Data Collection and Analysis

During the course of the experiment, the method for taking and analyzing data has developed. As summary of the current method is provided here.

Experimental Process

Three different types insulation were tested: Polystyrene, fiberglass, and cellulose. To test these three boxes were constructed and a drywall box wall also constructed. The boxes of insulation were built to fit around the drywall box. Two holes were bored in the drywall box, on for a 25W light bulb, and one for a thermocouple.

figure 1

Each insulation box was set up as the cellulose box is set up in figure 1. The light was then turned on, and left on for an hour. The light was then unplugged, and an external and initial internal temperature was recorded. The internal temperature was then taken at regular intervals for three to seven hours. The interval and duration was determent by the type of insulation. The goal was for the temperature to fall less than three tenths of a degree (C) between data points and approximately 25C between the first and last data point.

Analysis of Raw Data

figure 2

The equation used to calculate the thermal resistivity was ln((T(t)-T_u)/(T_i-T_u))=-USt/mc. Where T(t) is the u is the temperature outside the experiment, Ti is the initial temperature in the box, S is the surface area, t is the time, m is the mass, m is the mass, c is the heat capacity, and U is the thermal conductivity. Thermal resistivity (R) is the inverse of  conductivity (U). To find U, we simplified the equation to γ=βt, where γ is ln((T(t)-T_u)/(T_i-T_u)) and β is -US/mc. This simplified things because the slope of γ versus t is β(figure 2). m, c, S are all physical constants so R is S/(mcβ).
temperature at time t, T

Economic Analysis

The economic analysis was based off a hypothetical building with certain constraints. The hypothetical building had a square footage of 14000 and 6 floors with 10 foot ceilings. All of the data that was calculated was based off of these constraints. The price to install each insulation and the cost of energy was calculated in this analysis. 

Building specs:                                                                                                    

14000sqft                                                                                                                          

6 floors

10 ft ceilings

total wall area 86400 sqft

Installment costs

Cost of parts and labor = .85$ per sqft

Fiber glass:                                                  Cellulose:                                                 Polystyrene:

1.06$ per sqft                                             1.90$ per sqft                                          .80$ per sqft

Cost= 165024$                                         Cost= 237600$                                      Cost= 69120$

Loan cost

Fiber glass:                                                  Cellulose:                                                 Polystyrene:

Loan=170,00$                                            Loan= 240,000$                                     Loan= 70,000$

Interest = 5.25%                                         Interest = 5.25%                                     Interest = 5.25%

10 years                                                     10 years                                                   10 years

1823.96$ per month                                   2575.00$ per month                                 751.04$ per month

Building Energy Output

Average Electricity Output, 23 KW-H/sqft/year

total= 322,000 KW-H per year

Heating (19% of total)                                                          Cooling(7% of total)

61180 KW-H                                                                      22540 KW-H 

Annual Average cost for Electricity, 1.34$ per sqft

Heating (19% of total)                                                          Cooling(7% of total)

.254$ per sqft                                                                       .093$ per sqft

Cost= 21997.40$ per year                                                   Cost= 8104.32$ per year