I Planck's Impedance: Exploring the Mystery of a Fictional Measurement System

[AlexB23]

TL;DR

Hello guys, and am new here. A week ago I was working on a fictional measurement system, and the Planck's impedance came out of it after some dimensional analysis.

The measurements system is defined by the following base units:

1 Berkel = 0.8590488 seconds (1,220,197,850 oscillations of the hydrogen atom in a hyperfine state)

1 Dist'al = 0.2575363 meters
(Speed of light multiplied by 1×10⁻⁹ Berkels)

1 Hef'al = 17.08109 kg
(Mass of 1 cubic dist'al of water at 4°C)

1 Muncie = 0.2441514114 Amp
(Amount of force per dist'al of two infinite wires separated by one dist'al is equal to 2×10⁻⁹ force units when the current is 1 Muncie)

Somehow, the derived unit of resistance in this fictional measurement system is equal to 29.9792458 Ohms, when doing the dimensional analysis, which is the same value as Planck's impedance. Why is that?

 

[Ibix]

Welcome to PF.

You can define a unit system any way you want. The trick is getting anyone to use it. Is there a question here?

 

[AlexB23]

You can define a unit system any way you want. The trick is getting anyone to use it. Is there a question here?

I had to edit the question and post my measurement base units, but it is now there.

 

[PeroK]

I had to edit the question and post my measurement base units, but it is now there.

Just a numerical coincidence unless you picked the units to coincide in some way.

 

[AlexB23]

Just a numerical coincidence unless you picked the units to coincide in some way.

I didn't pick the time unit to coincide in that way. The time unit is equal to 1/100,000th the length of a day on a fictional planet. The day length is 85,904.88 seconds, or 100,000 Berkels in this measurement system. Could it be the fact that the dist'al is defined as the distance light travels in 10⁻⁹ Berkels? Or that the Muncie is defined as being the current that generates 2×10⁻⁹ force units/dist'al between two wires separated by a dist'al?

Also, I have noticed that the Planck's impedance expressed in SI units is 29.97 Ohms, which is coincidentally, and exactly 1/10 million times the value of the speed of light in m/s without the units attached.