TGM
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TGM is a coherent and gravitational system of measurement proposed by Tom Pendlebury. It is a complete system, with units for all physical quantities, which focuses on four main traits:
1.) A one-to-one correspondence between all basic units, wherever this is possible. It achieves this, breaking 1:1 correspondence only in the shift to electrical units and light units, which is really necessary to obtain usable unit sizes.
2.) Links to accessible physical realities (the length of the day, mean gravitational acceleration, and so forth), while still maintaining the precision of formal definitions according to physical constants.
3.) Consistently Base 12 in all respects.
4.) All units can be consistently derived from the base unit.
The name is an abbreviation for Tim-Grafut-Maz, its units of time, length, and mass.
Design Edit
Measurement systems tend to begin with the unit of length. TGM begins instead with the unit of time. Adopting our current Base 12 division of the day, TGM divides the hour into twelve units of five minutes, or 1/12 hour (unciaHours); unciaHours into twelve units of 5/12 minutes (25 seconds), or 1/12^{2} hour (biciaHours); biciaHours into twelve units of 25/12 seconds, or 1/12^{3} hour (triciaHours); and finally triciaHours into twelve units of 25/12^{2} seconds, or 1/12^{4} hour (quadciaHours). These quadciaHours produce the best final system of measurement, so they are the unit of time.
This unit of time is called the Tim; and all of TGM flows, directly or indirectly, from it.
The unit of length, for example, the Grafut, is easily derived from the Tim. Taking the Tim as the unit of time, mean Earth gravity accelerates an object by a certain velocity per Tim. That velocity is itself a certain distance per Tim. That distance is the unit of length, called the Gravity Foot, or Grafut.
The unit of volume is the cubic Grafut; this is used frequently enough that it is given its own name, the Volm.
All other units can be derived consistently in the same way.
Units Edit
Base Units Edit
Unit Name | Unit Symbol | Quantity | Conceptual Definition | Standardization Definition | SI Equivalent |
---|---|---|---|---|---|
Tim | Tm | Time | 1/12^{4} hour | 1 595 943 015 periods of radiation corresponding to the transition between the two hyperfine levels of the ground state of Cesium 133 | 0.173 611 111 043 121 88 s |
Gee | G | Acceleration | Acceleration due to gravity at Earth's surface | Polar diameter of Earth = 42998169.6 gf. Speed of light = 176 024 043 Vl exactly. | 9.810 049 407 604 21 m/s^{2} |
Denz | Dz | Density | Density of water | under a pressure of one standard atmosphere, and temperature of maximal density (3.98°C) | 999.972 kg/m^{3} |
Calg | Cg | Temperature | Temperature increase when 1 Wg of heat is applied to 1 Mz of water | Exactly 1/1440 kelvin. Triple point of water is exactly (dec) 393 350.4 Cg. | 0.000 694 444... K |
Kur | Kr | Electric Current | The amount of current that, if maintained in two parallel conductors placed 1 Gf apart, produces a force between them equal to 1/12^{9} Mg for each Grafut of length. | 0.495 722 068 629 349 2 A | |
Molz | Mlz | Amount of Substance | The amount of substance that contains as many elementary particles as there are atoms in 12 Mz of Carbon 12. | 25 850.355 623 275 307 mol |
Derived Units Edit
Unit Name | Unit Symbol | Quantity | Derivation | SI Equivalent |
---|---|---|---|---|
Vlos | Vl | Velocity or Speed | G × Tm | 1.703 133 577 042 086 3 m/s |
Grafut | Gf | Length | G × Tm^{2} | 0.295 682 912 565 123 m |
Surf | Sf | Area | Gf^{2} | 0.087 428 384 782 994 18 m^{2} |
Volm | Vm | Volume | Gf^{3} | 0.025 851 079 453 500 004 m^{3} |
Maz | Mz | Mass | Vm × Dz | 25.850 355 623 275 306 kg |
Mag | Mg | Force | Mz × G | 253.593 265 868 470 04 N |
Prem | Pm | Pressure or Stress | Mg / Sf | 2 900.582 762 656 697 5 Pa |
Werg | Wg | Work or Energy | Mg × Gf | 74.983 195 458 890 82 J |
Pov | Pv | Power | Wg / Tm | 431.903 206 012 352 2 W |
Penz | Pz | Power Density | Pv / Sf | 4 940.079 896 070 119 W/m^{2} |
Pel | Pl | Electric Potential | Pv / Kr | 871.260 799 840 012 2 V |
Og | Og | Electric Resistance | Pl / Kr | 1 757.559 033 530 647 2 Ω |
Quel | Ql | Electric Charge | Kr × Tm | 0.086 062 859 103 336 03 C |
Kap | Kp | Electric Capacitance | Ql / Pl | 98.779 675 522 116 42 µF |
Kurn | Kn | Magneto-Motive Force | Kr × Turn | 0.495 722 068 629 349 2 ampere-turn (AT) |
Magra | Mgr | Magnetic Field Strength | Kn / Gf | 1.676 532 689 457 218 1 AT/m |
Flum | Fm | Magnetic Flux | Wg / Kr | 151.260 555 468 543 54 Wb |
Flenz | Fz | Magnetic Flux Density | Fm / Sf | 1 730.108 086 109 414 7 T |
Meab | Mb | Permeability | Fz / Mgr | 1 031.956 070 400 000 3 N/A^{2} |
Gen | Gn | Inductance | Pl × Tm / Kr | 305.131 776 535 131 17 H |
Quenz | Qz | Electric Flux Density | Ql / Sf | 0.984 381 208 882 589 7 C/m^{2} |
Elgra | Egr | Electric Field Strength | Pl / Gf | 2 946.605 173 364 965 V/m |
Mit | Mt | Permittivity | Qz / Egr | 0.000 334 072 992 805 631 2 F/m |
Molv | Mlv | "Molvity" (Molarity) | Mlz / Vm | 999 972 mol/m^{3} |
Molm | Mlm | "Molmity" (Molality) | Mlz / Mz | 1000 mol / kg (exactly) |