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Project Grant Team
John S. Pazdar Peter A. Wursthorn Project Director Principal Investigator Capital Community College Capital Community College Hartford, Connecticut Hartford, Connecticut This project was supported, in part, by the Patricia L. Hirschy National Science Foundation Principal Investigator Opinions expressed are those of the authors Asnuntuck Community College and not necessarily those of the Foundation Enfield, Connecticut
SPINOFFS
Spinoffs are relatively short learning modules inspired by the LTAs. They can be easily
implemented to support student learning in courses ranging from prealgebra through calculus.
The Spinoffs typically give students an opportunity to use mathematics in a real world context.
LTA - SPINOFF 12A Finding the Rate of Return for
Energy Saving Investment
LTA - SPINOFF 12B Fitting a Sine or Cosine Curve to
NASA Energy Use Data
LTA - SPINOFF 12C Rocket Spies: Codes and Rockets
in the 1950’s and 1960’s
Alice Kaseberg - AMATYC Writing Team Member
Lane Community College, Eugene, Oregon
Janet Tarjan - AMATYC Writing Team Member
Bakersfield Community College, Bakersfield, California
Catherine Alexander - NASA Scientist/Engineer
Kennedy Space Center, Florida
NASA - AMATYC - NSF
SPINOFF 12B
Fitting a Sine or Cosine Curve to NASA Energy Use Data
Monthly energy related data may fit a sine or cosine curve. The following exercises refer to data found
in the tables on the next two pages. These tables provide a record of the monthly electrical energy use
for three buildings (Hanger AF, Hanger S, E&O Building) at the Cape Canaveral Air Station in Florida.
Before undertaking this Spinoff, you should read pertinent parts of LTA 12, namely “Background
Information” and Section 2.
Exercises
1) Choose one building. It may be Hangar AF, Hangar S, or the E&O Building.
2) Use a graphing calculator and follow the steps below to fit a sine curve (or cosine curve) to the
NASA electric usage data for 18 months (FY97 and the first 6 months of FY98) for the building
you selected.
a) Number the first list in your graphing calculator with 1 to 18.
b) Select a building and enter its energy use data for all 12 months of FY97 and the first six months
of FY98.
b) Calculate one-variable statistics on the second list.
c) Record the mean and range for the data.
d) Set a viewing window with Xmin = 0, Xmax = number of data points (18), Xscl = 2, Ymin
= lowest number in second list, Ymax = highest number in second list,
Yscl = range/10.
e) Use Statistical Plot to graph the data.
f) Enter the mean as one equation, Y = mean, in [y=]. Does the mean pass horizontally through
the middle of the data?
g) In [MODE] select [Radian] option.
Set up a first guess for the equation using these suggestions for starting values.
Y = a⋅sin( bx + c ) + d
Let a = range/2.
Let b = 0.5.
We expect there to be a 12 month seasonal cycle or period.
The period for the general sine function (y = k⋅sin x) is 2π or
approximately 6.28 radians.
The value of b, the coefficient of x, determines the period according to the
formula: period = 2π/b.
We want a period close to 12 radians so we let b = 0.5.
The coefficient b = 0.5233333 is more precise but 0.5 works adequately.
Let d = mean.
h) Enter the sine equation into a second equation in [y=].
i) Use guess and check to set the parameter c (the source of the shift left or right) so as to match
any cyclic behavior in the graph of the data.
NASA - AMATYC - NSF
Table 2 Hangar S - Electricity Use in kWh
Month FY
(kWh)
FY
(kWh)
FY
(kWh)
Oct 92,890 116,360 97, Nov 81,200 100,000 82, Dec 69,940 80,180 71, Jan 61,890 84,320 67, Feb 59,000 77,520 61, Mar 61,990 101,440 59, Apr 70,120 94,600 64, May 81,410 87,840 74, Jun 93,080 95,240 86, Jul 102,290 103,440 97, Aug 106,780 92,240 104, Sep 105,440 101,240 106,
# The data for FY97 and Oct to Mar FY98 are actual data from NASA. Other data are estimated from NASA data.
Hangar S is the building where the Self-Contained Atmospheric Pressurized Ensemble (SCAPE) suits are maintained, cleaned, and refurbished. The SCAPE Suits protect workers as they load the hydrazine fuel into the Orbiter’s maneuvering engines
Table 3 Hangar AF - Electricity Use in kWh *
Month FY
(kWh)
FY
(kWh)
FY
(kWh)
Oct 120,230 288,000 139, Nov 134,270 218 ,880 103, Dec 166,850 229,120 125, Jan 210,000 236,800 122, Feb 253,150 264,960 149, Mar 285,730 296,960 154, Apr 299,780 248,320 253, May 291,830 268,800 285, Jun 222,700 199,680 299, Jul 178,430 376,320 291, Aug 141,890 185,600 263, Sep 152,020 162,560 180, ***** The data for FY97 and Oct to Mar FY98 are actual data from NASA. Other data are estimated from NASA data. When the two white Solid Rocket Boosters are recovered from the Atlantic Ocean after Shuttle launch, they are taken to Hangar AF. They are then refurbished before being refueled for another launch.
