I Believe I can fly

I Believe I can flyAP Calculus BC Phillip Wong Gar Mint Hung Yazhan LinGroup Project:In Reality!

What's a real world problem?How does airplane fly?(make it stand out)Paper Airplane demonstration

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.How Does a Airplane Fly?

Lower sideSeparating pointEnd pointWhen wind blade touch. Compresses molecules. Closer the lines the closer the molecules, forming greater pressure. 4At this point, can anyone answer how does the paper plane stay balanced?

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?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 FormulaUsed 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.

TrigonometryCalculation neededRelated rate of changeUsed 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 attackAngle of attack- the angle between the lifting body's reference line and the oncoming flow. Fluid MechanicsFinding average pressure that the body of the plane applies on the air below it.Application of Physics and CalculusGeneral Forms of Needed Formulas

Choice of Plane: Concorde

Find the arc length of the upper side Find the arc length of the lower sideThe Following Graph Is a Left Side Image of ConcordeEnding PointSeparating Point

Find the arc length of the upper side Find the arc length of the lower sideThe Following Graph Is a Cross-Section of the Wind Blade yxSeparating PointEnd PointUpper side is represented by a function U(x)Angle of AttackLength of the wind blade: LLower side is represented by a function D(x)The Average Velocity of Flowing Air Molecules

Pressure differenceHow Much Time Do We Need?

xArea of the Plane

B(X)A(X)baFinal Battle!precisely find out the minimum pressure difference to lift up the plane

With all these knowledge, you can make yourself fly. Didnt pay attention?!?!Feeling regretful?!?!Dont Worry, feel free to contact usConclusionTEHECitation