-: Dimension Numbers :-

Wendy's: Home Nines Magnet UES

Nines Numbers

The nines system is one that purely depends on the length of the time unit. The table below shows the NNA system, with time dependencies. To keep the exact Nines definition with the local time system, the units of length, mass and time vary directly with time.
time T s = 1.000 000 000 000 t
length T c c=0.299792458 m = 3.335 640 951 981 t
mass T c³/G G=0.0667258 kg = 2.476 462 069 977 t
charge T c²/√(Gμ/4π) μ4π=100 C = 28.741 239 181 087 t

One can then do a time dependence of all of the named SI units, according to this scale. So if this system was exported to Mars, the size of the Nines units would change accordingly. One can get a rough conversion simply by using your ruler and a local ruler.

t=1 m, kg, s, F, C, J, Wb, H, m³/s²
t=0 S, A, W, V, Ω, m/s, N
t=-1 m/s², Hz
t=-2 Pa, kg/m³

The dependence of mass on length does not scale well when one takes it to the extremes of atomic or astronomical scales. Over this range of dimensions, we notice that density and velocity are relatively constant.

Accordingly, one designs a scale based on density, velocity and time.

d=0 v = 0 v = 1 v = 2 v = 3
t=-1 frequency acceleration
t=0 unit velocity spec mass
t=1 time length kin viscos traction
t=2 area volume flow
t=3 volume

v = 0 v = 1 v = 2 v = 3 v=4 v=5
t=0 density pressure power flux
t=1 mass/area dyn viscos surface tension
t=2 1/G mass/length mass flow force power
t=3 mass momentum energy
t=4 mmt of mass action

This table becomes neater, if one makes the verticals run with length rather than time. Also, one can see if one places d=100, v=10 and t=1, one gets relatively easy numbers to use, to add up to form the dimension number.

The bulk of the electrical units fit into the middle, so it is more sensible to start with d=200. Also, some mechanical quantities are based on sqrt(force) or sqrt(density), so it's a useful change.

This scale is the CGS numbers.

0 +10 +20 +30
-21 -11 1/length -1 frequency 9 acceleration
-10 0 UNITY 10 velocity 20 spec energy
1 1 time 11 length 21 kin viscosity 31 traction
12 22 area 32 mass flow
23 33 volume


200 density


220 pressure

230 power flux
211 211 mass/area 221 dyn visc 231 241
222 222 mass/line 232 mass flow 242 force 252 power
233 233 mass 243 momentum 253 power
244 244 mass moment 254 action

Dimension Numbers

The placing of the electrical quantities into the dimensional scale took some effort, much work was centred on a thing called the DC triangle.

In essence, all quantities that i could round up had SI units, that after removing length and time, maps onto one of the following measures: 1, watt, ampere, volt, ohm and siemens.

© 2003-2004 Wendy Krieger