Difference between revisions of "Units"
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| + | {| class="zebra c1r c2bl c4c c4sm c5bl c8bl c8c c9c c10c c11c c12c" | ||
| + | |- | ||
| + | ![https://www.ibiblio.org/units/ Rowlett] !!class=in1|Tower<br>Grain !!Troy<br>Grain !!Gram !!Tower<br>Ounce !!Troy<br>Ounce !!Avoir.<br>Ounce !!Tower<br>Pound !!Troy<br>Pound !!<small>Merchant</small><br>Pound !!<small>London</small><br>Pound !!Avoir.<br>Pound | ||
| + | |- class=subsection | ||
| + | |Tower Pound ||class=in1|'''7680''' ||5400 ||349.914 ||'''12''' ||11¹⁄₄ ||12¹²⁄₃₅ ||1 ||¹⁵⁄₁₆ ||⁴⁄₅ ||³⁄₄ ||²⁷⁄₃₅ | ||
| + | |- | ||
| + | |'''Troy Pound''' ||class=in1|8192 ||'''5760''' ||373.242 ||12⁴⁄₅ ||'''12''' ||13²⁹⁄₁₇₅ ||¹⁶⁄₁₅ ||1 ||⁶⁴⁄₇₅ ||⁴⁄₅ ||¹⁴⁴⁄₁₇₅ | ||
| + | |- | ||
| + | |Merchant Pound ||class=in1|'''9600''' ||6750 ||437.393 ||'''15''' ||14¹⁄₁₆ ||15³⁄₇ ||⁵⁄₄ ||⁷⁵⁄₆₄ ||1 ||¹⁵⁄₁₆ ||²⁷⁄₂₈ | ||
| + | |- | ||
| + | |London Pound ||10240 ||'''7200''' ||466.552 ||'''16''' ||'''15''' ||16¹⁶⁄₃₅ ||⁴⁄₃ ||⁵⁄₄ ||¹⁶⁄₁₅ ||1 ||³⁶⁄₃₅ | ||
| + | |- | ||
| + | |'''Avoir. Pound''' ||class=in1|9955⁵⁄₉ ||'''7000''' ||453.592 ||15⁵⁄₉ ||14⁷⁄₁₂ ||'''16''' ||³⁵⁄₂₇ ||¹⁷⁵⁄₁₄₄ ||²⁸⁄₂₇ ||³⁵⁄₃₆ ||1 | ||
| + | |- class=subsection | ||
| + | |Tower Ounce ||class=in2|640 ||class=in1|450 ||class=in1|29.160 ||class=center|1 ||class=center|¹⁵⁄₁₆ ||class=center|³⁶⁄₃₅ ||'''¹⁄₁₂''' ||⁵⁄₆₄ ||'''¹⁄₁₅''' ||'''¹⁄₁₆''' ||⁹⁄₁₄₀ | ||
| + | |- | ||
| + | |'''Troy Ounce''' ||class=in2|682²⁄₃ ||class=in1|480 ||class=in1|31.103 ||class=center|¹⁶⁄₁₅ ||class=center|1 ||class=center|¹⁹²⁄₁₇₅ ||⁴⁄₄₅ ||'''¹⁄₁₂''' ||¹⁶⁄₂₂₅ ||'''¹⁄₁₅''' ||¹²⁄₁₇₅ | ||
| + | |- | ||
| + | |'''Avoir. Ounce''' ||class=in2|622²⁄₉ ||class=in1|437¹⁄₂ ||class=in1|28.350 ||class=center|³⁵⁄₃₆ ||class=center|¹⁷⁵⁄₁₉₂ ||class=center|1 ||³⁵⁄₄₃₂ ||⁶⁄₇₉ ||⁷⁄₁₀₈ ||³⁵⁄₅₇₆ ||'''¹⁄₁₆''' | ||
| + | |} | ||
| + | |||
==AD&D== | ==AD&D== | ||
| − | * 200 cp = __ sp = 2 ep = 1 gp = 1/5 pp= 1.6 avoir. oz. | + | * 240 {{abbr|p|2=“1p” = 1 Pence}} = 12 {{abbr|s|2=“1s” = 1 Shilling}} = 2 {{abbr|C|2=“1C” = Two Crown}} = 1 {{abbr|£|2=“1£” = 1 Pound}} = ¹⁄₅ {{abbr|G|2=“1G” = Five Guinea}} (pre-decimal Britain) |
| + | * 200 cp = __ sp = 2 ep = 1 gp = 1/5 pp = 1.6 avoir. oz. | ||
* 10 gp = 1 pound | * 10 gp = 1 pound | ||
| Line 27: | Line 49: | ||
|1,000 {{abbr|''passus''|“paces” (Roman unit)}} (5,000 {{abbr|''pedes''|“feet” (Roman unit)}}) | |1,000 {{abbr|''passus''|“paces” (Roman unit)}} (5,000 {{abbr|''pedes''|“feet” (Roman unit)}}) | ||
|- | |- | ||
| − | |mile, imperial | + | |mile, imperial<sup>UK</sup> |
|{{formatnum:{{#expr: 5280 / 3 * 0.9143969 round 3 }}}} | |{{formatnum:{{#expr: 5280 / 3 * 0.9143969 round 3 }}}} | ||
|5,280 imperial feet | |5,280 imperial feet | ||
| Line 35: | Line 57: | ||
|5,280 international feet | |5,280 international feet | ||
|- | |- | ||
| − | |mile, survey | + | |mile, survey<sup>US</sup> |
|{{formatnum:{{#expr: 5280 * 12 / 39.37 round 3 }}}} | |{{formatnum:{{#expr: 5280 * 12 / 39.37 round 3 }}}} | ||
|5,280 survey feet | |5,280 survey feet | ||
|- | |- | ||
| − | |mile (AD&D) | + | |mile <small>(AD&D)</small> |
|{{formatnum:{{#expr: 299792458 / 186000 round 3 }}}} | |{{formatnum:{{#expr: 299792458 / 186000 round 3 }}}} | ||
| − | |{{abbr|186,000 miles | + | |{{abbr|1=186,000 miles = 1 light second|2=“In the latter case distance is not a factor as long as the telepath and the receiver are on the same plane of existence and not separated by distances greater than 186,000 miles (1 light second)”.{{br}}1 light second ≝ 299,792,458 m = 186,282.4 statute miles}} |
|- | |- | ||
| − | |mile (d20) | + | |mile <small>(d20)</small> |
|{{formatnum:{{#expr: .0254 * 12 * 6000 }}}} | |{{formatnum:{{#expr: .0254 * 12 * 6000 }}}} | ||
|6,000 feet | |6,000 feet | ||
| Line 51: | Line 73: | ||
|{{unit|deg||1|60}} lattitude | |{{unit|deg||1|60}} lattitude | ||
|- | |- | ||
| − | |mile, Admiralty | + | |mile, Admiralty<sup>UK</sup> |
|{{formatnum:{{#expr: 6080 *12 * 0.0254 round 3}}}} | |{{formatnum:{{#expr: 6080 *12 * 0.0254 round 3}}}} | ||
|6,080 Imperial feet | |6,080 Imperial feet | ||
| Line 57: | Line 79: | ||
|mile, nautical<sup>US</sup> | |mile, nautical<sup>US</sup> | ||
|{{formatnum:{{#expr: 6080.20 * 12 * 0.0254 round 3 }}}} | |{{formatnum:{{#expr: 6080.20 * 12 * 0.0254 round 3 }}}} | ||
| − | |6,080.20 statute | + | |6,080.20 statute feet |
|- | |- | ||
|light-second | |light-second | ||
| Line 74: | Line 96: | ||
: 1 furlong = 10 chains = 40 rods = 1000 links | : 1 furlong = 10 chains = 40 rods = 1000 links | ||
| + | |||
| + | |||
| + | ==Other units== | ||
| + | A d20/D&D mile ({{unit|miD}}) is {{unit|feet|6,000}}, and thus apparently a fantasy equivalent to the {{unit|foot|6,076|v=~~}} nautical mile rather than the {{unit|foot|5,280}} land mile. | ||
| + | |||
| + | A nautical mile ({{unit|miN}}) is one minute of latitude ({{unit|'m|1}} = {{unit|°a|1|60}}), making Earth’s meridional circumference {{unit|miN|21,600}}. Since Earth is not a perfect sphere, the actual length of a minute of latitude varies between {{unit|m|1,813}} and {{unit|m|1,861}} with a ''de jure'' average of {{unit|m|1,852}} ({{unit|ft|6076.12|v=~~}}). | ||
| + | |||
| + | The original intent for the meter was to be one ten-millionth of 90° latitude, such that {{unit|km|40,000}} would equal Earth’s meridional circumference. The best measurements of the 1800s were slightly off and Earth’s actual m. circ. in standard meters is {{unit|km|40,008|v=~~}}. | ||
| + | |||
| + | From this one can extrapolate that a standard D&D fantasy world could be: | ||
| + | # a {{unit|miN|21,600}} ≈ {{unit|km|40,008}} m.circ. spheroid like Earth, | ||
| + | # a {{unit|miD|21,600}} ≈ {{unit|km|39,502}} m.circ. spheroid with {{abbr|2½%|2.4891%}} less surface area than Earth, or | ||
| + | # a {{unit|miD|21,600}} = {{unit|km|40,000}} m.circ. sphere with D&D feet/inches etc. {{abbr|1¼%|1.2598% • 1 D&D inch ≈ 25.72 ㎜}} longer than standard feet/inches. | ||
| + | |||
| + | ;Greek | ||
| + | : 1 ''million'' (∼mile) = 5,000 ''podes'' | ||
| + | : 1 ''stade'' (∼furlong) = 600 ''podes'' | ||
| + | : 1 ''plethron'' = 100 ''podes'' (∼feet) | ||
| + | |||
| + | ;Roman | ||
| + | : 1 ''mille passus'' (∼mile) = 8 ''stadia'' = 1,000 ''passus'' = 6,000 ''pedes'' | ||
| + | : 1 ''stadium'' (∼furlong) = 125 ''passus'' = 625 ''pedes'' | ||
| + | : 1 ''passus'' (∼pace) = 5 ''pedes'' (∼feet) | ||
| + | |||
| + | The minum (♏︎) was originally defined in 1809 by Timothy Lane, {{wp|Fellow of the Royal Society|FRS}} as {{frac|61440}} of the [Queen Ann] wine gallon (i.e. 231 in³ or 58,176 gr.t. H₂O at 29.52″ Hg<sub>63 °F</sub>) [https://books.google.com/books?id=pCPrAAAAMAAJ&pg=PR45-IA5 ''Pharmacopoeia''] In the UK, the minim was redefined as {{frac|76800}} of the new Imperial gallon (10 lb. H₂O at 62 °F<!-- 30″ Hg<sub>62 °F</sub> -->) [https://www.sizes.com/library/British_law/5GeorgeIVcap74.pdf 1824 act] The Weights and Measures Act of 1878 (41 & 42 Vict. c 49) | ||
Latest revision as of 04:47, 26 January 2021
| Rowlett | Tower Grain |
Troy Grain |
Gram | Tower Ounce |
Troy Ounce |
Avoir. Ounce |
Tower Pound |
Troy Pound |
Merchant Pound |
London Pound |
Avoir. Pound |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Tower Pound | 7680 | 5400 | 349.914 | 12 | 11¹⁄₄ | 12¹²⁄₃₅ | 1 | ¹⁵⁄₁₆ | ⁴⁄₅ | ³⁄₄ | ²⁷⁄₃₅ |
| Troy Pound | 8192 | 5760 | 373.242 | 12⁴⁄₅ | 12 | 13²⁹⁄₁₇₅ | ¹⁶⁄₁₅ | 1 | ⁶⁴⁄₇₅ | ⁴⁄₅ | ¹⁴⁴⁄₁₇₅ |
| Merchant Pound | 9600 | 6750 | 437.393 | 15 | 14¹⁄₁₆ | 15³⁄₇ | ⁵⁄₄ | ⁷⁵⁄₆₄ | 1 | ¹⁵⁄₁₆ | ²⁷⁄₂₈ |
| London Pound | 10240 | 7200 | 466.552 | 16 | 15 | 16¹⁶⁄₃₅ | ⁴⁄₃ | ⁵⁄₄ | ¹⁶⁄₁₅ | 1 | ³⁶⁄₃₅ |
| Avoir. Pound | 9955⁵⁄₉ | 7000 | 453.592 | 15⁵⁄₉ | 14⁷⁄₁₂ | 16 | ³⁵⁄₂₇ | ¹⁷⁵⁄₁₄₄ | ²⁸⁄₂₇ | ³⁵⁄₃₆ | 1 |
| Tower Ounce | 640 | 450 | 29.160 | 1 | ¹⁵⁄₁₆ | ³⁶⁄₃₅ | ¹⁄₁₂ | ⁵⁄₆₄ | ¹⁄₁₅ | ¹⁄₁₆ | ⁹⁄₁₄₀ |
| Troy Ounce | 682²⁄₃ | 480 | 31.103 | ¹⁶⁄₁₅ | 1 | ¹⁹²⁄₁₇₅ | ⁴⁄₄₅ | ¹⁄₁₂ | ¹⁶⁄₂₂₅ | ¹⁄₁₅ | ¹²⁄₁₇₅ |
| Avoir. Ounce | 622²⁄₉ | 437¹⁄₂ | 28.350 | ³⁵⁄₃₆ | ¹⁷⁵⁄₁₉₂ | 1 | ³⁵⁄₄₃₂ | ⁶⁄₇₉ | ⁷⁄₁₀₈ | ³⁵⁄₅₇₆ | ¹⁄₁₆ |
AD&D
- 240 p = 12 s = 2 C = 1 £ = ¹⁄₅ G (pre-decimal Britain)
- 200 cp = __ sp = 2 ep = 1 gp = 1/5 pp = 1.6 avoir. oz.
- 10 gp = 1 pound
- Feet =
- 1 inch (1″) = 10 feet (10′) indoors = 10 yards (30′) outdoors
- League = 3 miles
- 186,000 miles = 1 light second (PHB-116)
| Unit | Length (m) | Notes |
|---|---|---|
| kilometre | 1,000 | |
| mille passus | 1,479.5 | 1,000 passus (5,000 pedes) |
| mille passus | 1,480 | 1,000 passus (5,000 pedes) |
| mile, imperialUK | 1,609.339 | 5,280 imperial feet |
| mile, international | 1,609.344 | 5,280 international feet |
| mile, surveyUS | 1,609.347 | 5,280 survey feet |
| mile (AD&D) | 1,611.787 | 186,000 miles = 1 light second |
| mile (d20) | 1,828.8 | 6,000 feet |
| mile, nauticalInt. | 1,852 | 1⁄60° lattitude |
| mile, AdmiraltyUK | 1,853.184 | 6,080 Imperial feet |
| mile, nauticalUS | 1,853.245 | 6,080.20 statute feet |
| light-second | 299,792,458 | 186,282.4 statute miles |
1 cubic-pes of water = 64 lībrae
- 1 foot = 12 inches
- 3 feet = 1 yard
- 5 feet = 1 pace
- 6 feet = 1 fathom
- 5000 feet = 1 mile (land)
- 6000 feet = 1 mile (nautical)
- 1 furlong = 10 chains = 40 rods = 1000 links
Other units
A d20/D&D mile (𝗆𝗂𝖣) is 6,000 feet, and thus apparently a fantasy equivalent to the ≈ 6,076-foot nautical mile rather than the 5,280-foot land mile.
A nautical mile (𝖭𝗆𝗂) is one minute of latitude (1′ = 1⁄60 °), making Earth’s meridional circumference 21,600 𝖭𝗆𝗂. Since Earth is not a perfect sphere, the actual length of a minute of latitude varies between 1,813 𝗆 and 1,861 𝗆 with a de jure average of 1,852 𝗆 (≈ 6076.12-ft).
The original intent for the meter was to be one ten-millionth of 90° latitude, such that 40,000 ㎞ would equal Earth’s meridional circumference. The best measurements of the 1800s were slightly off and Earth’s actual m. circ. in standard meters is ≈ 40,008 ㎞.
From this one can extrapolate that a standard D&D fantasy world could be:
- a 21,600 𝖭𝗆𝗂 ≈ 40,008 ㎞ m.circ. spheroid like Earth,
- a 21,600 𝗆𝗂𝖣 ≈ 39,502 ㎞ m.circ. spheroid with 2½% less surface area than Earth, or
- a 21,600 𝗆𝗂𝖣 = 40,000 ㎞ m.circ. sphere with D&D feet/inches etc. 1¼% longer than standard feet/inches.
- Greek
- 1 million (∼mile) = 5,000 podes
- 1 stade (∼furlong) = 600 podes
- 1 plethron = 100 podes (∼feet)
- Roman
- 1 mille passus (∼mile) = 8 stadia = 1,000 passus = 6,000 pedes
- 1 stadium (∼furlong) = 125 passus = 625 pedes
- 1 passus (∼pace) = 5 pedes (∼feet)
The minum (♏︎) was originally defined in 1809 by Timothy Lane, FRS as 1⁄61440 of the [Queen Ann] wine gallon (i.e. 231 in³ or 58,176 gr.t. H₂O at 29.52″ Hg63 °F) Pharmacopoeia In the UK, the minim was redefined as 1⁄76800 of the new Imperial gallon (10 lb. H₂O at 62 °F) 1824 act The Weights and Measures Act of 1878 (41 & 42 Vict. c 49)
