Transcript Geometry, Airplanes and Flight

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
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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
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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
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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
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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.
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Shapes
Parallel lines
Perpendicular lines
Types of angles
Measuring distances
Bisecting lengths
Bisecting angles
Vocabulary and Concepts:
Distinguish, Diagram and Explain Verbally
symmetry
vertical
horizontal
diagonal
vertex (corner point)
edge
bisect
midpoint
angle bisector
trisect
congruent
parallel lines
perpendicular lines
axis
flip (reflection)
turn (rotation)
slide (translation)
convex (valley fold)
concave (mountain fold)
square
rectangle
parallelogram
rhombus
kite
equilateral
isosceles
scalene
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.
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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
Pitch
Nosedive
(nose down)
or stall (nose
rises up)
Yaw
Flat spin
Rotation
around
forwardbackward
axis
Rotation
around leftright axis
Rotation
around updown axis
Adjust
dihedral
angle
Bend wing
back corners
up (for dive)
or down (for
stall)
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/K12/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