Embed Size (px)
Citation preview
ICTCM - 2013
“Toy” Helicopters in Math and Science ClassesIntroduction
John Bacon (1)[email protected]
Bryndol Sones (2)[email protected]
Johann Thiel (1)[email protected]
Victor Trujillo (1)[email protected]
Frank Wattenberg (Speaker) (1)[email protected]
(1) Department of Mathematical Sciences(2) Department of Physics and Nuclear Engineering
United States Military Academy
The Parrot Drone
ICTCM - 2013
• Under $300• Available at Brookstone, Amazon,
Barnes and Noble• Flight Time about Ten Minutes• Extra Batteries $40• Li Polymer• Two Cameras
Controls
ICTCM - 2013
• iOS (iPad, iPhone) or Android• Four Rotor -- Inherently Stable• Downward Facing Sonar• Downward Facing Camera• Gyroscopes• Uses Controller’s Compass and
Accelerometer• Easiest -- Line-of-Sight
ICTCM - 2013
Streaming video from the drone allows it to be controlled without line-of-sight
What Makes it Work?
ICTCM - 2013
• Mathematics• Addition, Subtraction, Multiplication, Division, and Circles• The Pythagorean Theorem and Trigonometry• Vectors• Linear Algebra and Coordinate Transformations• Differential Equations• Fluid Flow -- Airfoils• Statistics
• Physics• Speed, Velocity, Acceleration, and Force• Work and Energy• Air Pressure• Torque and Angular Momentum
• Chemistry -- Batteries
• Middle School, High School, and College
• Intuitive and ...
ICTCM - 2013
First Questions• How Fast Can it Fly?• How Long Can it Fly?
First Experiments• Work in a large indoor space -- a hallway or gym• Record distance and time for several flights• Each student makes at least one flight• Record total flight time on a single charge
ICTCM - 2013
Planning for the Real (and Windy) World
Suppose the drone flies indoors at a speed of five feet per second and there is a two feet per second wind. How fast can the drone fly?
ICTCM - 2013
Planning a Round Trip Mission
Suppose that you want to fly from your base to a point that is 150 feet due north and return. Your flying speed is five feet per second.
• How long will the round-trip take if there is no wind?• Suppose there is a two feet per second wind blowing
from north to south. How will this affect your total flight time?
• How long will the outbound leg take?• How long will the return leg take?• What if the wind speed was six feet per second?
ICTCM - 2013
Flight Simulator
Students persevere and are more confident in their answers when they check them in a simulator or a
physical experiment instead of the back of the book.
ICTCM - 2013
Flight Planning in the Classroom
ICTCM - 2013
ICTCM - 2013
Flight Planning in a Simulator
ICTCM - 2013
Simulating “Seat-of-the-Pants” Flying
ICTCM - 2013
What Can We Learn About RotaryWing Aircraft from Fixed Wing Aircraft?
• What changes in the wings do you observe for take-off and landing?
• Why?
What Can We Learn About Wingsand Blades from Cardboard?
Why Four Rotors?
ICTCM - 2013
Linear Transformations and Aerial Photographs
ICTCM - 2013
The Basic Idea
ICTCM - 2013
Problems
• Given photograph coordinates for several features find the ground coordinates.
• Find a transformation that converts ground coordinates to photograph coordinates (matrix inverse).
• Given ground and photograph coordinates of three recognizable features find the entries for A and b (systems of equations).
ICTCM - 2013
A Chance to be Creative -- Mission Planning
ICTCM - 2013
