Forces and Flight

In discussing forces and flight, there are generally four primary forces discussed. As can be seen in the illustration below these forces are: (1) lift, (2) weight, (3) thrust, and (4) drag.

The first force we will discuss is that of weight. Weight is the force an object experiences as a result of gravity. Weight always acts downward and in this case, opposes lift. Weight is the force that must be "overcome" in order for a plane to lift off. The SI unit of weight is the Newton, and the mathematical equation for determining weight is:

W = mg

Where:

• m = mass (in kilograms)
• g = 9.81 m/s2 (acceleration due to gravity near the surface of the Earth)

Example: What is the weight of a small airplane which has a mass of 2800 kg?

W = mg
W = (2800kg)(9.81 m/s2)
W = 27,468 N

The second force is that of Lift. Lift is required to make and keep the aircraft airborne. In order for a plane to achieve liftoff the lift force must be greater than the force weight. The lift is perpendicular to the drag and thrust forces and is primarily produced as a result of Bernoulli's Principle. The equation for determining lift is:

L = (Cl)(.5)(p)(v2)(S)

Where:

• Cl = coefficient of lift (dimensionless unit)
• p = air density (kg/m3)
• v = velocity (m/s)
• S = wing area (m2)

As can be seen by the equation the pilot can change the lift by changing either the velocity of the plane or the wing area. The velocity is changed by either increasing or decreasing the thrust (provided by the engine). The pilot can change the wing area by extending or retracting the flaps on the wings. Next time you fly watch the wings during takeoff, you will notice initially that the flaps are fully extended, thus providing the greatest area resulting in an increase in lift. Shortly after takeoff you will hear a "grinding" noise, this is due to the flaps being retracted, thereby decreasing the surface area and the lift. Then, prior to landing you will hear the flaps being extracted, once again this is to increase the lift force. One might ask why not leave the flaps out and maximize lift all the time? The reason for this is that the extended flaps increase the total drag (which is a bad thing) and once airborne all the lift needed is that to overcome gravity.

I should point out the the coefficient of lift is a dimensionless quantity which indicates the lifting capability of an airfoil (wing). This value is general determined in a wind tunnel which includes varies Angles of attack (the angle between the wing and the relative wind) and frictional airfoil shapes. In addition, the pilot can change the coefficient of lift by changing the angle of attach.

Example: What is the lift produced by a plane that has a total wing area of 15-m2 and a velocity of 70 m/s. Assume the density of air to be 1.29-kg/m3 and the coefficient of lift to be .75.

L = (CL)(.5)(p)(v2)(S)
L = (.75)(.5)(1.29)(70)2(15)

L = 35555 N

The third force is that of thrust. This force is exerted on the atmosphere by the engine and is responsible for moving the aircraft forward. This forward motion is either achieved by "pushing" or "pulling" the aircraft. The thrust force must be greater than the drag force in order for the aircraft to move forward.

The fourth and final force is that of drag. This is the force that the atmosphere exerts on the aircraft that is opposite of the motion of the plane. This force is produced as a result of the friction of the air as it passes over the airplane. The greater the surface area exposed to the air the greater the drag.

Conclusion:

There are four primary forces (somewhat of an over simplification) involved with flight; these are thrust, drag, weight, and lift. In a constant unaccelerated flight, the sum of the forces acting on the plane is zero. In other words the weight must equal the lift and the thrust must equal the drag. An example is that in order to accelerate the plane in the forward direction the thrust must be greater than the drag and in order to land the plane the weight force must be greater than the lift force. This application is a good illustration of Newtonian Physics.

Wind Effects
How Does the Wind Effect Flight?

One primary influence of wind on flight is that of influencing the ground speed of the airplane and the direction of flight. The wind can influence the speed by either opposing the thrust force (head wind) or acting in the same direction as the thrust force (tail wind). In addition, it can also act perpendicular (crosswind) to the direction of thrust. All of these influences must be carefully considered when determining the length of flight as well as the direction the aircraft must fly in order to reach its final destination.

Example: An airplane traveling with a ground speed of 100m/s encounters a headwind of 20 m/s. (a) What is the new ground speed of the plane? (b) What is the ground speed if the wind is a tail wind?

(a) ground speed = 100m/s - 20m/s = 80m/s

(b)ground speed = 100m/s + 20m/s = 120m/s

As can be seen the "actual" speed of the aircraft (and therefore the time of a trip) is greatly influenced by the direction and speed of the wind!

 National Science Education Content Standards [9-12] Content Standard B: Motions and Forces[9-12] Content Standard E: Abilities of Technological Design[9-12] Content Standard G: Science as a Human Endeavor, Historical Perspectives Principles and Standards for School Mathematics [9-12] Number and Operations Standard: Compute fluently and make reasonable estimates. [9-12] Measurement Standard: Apply tools and formulas to determine measurements.[9-12] Data Analysis and Probability Standard: Develop and evaluate predictions based on data.[9-12] Problem Solving Standard: Build new mathematical knowledge through problem solving. [9-12] Connections Standard: Apply mathematics in contexts outside of mathematics.