Defining Gbar units

Let's begin with the mass, length, duration units just as if we were going to the NIST fundamental constants website to look up the conventional Planck units.

http://physics.nist.gov/cuu/Constants/

At this site, in the "Universal" section, there are metric values for the conventional Planck mass, length, duration, and temperature

http://physics.nist.gov/cgi-bin/cuu/Category?view=html&Universal.x=87&Universal.y=12


For this preliminary rough calculation I wont show error bounds or round off.  Here are the corresponding Gbar quantities: what you get if you use
Gbar = 8 pi G, instead of G itself. Besides the mass, length, duration, and temperature quantities analagous to what NIST lists, an energy unit has been added.

  mass unit = 4.34139 micrograms
  length unit = 8.10263 × 10-35 meters
  duration unit = 2.70275 × 10-43 seconds
  temperature unit = 0.282609 × 1032 kelvin
  energy unit = 3.90185 × 108 joule


This is what you get for basic units if you set the values of Gbar, hbar, c, and k equal to 1.
Later we will include the elementary charge e (the charge on the electron)

|Gbar| = |hbar| = |c| = |k| = |e| = 1

Because the sizes of the Planck quantities are extreme, we will here use some
named power-of-ten scaled versions.


  108 mass units = 434 grams = pound  (because it's about a pound of mass)
  1033 length units = 8.10 centimeters = hand (because it's some 3 and 1/4 inches, about a handbreadth)
  1042 duration units = 0.270275 second = count (because at 222 to the minute it's about as fast as I can count)
  10-32 temperature unit = 0.282609 kelvin = degree Fahrenhalf (because it's about half a Fahrenheit degree)
  10-10 energy unit = 0.0390185 joule = jot (placeholder name, because it's a tiny amount of energy)


The same humanscale units can be defined by assigning these power-of-ten values to the fundamental constants
Gbar = 10-7 hand3count-2pound-1
c = 109 hand count-1
hbar = 10-32 jot count
k = 10-22 jot degree-1
e = 10-18 dram (charge unit)

Here for reference are sizes of the main humanscale Gbar units:
the time unit (count) comes out 222 to the minute.
the temperature degree turns out to be about half a Fahrenheit
the mass unit pound comes out to 434 grams, roughly one conventional pound.
the length unit hand is 8.10 centimeters (around 3 and 1/4 inches)
the force unit mark is 0.4816 newton, a couple of ounces of force.
the energy unit jot works out to around 0.04 joule or 1/100 of a calorie.
the charge unit dram since it is 1018 electron's worth, has a metric equivalent of 0.1602 Coulomb
the unit current is about 2/3 of a conventional ampere
the unit voltage quartervolt (Q) is about 1/4 of a conventional volt.
the power unit jot per count is approx. 1/6 watt.
the area unit  square hand is about 65.65 square centimeters.
the volume unit cubic hand comes out to 532 cubic centimeters, somewhat more than an ordinary pint.
the pressure unit  mark per square hand is about 73.3 pascals.
the mass density unit pound per cubic hand  is about 0.816 standard (g/cc) density.
the acceleration unit hand per square count  is about 1.11 meters per sq. second,
roughly a ninth of the conventional gee.

eQ = 10-18 jot
k = 10-22 jot degree-1 =10-4 eQ degree-1
hbar = 10-14 eQ count
hbar × c = 10-5 eQ hand  = 10 eQ microhand

Light with angular wavelength of 1 microhand is green, and has photon energy 10 eQ.
By way of comparison the surface temperature of the sun is 20,000 degrees, in energy terms 2 eQ.
It may be useful to know that the pound defined here is equal to about 2.6E26 proton masses.
Rough approximations of conditions at the earth's surface, for working the exercises:
pressure 1400 mk per sq. hd, absolute temperature 1000 deg, gravity 9 hd per sq. ct.

One reason you might regard 8piG (or "Gbar") as more fundamental than G is that the 1915 Einstein equation, the main classical equation about gravity, is often written:

Gab = (8piG)Tab

This already assumes that the units have been adjusted to make c = 1, because the actual coefficient is 8piG/c4. Then, by adjusting units so that 8piG = 1, relativists will often write the main gravity equation in this squeaky clean form:
Gab = Tab
The coefficient 8piG/c4 in the Einstein equation is the reciprocal of a force c4/8piG which is the unit of force in this version of Planck units. In our humanscale system, the force amounts to exactly 1043 mark.