# Happiness Calculations

Where:

• C = Mass consumed by population (lb/year)
• H = Happiness (fraction)
• F = Ecological footprint (hectares/year)
• P = World population (people)
• S = Transport speed (miles/hr)
• Rmax = Initial resources in 1 AD (lb)
• Rearth = Resources produced by biosphere per year, "natural capacity" (lb)
• Hmax = Maximum happiness (1)
• Hearth = Happiness when C = Rearth
• Hmaxr = Happiness when C = Rmax
• Hcrash = Ideal happiness when population crashes (linear model)
• Hlight = Happiness at S = speed of light
• Cmax = Consumption at Hmax
• Cmin = Consumption in 1 AD
• Cpeak = Consumption at projected peak population
• Pmin = Population in 1 AD
• Ppeak = Population at projected peak population
• Pmax = Population at Hmax
• Slight =Speed of light
• Smax = Speed at Hmax
Relationships:

C: k*F*P = k*n*EXP(2*(H-j)/g) lb/yr
H: g*LN(F) +j
P: n*F people
S: m*C mi/hr
F: EXP((H-j)/g) hectares/yr

Constants (empirical):

g: 0.124494544
j: 0.492513147
k: 1000
n: 2.51E+09
m: 2.78431E-11

Miscellaneous:

Cmax: 8.71708E+15 lb/yr
Cmin: 2.51409E+10 lb/yr
Smax: 2.42710E+05 mi/hr
Slight:
 6.70615e+07
mi/hr
Pmax: 1.47918E+11 people
Ppeak: 8.16562E+09 people
Rearth: 1.19E+13 lb
Cmax/Pmax: 58931.6
Cmax/Rmax: 7.6
Cmax/Rearth: 732.5
Cmax/Cmin: 346728.7
Pmax/Pmin: 588.4
Cmax/Cpeak: 328.7
Pmax/Ppeak: 18.1
Cmax/day: 2.38824E+13
Smax/Slight: 3.61922E-04
lSlight/Smax: 2763.0
Cmax/Cpeak/12: 27.4
Lunar Periods: 1.0
n/Pmin: 10.0
Asteroid Diameter(Cmax): 18.0 km
Hearth: 0.59
Hmax: 1
Hmaxr: 0.87
Hcrash:
 0.65

Hlight: 1.49
Hearth/Hmaxr: 0.67
Hcrash/Hmax:
 0.65

Hmax/Hlight: 0.67

Note: H(2/3 Hearth): 0.392923895 occurred in 1857, when max H was 0.581386935 (nearly Hearth, which was reached in 1861).