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 forwardFold behindFold, then unfoldFold dot to dotUnfoldTurn overMake equal distancesMake 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 squarebisect rectanglemidpoint parallelogramangle bisector rhombus trisect kitecongruent equilateralparallel lines isoscelesperpendicular lines scaleneaxis 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 ResourcesBlackburn, 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