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Abstract

This project’s purpose was to test the thermal conductivity in roofing materials when the degree of pitch

of a roof is changed. This was accomplished by building three roof systems of the same material and

only changing the pitch of the roof. In building construction, the numerical measure of the steepness of a

roof is referred to as the roof’s pitch. The systems were built with a 10°, 30°, and 60° roof pitches to

represent different architectural designs.

Problem Statement

In today’s world a growing concern is being “greener” meaning being less dependent on non-renewable

resources and energy. In the construction industry, if we can build and design buildings to conserve and

save energy we can cut back our dependence on non-renewable resources. If these practices show to be

not only profitable but also inexpensive to implement then the industry can strive to create “greener”

building practices.

Solution

Through research we can determine if it is possible to create such energy-saving practices. This project

was designed to test and research just that. The roof systems were designed so that they would represent

different building designs that are commonly found in homes across the country. The roof systems that I

created and tested were built with common asphalt shingles and underlayment just like thousands of

homes across America are. The roof systems each have their own pitch and were tested identically. A

thermometer was placed inside each system to record the internal temperature and the surface temperature

of the asphalt shingles was also recorded to show relationships.

To create the roof systems with the same interior volume I used formulas for volume of a triangular prism

and volume of a rectangular prism. The 60° roof system was the system that the other two derived their

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volumes from. Since the 60° roof system was the steepest pitch I built it as a triangular prism. Being

only a triangular prism, the others having rectangular volume under the triangular volume, the 60°

system’s volume was calculated to be 7308in³. The dimensions are: base 21”; height 29”; and length of

24” giving me the volume in inches³. V=12(21 )(29)¿ To calculate the volume for the 10° roof system I

calculated the volume of a triangular prism and also the volume of a rectangle. The volume of the

triangular prism: V=(23.8 )( 3 )(24) giving me a volume of 856.8in³. From here, I subtracted this

volume from the volume for the 60° roof system 7308 in3−856.8 in3=6451.8i n3 after finding this the

height of the rectangle was found using the equation Vol rect=l x w xh after solving the height was

found to be 11.3 inches so I added this to the height of triangular prism and these two together gives you

the same volume of the 60° roof system. The 30° system calculations were derived the same way, the

triangular volume: V = (22.5”)(8”)(24”) giving me a volume of 2169in³. So 7308in³-2169in³ = 5139in³

and after solving for the height of rectangular prism I determined the height to be 9.5in. So with the

addition in volume of rectangular prism to the volume of each triangular prism all volumes equal 7308in³.

This was the control of the experiment for this semester, since I was testing for affect on internal

temperature the volume of the systems needed to be equal.

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60° Roof System (above) 10° Roof System (below)

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30° Roof System

All roof systems were built using the same standard building materials. The frame was built using 2” x

4” boards and the roofs and sides were covered with 3/8” plywood. The shingles were common 3 tab

asphalt shingles. Asphalt shingles are composed of: a base material, either organic felt or glass-fiber mat,

that provides support for the weather-resistant components and gives a shingle strength; asphalt and

fillers; and surfacing material, generally in the form of mineral granules, that provides protection from

impact and UV degradation and improves fire resistance. The underlayment or “felt-paper” serves two

primary functions, one is temporary weather protection until the shingles are installed and the other is a

secondary waterproofing barrier in case moisture infiltrates the shingles.

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Completed roof systems (above)

Testing Equipment For measuring the temperatures of the internal space and the surface temperature of the shingles I used two methods. The internal temperature was measured using a thermometer that extended into the space and had a digital readout on the back side of each system. The surface temperature was measured with a infrared non-contact laser thermometer.

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Results Thus far data has been fairly similar across the board with the three roof systems. All readings were taken between the hours of 7-9am and 2-4pm. The internal temperatures did vary but only minimal amounts. The data did point out a few patterns that are starting to emerge though. The 60° system shows that in the morning hours of testing it produces a warmer internal temperature compared to the other two systems. And the 10° system showing that it produces a warmer internal temperature during the pm testing hours. This data will continue to be collected throughout the winter break and run the entire length of the Spring 2012 semester.

10°,30°,60° Roof System TemperaturesDate/ Time Roof System Internal Temp. (°F) Surface Temp. (°F)

11-15-11 a.m. 10° 73.3 80.2a.m. 30° 75.2 80.3a.m. 60° 72.3 79.511-15-11 p.m. 10° 78.6 80.1p.m. 30° 77.5 80.5p.m. 60° 78.2 79.811-16-11 a.m. 10° 74.8 82.1a.m. 30° 74.7 81.5a.m. 60° 74.7 80.611-16-11 p.m. 10° 79.7 80.3p.m. 30° 80.1 80.3p.m. 60° 79.9 80.111-17-11 a.m. 10° 54.7 58.1a.m. 30° 54.7 58.3a.m. 60° 54.9 59.311-17-11 p.m. 10° 65.4 70.2

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p.m. 30° 65.1 71.3p.m. 60° 64.2 71.211-18-11 a.m. 10° 39.6 38.3a.m. 30° 38.5 37.4a.m. 60° 39.9 39.511-18-11 p.m. 10° 62.1 60.2p.m. 30° 62.1 60.8p.m. 60° 62.2 62.011-21-11 a.m. 10° 70.7 74.8a.m. 30° 70.5 75.5a.m. 60° 70.2 75.211-21-11 p.m. 10° 77.4 77.9p.m. 30° 77.4 77.6p.m. 60° 77.7 77.911-22-11 a.m. 10° 75.7 84.5a.m. 30° 75.4 83.0a.m. 60° 75.2 82.111-22-11 p.m. 10° 79.8 83.1p.m. 30° 78.4 84.2p.m. 60° 77.8 83.711-23-11 a.m. 10° 62.1 64.3a.m. 30° 61.9 65.7a.m. 60° 61.9 65.611-23-11 p.m. 10° 69.8 75.2p.m. 30° 67.5 74.3p.m. 60° 68.7 75.111-24-11 a.m. 10° 62.2 65.7a.m. 30° 61.7 65.1a.m. 60° 62.7 66.211-24-11 p.m. 10° 71.8 73.2p.m. 30° 70.5 74.5p.m. 60° 72.0 74.311-25-11 a.m. 10° 62.6 69.8a.m. 30° 61.5 66.8a.m. 60° 63.7 70.111-25-11 p.m. 10° 72.5 71.3p.m. 30° 72.5 71.3p.m. 60° 72.5 72.111-27-11 a.m. 10° 51.6 53.6a.m. 30° 51.4 54.2a.m. 60° 51.1 53.911-27-11 p.m. 10° 51.1 53.6p.m. 30° 50.4 54.4p.m. 60° 50.5 54.8

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A.M. Internal Temperature Readings

10° am readings 30° am readings 60° am readings

Degrees Fahrenheit

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01020304050607080

P.M. Internal Temperature Readings

10° p.m. Temperatures30° p.m. Temperatures60° p.m. Temperatures

Degrees Fahrenheit

As you can see the desired difference we were testing for has not yet appeared. This is why the testing will continue.

Next SemesterFor the upcoming semester three new roof systems will be built with one constant pitch. For this semester the roofing materials will be changed and include an asphalt shingle roof, a metal roof, and ceramic tile roof. The desired pitch has not yet been decided. The six roof systems will be tested for internal and surface temperature and other parameters. These systems will also to be built with spray foam insulation.