Geometry, Airplanes and Flight What makes a “good” paper airplane? Why might a paper airplane not fly well? Fold one yourself from plain white paper.

Rationale and Skills Developed Satisfaction of creating an object yourself Physical motions of folding Read technical diagrams Multiple intelligences Differentiation Low cost! Connections: geometry, engineering design, literature, physical science

Measurement, Modeling and Multiple Representation Standards Measurement: area, length, angle Classify shapes Identify (geometrical) properties Visualize, represent and transform two dimensional and three dimensional shapes Use maps and scale drawings to represent real objects Use appropriate tools to construct and verify geometrical relationships

Engineering Design and Physical Science Standards Design process (iterative) Optimization, given constraints Identify needs, invent, innovate Generate alternative plans Predict outcomes Create models, exhibit craftsmanship Test, modify, retest, … Study physical forces that effect flight

Folding Basics Use a hard surface. Take your time. Be accurate. Eyeball before you make the actual crease Press firmly to make crisp folds. Smooth layers flat. You learn more each time you start over.

Note Symbols and Perform Actions Valley fold - - - - - - - (fold up toward you) Mountain fold _ .._.._.._.. (fold back away from you) Existing crease Fold forward Fold behind Fold, then unfold Fold dot to dot Unfold Turn over Make equal distances Make equal angles

Fold and Think Geometry Wide Wing (green) Stacked Over Logan (blue) Your table’s assigned model (varies) Try the others if you like.

Fold and Think Geometry Wide Wing (green) Stacked Over Logan (blue) Your table’s assigned model (varies) Try the others if you like. Shapes Parallel lines Perpendicular lines Types of angles Measuring distances Bisecting lengths Bisecting angles

Vocabulary and Concepts: Distinguish, Diagram and Explain Verbally symmetry flip (reflection) vertical turn (rotation) horizontal slide (translation) diagonal convex (valley fold) vertex (corner point) concave (mountain fold) edge square bisect rectangle midpoint parallelogram angle bisector rhombus trisect kite congruent equilateral parallel lines isosceles perpendicular lines scalene axis trapezoid pentagon

Which plane will fly “best”? Why? How will you know? What is “best”?

Launch Factors Angles: vertically straight up, some angle up, horizontal, some angle down Hold underneath - near front, at center, near back Hold “over” (between fingers) Speed/force of launch: gentle, snap, …

Engineering Design Lab Test: Go fly, describe, record. What’s happening? Analyze. “Trim” (modify) your plane to improve (optimize) its flight. Fly again, describe, record.

Flight Principle #1: The forward thrust must be greater than the drag. Drag activity with paper Posterboard relay race Drag in folded planes? Thrust in folded planes?

Flight Principle #2: The lift from the wings must be greater than the effect of gravity. Lift activity with paper strips Bernoulli Principle Galileo gravity activity with objects

Shape of Airplane Wing Bernoulli’s Principle: Faster moving air (above wing) exerts less pressure than slower moving air (below wing). This causes lift. The amount of lift is proportional to the area of the wing.

Unstable Flight What do you call it? What does it look like? Math or physical explanation How can you fix it?

Unstable Flight Roll Wing dips, barrel roll, corkscrew Rotation around forward-backward axis Adjust dihedral angle Pitch Nosedive (nose down) or stall (nose rises up) Rotation around left-right axis Bend wing back corners up (for dive) or down (for stall) Yaw Flat spin Rotation around up-down axis Add fuselage and rudders (vertical surfaces)

Airplane Resources Blackburn, K. Guinness Book Record Holder website http://paperplane.org/ Green, S.N., Take off with scientific methodology. Science and Children, Nov/Dec 1988, 38-43, 71 Hurst, C. Children’s Literature Site contains numerous links and article Flight and Children’s Literature. Teaching K-8. http://www.carolhurst.com/subjects/flight.html Jackson, P. Championship Paper Planes, Barnes and Noble Books, 2000. ISBN 0-7607-2185-8 NASA website. http://www.grc.nasa.gov/WWW/K-12/airplane/airplane.html Schneidermeyer, K. Constructing flying disks. Science and Children, May 1999, 28-31 U.S. Centennial of Flight Commission website includes resources http://www.centennialofflight.gov/essay/Theories_of_Flight/airplane/TH2.htm