22.16853 centimeters d|8.72778 inches
′trina-unqualengthel ′3ULnℓ ′foot =
′trihand
~ 1 Grafut d|29.558 centimeters d|11.637 inches =
d|0.96975 foot
′quadhexalengthel ′46Lnℓ ′cubit =
′bispan =
′hexapalm =
′unhexathumb =
′quadhexakernel
~ 16 unciaGrafut d|22.16853 centimeters d|8.72778 inches
′ennea-unqualengthel ′9ULnℓ ′yard =
′trifoot =
′enneahand
~ 3 Grafut d|88.674 centimeters d|34.911 inches =
d|2.9093 feet
′hexa-quadqualengthel ′6QLnℓ ′kay =
′hexastadium
~ 2 triquaGrafut d|1.02152 kilometers d|0.63475 miles =
d|0.55159 nautical miles
′ennea-quadqualengthel ′9QLnℓ ′mile =
′enneastadium
~ 3 triquaGrafut d|1.53229 kilometers d|0.95212 miles =
d|0.82739 nautical miles

[TBD: Talk a bit about each of the colloquialisms. Fill in the higher powers up to the limit of the known universe, and take the uncial powers down to the Planck distance. Create entries for 1 astronomical unit (′astronomel? ′interplanetel?) and 1 light year (′interstellarel?).]

Top
Kodegadulo
Posted: Apr 14 2013, 05:40 AM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



I thought I should pick up where I left off last year and resume developing the Primel metrology. I did a bit more fleshing out of the Primel Length Units (just above this post).
  • Added the uncial powers down to the ′unnilcialengthel (femtometer range).
  • Discovered that the ′lengthel approximated spacing of ruled paper, and that its immediate unqual powers, without multiplier factors, were already useful as human-sized units.
  • Added colloquialisms for key unqual powers ′line, ′hand, ′ell, ′trekel.
  • Moved multiples of unqual powers off into an auxiliary units table.
  • Added examples of human height in ′lines, ′hands, ′ells.
Top
Kodegadulo
Posted: Apr 14 2013, 12:42 PM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



Did a bit more work on the Primel Length Units:
  • Added the ′chain and the ′furlong, between the ′ell and the ′trekel. Not very good fits but the closest analogs at their scales.
Top
Kodegadulo
Posted: Apr 14 2013, 04:49 PM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



I'm rethinking the colloquialisms for the Primal Time Units.

I think the unciaday really needs a compelling colloquialism, one that is not derivative of "hour" like "bihour" or "duor". It probably should somehow derive from the Latin uncia in the same way that English ounce and inch did, but with a sense of "time of day".

(The ancient Greek for "time of day" was in fact hora (ὥρα), whence English hour. Originally it had only a vague sense that could have covered any portion of a day (or even "season"), but of course it was co-opted centuries ago for the specific meaning of "semiunciaday".)

Hmm, if we combine "when" with "ounce", we could call the unciaday a "whence". But that won't work because "whence" means "from where", or "from which", not "from when".

I've already got something I like for the triciaday: the "trice". I toyed with simply calling it a "′minute", since at d[50] (z[42]) seconds, it's very close to the sexagesimal minute. But "trice" is nice because it's already a perfectly good English word meaning a minute ("my-newt") amount of time, without simply aping the word minute ("minnit"). And of course it carries the sense of "threeness" coming from it being at once the triqua of the ′timel and the tricia of the day. It could even be interpreted as referring to the fact that you get it by dividing a day dozenally--thrice.

Well, you get the unciaday by dividing a day dozenally, once. So perhaps we need a word that combines the sense of "once" and "uncia". "Unce"? Hmm.

How about the biciaday? It's a decaminute, or "temin". However, it makes no sense to give it a colloquialism that mentions not only the non-dozenal base ten, but also the non-dozenal sexagesimal minute. So we need something else. Well, you get a biciaday by dividing the day dozenally, twice. But "twice" and "trice" are too close together in sound and could be easily confused, especially with certain British accents and certain speech impediments. But if an unciaday is an "unce", and a triciaday is a "trice", then perhaps a biciaday should be ... a "bice"? Hmm.

What about plurals of these words? Let's try them out: "There are one dozen trices in a bice, one gross trices in an unce, and one zagier trices in a day. There are one dozen bices in an unce, and one gross bices in a day. There are one dozen unces in a day. I work four unces a day, although often as much as five or six unces, but only get three bices for lunch, or equivalently, threezen trices."

Meanwhile, I'm second-guessing using "twinkling" as a colloquialism for the ′timel. It may be more appropriate for the ′unquatimel instead. A "twinkling" is defined as "the time required for a wink". At approximately a third of a second, the ′unquatimel is about right for that.

So I need a different colloquialism for the ′timel. I'm thinking now it should be the "jiffy" because that has a non-specific meaning of a very short period of time. It's used technically to indicate specific tiny amounts of time, but at wildly different scales in different fields of science and engineering. So perhaps I can co-opt it for the ′timel, especially if I cast it as the "′jiffy".

I don't have anything good for the ′biquatimel. It's z[4.2] seconds long. About the time needed to breathe in an out when at rest. Call it a "breathing"?

So what have we got?

A dozen jiffies in a twinkling.
A dozen twinklings in a breathing.
A dozen breathings in a trice.
A dozen trices in a bice.
A dozen bices in an unce.
A dozen unces in a day.

Thoughts? Suggestions?

Top
Kodegadulo
Posted: Apr 14 2013, 09:36 PM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



Primel Area Units

The Primel base unit for area, the ′areael, is derived by squaring the ′lengthel. This results in a square approximately 8 millimeters, or 5/14z of a customary inch, to a side, equivalent to about 0.6741d square centimeters or d|0.1045 square inches.

A square centimeter is equivalent to about 1.483d (1.597z) ′areaels. A square inch is approximately 9.57d (9.6Xz) ′areaels.

Just as for the ′lengthel, the ′areael might seem rather small for a base unit of measure. But quadrille-ruled paper marked off in ′areaels would be quite useful for drafting and so forth. And when the ′areael is considered together with its dozenal powers, the suite of units proves to be useful for a variety of purposes:

Here are some unqual powers of the ′areael:

Primel Unit Symbol Colloquialism TGM Equivalent SI Equivalents Customary Equivalents
bicia′areael b↓′Arℓ ′pointareael ~14z quadciaSurf 0.4681488101d square millimeters 3.761676842d square points
uncia′areael u↓′Arℓ   ~14z pentciaSurf 5.617785721d square millimeters 45.1401221d square points
′areael ′Arℓ ′kernelarea
′spacingarea
~14z quadciaSurf 67.41342865d square millimeters 0.104491023d square inches
541.68146524d square points
unqua′areael u↑′Arℓ   ~14z triciaSurf 8.089611438d square centimeters 1.253892281d square inches
biqua′areael b↑′Arℓ ′handarea ~14z biciaSurf 0.970753373d square decimeters 15.04670737d square inches
triqua′areael t↑′Arℓ   ~14z unciaSurf 11.64904047d square decimeters 1.253892281d square feet
quadqua′areael q↑′Arℓ ′ellarea ~14z Surf 1.397884856d square meters 15.04670737d square feet=
1.671856374d square yards
pentqua′areael p↑′Arℓ   ~14z unquaSurf 16.77461828d square meters 20.06227649d square yards
hexqua′areael h↑′Arℓ ′remulcumarea ~14z biquaSurf d|2.012954193d ares d|240.7473179d square yards
septqua′areael s↑′Arℓ   ~14z triquaSurf 24.15545032d ares =
0.2415545032d hectares
0.596894177d acres
octqua′areael o↑′Arℓ ′stadiumarea ~14z quadquaSurf 2.898654038d hectares 7.162730119d acres
ennqua′areael e↑′Arℓ   ~14z pentquaSurf 34.78384846d hectares 85.95276143d acres
decqua′areael d↑′Arℓ ′dromicumarea ~14z hexquaSurf 4.174061815d square kilometers 1.611614277d square miles
levqua′areael ℓ↑′Arℓ   ~14z septquaSurf 50.08874178d square kilometers 19.33937132d square miles
unnilqua′areael un↑′Arℓ ′itinerumarea ~14z octquaSurf 601.0649014d square kilometers 232.0724559d square miles

The biqua′areael is one square ′hand, and might be referred to colloquially as a ′handarea. This is almost exactly one square decimeter (about d|97 square centimeters) or d|15 square inches. This unit might be good for measuring surface areas of everyday objects such as furniture and equipment. A square decimeter is approximately d|1.03 ′handareas. A square foot is about d|9.57 ′handareas.

The quadqua′areael is one square ′ell, and might be referred to colloquially as an ′ellarea. This is approximately d|1.4 square meters, or d|15 square feet, or d|1.67 square yards. This unit might be good for measuring floor plans, floor covering, and so forth. A square meter is about d|0.715 ′ellareas. A square yard is about d|0.598 ′ellareas.

The hexqua′areael is one square ′remulcum, and might be referred to colloquially as a ′remulcumarea. This is approximately d|2.01 ares, or d|240.75 square yards. This unit might be good for measuring architectural plots for building and landscaping plans, smaller farming properties, and so on. A hectare is approximately d|49.7 (z|41.8) ′remulcumareas. An acre is about d|13.96 (z|11.E6) ′remulcumareas.

The octqua′areael is one square ′stadium, and might be referred to colloquially as a ′stadiumarea. This is approximately d|2.9 hectares, or d|7.2 acres. This unit might be good for measuring larger farming properties, institutional building plans, city block maps, etc. A square kilometer is about d|23.96 (z|1E.E6) ′stadiumareas. A square mile is approximately d|62.05 (z|52.07) ′stadiumareas.

The decqua′areael is one square ′dromicum, and might be referred to colloquially as a ′dromicumarea. This is approximately 4 square kilometers or d|1.6 square miles. This unit might be good for measuring area on maps at urban and regional scales.

The unnilqua′areael is one square ′itinerum, and might be referred to colloquially as an ′itinerumarea. This is approximately d|601 square kilometers or d|232 square miles. This unit might be good for measuring area on maps at national or continental scales.

Top
Kodegadulo
Posted: Apr 17 2013, 04:29 AM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



Finished write-up on Primel Area Units and linked to it from the table in the original post.
Top
Kodegadulo
Posted: Apr 17 2013, 12:54 PM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



Primel Time Units

NOTE: This post supplants this previous post and institutes some changes to the colloquialisms. I'm keeping the old post for historical reasons rather than editing it.

The mean solar day is a fundamental reality of Primel, just as it is for TGM. However, Primel will use a round dozenal power of the day, the hexciaday, as its base unit of time, the ′timel. This contrasts with TGM, which first divides the day in half, and then takes the pentcia of the semiday as its base time unit, the Tim. As a consquence, the ′timel is equivalent to one-sixth of a Tim. This makes the ′timel a very fleeting moment of time, just beyond human perception. I have proposed calling it, colloquially, a ′jiff. Nevertheless, it is a useful quantity for precision scientific and engineering purposes, and its scale will have interesting effects on the rest of the Primel metrology.

On the other hand, the unqual powers of the ′timel, starting with the ′unquatimel, do fall within the human scale. The table below shows a range of dozenal powers of the ′timel, from ennqua down to enncia. The ′timel itself is highlighted in blue, and the "human scale" powers up to the full day are shown in green. Each of these is equivalent to an uncial power of the day, and these equivalents can be used as synonyms. One useful feature to note at the top of the scale is that higher powers of the ′timel correspond to whole powers of the day, so there is a seamless transition from large-scale measures of time based on the day and smaller-scale measures of time.

Prefixes indicate base: d| = decimal, z| = dozenal. See Radix Prefixes for more details.

Primel Unit Symbol Derivation
(and Synonym)
Colloquialism TGM Equivalent SI Equivalents Customary Equivalents
ennqua′timel e↑′Tmℓ triquaday (t↑Dy) 2 octquaTim (o↑Tm) 1000z days
octqua′timel o↑′Tmℓ biquaday (b↑Dy) 2 septquaTim (s↑Tm) 100z days
septqua′timel s↑′Tmℓ unquaday (u↑Dy) 2 hexquaTim (h↑Tm) 10z days
hexqua′timel h↑′Tmℓ day 2 pentquaTim (p↑Tm) 20z hours = 42,000z seconds
pentqua′timel p↑′Tmℓ unciaday (u↓Dy) unce
′whiling
′stound
′dwell
2 quadquaTim (q↑Tm) 1 "duor" = 1 bihour = 2 hours = 4200z seconds
quadqua′timel q↑′Tmℓ biciaday (b↓Dy) bice
′block
′bout
′breather
2 triquaTim (t′Tm) 1 "temin" = 1 decaminute = d|10 minutes = 420z seconds
triqua′timel t′′Tmℓ triciaday (t↓Dy) ′trice 2 biquaTim (b↑Tm) 50d seconds = 42z seconds
biqua′timel b↑′Tmℓ quadciaday (q↓Dy) ′breathing
′waltzing
′lull
2 unquaTim (u↑Tm) 4.16d seconds = 4.2z seconds
unqua′timel u↑′Tmℓ pentciaday (p↓Dy) ′twinkling 2 Tim ( Tm ) 347.2d milliseconds =
420z triciaseconds =
20.83d thirds (1/60d seconds)
′timel ′Tmℓ hexciaday (h↓Dy) ′jiff 2 unciaTim (u↓Tm) 28.93518d milliseconds =
42z triciaseconds =
1.7361d thirds (d|1/60 seconds)
uncia′timel u↓′Tmℓ septciaday (s↓Dy) 2 biciaTim (b↓Tm) 2.4113d milliseconds =
4.2z triciaseconds
′biciatimel ′b↓Tmℓ octciaday (o↓Dy) 2 triciaTim (t&diwnarrow,Tm) 200.94d microseconds =
420z hexciaseconds
′triciatimel ′tTmℓ ennciaday (eDy) 2 quadciaTim (qTm) d|16.745 microseconds =
z|42 hexciaseconds
′quadciatimel ′qTmℓ decciaday (dDy) 2 pentciaTim (pTm) d|1.3954 microseconds =
z|4.2 hexciaseconds
′pentciatimel ′pTmℓ levciaday (ℓDy) 2 hexciaTi (hTm) d|116.28 nanoseconds =
z|420 ennciaseconds
′hexciatimel ′hTmℓ unnilciaday (unDy) 2 septciaTim (sDy) d|9.6903 nanoseconds =
z|42 ennciaseconds
′septciatimel ′sTmℓ ununciaday (uuDy) 2 octciaTim (oTm) d|807.53 picoseconds =
z|4.2 ennciaseconds
′octciatimel ′oTmℓ unbiciaday (ubDy) 2 ennciaTim (eTm) d|67.294 picoseconds =
z|420 unnilciaseconds
′ennciatimel ′eTmℓ untriciaday (utDy) 2 decciaTim (dTm) d|5.6078 picoseconds =
z|42 unnilciaseconds

The ′unquatimel is a dozen jiffies, equivalent to 2 Tims or about a third of a second. It is approximately the time needed for a wink. Therefore an appropriate colloquialism for it may be the twinkling. It is also equivalent to a beat of a metronome in the presto range. Counting ′unquatimels in threes approximates the tempo of a Viennese waltz.

The ′biquatimel is a dozen twinklings, equivalent to 2 unquaTim or z|4.2 seconds. It is about the time needed to inhale and exhale while at rest. Therefore an appropriate colloquialism for this unit may be a breathing. It is about the time needed to play four measures of a musical piece set in 3/4 time or waltz rhythm, enough to state the melodic theme of the Blue Danube for instance. Therefore an appropriate colloquialism for this unit may be a ′waltzing.

The ′triquatimel is a dozen ′breathings ′waltzings, equivalent to 2 biquaTim or d|50 (z|42) seconds. The unit is noteworthy in that it is also the triciaday, making it exactly intermediary between the jiff and the day on the exponential scale. Calling it a ′trice as a colloquial name therefore makes for a nice play on words. This conveys the sense that, just like the traditional minute ("minnit"), which it approximates, it is a minute ("my-newt") amount of time, yet the name does not simply ape a sexagesimal unit. It also conveys the sense of "threeness" that it embodies.

The ′quadquatimel, or biciaday, is a dozen ′trices, equivalent to 2 triquaTim or ten conventional minutes. The ′pentquatimel, or unciaday, is a gross of ′trices, equivalent to a long hundred (d|120) conventional minutes, which is the same as 2 conventional hours. Using SDN prefixes, we might call the former a "decaminute" and the latter a "bihour", but less derivative expressions might be more appropriate to colloquialize these units.

First attempt: The unciaday, biciaday, and triciaday dozenally divide the day, respectively, once, twice, and thrice. Since we've given the triciaday the nickname trice, perhaps we can give the unciaday and biciaday the nicknames unce and bice.

Second attempt: A good nickname for the unciaday might be the ′whiling (as in "whiling away a couple of hours"). The biciaday, a ten-minute block of time, might be nicknamed the ′block.

Third attempt: A good nickname for the unciaday might be the ′stound. "Stound" is an archaic English word with roots hearkening back to Old English. It was actually the word for "hour" or "time of day" (cognate with the German Stunde), until the Norman conquest supplanted it with "hour" borrowed from the French. The biciaday might be nicknamed a ′bout. Some of the definitions of "bout" include "period; session; spell" and "a turn at work or any action". The fast hand on the DSGB clock suffers a "bout" of a dozen spins during one biciaday. In a Primel world, when you want to take a break, instead of telling everyone to "take ten" (minutes) or even "take a dozen" (′trice), you could say "take about a ′bout". smile.gif

Although the TGM time units are not whole dozenal powers of the ′timel, they are all a simple multiple of one, so we could certainly incorporate them into Primel as auxiliary units:

Auxiliary Unit Colloquialism Primel Equivalent SI Equivalents Customary Equivalents
semiday pentquaTim = clock 6 ′pentquatimels = 6 unces whilings stounds z|10 hours = z|21,000 seconds
unciasemiday quadquaTim = hour 6 ′quadquatimels = 6 bices blocks bouts = z|60 trices 1 hour = d|60 minutes = z|2100 seconds
biciasemiday triquaTim = ′semiblock 6 ′triquatimels = 6 trices 5 minutes= z|210 seconds
triciasemiday biquaTim 6 ′biquatimels = 6 ′breathings ′waltzings d|25 seconds = z|21 seconds
quadciasemiday unquaTim 6 ′unquatimels = 6 ′twinklings d|2.083 seconds = z|2.1 seconds
pentciasemiday Tim 6 ′timels = 6 ′jiffies d|173.61 milliseconds = z|210 triciaseconds

Here are a few additional auxiliary units that are all interesting multiples of some dozenal power of the ′timel:

Auxiliary Unit Colloquialism Primel Equivalent SI Equivalents Customary Equivalents
septaday week ′septa-hexquatimel 1 week = 7 days
biweek = unbinaday fortnight ′unbina-hexquatimel z|12 days = d|14 days = 2 weeks
bihexaday short Gregorian month ′bihexa-hexquatimel z|26 days = d|30 days
biseptaday long Gregorian month ′bisepta-hexquatimel z|27 days = d|31 days
bihexpentaday Gregorian year ′bihexpenta-hexquatimel z|265 days = d|365 days
bihexhexaday Gregorian leap year ′bihexhexa-hexquatimel z|266 days = d|366 days
quadraweek = biquadraday Perennial-Calendar short month ′biquadra-hexquatimel z|24 days = d||28 days = 4 weeks
pentaweek = bilevaday Perennial-Calendar long month ′bileva-hexquatimel z|2E days = d|35 days = 5 weeks
ununiweek = septseptaday Perennial-Calendar regular quarter ′septsepta-hexquatimel z|77 days = d|91 days = z|11 weeks = d|13 weeks = 3 months
unbinaweek = octbinaday Perennial-Calendar leaping quarter octbina-′hexquatimel z|82 days = d|98 days = z|12 weeks = d|14 weeks = 3 months + leap week
quadquadraweek = bihexquadraday Perennial-Calendar year ′bihexquadra-hexquatimel z|44 weeks = d|52 weeks = z|264 days = d|364 days
quadpentaweek = bihexlevaday Perennial-Calendar leap year ′bihexleva-hexquatimel z|45 weeks = d|53 weeks = d|26E days = d|371 days

A Perennial Calendar can be constructed where every year and month starts on the same day of the week, where every year and month contains a whole number of weeks, and where a leap year adds a leap week onto the last month of the year, rather than a leap day in February. The pattern of leap years would be quite different, of course. When such a calendar is interpreted in dozenal, there's a nice sort of correspondence between how each month is either z|24 or z|2E days and how each year is either z|264 or z|26E days; or equivalently, how each month is either 4 or 5 weeks and how each year is either z|44 or z|45 weeks. (This is essentially a dozenalization of Irv Bromberg's Symmetry 454 Calendar, which was discussed along with other perennial calendars in this thread.)

[z] The following is all in dozenal.

WkJanuary
MTWTFSS
0101020304050607
0208090X0E101112
0313141516171819
041X1E2021222324
WkFebruary
MTWTFSS
0501020304050607
0608090X0E101112
0713141516171819
081X1E2021222324
0925262728292X2E
WkMarch
MTWTFSS
0X01020304050607
0E08090X0E101112
1013141516171819
111X1E2021222324
WkApril
MTWTFSS
1201020304050607
1308090X0E101112
1413141516171819
151X1E2021222324
WkMay
MTWTFSS
1601020304050607
1708090X0E101112
1813141516171819
191X1E2021222324
1X25262728292X2E
WkJune
MTWTFSS
1E01020304050607
2008090X0E101112
2113141516171819
221X1E2021222324
WkJuly
MTWTFSS
2301020304050607
2408090X0E101112
2513141516171819
261X1E2021222324
WkAugust
MTWTFSS
2701020304050607
2808090X0E101112
2913141516171819
2X1X1E2021222324
2E25262728292X2E
WkSeptember
MTWTFSS
3001020304050607
3108090X0E101112
3213141516171819
331X1E2021222324
WkOctober
MTWTFSS
3401020304050607
3508090X0E101112
3613141516171819
371X1E2021222324
WkNovember
MTWTFSS
3801020304050607
3908090X0E101112
3X13141516171819
3E1X1E2021222324
4025262728292X2E
WkDecember
MTWTFSS
4101020304050607
4208090X0E101112
4313141516171819
441X1E2021222324
Leap Week
4525262728292X2E

Additional material at: Names for Some Fractions of the Day

Top
Kodegadulo
Posted: Apr 17 2013, 11:43 PM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



Discovered that one version of the ancient Greek stadium measure is very close to the length of the ′quadqualengthel, much better than the English furlong. So replaced the colloquial name to be ′stadium. Also the ′octquasquarel (the square ′quadqualengthel) is now a ′stadiumsquare.
Top
Leopold Plumtree
Posted: Apr 20 2013, 01:13 AM


Regular


Group: Members
Posts: 346
Member No.: 59
Joined: 26-May 06



Nice to see the Primel system moving forward! biggrin.gif I'm bit of a fan.
Top
Kodegadulo
Posted: Apr 21 2013, 11:24 PM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



Primel Volume Units

The Primel base unit for volume, the ′volumel, is derived by cubing the ′lengthel. This results in a cube approximately 8 millimeters, or z[5/14] of a customary inch, to a side, equivalent to about d[0.5535] milliliters, or d[33.78×10-3] cubic inches, or d[18.72×10-3] U.S. customary fluid ounces, or about a 1/9 of a U.S. customary teaspoon, or about z[54] hexciaVolm.

A milliliter is equivalent to about d[1.807] (z[1.982]) ′volumels. A cubic inch is approximately d[29.61] (z[25.73]) ′volumels. A U.S. customary fluid ounce is equivalent to about d[53.43] (z[45.52]) ′volumels. A U.S. customary teaspoon (approximately 5 ml) is about 9 ′volumels. A TGM Volm is equivalent to about z[23,000] ′volumels. (This makes sense because this z[23,000 = 303], and the TGM Grafut is equivalent to about z[30] ′lengthels.

Just as for the ′lengthel, the ′volumel might seem rather small for a base unit of measure. However, there are certain commonplace volume measurements at the fine end of the scale, such as measuring quantities of liquid medications, that it would be perfectly suitable for. And when the ′volumel is considered together with its dozenal powers, the suite of units proves to be useful for a variety of purposes:

Primel Unit Symbol Colloquialism TGM Equivalent SI Equivalents Customary Equivalents
′triciavolumel ′tVoℓ ′pointvol(ume) ~ z[54] octciaVolm d[0.320313974] microliter  
′biciavolumel ′bVoℓ   ~ z[54] septciaVolm d[3.843767689] microliter  
′unciavolumel ′uVoℓ   ~ z[54] hexciaVolm d[46.12521227] microliter  
′volumel ′Voℓ ′kernelvol(ume)
′spacingvol(ume)
~ z[54] hexciaVolm d[0.553502547] milliliters d[0.033776798] cubic inches =
d[0.018716148] fluid ounces
′unquavolumel ′UVoℓ   ~ z[54] pentciaVolm d[6.642030567] milliliters d[0.405321574] cubic inches =
d[0.224593772] fluid ounces
′biquavolumel ′BVoℓ   ~ z[54] quadciaVolm d[79.70436681] milliliters d[2.695125265] fluid ounces =
d[4.863858883] cubic inches
′triquavolumel ′TVoℓ ′handvol(ume) ~ z[54] triciaVolm d[956.452402] milliliters =
d[0.956452402] liters
d[32.34150318] fluid ounces =
d[1.010671974] quarts =
d[58.3663066] cubic inches
′quadquavolumel ′QVoℓ   ~ z[54] biciaVolm d[11.47742882] liters d[3.032015923] gallons =
d[700.3956792] cubic inches = d[0.405321574] cubic feet
′pentquavolumel ′PVoℓ   ~ z[54] unciaVolm d[137.7291458] liters d[36.38419108] gallons =
d[4.863858883] cubic feet
′hexquavolumel ′HVoℓ ′ellvol(ume) ~ z[54] Volm d[1652.74975] liters =
d[1.65274975] cubic meters
d[436.610293] gallons =
d[58.3663066] cubic feet =
d[2.161715059] cubic yards

The ′triquavolumel is one cubic ′unqualengthel, or cubic ′hand, and so might be referred to colloquially as a ′handvolume, or ′handvol for short. As a result of the ′hand being such a close approximation of the decimeter, the ′handvol is remarkably close to one liter: about d[956] milliliters.

More interestingly, the ′handvol is intermediate between a liter and a U.S. customary quart, and is actually extremely close to the latter: about d[1.01] quart. This makes it an even better approximation to a quart than Pendlebury's "quartol" (hexa-biciaVolm). Indeed, if a liter is (as the old adage says) "a leeter bit more than a quart", then a TGM quartol is a "leeter bit more again". In fact, if the TGM Gee had been identical to the ′gravitel (which equals the SI standard gravity), then the quartol would have been exactly 9/8 of a ′handvol (z[1.16] ′handvols). This makes the TGM quartol nearly d[8%] larger than a liter, and nearly d[14%] larger than a quart. Whereas the ′handvol is only d[1%] over the quart, and less than d[5%] under the liter. All in all, users of both the SI and U.S. customary systems may be a "leeter-bit" happier adjusting to the ′handvol than to the TGM quartol.

If the ′triquavolumel is so close to the liter and the quart, then why not colloquialize it as either a "primel liter" or a "primel quart", or even as both? Well, first of all, such names would imply that Primel units are somehow derivative of either customary or SI units, but in fact they are quite independent. It would be preferable to relate the ′unqualengthel, and by extension the ′triquavolumel, to some object such as the human hand which provides an intuitive sense of scale.

Second, the "quart" itself derived its name from the fact that it is a quarter of a U.S. customary gallon. Why should the name of a Primel unit make reference to a fractional relationship between units in another metrology? We could just as easily stand this on its head and characterize the gallon as being a U.S. customary "quadra-handvol".

In fact, let's relate some other U.S. customary measures to the ′volumel and the ′handvol:

U.S. Customary Primel Approximation Primel Colloquialization
gallond[128] fl. oz.z[4000] ′volumelsz[4] ′handvols′galvol
half-gallond[64] fl. oz.z[2000] ′volumelsz[2] ′handvolshalf ′galvol
quartd[32] fl. oz.z[1000] ′volumelsz[1] ′handvol′handvol
pintd[16] fl. oz.z[600] ′volumelsz[1/2] ′handvol′pintvol
cupd[8] fl. oz.z[300] ′volumelsz[1/4] ′handvol′cupvol
half-cupd[4] fl. oz.z[160] ′volumelsz[1/8] ′handvolhalf ′cupvol
quarter-cupd[2] fl. oz.z[90] ′volumelsz[1/14] ′handvolquarter ′cupvol
fluid ounced[1] fl. oz.z[46] ′volumelsz[1/28] ′handvol′ozvol
tablespoond[1/2] fl. oz.z[23] ′volumelsz[1/54] ′handvol′supvol
teaspoond[1/6] fl. oz.z[9] ′volumelsz[1/140] ′handvol′sipvol

Moving up the scale:

The ′quadquavolumel, colloquially known as the ′unquahandvol, is about a dozen liters or 3 U.S. customary gallons. This is about the amount of water per flush in a typical old-style (pre-d[1990]s) flush toilet.

The ′pentquavolumel, colloquially known as the ′biquahandvol, is about a gross liters or three dozen U.S. customary gallons. This is about the capacity of a typical tall kitchen trash bag, or about the volume of water needed to fill a typical bathtub.

The ′hexquavolumel is one cubic ′biqualengthel, or one cubic ′ell, and so might be colloquialized as an ′ellvolume, or ′ellvol for short. This is about d[1.65] cubic meters, or d[2.16] cubic yards. This unit may be appropriate for measuring large industrial vats or tanks.

The ′ennquavolumel, is one cubic ′triqualengthel, or one cubic ′chain, and so might be colloquialized as a ′chainvolume, or ′chainvol for short. This is about d[2856] cubic meters, or d[3735] cu yards.

The ′unnilquavolumel is one cubic ′quadqualengthel, or one cubic ′stadium, and so might be colloquialized as a ′stadevolume, or ′stadevol for short. This is about d[4.935] million cubic meters, or d[6.455] million cubic yards.

The ′untriquavolumel is one cubic ′pentqualengthel, or one cubic ′trekel, and so might be colloquialized as a ′trekelvolume, or ′trekelvol for short. This is about d[8.528] cubic kilometers, or d[2.046] cubic miles.

Other interesting posts about volume units:

Comparison of Primel, TGM, and USC volume units.

Top
Kodegadulo
Posted: Dec 15 2013, 06:05 AM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



After neglecting this project for too long, I figure it's high time I pick up where I left off. Note that I've done some sprucing up of the previous posts in the chain, so it may be worth it for you to look them over again.

Primel Mass Units

The Primel base unit for mass, the ′massel (′Msℓ), is the mass of one ′volumel of water at maximal density. This makes the ′massel equivalent to about d|0.5535 grams, or d|0.01952 ounces, or d|8.542 grains. Since the ′volumel is colloquially a cubic ′kernel, or ′kernelvol, the ′massel can be colloquialized as a ′kernelmass.

At a bit over a half a gram, the ′massel shares with the gram the disadvantage of being relatively small for a base unit of measure. Even so, it certainly has applications for fine measurements of mass.

Furthermore, the ′massel's third dozenal scaling, the ′triquamassel (′TMsℓ), turns out to be remarkably close to the gram's third decimal scaling, which is of course the kilogram. At about d|956.4 grams, it is less than d|5% off from the kilogram. This makes it at least as applicable to everyday uses as the kilogram is. People accustomed to using SI units would find it easy to adapt to using ′triquamassels.

Moreover, by being a little less than the kilogram, the ′triquamassel comes even closer than the kilogram does to being a double pound. At d|2.109 pounds, or d|33.74 ounces, it comes within about d|5% of a bipound. Simply dividing customary avoirdupois masses by two provides a reasonable rough approximation of the equivalent in ′triquamassels. So users of the avoirdupois system would also find it relatively easy to adapt to using ′triquamassels.

So should we colloquialize the ′triquamassel as a "primel kilogram", or a "primel bipound"? That would imply that the primel unit is somehow based on the kilogram or the pound, but this is not the case at all. A better choice would be to exploit the fact that the ′triquamassel is the mass of a cubic ′hand, or ′handvol, of water. So by extension we could call it a ′handmass.

Here are a number of dozenal powers of the ′massel:

Primel Unit Symbol Colloquialism TGM Equivalent SI Equivalents Customary Equivalents
′ennciamassel ′eMsℓ   ~ z|5.4 ununciaMaz d|0.10727 nanograms  
′octciamassel ′oMsℓ   ~ z|5.4 unnilciaMaz d|1.2872 nanograms  
′septciamassel ′sMsℓ   ~ z|5.4 levciaMaz d|15.447 nanograms  
′hexciamassel ′hMsℓ   ~ z|5.4 decciaMaz d|0.18536 micrograms  
′pentciamassel ′pMsℓ   ~ z|5.4 ennciaMaz d|2.2243 micrograms  
′quadciamassel ′qMsℓ   ~ z|5.4 octciaMaz d|26.692 micrograms  
′triciamassel ′tMsℓ ′pointmass ~ z|5.4 septciaMaz d|0.32031 milligrams  
′biciamassel ′bMsℓ   ~ z|5.4 hexciaMaz d|3.8437 milligrams  
′unciamassel ′uMsℓ   ~ z|5.4 pentciaMaz d|46.124 milligrams  
′massel ′Msℓ ′kernelmass
′spacingmass
~ z|5.4 pentciaMaz d|0.55349 grams d|0.019524 ounces
′unquamassel ′UMsℓ   ~ z|5.4 quadciaMaz d|6.6418 grams d|0.23428 ounces
′biquamassel ′BMsℓ   ~ z|5.4 triciaMaz d|79.7029 grams d|2.8114 ounces
′triquamassel ′TMsℓ ′handmass ~ z|5.4 biciaMaz d|0.95642 kilograms d|2.1086 pounds =
d|33.737 ounces
′quadquamassel ′QMsℓ   ~ z|5.4 unciaMaz d|11.477 kilograms d|25.303 pounds
′pentquamassel ′PMsℓ   ~ z|5.4 Maz d|137.73 kilograms d|303.63 pounds
′hexquamassel ′HMsℓ ′ellmass ~ z|5.4 unquaMaz d|1652.7 kilograms =
d|1.6527 metric tons
d|3643.6 pounds =
d|1.8218 tons
′septquamassel ′SMsℓ   ~ z|5.4 biquaMaz d|19.832 metric tons d|21.862 tons
′octquamassel ′OMsℓ   ~ z|5.4 triquaMaz d|237.99 metric tons d|262.34 tons
′ennquamassel ′EMsℓ ′chainmass ~ z|5.4 quadquaMaz d|2.8559 kilotons d|3.1488 kilotons
′decquamassel ′DMsℓ   ~ z|5.4 pentquaMaz d|34.270 kilotons d|37.777 kilotons
′levquamassel ′LMsℓ   ~ z|5.4 hexquaMaz d|411.25 kilotons d|453.32 kilotons
′unnilquamassel ′UNMsℓ ′stademass ~ z|5.4 septquaMaz d|4.9349 megatons d|5.4399 megatons

The ′quadquamassel (′QMsℓ) is noteworthy in being quite close to d|25 pounds, which is a handy round number for users of avoirdupois units.

The ′hexquamassel (′HMsℓ), being three dozenal orders larger than the ′triquamassel, could play the same role as the U.S. or metric ton, but as a somewhat larger brother to both. But rather than colloquially call it a "primel ton", we should take note that it is the mass of water in a cubic ′ell, or ′ellvol, and therefore call it a ′ellmass.

We can also relate the ′massel and ′handmass to the U.S. customary pound and ounce; and we can exploit the relationship between mass and volume to derive some additional colloquial unit names:

U.S. Customary Analog [d] Primel Approximation [z] Primel Colloquialization Actual Equivalents [d]
8 pounds ~ gallon mass128 oz.4000 ′massels4 ′handmass′galmass8.434 lb134.9 oz3825 g
4 pounds ~ half gallon mass64 oz.2000 ′massels2 ′handmasshalf ′galmass4.217 lb67.5 oz1913 g
2 pounds ~ quart mass32 oz.1000 ′massels1 ′handmass′handmass2.109 lb33.7 oz956 g
1 pound ~ pint mass16 oz.600 ′massels1/2 ′handmass′pintmass1.054 lb16.9 oz478 g
half pound ~ cup mass8 oz.300 ′massels1/4 ′handmass′cupmass0.527 lb8.4 oz239 g
quarter pound ~ half cup mass4 oz.160 ′massels1/8 ′handmasshalf ′cupmass0.264 lb4.2 oz120 g
eighth pound ~ quarter cup mass2 oz.90 ′massels1/14 ′handmassquarter ′cupmass0.132 lb2.1 oz60 g
ounce ~ fl oz mass1 oz.46 ′massels1/28 ′handmass′ozmass0.066 lb1.05 oz29.88 g
half ounce ~ tablespoon mass1/2 oz.23 ′massels1/54 ′handmass′supmass0.033 lb0.527 oz14.94 g
sixth ounce ~ teaspoon mass1/6 oz.9 ′massels1/140 ′handmass′sipmass0.011 lb0.176 oz4.98 g
Top
Kodegadulo
Posted: Dec 15 2013, 01:57 PM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



Primel Units of Force or Weight

The Primel base unit for force, the ′forcel (′Fcℓ), is the force that imparts an acceleration of one ′accelerel upon a mass of one ′massel. Since force and weight are synonyms for the same kind of quantity, this unit can also be called the ′weightel (′Wtℓ), and can be described as the weight that a one ′massel object has within a one ′gravitel gravitational field.

This makes the ′forcel or ′weightel equivalent to about d|5.24279 millinewtons, or d|0.5535 grams-force, or d|0.01952 ounces-force. Since this is the weight of a cubic ′kernel of water (in a standard Earth gravity), we could colloquialize this force unit as a ′kernelforce or ′kernelweight.

Indeed, because the Primel system equates the ′accelerel with the ′gravitel, there is a one-to-one correspondence between each of the dozenal scalings of the ′massel and the same dozenal scalings of the ′forcel or ′weightel. So all the colloquializations for the mass units can be extended to the force/weight units:

Primel Unit Symbol Colloquialism TGM Equivalent SI Equivalents Customary Equivalents
′ennciaforcel
′ennciaweightel
′eFcℓ
′eWtℓ
  ~ z|5.4 ununciaMag d|1.0520 piconewtons
d|0.10727 nanograms-force
 
′octciaforcel
′octciaweightel
′oFcℓ
′oWtℓ
  ~ z|5.4 unnilciaMag d|12.623 piconewtons =
d|1.2872 nanograms-force
 
′septciaforcel
′septciaweightel
′sFcℓ
′sWtℓ
  ~ z|5.4 levciaMag/td> d|151.48 piconewtons =
d|15.447 nanograms-force
 
′hexciaforcel
′hexciaweightel
′hFcℓ
′hWtℓ
  ~ z|5.4 decciaMag d|1.8178 nanonewtons =
d|0.18536 micrograms-force
 
′pentciaforcel
′pentciaweightel
′pFcℓ
′pWtℓ
  ~ z|5.4 ennciaMag d|21.813 nanonewtons =
d|2.2243 micrograms-force
 
′quadciaforcel
′quadciaweightel
′qFcℓ
′qWtℓ
  ~ z|5.4 octciaMag d|261.76 nanonewtons =
d|26.692 micrograms-force
 
′triciaforcel
′triciaweightel
′tFcℓ
′tWtℓ
′pointforce
′pointweight
~ z|5.4 septciaMag d|3.1411 micronewtons =
d|0.32031 milligrams-force
 
′biciaforcel
′biciaweightel
′bFcℓ
′bWtℓ
  ~ z|5.4 hexciaMag d|37.693 micronewtons =
d|3.8437 milligrams-force
 
′unciaforcel
′unciaweightel
′uFcℓ
′uWtℓ
  ~ z|5.4 pentciaMag d|452.32 micronewtons =
d|46.124 milligrams-force
 
′forcel
′weightel
′Fcℓ
′Wtℓ
′kernelforce
′kernelweight
~ z|5.4 pentciaMag d|5.4279 millinewtons =
d|0.55349 grams-force
d|0.019524 ounces-force
′unquaforcel
′unquaweightel
′UFcℓ
′UWtℓ
  ~ z|5.4 quadciaMag d|65.134 millinewtons =
d|6.6418 grams-force
d|0.23428 ounces-force
′biquaforcel
′biquaweightel
′BFcℓ
′BWtℓ
  ~ z|5.4 triciaMag d|781.61 millinewtons =
d|79.7029 grams-force
d|2.8114 ounces-force
′triquaforcel
′triquaweightel
′TFcℓ
′TWtℓ
′handforce
′handweight
~ z|5.4 biciaMag d|9.3783 newtons =
d|0.95642 kilograms-force
d|2.1086 pounds-force =
d|33.737 ounces-force
′quadquaforcel
′quadquaweightel
′QFcℓ
′QWtℓ
  ~ z|5.4 unciaMag d|112.55 newtons =
d|11.477 kilograms-force
d|25.303 pounds-force
′pentquaforcel
′pentquaweightel
′PFcℓ
′PWtℓ
  ~ z|5.4 Mag d|1.3506 kilonewtons =
d|137.73 kilograms-force
d|303.63 pounds-force
′hexquaforcel
′hexquaweightel
′HFcℓ
′HWtℓ
′ellforce
′ellweight
~ z|5.4 unquaMag d|16.207 kilonewtons =
d|1652.7 kilograms-force =
d|1.6527 metric tons-force
d|3643.6 pounds-force =
d|1.8218 tons-force
′septquaforcel
′septquaweightel
′SFcℓ
′SWtℓ
  ~ z|5.4 biquaMag d|194.49 kilonewtons =
d|19.832 metric tons-force
d|21.862 tons-force
′octquaforcel
′octquaweightel
′OFcℓ
′OWtℓ
  ~ z|5.4 triquaMag d|2.3339 meganewtons =
d|237.99 metric tons-force
d|262.34 tons-force
′ennquaforcel
′ennquaweightel
′EFcℓ
′EWtℓ
′chainforce
′chainweight
~ z|5.4 quadquaMag d|28.007 meganewtons =
d|2.8559 kilotons-force
d|3.1488 kilotons-force
′decquaforcel
′decquaweightel
′DFcℓ
′DWtℓ
  ~ z|5.4 pentquaMag d|336.07 meganewtons =
d|34.270 kilotons-force
d|37.777 kilotons-force
′levquaforcel
′levquaweightel
′LFcℓ
′LWtℓ
  ~ z|5.4 hexquaMag d|4.0329 giganewtons =
d|411.25 kilotons-force
d|453.32 kilotons-force
′unnilquaforcel
′unnilquaweightel
′UNFcℓ
′UNWtℓ
′stadeforce
′stadeweight
~ z|5.4 septquaMag d|48.395 giganewtons
d|4.9349 megatons-force
d|5.4399 megatons-force

We can do similar with weights associated with common U.S. customary volume measures:

U.S. Customary Primel Approximation Primel Colloquialization
8 pounds-forced|128 ounces-forcez|4000 ′weightelsz|4 ′handweight′galweight
4 pounds-forced|64 ounces-forcez|2000 ′weightelsz|2 ′handweighthalf ′galweight
2 pounds-forced|32 ounces-forcez|1000 ′weightelsz|1 ′handweight′handweight
1 pound-forced|16 ounces-forcez|600 ′weightelsz|1/2 ′handweight′pintweight
half pound-forced|8 ounces-forcez|300 ′weightelsz|1/4 ′handweight′cupweight
quarter pound-forced|4 ounces-forcez|160 ′weightelsz|1/8 ′handweighthalf ′cupweight
eighth pound-forced|2 ounces-forcez|90 ′weightelsz|1/14 ′handweightquarter ′cupweight
ounce-forced|1 ounces-forcez|46 ′weightelsz|1/28 ′handweight′ozweight
half ounce-forced|1/2 ounces-forcez|23 ′weightelsz|1/54 ′handweight′supweight
sixth ounce-forced|1/6 ounces-forcez|9 ′weightelsz|1/140 ′handweight′sipweight
Top
Kodegadulo
Posted: Dec 15 2013, 05:39 PM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



Primel Units of Work or Energy

The Primel base unit for work, the ′workel (′Wkℓ), is the work performed by applying a force of one ′forcel over a distance of one ′lengthel. Since work and energy are synonyms for the same kind of quantity, this unit can also be called the ′energel (′Ngℓ).

This makes the ′workel or ′energel equivalent to about d|44.566 microjoules, or d|445.66 ergs. Since this is, colloquially, the work performed by applying one ′kernelforce over a distance of one ′kernel, we could colloquialize this as one ′kernelwork or ′kernelenergy.

Compared to the SI joule, the ′workel is quite small. But compared to the old CGS unit of energy (the erg), it's actually rather large. Of course, those used to thinking in joules may find this unit inconvenient except for fine energy measurements. However, we have an easy out for this, by dozenally scaling the ′workel using SDN prefixes.

Consider the ′quadquaworkel. We could characterize this as the work performed by applying one ′handforce (′triquaforcel) over a distance of one ′hand (′unqualengthel). So it would be very appropriate to call this unit, colloquially, a ′handwork. As it turns out, this unit happens to be quite close to one joule! (It's equivalent to about d|0.9241 J.) So the ′quadquaworkel would be approximately as convenient to use as the joule.

However, it's arguable that even the joule is rather too small a unit for many applications. For instance, we have to go to kilojoules in order to describe the energy in just one dietary calorie (approximately d|4.184 kJ). And we count a daily diet in thousands of such calories.

Even more poignantly, we never hear domestic or commercial energy usage expressed in joules. Instead, it's usually expressed in kilowatt-hours. One kilowatt-hour is equivalent to d|3.6 megajoules -- more than 6 decimal orders of magnitude over the base unit! This scheme of leveraging a largish power unit multiplied by a largish time unit certainly can produce a big scaling up of a smallish energy unit. Unfortunately, doing this in SI makes the kilowatt-hour an oddball unit, because the large time unit it is based on (the hour) is not a simple decimal power of the base time unit (the second).

Fortunately, TGM and Primel don't need to suffer this problem. We could certainly measure energy using Pov-hours or ′handpower-days. However, these would be indirect ways of applying dozenal powers to the base units, and this can be done more simply and directly with SDN prefixes: The Pov-hour would be just another name for the quadquaWerg. Likewise, the ′handpower-day would be just another name for the ′hexquahandwork or ′decquaworkel. This unit turns out to be equivalent to about three-quarters of a kilowatt-hour (approximately d|766.50 W-hr), so it would be useful for measuring energy consumption.

Notice that the ′ellwork, the energy necessary to take one ′ellmass (d|1.653 metric tons) and raise it by one ′ell (d|1.182 meters) against one standard ′gravitel, is only d|19.162 kilojoules -- which is only d|4.58 (kilo)calories! That's about the chemical energy in a quarter of a packet of sugar! Just goes to show how "compact" chemical energy is compared to simple kinetic energy or gravitational potential energy. Certainly if one considers the amount of kinetic energy that can be unleashed by igniting a small amount of some explosive chemical, this makes a lot of sense.

Primel Unit Symbol Colloquialism TGM Equivalent SI Equivalents
′workel
′energel
′Wkℓ
′Ngℓ
′kernelwork
′kernelenergy
~ z|1.94 hexciaWerg d|44.566 microjoules =
d|445.66 ergs
′unquaworkel
′unquaenergel
′UWkℓ
′UNgℓ
  ~ z|1.94 pentciaWerg d|534.79 microjoules =
d|5.3479 kiloergs
′biquaworkel
′biquaenergel
′BWkℓ
′BNgℓ
  ~ z|1.94 quadciaWerg d|6.4175 millijoules =
d|64.175 kiloergs
′triquaworkel
′triquaenergel
′TWkℓ
′BNgℓ
  ~ z|1.94 triciaWerg d|77.010 millijoules =
d|770.10 kiloergs
′quadquaworkel
′quadquaenergel
′QWkℓ
′QNgℓ
′handwork
′handenergy
~ z|1.94 biciaWerg d|924.12 millijoules =
d|9.2412 megaergs
′pentquaworkel
′pentquaenergel
′PWkℓ
′PNgℓ
  ~ z|1.94 unciaWerg d|11.089 joules =
d|110.89 megaergs
′hexquaworkel
′hexquaenergel
′HWkℓ
′HNgℓ
  ~ z|1.94 Werg d|133.07 joules =
d|1.3307 gigaergs
′septquaworkel
′septquaenergel
′SWkℓ
′SNgℓ
  ~ z|1.94 unquaWerg d|1.5969 kilojoules =
d|15.969 gigaergs
′octquaworkel
′octquaenergel
′OWkℓ
′ONgℓ
′ellwork
′ellenergy
~ z|1.94 biquaWerg d|19.162 kilojoules =
d|[191.62 gigaergs
′ennquaworkel
′ennquaenergel
′EWkℓ
′ENgℓ
  ~ z|1.94 triquaWerg d|229.95 kilojoules =
d|2.2995 teraergs
′decquaworkel
′decquaenergel
′DWkℓ
′DNgℓ
  ~ z|1.94 quadquaWerg d|2.7594 megajoules =
d|27.594 teraergs
′levquaworkel
′levquaenergel
′LWkℓ
′LNgℓ
  ~ z|1.94 pentquaWerg d|33.113 megajoules =
d|331.13 teraergs
′unnilquaworkel
′unnilquaenergel
′UNWkℓ
′UNNgℓ
′chainwork
′chainenergy
~ z|1.94 hexquaWerg d|397.35 megajoules =
d|3.9735 petaergs
Top
Kodegadulo
Posted: Dec 15 2013, 11:49 PM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



Primel Power Units

The Primel base unit of power, the ′powerel (′Pwℓ), is a rate of energy consumption equal to one ′workel in each ′timel (′Wkℓ/′Tmℓ). Colloquially, this is equivalent to a rate of one ′kernelwork per ′jiffy, so we could give this unit the colloquial name ′kernelpower.

This makes the ′powerel equivalent to about d|1.5402 milliwatts, or d[15.402 kiloergs/second. As with other Primel units, the ′powerel is relatively small compared to the analogous SI unit (the watt), but quite large compared to the equivalent CGS unit (erg/second). Although the ′workel was even tinier compared to its SI analog, being in the microjoules, the ′powerel has gained some ground simply because we divide by the ′jiff, and the ′jiff is tiny compared to the SI second. But once again, we can mitigate any size inconvenience by using SDN prefixes to scale the ′powerel.

For instance, the ′triquapowerel (′TPwℓ) is equivalent to d|2.6615 watts. This is a rate of energy consumption of one ′quadquaworkel (′QWkℓ) per ′unquatimel (′UTmℓ). Colloquially, this is a rate of one ′handwork per ′twinkling, so it can also be called a ′handpower.

As an example, standard d|40 watt, d|60 watt and d|100 watt light bulbs could be approximated as one-and-a-quarter dozen (z|13) ′handpower, one-and-seven-eighths dozen (z|1X.6) ′handpower, and three-and-one-eighth dozen z|31.6 ′handpower. Or perhaps these could be rounded to z|10 ′handpower, z|20 ′handpower, and z|30 ′handpower, respectively.

The ′hexquapowerel, known colloquially as the ′ellpower, is the rate of energy consumption needed to take an ′ellmass (d|1.652 metric tons) and raise it in a one ′gravitel field to a height of one ′ell (d|1.1823 meters) within one ′biquatimel (one ′breathing one ′waltzing, d|4.0833 seconds). This is approximately d|4.5890 kilowatts or d|6.1673 horsepower.

Primel Unit Symbol Colloquialism TGM Equivalent SI Equivalents Customary Equivalents
′powerel ′Pwℓ ′kernelpower ~ z|X.8 hexciaPov d|1.5402 milliwatt =
d|15.402 kiloergs/second
′unquapowerel ′UPwℓ   ~ z|X.8 pentciaPov d|18.482 milliwatts =
d|184.82 kiloergs/second
′biquapowerel ′BPwℓ   ~ z|X.8 quadciaPov d|221.79 milliwatts =
d|2.2179 megaergs/second
′triquapowerel ′TPwℓ ′handpower ~ z|X.8 triciaPov d|2.6615 watts =
d|26.615 megaergs/second
′quadquapowerel ′QPwℓ   ~ z|X.8 biciaPov d|31.937 watts =
d|319.37 megaergs/second
′pentquapowerel ′PPwℓ   ~ z|X.8 unciaPov d|383.25 watts =
d|3.8325 gigaergs/second
d|0.51395 horsepower
′hexquapowerel ′HPwℓ ′ellpower ~ z|X.8 Pov d|4.5990 kilowatts =
d|45.990 gigaergs/second
d|6.1673 horsepower
′septquapowerell ′SPwℓ   ~ z|X.8 unquaPov d|55.188 kilowatts =
d|551.88 gigaergs/second
d|74.008 horsepower
′octquapowerel ′OPwℓ   ~ z|X.8 biquaPov d|0.66225 megawatts =
d|[6.6225 teraergs/second[/color]
d|888.10 horsepower
′ennquapowerel ′EPwℓ ′chainpower ~ z|X.8 triquaPov d|7.9471 megawatts =
d|79.471 teraergs/second
′decquapowerel< ′DPwℓ   ~ z|X.8 quadquaPov d|95.365 megawatts =
d|953.65 teraergs/second
′levquapowerel ′LPwℓ   ~ z|X.8 pentquaPov d|1.1444 gigawatts =
d|11.444 petaergs/second
′unnilquapowerel ′UNPwℓ ′stadepower ~ z|X.8 hexquaPov d|13.733 gigawatts =
d|137.33 petaergs/second
Top
Kodegadulo
Posted: Dec 16 2013, 11:49 AM


Obsessive poster


Group: Moderators
Posts: 4,184
Member No.: 606
Joined: 10-September 11



Note: I've updated the summary table in the original post:
  • Added links to the new detail posts on Primel Mass Units, Primel Force Units, Primel Energy Units, Primel Power Units.
  • Added numerous other units and reorganized the table into sections on Mechanics, Heat/Thermodynamics, Electromagnetism, Chemistry. (I'll eventually add detail posts about these.)
  • Settled on the basis for the electromagnetic units. Just as with TGM, everything hinges on the choice for Ampere's magnetic force constant kA. The size of the force chosen determines the size of the base unit of current, by definition. All the other units follow from that. But the choice is completely arbitrary. Historically, people have picked "round" numbers in their chosen base that yielded "convenient sized units". SI picked d[10-7] newton/amp2. Pendlebury picked z[0.6×10-9] Mag/Kur2. After some trial and error with a spreadsheet, I picked z[0.6×10-5] ′forcel/′currentel2. This leads to a ′capacitel of about 2 farads, and a ′fluxdensitel of about 2 tesla. Deviating from this choice of kA in either direction shrinks one of these at the expense of blowing up the other to an unreasonable size.
  • Settled on the temperature unit (′thermel) EDIT: (′temperatel). Pendlebury started with the "specithermacity" (specific thermal capacity) of water, determined a rough value for the Calg, saw that the biquaCalg was coincidentally close to a round decimal number of kelvins (d[0.1] K), and rounded the biquaCalg so that a whole number of them (d[1000] = z[6E4]) would cover the Celsius range. I followed the same program and discovered a similar coincidence with the ′quadquathermel ′quadquatemperatel, and rounded it to d[0.4] kelvins, so that exactly d[250] = z[18X] of them cover the Celsius range. This causes the Calsp and the ′specithermacitel to be slightly below the actual range of values for the specithermacity of water, but so be it.
Top
« Next Oldest | The Primel Metrology | Next Newest »
zIFBoards - Free Forum Hosting
Create your own social network with a free forum.
Learn More · Sign-up for Free

Topic OptionsPages: (19) [1] 2 3 ... Last »



Hosted for free by zIFBoards* (Terms of Use: Updated 2/10/2010) | Powered by Invision Power Board v1.3 Final © 2003 IPS, Inc.
Page creation time: 0.2232 seconds · Archive