2. What's a real world problem?

4.  In these three pictures, it demonstrates how the wind molecules flow as it comes in contact with the wing blade.  The closer the lines are, the closer the air molecules are, which forms greater pressure. (Lower side has closer lines)  Note: Pressure difference creates net force (Pressure=Force/Area)  Net force at the bottom of the plane cancels and the gravitational force and lifts up the plane. Lower side Separating point End point

5. Once we understood the concept, we can start to do a real world question! How to calculate the minimum pressure difference that ‘s needed to lift up a plane?

6.  In order to precisely find out the minimum pressure difference (the minimum net force ) to lift up the plane, we must incorporate: Bernoulli Equation - Used to establish the relationship between velocity of air molecules and air pressure. Integration & Arc Length Formula Used to calculate the total distance that the air molecules traveled (Both the molecules on the upper side and the molecules on the lower side) Mean Value Theorem(Average Value of Y) Used to evaluate the average velocity of the flowing air molecules. Trigonometry Calculation needed Related rate of change Used to find out the time it takes for air molecules to travel from the separating point to the ending point respects to different angles of attack Angle of attack- the angle between the lifting body's reference line and the oncoming flow. Fluid Mechanics Finding average pressure that the body of the plane applies on the air below it. Application of Physics and Calculus

7. General Forms of Needed Formulas

8. General Information: Length: 202 ft 4 in (61.66 m) Wingspan: 84 ft 0 in (25.6 m) Height: 40 ft 0 in (12.2 m) Wing area: 3,856 ft2 (358.25 m2) Empty mass: 173,500 lb (78,700 kg) Useful load: 245,000 lb (111,130 kg) Choice of Plane: Concorde

9. Find the arc length of the upper side Find the arc length of the lower side The Following Graph Is a Left Side Image of Concorde Ending Point Separating Point

10. Find the arc length of the upper side Find the arc length of the lower side The Following Graph Is a Cross-Section of the Wind Blade y x Separating Point End Point Upper side is represented by a function U(x) Angle of Attack Length of the wind blade: L Lower side is represented by a function D(x)

11. The Average Velocity of Flowing Air Molecules

12. Pressure difference

13. How Much Time Do We Need? x

14. Area of the Plane B(X) A(X) b a

15. Final Battle! precisely find out the minimum pressure difference to lift up the plane

16.  With all these knowledge, you can make yourself fly.  Didn’t pay attention?!?!  Feeling regretful?!?!  Don’t Worry, feel free to contact us Conclusion

17.  TEHE Citation