Physics of Flight
For my physics news I decided to look at the physics of flight. There are four main forces involved in flight. They consist of an upward force, lift, a downward force, weight, a forward force, thrust, and a backward force, drag. In order for flight to occur, lift must be greater than or equal to the weight and thrust must be equal to or greater than drag.
The wings of a plane are responsible for providing the lift. This concept can be explained by both Bernoulli’s principle and by Newton’s third law. As air currents pass by the wings of a plane, their shape, airfoil, establishes a differential pressure gradient. The distance the air has to travel is greater above the wing than below the wing. Since the air travels past the wing in the same amount of time, the air above the wing moves faster than the air below the wing. Bernoulli’s equation (P1 + .5pv1^2= P2 + .5pv2^2) indicates that this increase in speed causes a decrease in pressure above the wing and an increase in pressure below the wing. This unequal pressure causes dynamic lift, which pushes the plane upwards. The angle of the wing also plays a role in providing lift. The wing directs wind downwards as the plane flies. As established by Newton’s third law, the downward wind molecules push the wing in the opposite direction that they are traveling.
The thrust of the plane comes from the engine or propeller. Like lift, it also utilizes Newton’s third law. Air is sucked in to the engine and pushed backward. As the air moves back at a rapid rate, the plane gets pushed forward. With the aide of an engine, the air traveling back causes a greater force than the wind on the body of the plane.
Both Drag and weight limit the ability of the plane to fly. As wind hits the plane, it pushes the plane in the opposite direction that it wants to travel. In order to limit drag, planes have been designed to lower the surface area of the body. By doing this, the path of the air is less hindered, therefore causing less drag. The weight force is simply the force of gravity and the mass of the plane.
Now that I have explained the physics behind flight I will look specifically at the Boeing 747 jet airplane to mathematically show these principles.
Force Weight= mg
Force Thrust= ma
Force Lift= C* (.5pv^2) *wing A
Force Drag= C* (.5pv^2)*Total A
FT=(333,390kg)(a) FT= 4(223000N)
(4*223,000N)/333,390kg = 2.7m/s^2
Acceleration seemed slow to me but this is due to the fact that it is a commercial plane. They accelerate very slowly over a long period of time.
FW=FL 3267222N= C* (.5*1.29*(265.3m/s)^2*510.95m^2 C=.14 constant
FD=FT 892000N= .022* (.5*1.29*(265.3m/s)^2 *A A=893m^2