The Physics of Planes

   The Physics of Planes 

          Airplanes are constructed in a way that the airflow pattern around them generates lift, which enables them to fly. The airflow is produced by the forward motion of the plane relative to the air. This forward motion is produced by engine thrust, delivered by way of propeller engines or air-breathing engines, otherwise known as turbines. Airplane engines produce thrust by accelerating the airflow in the rearward direction. This backwards acceleration of the airflow exerts a "push" force on the airplane in the opposite direction, by Newton's third law that there is an equal and opposite reaction, causing the airplane to move forward. 

Airfoils

          In aerodynamics, airplane wings are called airfoils. They have a cambered shape which enables them to produce lift, even for angles of attack (α) equal to zero. The figure below is a cross-sectional view of an airfoil. 

           The orientation of the airfoil relative to the airplane body is shown below. The angle of incidence is defined as the angle between the chord line and the longitudinal axis of the plane. For general aviation designs, an angle of incidence commonly used is about 6 degrees. 

Forces acted on the Plane 

The figure below shows the resultant forces acting on an airplane in level flight, moving at constant velocity. 

 

Since the airplane is moving at constant velocity it is experiencing zero acceleration, and the forces must balance. This means that the lift force (L) generated by the airplane wings must equal the airplane weight (W), and the thrust force (T) generated by the airplane engines must equal the drag force (D) caused by air resistance. This balance allows the plane to stay in te sky and produce a safe flight.

Taking off and Landing 

          An airplane undergoing takeoff, or landing, experiences similar forces acting on it. The figure below shows the typical forces acting on an airplane during takeoff. Note that the lift force (L) is defined as perpendicular to the velocity (V) of the plane relative to the air. The drag force (D) is defined as parallel to the velocity (V). As one would expect, the thrust force (T) is in the same direction as (V). The weight (W) of the plane points straight down in the direction of gravity. Now, W = mg, where m is the mass of the plane and g is the acceleration due to gravity, where g = 9.8 m/s². 

 

If the plane is moving at constant velocity with respect to ground then all the forces acting on the plane must be balanced. This means that in the vertical direction the sum of the forces is equal to zero, and in the horizontal direction the sum of the forces is equal to zero. Mathematically, in the vertical direction:

Equation: Lcosθ + Tsinθ - Dsinθ - W = 0

In the horizontal direction: 

Equation: Tcosθ - Dcosθ - Lsinθ = 0. 

If the plane is experiencing acceleration one can use these force equations, by including acceleration terms in the force equations, using Newton's second law.

Maneuvering and Navigation

             Airplanes control their navigation path and attitude (orientation relative to the direction of air flow) by adjusting physical elements on the outside of the airplane, elements which modify the airflow pattern around the plane, causing the plane to adjust its attitude and flight path. These physical elements are called control surfaces and consist of ailerons, elevators, rudders, spoilers, flaps, and slats. Adjusting a plane's flight path always involves either pitching, rolling, or yawing, or a combination of these. The figure below illustrates what these are. 

 

 

We can analyze this as follows. 

By Newton's second law, the force balance for the centripetal acceleration, in the lateral direction, is given by 

 

where θ is the bank angle, m is the mass of the plane, V is the velocity of the plane (normal to the page) with respect to ground, and R is the radius of the turn. 

The force balance in the vertical direction is given by 

 

Combine the above two equations to give the radius of the turn. We have 

 

sources:

http://www.portageinc.com/community/pp/flight.aspx

http://www.lcse.umn.edu/~bruff/bernoulli.html

http://www.real-world-physics-problems.com/how-airplanes-fly.html

https://www.grc.nasa.gov/www/k-12/airplane/forces.html