1. ICTCM - 2013 “Toy” Helicopters in Math and Science Classes Introduction John Bacon (1) John.Bacon@usma.edu Bryndol Sones (2) Bryndol.Sones@usma.eduedu Johann Thiel (1) Johann.Thiel@usma.edu Victor Trujillo (1) Victor.Trujillo@usmaVictor.Trujillo@usma.edu Frank Wattenberg (Speaker) (1) Frank.Wattenberg@usma.eduWattenberg@usma.edu (1)(1) Department of Mathematical Sciences (2) Department of Physics and Nuclear Engineeringhysics and Nuclear Engine United States Military Academy

2. 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

3. 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

4. ICTCM - 2013 Streaming video from the drone allows it to be controlled without line-of-sight

5. 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...

6. 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

7. 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?

8. 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?

9. 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.

10. ICTCM - 2013 Flight Planning in the Classroom

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12. Flight Planning in a Simulator

13. ICTCM - 2013 Simulating “Seat-of-the-Pants” Flying

14. ICTCM - 2013 What Can We Learn About Rotary Wing Aircraft from Fixed Wing Aircraft? What changes in the wings do you observe for take- off and landing? Why? What Can We Learn About Wings and Blades from Cardboard? Why Four Rotors?

15. ICTCM - 2013 Linear Transformations and Aerial Photographs

16. ICTCM - 2013 The Basic Idea

17. 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).

18. ICTCM - 2013 A Chance to be Creative -- Mission Planning

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