Lesson 14 Economic Thickness.ipynb

Kernel:

When should we stop insulating a home?

One criteria is when the cost of insulation is higher than the energy it offsets.

from pint import UnitRegistry
u = UnitRegistry()
u.define('dollar=[]')

# simple cubic cabin floating in space

sheets = 7
side = 15 * u.feet

area = 6 * side**2
price_insulation = 10.48 * u.dollar / (4 * u.foot * 8 * u.foot)
print('price of insulation =', price_insulation)
# cost for each layer
cost_insulation = price_insulation * area * sheets
print('total cost of insulation =', cost_insulation)
r_value = 3.85 * u.hour * u.foot**2 * u.delta_degF / u.BTU * sheets
UA_value = area / r_value
print('UA value =', UA_value)
# assume 3000 heating degree days

degree_days = 3000 * u.delta_degF * u.day
yearly_energy = (UA_value * degree_days).to(u.therm)
CRF = 0.1
yearly_cost_insulation = cost_insulation * CRF
print('Yearly energy cost =', yearly_energy)
print('Yearly insulation cost =', yearly_cost_insulation)

price of insulation = 0.3275 dollar / foot ** 2
total cost of insulation = 3094.875 dollar
UA value = 50.09276437847866 btu / delta_degF / hour
Yearly energy cost = 36.06679035250464 thm
Yearly insulation cost = 309.4875 dollar

We compare to the cost of one sheet of insulation to multiple sheets.

1 sheet cost is $44 per year and 250 therms burned

# 2 sheets

#(25 - 12.6) * u.BTU / ((88 - 44) * u.dollar)
(88 - 44) * u.dollar / ((252 - 126 ) * u.therm)

0.3492063492063492 dollar/thm

# 3 sheets

(132 - 44) * u.dollar / ((252 - 84 ) * u.therm)

0.5238095238095238 dollar/thm

# 4 sheets

(176 - 44) * u.dollar / ((252 - 63 ) * u.therm)

0.6984126984126984 dollar/thm

(309 - 44) / (252 - 36)

1.2268518518518519

6 * 3.85

23.1

# test for visibility