Deriving a system of scientific units

The dominant society on my conworld is at a level of technological and scientific development not unlike our own, with minor differences here and there. Scientific standards are decided by Academy of Science (for want of a better translated term), and this includes the system of measurements, which in this world is similar to the Terrestrial Imperial system, but with derived units in a manner similar to SI derived units. The native numeral system is dozenal (or duodecimal, or base-12), so a lot of the unwieldy aspects of an Imperial system of measurement can be handwaved away (12" to a foot is nice and round, for example).

So far, I've got units of length, area, time, temperature, and mass. Following the example set by the SI derived units, I've also come up with equivalents for force, pressure, and energy (newton, pascal, and joule), though I haven't thought of appropriate names for these units.

How can I derive units for electromagentism (e.g. volt, ohm, watt, ampere), as the SI definitions seem to be a bit confusing in this regard? The ampere is currently the base SI unit for current, but how did they decide exactly what one ampere is?

For more context, I've listed all units in this system of measurements as they're currently defined below. Note that whilst I'm using the same names as common Imperial units, the actual definitions vary quite considerably.

Base Units

• Length: foot = 267 mm
• Mass: pound = 528.72675 g
• Time: second = 0.8544 s
• Temperature: Originally defined by assigning 0° to the freezing point of water, and 144° to the boiling point of water, but supplanted in physics and chemistry with a unit using the same graduations but measured from absolute zero instead, analogous to degrees Celsius and kelvins.
• Molar weight is the amount of substance which contains as many elementary entities as there are atoms in one ounce of carbon-12, which makes it slightly less than one SI mol. The analogue of Avogadro's constant is correspondingly adjusted.
• Ampere equivalent?
• Candela equivalent?

Length

• Point = 0.309 mm ($\frac{1}{72}$ of an inch)
• Line = 6 points = 1.854 mm ($\frac{1}{12}$ of an inch)
• Inch = 12 lines = 22.25 mm ($\frac{1}{12}$ of a foot)
• Foot = 12 inches = 267 mm (Base unit of distance)
• Yard = 4 feet = 1.068 m (Less commonly used instead of feet)
• Chain = 18 yards = 19.224 m (Commonly used in surveying (miles-chains))
• Mile = 72 chains = 1384.128 m (Common unit of large distances)
• League = 4 miles = 5536.512 m (4 miles, or the distance a person can walk in an hour)
• Pica = $\frac{1}{6}$ in = 3.7083 mm ($\frac{1}{72}$ of a foot)
• Furlong = 9 chains = 173.016 m ($\frac{1}{8}$ of a mile)
• Link = $\frac{1}{144}$ chain = 133.5 mm (Surveying unit)
• Rod = 24 links = 3.204 m (Surveying unit equal to $\frac{1}{6}$ of a chain)

Time

• Second = 0.8544 Earth seconds
• Minute = 72 seconds = 1.02528 Earth minutes
• Hour = 72 minutes = 1.230336 Earth hours
• Day = 24 hours = 29.528064 Earth hours
• Year = 241 days ≈ 297 Earth days

Mass

The base unit of mass is the pound, but the modern ounce was originally defined as the mass of one cubic inch of water.

• Grain = = $\frac{1}{6912}$ lb ≈ 0.019 g
• Dram = 48 grains = $\frac{1}{144}$ lb ≈ 0.918 g
• Ounce = 12 drams = $\frac{1}{48}$ lb = 11.015140625 g
• Quarter(-pound) = 12 ounces = $\frac{1}{4}$ lb = 132.1816875 g
• Pound = 4 quarters = 1 lb = 528.72675 g
• Stone = 12 pounds = 12 lb = 6.344721 kg
• Hundredweight = 12 stones = 144 lb = 76.136652 kg
• Ton = 12 hundredweights = 1728 lb = 913.639824 kg

Derived Units

So far, I haven't thought of what names to give these derived units

• Force: poundal (pdl) = 1 lbâ‹…ft / s ≈ 0.193 N (probably only used with prefixes much like our kilogram?)
• Pressure: poundal per square foot ≈ 2.713 Pa (could also use pounds per square inch: 1 psi = 390.625 Pa)
• Energy: poundalâ‹…foot ≈ 0.052 J (possibly also only used with prefixes)

posted over 6 years ago

Robbie‭

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