Geometry, Airplanes and Flight What makes a “good” paper airplane? Why might a paper airplane...
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Transcript of Geometry, Airplanes and Flight What makes a “good” paper airplane? Why might a paper airplane...
![Page 1: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072014/56649e8a5503460f94b8edb6/html5/thumbnails/1.jpg)
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.
![Page 2: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072014/56649e8a5503460f94b8edb6/html5/thumbnails/2.jpg)
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
![Page 3: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072014/56649e8a5503460f94b8edb6/html5/thumbnails/3.jpg)
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
![Page 4: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072014/56649e8a5503460f94b8edb6/html5/thumbnails/4.jpg)
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
![Page 5: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072014/56649e8a5503460f94b8edb6/html5/thumbnails/5.jpg)
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.
![Page 6: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072014/56649e8a5503460f94b8edb6/html5/thumbnails/6.jpg)
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
![Page 7: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072014/56649e8a5503460f94b8edb6/html5/thumbnails/7.jpg)
Fold and Think Geometry
• Wide Wing (green)• Stacked Over Logan
(blue)• Your table’s assigned
model (varies)• Try the others if you
like.
![Page 8: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072014/56649e8a5503460f94b8edb6/html5/thumbnails/8.jpg)
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
![Page 9: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072014/56649e8a5503460f94b8edb6/html5/thumbnails/9.jpg)
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
![Page 10: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072014/56649e8a5503460f94b8edb6/html5/thumbnails/10.jpg)
Which plane will fly “best”?
• Why?
• How will you know?
• What is “best”?
![Page 11: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072014/56649e8a5503460f94b8edb6/html5/thumbnails/11.jpg)
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, …
![Page 12: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072014/56649e8a5503460f94b8edb6/html5/thumbnails/12.jpg)
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.
![Page 13: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072014/56649e8a5503460f94b8edb6/html5/thumbnails/13.jpg)
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?
![Page 14: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072014/56649e8a5503460f94b8edb6/html5/thumbnails/14.jpg)
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
![Page 15: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072014/56649e8a5503460f94b8edb6/html5/thumbnails/15.jpg)
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.
![Page 16: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072014/56649e8a5503460f94b8edb6/html5/thumbnails/16.jpg)
Unstable Flight
What do you call it?
What does it look like?
Math or physical explanation
How can you fix it?
![Page 17: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072014/56649e8a5503460f94b8edb6/html5/thumbnails/17.jpg)
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)
![Page 18: 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.](https://reader035.fdocuments.net/reader035/viewer/2022072014/56649e8a5503460f94b8edb6/html5/thumbnails/18.jpg)
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