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## Aerospace Engineering Algebra I Applications

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### Designed for secondary mathematics and science teachers ... Coordinate Plane Peregrine Falcon Hunts. Algebraic Expressions Nano Tubes ... – PowerPoint PPT presentation

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Title: Aerospace Engineering Algebra I Applications

1
Aerospace EngineeringAlgebra I Applications
• Leslie Woodard
• Houston Independent School District
• E3 Teacher Research
• Texas AM University

2
E3 Program Specs
• Designed for secondary mathematics and science
teachers
• Team with engineering professors to implement
research into curriculums
• Spark engineering interest in students

3
Secondary Mathematics Supplementary Applications
• Petroleum Engineering
• Solve Linear Equations and Inequalities
-Maintaining well pressure when drilling for oil
• Chemical Engineering
• Solve Linear Equations - Extraction of sulfur
from diesel fuel
• Exponential Growth and Decay - Stretching of
Polypropylene
• Aerospace Engineering
• Slope and Angle Measures - Landing of Commercial
Airplanes vs. Space Shuttle
• Ratio and Proportion - Exterior Commercial
Airplane Dimensions

4
Algebra I ApplicationsModules for Webpage
• Analysis of Data Birds to Planes
• Coordinate Plane Peregrine Falcon Hunts
• Algebraic Expressions Nano Tubes
• Linear Equations Canadian Goose Wingspan
• Linear Inequalities How much to lift off?
• Linear Equations First Plane Lift

5
Aerospace Engineering Mathematics Education
Objective
• Implement knowledge of basic aerodynamics into
curriculum
• Aerodynamics the study of forces and the
resulting motion of objects through the air

6
Aerospace Engineering Mathematics Education
Objective cont.
• Implement knowledge of TiiMS Research
• Texas Institute for Intelligent Bio-Nano
Materials and Structures for Aerospace
Engineering
• TiiMS Research
• Intelligent Systems
• Functionalized Nano-Materials
• Multifunctional Material Systems
• Biomaterials and Device

7
Focus on TiiMS Research
• Intelligent Systems
• Mimicking flight ability of birds
• Strength to weight ratios
• Reconfigurability
• Integration of sensing and actuation
• Functionalized Nano-materials
• Develop materials with tunable, adaptive, stress
smart sensing systems
• Increase intelligence
• Reduce weight, mass, size, and power consumption

8
Module Specs
• Objective Solve linear inequalities with one
variable using aerodynamics and TiiMS research
for real world applications
• Texas Essential Knowledge and Skills (TEKS)
• (b)1C, (b)1D, (b)3A, (b)3B, (c)3B, (c)3C
• National Council for Teachers of Mathematics
Standards (NCTM)
• 1, 2, 3, 4, 5, 8

9
Applicable Problem
• Aerospace Engineers of the Boeing aircraft must
add the weight of the engines, fuel, passengers,
cargo, and frame of the plane when programming
the planes intelligent system to sense safe take
off weights. Afterwards, the engineers want to
build a plane with a frame made of materials with
nano-tubes to determine how many more passengers,
how much more cargo, or how much more fuel the
plane can carry.

10
Boeing 717 Specs
• take off weight 110,000 lbs t
• engine 18,500 lbs e
• fuel 24,609 lbs f
• passengers 13,250 lbs p
• cargo 13,250 lbs c
• plane frame ? pf
• Inequality
• e f p c pf lt t

11
Weight of Frame
• What is the maximum that the frame of the plane
can weigh?
• e f p c pf lt t
• (18500 24609 13250 13250) pf lt 110000

69609 p lt 110000 -69609 -
69609 p lt 40391 The Plane
frame can weigh up to 40,391lbs
12
Nano-materials and a New Plane Frame
• What would be the new weight of a plane frame
built with nano-materials, if nano-materials
decrease the original weight of the plane frame
by 1/6?
• Old Plane Frame (1/6)Old Plane Frame New
Plane Frame
• 40391 6731.833 33659.167

13
More Luggage
• How much cargo (luggage) can the passengers
bring on the plane with a frame made of
nano-materials.
• e f p c pf
lt t
• 18500 24609 13250 C 33659.167 lt
110000
• 90018.167 c lt 110000
• -90018.167
-90018.167

• c lt 19981.833

14
Boeing 747 Specs
• take off weight 875,000 lbs t
• engine 184,900 lbs e
• fuel 334,632 lbs f
• passengers 78,600 lbs p
• cargo 52,400 lbs c
• plane frame ? pf

15
INDEPENDENT PRACTICE
• What is the maximum that the plane frame can
weigh?
• What would be the new weight of a plane frame
built with nano-materials, if nano-materials
decrease the original weight of the plane frame
by 1/5?
• How much cargo (luggage) can the passengers
bring on the plane with a frame made of
nano-materials.
e.html
• www.nasa.gov
• Try your hand at the design of a 200 passenger
airliner, flying from Washington D.C. to the
• You may modify the airplanes wings, tails,
engine, fuselage, and cruise settings by
clicking on the small pictures above. Then click
on the image in the upper right to analyze and

16
Wright Brothers Airplane1903

17
Basic AerodynamicsSolving Equations
• Notes Force ( N ) mass (kg) x acceleration
(m/s)
• gravity (g) 9.80 m/s2
• 1 kg 2.205 lbs
• 1 ft 0.3048 m
• What is the mass of the airplane in kilograms if
it weighed 700lbs.
• Calculate the force on the plane.

18
Cont.
• Calculate the speed in f/s if the plane flew 122
feet in 11 seconds. Then draw a distance time
graph.
• Convert this speed to meters/second.

19
Independent Practice
• Go onto the Boeing Website and find commericial
airplane information.
• www.boeing.com
• Repeat the same process for the
• Boeing 717
• Boeing 757

20
References
• Garcia, D. (Ed.). (1998). Algebra I Explorations
and Applications Texas Teachers Edition.
Evanston, Illinois McDougal Littel.
• Gay, L.R. Airasian, Peter (Eds.). (2003).
Educational Research Competencies for Analysis
and Applications. New Jersey Pearson Education.
• http//tiims.tamu.edu June 18, 2003. Intelligent
Systems Functionalized Materials
• www.boeing.com June 24, 2003. Commercial
• www.houstonisd.org June 9, 2003. Project Clear.
• www.nctm.org June 9, 2003. NCTM Standards An
Overview of Principles and Standards for School
Mathematics
• http//www.lerc.nasa.gov/WWW/K-12/airplane/bga.htm
l
• June 23, 2003. K-12 Lessons