Aerospace Engineering Algebra I Applications

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Aerospace EngineeringAlgebra I Applications

• Leslie Woodard
• Houston Independent School District
• E3 Teacher Research
• Texas AM University

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E3 Program Specs

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

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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

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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?

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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

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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

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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

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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

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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.

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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

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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
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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

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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

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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

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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.

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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