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Jupyter notebook Final Project/project_report.ipynb

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Kernel: Anaconda (Python 3)

Final Project

Team Name: Lost Vikings

Team Members: Brooke Beesley, Jon Janikowski, Riley Larcher, Lenina Pascua

Design Objectives

What performance objectives you set (temperature, price, etc.)

The goal of this project is to design a cardboard box that contains the basic energy goals of a human home. Homes usually want to maintain a mild indoor temperature, let in natural sunlight and fresh air, and use as little energy as possible. For this box, instead of having an energy source, we are going to use thermal mass and not let in fresh air, so our main goal is to keep a cardboard box at a comfortable temperature for humans to live in. We aimed to keep the maximum temperature of the box at 75 degrees F and the minimum temperature of the box at 65 degreees F.

Design Strategy

What was your overall strategy?

Our overall contruction of the box included a double layer of R-1.93 foam for insulation and a 12inch-by-8inch south-facing window made of clear plastic. As our source of thermal mass, we used eight 16.9oz water bottles, which is about 1.06 gallons of water. For our second run, we focused on the window and thermal mass. We chose to patch up half of our 96 sq.inch window horizontally, making it a 12inch-by-4inch window or 48 sq.inches and we added 33.8 ounces of water to our thermal mass.

Estimation of Performance

Prove to yourself and your reader how you went about estimating your design needs

How did you determine the amount of insulation needed?

We used a double layer of the foam insulation because our biggest worry was the amount of energy that would exit the box throughout the night, and we did not think that a single layer was going to be sufficient.

How did you determine the amount of window needed?

We thought that our biggest problem was going to be heat loss during the nighttime, so to combat a high thermal loss, we decided to make a 96 sq.inch window to allow a high amount of solar energy to enter the box.

How did you determine the type and amount of thermal mass you used?

We decided to use water as our thermal mass because water has a high specific heat capacity (4.186 J/gK) and is a relatively cheap option for this project. The higher specific heat capacity helps keep the solar energy gained during the day from leaving the box during the night. We decided to use eight 16.9oz water bottles because that was the amount of bottles that fit as a bottom layer for our box and that roughly amounted to 1.06 gallons of water.

How did you estimate the highest and lowest temperature you would observe?

Assuming that humans are going to live in this house, we tried to keep the box at temperatures between 65 and 75 degrees Fehrenheit, which is the range of temperatures that humans are most comfortable living in.

Clearly show the basic details of your calculations.

KNOWN

  • Box Dimensions: 12inch x 12inch x 16 inch

  • R-Value Cardboard:.4375 ft^2Fhr/BTU

  • Thickness of Cardboard: 0.125 inch

  • R-Value Foam Insulation: 1.93 ft^2 * degree_F * hr/ BTU , Double Layer: 3.86 ft^2 * degree_F * hr/ BTU

  • Thermal Mass: 1.06 gal of water

CALCULATIONS FOR RUN 1 Nightly Energy Loss

  • Surface Area of Box: 2(LW) + 2(WH) + 2(LH)= 2(1612)+2(1212)+2(16*12)= 7.33 ft^2

  • Surface Area of Window: 12in*8in= 96in^2= .67ft^2

  • Surface Area of Walls: 7.33ft^2 - .67ft^2 = 6.67 ft^2

  • R-value of the wall: 2*1.93 + .4375= 4.2975

  • U-Value of walls: 1/ 4.2975= .233 BTU/ft^2Fhr

  • UA product of walls: .233 BTU/ft^2Fhr * 6.67ft^2= 1.55 BTU/F*hr

  • R-value of the window: .68+ .7+ .17= 1.55 ft^2Fh/BTU

  • U-value of the window: 1/ 1.55 ft^2= .645 BTU/ft^2Fhr

  • UA product of window: .645 BRU/ft^2Fhr * .67ft^2= .43 BTU/F*hr

  • Total UA product: 1.55 BTU/Fhr + .43 BTU/Fhr = 1.98 BTU/F*hr

  • Q=UAdeltaT

  • Q=UAdeltaTtime

  • Q= Nightly energy loss

  • UA: 1.98 BTU/F*hr

  • DeltaT: Day temp- night temp= 80F-55F= 25F

  • time period of night: 10 hours

  • Q= 1.98 BTU/F*hr * 25F * 10hr = 495 BTU

  • **Nightly Energy Loss: 495 BTU

CALCULATIONS FOR RUN 1 DAILY SOLAR GAIN

  • Average Solar Insolation for Sacramento: 960 BTU/ft^2*day (from NREL pdf, south facing window)

  • Average Solar Insolation for San Francisco: 745 BTU/ft^2*day (from NREL pdf, south facing window)

  • Solar Insolation (Average between Sac and SF): (960+ 745)/2= 852 BTU/Ft^2*day

  • Rohnert Park Daily Solar gain: daily solar insolation* area of window = 852 BTU/Ft^2*day * .67ft^2 = 570.84 BTU/day

  • Daily Solar Gain: 570.84 BTU/day

TEMPERATURE RISE OF THE THERMAL MASS

  • Q=mcdeltaT

  • Q: Net Solar gain : 76 BTU/day = .96 J/s

  • m: mass of the water: 135.2 ounces = 3832.9 g

  • c: specific heat capacity of water: 4.186 J/g*K

  • DeltaT= .96 J/s / 3832.9g * 4.1866 J = 5.98 J/s

  • Delta T of the thermal mass: 5.98 K/s * 86,400 sec/day = 5.17 K = 9.3 F

  • Delta T of thermal mass: 9.3 F

CALCULATIONS FOR RUN 2

  • Window Area: 4 * 12 = 48 sq.inches = 0.33 ft^2

  • Window U-Value: 0.645 BTU/ ft^2Fhr

  • Window UA: 0.33 * 0.645 = 0.21 Btu/F*hr

  • Wall Area: 7.33ft^2 - 0.33 ft^2 = 7ft^2

  • Wall U-Value: 0.233 BTU/ft^2Fhr

  • Wall UA: 7.33 * 0.233 = 1.7 BTU/ F*hr

  • Total UA = 1.7 + 0.21 = 1.91 BTU/ F*hr

SOLAR GAIN

  • Average Solar Insolation for Sacramento: 960 BTU/ft^2*day (from NREL pdf, south facing window)

  • Average Solar Insolation for San Francisco: 745 BTU/ft^2*day (from NREL pdf, south facing window)

  • Solar Insolation (Average between Sac and SF): (960+ 745)/2= 852 BTU/Ft^2*day

  • Rohnert Park Daily Solar gain: daily solar insolation* area of window = 852 BTU/Ft^2*day * .33ft^2 = 281.16 BTU/day

  • Daily Solar Gain: 281.16 BTU/day

NIGHTLY ENERGY LOSS

  • Q=UAdeltaT

  • Q=UAdeltaTtime

  • Q= Nightly energy loss

  • UA: 1.91 BTU/F*hr

  • DeltaT: Day temp- night temp= 80F-55F= 25F

  • time period of night: 10 hours

  • Q= 1.91 BTU/F*hr * 25F * 10hr = 477.5 BTU

  • Nightly Energy Loss: 477.5 BTU

Clearly summarize the outputs of your calculations.

  • Run 1

    • UA product: 1.98 BTU/ degree_F * Hr

    • Expected solar gain: 571 BTU/day

    • Nightly thermal energy loss: 495 BTU/day

    • Net energy gain: 76 BTU/day

    • Delta T of thermal mass: 9.3 F

  • Run 2

    • UA product: 1.91 BTU/ degree_F * hr

    • Expected Solar gain: 281.16 BTU/ day

    • Nightly thermal energy loss: 477.5 BTU/day

    • Net energy gain: -196.34 BTU/day

Picture of Run 2

from IPython.display import Image
Image("IMG_3681.JPG")
Image in a Jupyter notebook
from pint import UnitRegistry
u = UnitRegistry()
area = 10 * u.feet**2
u.define('R_US = foot**2 * delta_degF * hour / BTU')
wall_r_value = (0.17 + 0.5 + 0.68) * u.R_US
UA_product = area / wall_r_value
print('Our UA product estimate is', UA_product.to(u.BTU/u.hour/u.delta_degF))
print('Our UA product estimate is', UA_product.to(u.watt/u.delta_degC))
Our UA product estimate is 7.4074074074074066 btu / delta_degF / hour Our UA product estimate is 3.9076142689629627 watt / delta_degC

Results

  • Include a graph of your temperature performance inside and the temperature outside

  • Include a graph of the temperature difference over time

  • Are the results what you expect?

  • What design improvements would you make?

Run 1

  • Window= 96 sq.inch

  • Thermal Mass = 135.2 oz / 1.06 Gallons of Water

%matplotlib inline
import matplotlib.pyplot as plt
import seaborn as sns
import pandas as pd

data = pd.read_csv('lost-vikings.csv', parse_dates=True, index_col=0)
data['t_diff'] = data['t_in_C'] - data['t_out_C']
data[['t_in_C', 't_out_C', 't_diff']].plot()
plt.title('Run 1')
plt.ylabel('Temperature (C)')
plt.show()
Image in a Jupyter notebook

Run 1 Results

  • In the box:

    • hottest 34 degrees_C or 93.2 degrees_F

    • coldest 12.9 degrees_C or 55.2 degrees_F

  • Outside:

    • hottest 34.125 degrees_C or 93.43 degrees_F

    • coldest 9.81 degrees_C or 49.66 degrees_F

  • The inside temperature got a lot hotter during the day than we anticipated because of the window size. During the night, a lot of heat also escaped and the box got a lot colder than we wanted it to.

** Design Improvements **

  • If we were to do more runs, we would make the window smaller because the size of our window was pretty big and let too much solar energy to come in the box and let too much heat leave at night time. We would also add more thermal mass to absorb and keep the heat in.

Run 2

  • Window= 48 sq.in

  • Thermal Mass = 168.2 oz / 1.3 gallons of water

%matplotlib inline
import matplotlib.pyplot as plt
import seaborn as sns
import pandas as pd

data = pd.read_csv('lost-vikings_2 (1).csv', parse_dates=True, index_col=0)
data['t_diff'] = data['t_in_C'] - data['t_out_C']
data[['t_in_C', 't_out_C', 't_diff']].plot()
plt.title('Run 2')
plt.ylabel('Temperature (C)')
plt.show()
Image in a Jupyter notebook

Run 2 Results

  • In the box:

    • hottest 27.8 degrees_C or 82 degrees_F

    • coldest 12.8 degrees_C or 55 degrees_F

  • Outside:

    • hottest 24.125 degrees_C or 75.42 degrees_F

    • coldest 9.375 degrees_C or 48.88 degrees_F

  • After the first run, we made the window smaller and added more thermal mass. We thought that this would help let in less solar energy and keep the heat in longer. The inside temperature of the box did get less hot than the first run but it was still hotter than the goal of 75 degrees_F and it lost a lot of heat at night.

** Further Design Improvements **

  • The main thing we would do to improve our box from our second run is that we would need to add a lot more thermal mass. If we added more thermal mass, this would keep the heat inside more effectively which would emit later in the day resulting in a higher temperature at night.

Contributions

Each team member writes what their contributions to the project are. You can also comment on how you facilitated teamwork during your project.

Riley: I designed the box, made the cuts, assembled the materials, and built the box. I also cut the window, and built a filler to make the window smaller for our second run. I also arrived at 8am for the first and second runs.

Brooke: Did calcualations and Sage Math Cloud write up. Attempted to assist in construction but mostly provided moral support.

Jon: Worked with Riley in the design and construction of the box. Helped cut out and assemble materials. Wrote down information and data on Sage Math Cloud. Went Saturday at 8am to set up another run after the thermometer malfulctioned.

Lenina: Assisted calculations, did write up on sage math cloud, and kept team focused.