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Aerospace Engineering Algebra I Applications

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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.
  • http//connect.larc.nasa.gov/activities/adw/welcom
    e.html
  • www.nasa.gov
  • Try your hand at the design of a 200 passenger
    airliner, flying from Washington D.C. to the
    destination of your choice.
  • 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
    display your design.

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
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