Aerospace Engineering Algebra I Applications Leslie Woodard Houston Independent School District E3 Teacher Research Texas A&M University

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

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

Algebra I Applications Modules 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

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

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

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

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

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.

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 < t

Weight of Frame What is the maximum that the frame of the plane can weigh? e + f + p + c + pf < t ( ) + pf < p < p < The Plane frame can weigh up to 40,391lbs

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 – =

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 < t C < c < c <

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

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. 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.

Wright Brother’s Airplane 1903

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

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.

Independent Practice Go onto the Boeing Website and find commericial airplane information. Repeat the same process for the: Boeing 717 Boeing 757

References Garcia, D. (Ed.). (1998). Algebra I: Explorations and Applications Texas Teacher’s Edition. Evanston, Illinois: McDougal Littel. Gay, L.R. & Airasian, Peter (Eds.). (2003). Educational Research: Competencies for Analysis and Applications. New Jersey: Pearson Education. June 18, Intelligent Systems & Functionalized Materialshttp://tiims.tamu.edu June 24, Commercialwww.boeing.com June 9, Project Clear. June 9, NCTM Standards: An Overview of Principles and Standards for School Mathematicswww.nctm.org June 23, K-12 Lessons