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FACULTY NOTES
The LTAs and Spinoffs are designed so that each professor can implement them in a way that is consistent with his/her teaching style and course objectives. This may range from using the materials as out-of-class projects with minimal in-class guidance to doing most of the work in class. The LTAs and Spinoffs are amenable to small group cooperative work and typically benefit from the use of some learning technology. Since the objective of the LTAs and Spinoffs is to support the specific academic goals you have set for your students, the Faculty Notes are not intended to be prescriptive. The purpose of the Faculty Notes is to provide information that assists you to take full advantage of the LTAs and Spinoffs. This includes suggestions for instruction as well as answers for the exercises.
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FACULTY NOTES
LTA 12
Mission Control: We Have Energy Savings
Background Information
Math Prerequisites: Arithmetic Skills Averages Reading and reasoning Graphing
Learning Technologies Suggested: Scientific Calculator, Graphing Calculator
Approximate Class Time required for LTA 12: 2 hours
Comments
Students will gain experience with mathematical reasoning and problem solving as they meet the following objectives:
- Collect numerical data.
- Estimate data from personal life.
- Calculate sums of data.
- Measure rectangles and calculate areas.
- Calculate ratios.
- Calculate total cost given the unit cost and the number of units.
- Find to what fiscal year a given month belongs.
- Find the average of a set of numbers.
- Draw conclusions from data.
- Graph data.
- Draw conclusions from graphs.
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Part B Light Fixtures and Lamps
- The answers in columns 1 and 2 of the following table should be the same for all students. The estimated daily usage in column 3 will differ from student to student. Table 1: Light Fixtures and Lamp Information
Light Fixture or Lamp Watts Hours/Day (Watt-Hours Per Day) Kitchen: Fluorescent Light (4 bulbs @ 40 W)
Kitchen: Ceiling Fixture: (4 bulbs @ 60 W)
Living Room (LR): Ceiling Fixture (4 bulbs @ 60 W)
Living Room: 2 Floor Lamps (1 bulb @ 150 W)
First floor Bathroom: Recessed Light (4 bulbs @ 75 W)
First floor Hallway: Table Lamp (3 bulbs @ 60 W)
Family Room: 2 Reading Lamps (1 bulb @ 75 W)
Bedroom 1: Reading Lamp (1 bulb @ 75 W)
Bedroom 1: Ceiling Fixture (4 bulbs @ 60 W)
Bedroom 2: 2 Reading Lamps (1 bulb @ 75 W)
Bedroom 2: Ceiling Fixture (4 bulbs @ 60 W)
Second floor Hall: Reading Lamp (1 bulb @ 75 W)
Second floor Hall: Ceiling Fixture (4 bulbs @ 60 W)
Second floor Bathroom: Fluorescent Light (4 bulbs @ 40 W)
Bedroom 3: Table Lamp (3 bulbs @ 60 W)
Bedroom 3: Floor Lamp (1 bulb @ 150 W)
Bedroom 3: Ceiling Fixture (4 bulbs @ 60 W)
TOTAL --- --- 10,030 watt-hours
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- a) The prefix, kilo, means one thousand (1000) b) Divide watt-hours by 1000. Note: 1000 watt-hours = 1 kilowatt-hour. With reference to Exercise 13, 10,030 watt-hours = 10.030 kilowatt-hours. c) Multiply the number of kilowatt hours by $0.05. With reference to Exercise 13, the total cost is equal to ($0.05 per kWh)(10.030 kWh) = $0.5015. d) Answers vary. They should include the cost of electricity as well as a comparison to $0. used by NASA. e) Answers will vary. f) Answers will vary. An example of an assumption that may be used is that the year is not a leap year, and therefore the year has 365 days.
Part C Window to Wall Ratio
- Students follow the example of Table 2 to complete a table of window and wall dimensions. Students’ answers may vary slightly.
Window and wall information for House A
House A Front Wall
Window Dimension Window Area Exterior Wall Dimensions
Exterior Wall Area
windows (5) 8 mm by 20 mm 5·160 sq mm = 800 sq mm
113 mm by 33 mm
3,729 sq mm
door 13 mm by 29 mm
Totals --- 800 sq mm --- 3,729 sq mm
Window and wall information for House B House B Front Wall
Window Dimension Window Area Exterior Wall Dimensions
Exterior Wall Area
Left double window
12 mm by 8mm 96 sq mm
Rectangular windows (4)
8 mm by 21 mm 4·168 mm = 672 sq mm
Rectangular part of front wall: 118 mm by 25 mm
2,950 sq mm
Triangular windows (2)
Triangle b = 7 mm, h = 11 mm
77 sq mm
Triangular gable end: Trapezoidal windows (2)
altitude = 8 mm side 1 = 17 mm side 2 = 29 mm
368 sq mm
base = 60 mm, altitude = 45 mm
1,350 sq mm
Door 10 mm by 21 mm --- --- ---
Totals --- 1,213 sq mm --- 4,300 sq mm
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- a) The units of area cancelled out. b) The WWR would not have changed. c) If k is the scaling factor for inches and if c is the conversion factor from square millimeters to square inches, then we have the following. The true area of the windows = k (area of the windows in the diagram in square inches) =^2 k ·c (area of the windows in the diagram in square millimeters)^2
The true area of the wall = k (area of the wall in the diagram in square inches) =^2 k ·c (area of^2 the wall in the diagram in square millimeters)
Since constant factors cancel when we form the WWR ratio, it is not necessary to know the actual dimensions of the house. Any drawing done to scale is sufficient.
- a) Answers will vary. b) Answers will vary. c) Answers will vary. d) Wall W: Approximately 50% Wall X: Approximately 20% Wall Y: Approximately 30%
Part E Follow Up Exercises Related to NASA
- 3,010 hours per year which is obtained by solving the equation, (20.89kW) x = 62,878kWh.
- ($0.071)/kWh; calculation: ($4,471)/(62,878 kWh) = ($0.0711)/kWh
- 4,400 square feet; calculation: (88,000 sq ft)(0.05) = 4,400 sq ft
- $0.0481 per kWh; calculation: $96.00/1995kWh = $0.0481/kWh
- 31 years; calculation: $3,000.00/$96.00 per year = 31.25 years
Section 2
Establishing a Baseline for Energy Use
Comments
The contractor invests $12,000,000 in work and is paid back $23,000,000. The difference of $11,000,000 can be considered a return on the contractor’s investment. The government obtained the money to pay the contractor from savings created by reduced energy consumption and deferred maintenance. Deferred maintenance means that by installing new equipment, replacement of the old equipment is delayed for the life of the new equipment.
The finance option on some calculators permits finding interest rates or present values. For a more detailed discussion about rate of return on investment, see the Faculty Notes section for Spinoff 12 A.
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Part B Fiscal Year and Calendar Year - Baseline For Electricity Use
- January 1 and December 31
- Expenses such as instructor contracts are between August and June. Also, most tuition is paid at the beginning of the fall and winter terms. Thus, the major financial expenses for schools occur in the same fiscal year if the fiscal year is chosen to be July 1 to June 30.
- September 30, 1998
- FY 1998
- 1995
- 1997
- Answers are found in the far right column of each of the following tables.
Table 3 E & O (Engineering and Operations) Building Electricity Use in kWh
Month FY (kWh)
FY
(kWh)
FY
(kWh)
Baseline (Monthly Average) (kWh rounded to nearest hundred) Oct 79,130 70,320 87,120 78,
Nov 67,910 61,920 60,720 63, Dec 58,010 56,280 60,650 58,
Jan 51,870 80,720 56,280 63, Feb 50,990 52,560 47,880 50,
Mar 55,570 69,000 47,040 57, Apr 64,500 58,560 59,020 60,
May 75,600 71,760 69,210 72, Jun 75,600 77,520 80,400 77,
Jul 86,140 90,240 89,870 88, Aug 93,550 93,240 95,290 94,
Sep 96,010 97,920 95,330 96,
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Part C Exploring Electricity Use Patterns
- A graphing calculator or spreadsheet can be used to construct a connected line graph for the data in each table. Coded values (1 through 12) for the months should be recorded on the x-axis, with corresponding electricity use in kilowatt hours on the y-axis. Although the E&O building uses more electricity than Hangar S, the electricity use pattern for the two buildings is very similar. Both buildings use considerably less electricity from November through April than they do from May through September. For both buildings the electricity use for February is less than for any other month.
Hangar AF uses more electricity the other two buildings and its electricity use pattern is quite different. The electricity use for Hangar AF for the six month period from August through January is considerably lower than for the six month period from February through July. The lowest electricity use occurs in November.
No, the summer months may have higher air conditioning costs. Seasonal differences affect energy use. Building usage is another cause for variability in energy use. For example, more electricity is used in Hangar S and in Hangar AF for the months October through March FY97 than for the same months in FY98. This difference would not be attributable to seasonal differences. It may be due to higher building usage in FY97.
October through March FY98: 132,690 kWh April through September FY98: 262,400 kWh Usage for April through September is indeed higher than for October through March FY98.
Total electricity use for each fiscal year by building is shown in the following table.
Building FY96 FY97 FY E&O Building 854,880 880,040 848, Hangar S 986,030 1,134,420 975, Hangar AF (^) 2,456,880 2,976,000 2,370,
