# Physical Laws and Principles of Airflow #### Introduction There are several ways to explain how an airfoil generates lift. This publication discusses Newton’s laws of motion and Bernoulli’s principle. The “Newton” position is that lift is the reaction force on a body caused by deflecting a flow of gas, and the “Bernoulli” position is that lift is generated by a pressure difference across the wing. Both Bernoulli and Newton are correct, and we can use equations developed by each of them to determine the magnitude and direction of the aerodynamic force. *** ## Newton's Laws of Motion #### Overview Newton’s three laws of motion are inertia, acceleration, and action/reaction. These laws apply to the flight of any aircraft. A working knowledge of the laws and their applications assists in understanding aerodynamic principles discussed in this chapter. Interaction between the laws of motion and aircraft mechanical actions causes the aircraft to fly and allows aviators to control such flight. ### First Law: Inertia A body at rest will remain at rest, and a body in motion will remain in motion at the same speed and in the same direction unless acted upon by an external force. Nothing starts or stops without an outside force to bring about or prevent motion. Inertia is a body’s resistance to a change in its state of motion. For a constant mass, force ($$FF$$) equals mass ($$MM$$) times acceleration ($$AA$$), expressed in the formula ($$F=MAF=MA$$). Mass is then the property of matter that manifests itself as inertia. The force required to produce a change in motion of a body is directly proportional to its mass and rate of change in its velocity. Acceleration is a change in velocity with respect to time. It is directly proportional to force and inversely proportional to mass. This takes into account the factors involved in overcoming Newton’s First Law. It covers both changes in direction and speed, including starting up from rest (positive acceleration) and coming to a stop (negative acceleration or deceleration) expressed in the equation $$A=FMA=MF​$$. ### Third Law: Action/Reaction For every action, there is an equal and opposite reaction. When an interaction occurs between two bodies, equal forces in opposite directions are imparted to each body. In a helicopter, the rotor blades move air downward; consequently, the air pushes the rotor blades (and thus the helicopter) in the opposite direction (figure 1-1).
*** ## Bernoulli's Principle of Differential Pressure Bernoulli’s principle describes the relationship between internal fluid pressure and fluid velocity. It is a statement of the law of conservation of energy and helps explain why an airfoil develops an aerodynamic force. The concept of conservation of energy states energy cannot be created or destroyed and the amount of energy entering a system must also exit. A simple tube with a constricted portion near the center of its length illustrates this principle. An example is using water through a garden hose (figure 1-2). The mass of flow per unit area (cross-sectional area of the tube) is the mass flow rate. In figure 1-2, the flow into the tube is constant, neither accelerating nor decelerating; thus, the mass flow rate through the tube must be the same at stations 1, 2, or 3.
If the cross-sectional area at any one of these stations—or any given point—in the tube is reduced, the fluid velocity must increase to maintain a constant mass flow rate to move the same amount of fluid through a smaller area. Fluid speeds up in direct proportion to the reduction in area. Venturi effect is the term used to describe this phenomenon. Figure 1-3, page 1-3, illustrates what happens to the mass flow rate in the constricted tube as the dimensions of the tube change.
### Venturi Flow While the amount of total energy within a closed system (the tube) does not change, the form of the energy may be altered. Pressure of flowing air may be compared to energy in that the total pressure of flowing air always remains constant, unless energy is added or removed. Fluid flow pressure has two components—static and dynamic pressure. Static pressure is the pressure component measured in the flow but not moving with the flow as pressure is measured. Static pressure is also known as the force per unit area acting on a surface. Dynamic pressure of flow is that component existing as a result of movement of the air. The sum of these two pressures is total pressure. As air flows through the constriction, static pressure decreases as velocity increases. This increases dynamic pressure. Figure 1-4 depicts the bottom half of the constricted area of the tube, which resembles the top half of an airfoil. Even with the top half of the tube removed, the air still accelerates over the curved area because the upper air layers restrict the flow—just as the top half of the constricted tube did. This acceleration causes decreased static pressure above the curved portion and creates a pressure differential caused by the variation of static and dynamic pressures.
#### AIRFLOW AND THE AIRFOIL Airflow around an airfoil performs similarly to airflow through a constriction. As the velocity of the airflow increases, static pressure decreases above and below the airfoil. The air usually has to travel a greater distance over the upper surface; thus, there is a greater velocity increase and static pressure decrease over the upper surface than the lower surface. The static pressure differential on the upper and lower surfaces produces about 75 percent of the aerodynamic force, called lift. The remaining 25 percent of the force is produced as a result of action/reaction from the downward deflection of air as it leaves the trailing edge of the airfoil and by the downward deflection of air impacting the exposed lower surface of the airfoil. *** ## Vectors and Scalars Vectors and scalars are useful tools for the illustration of aerodynamic forces at work. Vectors are quantities with a magnitude and direction, while scalars are quantities described by size alone, such as area, volume, time, and mass. ### Vector Quantities Velocity, acceleration, weight, lift, and drag are examples of vector quantities. The direction of vector quantities is as important as the size or magnitude. When two or more forces act upon an object, the combined effect may be represented by the use of vectors. Vectors are illustrated by a line drawn at a particular angle with an arrow at the end. The arrow indicates the direction in which the force is acting. The length of the line (compared to a scale) represents the magnitude of the force. ### Vector Solutions Individual force vectors are useful in analyzing conditions of flight. The chief concern is with combined, or resultant, effects of forces acting on an airfoil or aircraft. The following three methods of solving for the resultant are most commonly used: parallelogram, polygon, and triangulation. ### Parallelogram Method This is the most commonly used vector solution in aerodynamics. Using two vectors, lines are drawn parallel to the vectors determining the resultant. If two tugboats push a barge with equal force, the barge moves forward in a direction that is the mean of the direction of both tugboats (figure 1-5).
### Polygon Method When more than two forces are acting in different directions, the resultant may be found by using a polygon vector solution. Figure 1-6, shows an example in which one force is acting at 90 degrees with a force of 180 pounds (vector A), a second force acting at 45 degrees with a force of 90 pounds (vector B), and a third force acting at 315 degrees with a force of 120 pounds (vector C). To determine the resultant, draw the first vector beginning at point 0 (the origin) with remaining vectors drawn consecutively. The resultant is drawn from the point of origin (0) to the end of the final vector (C).
### Triangulation Method This is a simplified form of a polygon vector solution using only two vectors and connecting them with a resultant vector line. Figure 1-7 shows an example of this solution. By drawing a vector for each of these known velocities and drawing a connecting line between the ends, a resultant velocity and direction can be determined.
### Vectors Used Figures 1-8 and 1-9, show examples of vectors used to depict forces acting on an airfoil segment and aircraft in flight.
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