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What is the primary factor that determines the amount of lift required to get an aircraft into the air?
What is the consequence of increased lift?
Why does an aircraft require more lift during a maneuver?
What is essential for a pilot to understand in order to comprehend an aircraft's performance?
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What is the result of increased drag?
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What is the force that opposes the thrust force and acts against the direction of the aircraft's motion?
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What is the result of the Earth's force of gravity acting on the aircraft's mass?
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What is the name of the force that sustains an aircraft in the air?
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What is the force that an aircraft needs to counter-balance its weight?
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What is the name of the force that propels an aircraft forwards through the air?
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What are the four principal forces acting on an aircraft in flight?
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Why does an aircraft need to be propelled forwards through the air?
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What is the purpose of the tailplane force?
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What is the mass of the air that fills a typical living room in an average family home?
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What happens to the air when a solid body moves through it?
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What determines the magnitude and direction of the reaction force on the body?
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What is the purpose of considering the diagram in Figure 3.2?
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What is the direction of the airflow at Point 1 in the diagram?
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What is the direction of the airflow at Point 2 in the diagram?
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What can be inferred about the air mass as it passes behind the box?
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What is the significance of the relative motion of the free-stream airflow in the diagram?
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What exerts a force on the air mass as it passes behind the box?
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What is the direction of the force exerted by the body of undefined characteristics on the air mass?
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What is the role of the wing in the scenario described?
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What is the purpose of analyzing the force exerted on the air mass behind the box?
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What principles of Physics must be considered to describe the generation of lift by a moving fluid?
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What level of mathematics is required for a complete discussion of lift?
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Why is a formal treatment of lift unnecessary for the average pilot?
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What is the purpose of this chapter's discussion of lift?
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Why do we assume air has zero viscosity when considering lift?
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What is the significance of the boundary layer near a wing's surface?
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Why do we need to consider air's viscosity when discussing drag?
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What is the implication of air's viscosity being low, but not zero?
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What is the assumption made about air in the context of airflow over an aircraft's wing?
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Under what condition does the airflow over an aircraft's wing become compressible?
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What is the speed of sound in the ICAO Standard Atmosphere at sea-level?
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What is the assumption made about air in the context of viscosity?
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Why is the assumption of incompressible air important for light aircraft pilots?
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What is the effect of compressing air?
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Why is the assumption of incompressible air made for low-speed flight?
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What happens when a child releases a blown-up balloon?
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What is the angle between the flat plate and the undisturbed airflow called?
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What is the name given to the component of the total reaction force acting at right angles to the relative airflow?
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What is the typical angle of attack for a light aircraft in steady, cruising flight?
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What happens to the air when a flat plate wing moves through it?
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What is the result of the total reaction force acting on the flat plate wing?
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What is the relative airflow in the context of an aircraft's wing?
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What is the primary advantage of using a wing with an aerofoil cross-section?
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How is the angle of attack measured on a wing with an aerofoil cross-section?
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What is the result of the airflow over a wing with an aerofoil cross-section compared to a flat plate wing?
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What is the key factor in the generation of lift by a wing with an aerofoil cross-section?
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Why is a wing with an aerofoil cross-section more efficient than a flat plate wing?
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What is the benefit of the curved surface of an aerofoil wing?
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What is the significance of the chord line in the context of a wing with an aerofoil cross-section?
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What is the importance of the ratio of the length of the lift vector to that of the drag vector for an aerofoil wing?
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Which two principles are used to explain how a wing moving through the air generates lift?
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Who formulated the equations that cover the conservation of energy within a moving fluid?
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What is the main difference between the Newtonian and Bernoulli explanations of lift?
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Why do aerodynamicists consider the Newtonian and Bernoulli explanations of lift as two perspectives of the same phenomenon?
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Who attempted to explain the phenomenon of lift?
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What is essential to understand lift generation by a moving fluid?
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What is the primary reason for the change in velocity of the airflow when it meets a wing?
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What happens to the airflow when a solid body moves through it?
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What is the result of a change in velocity of the airflow over a given time?
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What is the force that acts on the wing as a result of its motion through the air?
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Why is the wing more efficient than a flat plate in generating lift?
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What is the misconception about the airflow when it meets a wing?
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What is the effect of the wing's motion on the airflow?
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What is the relationship between the wing's shape and the airflow's direction?
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What is the force that the wing applies to the air to accelerate it?
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What is the principle expressed by Newton's 3rd Law of Motion?
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What is the quantity of motion possessed by a body or substance?
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What is the component of the total reaction force acting at right angles to the relative airflow?
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What is the result of the wing exerting a force on the air to change its velocity?
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What is the formula that expresses the force exerted by the wing on the air?
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What is the consequence of the wing imparting a downwash to the air?
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What is the principle that helps explain the nature of lift?
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What is the rate of change of momentum of the air proportional to?
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What is the purpose of considering the momentum implications in the production of lift?
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What is the primary factor that Bernoulli's Principle is concerned with?
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What happens to the pressure of a fluid when its velocity increases, according to Bernoulli's Principle?
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What is the result of drilling a small hole in the side of a pipe connected to the mains and closed off by a tap?
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What is the direction of the airflow changed to when air flows over a wing?
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What is the sum of the three types of energy in a system of fluid flow, according to Bernoulli's Principle?
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What is the consequence of the velocity of the airflow changing when air flows over a wing?
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What is the characteristic of the airflow near the surface of the wing?
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What is the significance of the observation that the velocity of the airflow varies in both magnitude and direction near the surface of the wing?
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What happens to the jet of water spurting from the hole when the tap is opened?
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What is the primary source of energy for the water in the pipe when the tap is closed?
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What is the relationship between the velocity of the air flowing over and under the wing?
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What is the direction of the force acting on the wing due to the pressure differential?
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What is the difference in airflow between a wing of aerofoil cross-section and a flat-plate wing?
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What is the result of the pressure differential across the wing?
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What is the relationship between the kinetic energy and pressure energy of the water?
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What is the effect of increasing the velocity of the main water stream on the jet of water spurting from the hole?
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What is the purpose of considering the airflow around a wing?
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What is the equation for force in relation to pressure and area?
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What is the point on a body through which the total reaction of all the aerodynamic forces affecting that body can be said to act?
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When an aircraft is in cruising flight, where is the Centre of Pressure approximately located?
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What is the angle of attack for an aircraft in cruising flight?
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What should not be confused with the Centre of Pressure?
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What is the total reaction of all the aerodynamic forces affecting a body composed of?
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What can be considered as an ideal fluid in airflow over a wing?
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What is the principle that explains the lift generated by a wing?
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What is the result of the downwards turning of air flowing around a wing?
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What is required to derive the equation that illustrates Bernoulli's Principle?
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Why is air considered an ideal fluid in the context of airflow over a wing?
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What is a streamline in the context of fluid flow?
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What is the direction of the velocity of a fluid particle at a point on a streamline?
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What is a region within a fluid flow containing a number of streamlines called?
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What is the principle that states that the mass of fluid flowing across two cross sections of a stream tube over any given period of time must be the same?
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What is the result of the Principle of Continuity?
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What is the significance of the Continuity Equation?
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What happens to the streamlines when the cross-sectional area of a stream tube decreases?
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What is the relationship between velocity and pressure in an ideal fluid?
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What is the direction of the net force acting on an aerofoil due to the pressure differential?
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What can be observed around an aerofoil at a small positive angle of attack?
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What is the significance of the stagnation point just under the leading edge of the aerofoil?
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What is the explanation for the lift force generated by an aerofoil?
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What is the relationship between the speed of the airflow over and under the wing?
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What is the result of the pressure differential across the wing?
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What is the principle that explains the variation of pressure with velocity in an ideal fluid?
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What is the fundamental relationship expressed in Bernoulli's Principle?
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Which of the following principles is NOT involved in the generation of lift by an aircraft wing?
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What is constant in an ideal fluid flow according to Bernoulli's Principle?
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What happens to the pressure of the fluid where the streamlines are widely spaced?
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What is the result of the Continuity Equation in terms of velocity and pressure?
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What is the underlying connection between Bernoulli's Principle and the two interpretations of lift?
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What is the implication of the streamlines being close together in a fluid flow?
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What is the purpose of drilling small holes into the upper and lower surfaces of an aerofoil in a wind tunnel?
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What happens to the static pressure over the upper surface of an aerofoil as the velocity of the airflow increases?
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What is the result of the pressure differential across an aerofoil, according to Bernoulli's Principle?
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What is the direction of the force exerted by the static pressure differential across an aerofoil?
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What is the relationship between total pressure and velocity in the airflow around an aerofoil, according to Bernoulli's Principle?
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What is the name of the pressure that an airflow exerts on an object due solely to its initial velocity?
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What is the name of the pressure that acts in all directions in an airflow?
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What is the total pressure of an airflow equal to?
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What is the purpose of the flat plate attached to a spring in Figure 3.15?
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What happens when moving air is brought to rest?
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What is the result of the dynamic pressure exerted on the object in Figure 3.15?
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What can be felt when holding a hand out of the window of a moving car?
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What is the relationship between total pressure and dynamic pressure in an airflow?
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What does ½ ρv² represent in Bernoulli’s Equation?
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What is the total pressure of the airflow in Bernoulli’s Equation?
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What is the direction of the aerodynamic force acting on the wing?
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What is the point on the wing through which the total reaction of all the aerodynamic forces acts called?
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What can be inferred from the streamlines in Figure 3.18?
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What happens to the stagnation point in the airflow at an angle of attack of about -5°?
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At what angle of attack is the upward-acting force equal to the downward-acting force?
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At what angle of attack is the stagnation point on the lower surface of the wing?
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According to NASA, what generates the net fluid force on a wing?
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Study Notes
Forces Acting on an Aircraft in Flight
- An aircraft in flight is affected by four main forces: weight, lift, thrust, and drag.
Weight
- Weight is the force exerted on an aircraft by the Earth's gravity, acting vertically downwards towards the center of the Earth.
- An aircraft's weight is equivalent to the force of gravity acting on its mass.
Lift
- Lift is the force that counter-balances an aircraft's weight, acting in the opposite direction.
- Lift is generated by the flow of air over an aircraft's surfaces, primarily its wings.
- The greater the weight of an aircraft, the more lift is required to get it into the air and maintain steady, straight flight.
Thrust
- Thrust is the force that propels an aircraft forward through the air, counter-acting drag.
- Thrust is required to create the flow of air over the wings, which generates lift.
Drag
- Drag is the force that opposes thrust, acting against the direction of an aircraft's motion.
- An increase in lift causes drag to increase, requiring more thrust to balance it.
Interrelationship of Forces
- The four principal forces are interconnected: a change in one force affects the others.
- Understanding the interrelationship of forces is crucial for a pilot to understand their aircraft's performance in various phases of flight or maneuvers.
Lift and Its Primary Cause
- Lift is the force that sustains an aircraft in the air and enables it to maneuver.
- Air possesses mass, which is a crucial property in generating lift.
- The mass of air in a typical living room is approximately 60 kilograms (132 pounds).
Displacement of Air Mass
- When a solid body moves through air, it displaces the air mass, causing an opposing force to be exerted on the body.
- The magnitude and direction of the reaction force depend on the body's motion and shape.
Generation of Lift
- Lift is generated by the displacement of air mass caused by a body moving through it.
- The direction of the reaction force on the body is opposite to the direction of the force exerted on the air mass.
The Role of the Wing
- The wing of an aircraft is an example of a body that displaces air mass, generating lift.
- The upwards reaction force experienced by the wing contributes to the force of lift.
- The shape and orientation of the wing affect the generation of lift.
Newton's Laws of Motion
- Newton's First Law of Motion states that a moving mass will continue to move at constant speed in a straight line unless acted on by a force.
- Newton's Third Law of Motion states that every action has an equal and opposite reaction.
The Nature of Lift
- Generation of lift by a moving fluid involves considering multiple laws of Physics
- Three principles are simultaneously considered:
- Principle of conservation of mass
- Principle of conservation of momentum
- Principle of conservation of energy
Limitations of Lift Theory
- A complete scientific discussion of how a wing produces lift would be complex and require advanced mathematics
- Such a formal treatment of lift is beyond the scope of this book and unnecessary for the average pilot
Assumptions in Aircraft Lift Generation
- Air is assumed to be an ideal fluid, allowing for three major assumptions about airflow properties.
- Incompressibility of Airflow: Airflow over a wing is assumed to be incompressible, maintaining constant density, as long as the speed is low (less than Mach 0.5) and constant altitude.
- Air can be compressed, but not during low-speed flight; compressibility becomes an issue at high speeds (Mach 0.5 or higher).
- The speed of sound at sea-level is approximately 662 knots (340.3 m/s or 1,116.4 ft/s), ensuring light aircraft fly at far less than half that speed.
Properties of Airflow
- Viscosity of Airflow: Air is assumed to be inviscid (zero viscosity), which is close to reality, except in the boundary layer (very thin layers next to the wing surface).
- Air's low viscosity is neglected when considering lift, but it must be accounted for when discussing drag.
- Steady Flow: Airflow around the wing is assumed to be steady, meaning the pattern of airflow doesn't change with time.
- At any given point in the airflow, velocity is constant, despite varying velocities at different points in the flow.
The Flat-Plate Wing
- A flat plate wing can change the direction of a horizontal airflow by moving through the air at a small positive angle to the airflow.
- The angle between the plate and the undisturbed airflow is called the angle of attack (α).
- The angle of attack is the angle between the wing and the relative airflow.
- In steady, cruising flight, a light aircraft typically has an angle of attack of around 4º.
Airflow and Reaction Force
- When a flat plate wing moves through the air, it induces a small upwash in front of the plate and a small downwash or downturn behind it.
- This "turning" of the air mass causes a reaction force to act on the flat plate wing, directed both backwards and upwards.
- The reaction force is called the total reaction.
- The total reaction force is the sum of the forces acting on the flat plate wing due to its motion through the air.
Components of the Total Reaction
- Lift is the component of the total reaction force acting at right angles to the relative airflow.
- The component of the total reaction force acting in the direction of the relative airflow is called drag.
- Drag is the subject of Chapter 5.
Wing Design Evolution
- Early aviation experiments used thin, flat, rectangular wing cross-sections, but pioneers soon discovered that curved cross-sections similar to bird wings produced more lift with less drag.
Aerofoil Cross-Section Advantages
- Wings with aerofoil cross-sections have a smooth airflow, which reduces turbulence and increases efficiency in producing downward airflow, resulting in more lift.
- The curved surface and depth of aerofoil cross-sections enable wings to be built with structural strength required for higher-performance aircraft.
- The angle of attack on an aerofoil wing is measured as the angle between the undisturbed relative airflow and the chord line (joining the leading and trailing edges).
Comparison to Flat Plate Wings
- Airflow over an aerofoil wing is much smoother than over a flat plate wing at equal angles of attack.
- Aerofoil wings have less turbulence, less tilted total reaction, and a higher lift-to-drag vector ratio, making them more efficient lifting surfaces than flat plates.
Importance of Lift/Drag Ratio and Angle of Attack
- The lift/drag ratio and angle of attack will be explored in later chapters, highlighting their significance in wing design.
Understanding Lift Generation
- Lift generation can be explained by considering three principles of physics: conservation of momentum, conservation of mass, and conservation of energy.
- The laws of motion by Sir Isaac Newton concern the conservation of momentum.
- The principle of conservation of energy in a moving fluid is covered by Daniel Bernoulli's equations.
- The work of both Newton and Bernoulli contributes to the full explanation of lift generation.
Newtonian Explanation of Lift
- The Newtonian explanation is based on the concept of force as defined by the rate of change of momentum.
- This explanation is viewed as one perspective of the lift-generation phenomenon.
Bernoulli Explanation of Lift
- The Bernoulli explanation is based on the Principle of the Conservation of Mass and Energy.
- Aerodynamicists have applied Bernoulli's work to explain lift, although Bernoulli himself did not attempt to explain the phenomenon.
- The Bernoulli explanation is viewed as another perspective of the lift-generation phenomenon, complementary to the Newtonian explanation.
The Newtonian Explanation of Lift
- Lift is generated by a wing turning the air downwards, resulting in a reaction force acting upwards on the wing.
- A wing with an aerofoil cross-section is more efficient than a flat plate in turning air downwards and generating lift.
Misconception of Air Deflection
- The air is not deflected downwards by "bouncing" off the inclined underside of the wing.
- Instead, the wing turns the air downwards due to the fluid's tendency to stay in contact with the body and be influenced by its shape or angle of inclination.
Wing's Action on Airflow
- The wing changes the direction of flow of an air mass, resulting in a change in velocity.
- This change in velocity is equivalent to an acceleration, which is a rate of change of velocity.
- The wing applies a force to the air to accelerate it, given by the formula: Force = mass × acceleration.
Reaction Force and Lift
- The change in velocity of the air generates a reaction force on the wing, acting in an upwards direction.
- This reaction force is the total reaction, with the component acting at right angles to the relative airflow being the lift force.
- The higher the aircraft's speed, the greater the lift force.
Momentum Implications
- The air possesses momentum due to its mass and velocity relative to the moving wing.
- Momentum is related to mass and velocity as: Momentum = mass × velocity.
- The wing brings about a change in momentum of the air by imparting a downwash.
- The wing must exert a force on the air to change its momentum, given by Newton's 2nd Law.
Conservation of Momentum
- The principle of conservation of momentum states that any physical substance in motion will continue moving at the same velocity unless acted upon by a resultant force.
- The wing's force on the air results in a change in momentum, which is proportional to the rate of change of momentum.
- The reaction force experienced by the wing is an equal and opposite reaction, as predicted by Newton's 3rd Law.
Lift Force Formula
- The lift force can be expressed by the formula: F = m × (v2 - v1) / t, which is equivalent to F = m × a.
- The lift force is the vertical component of the total reaction, acting perpendicularly to the relative airflow.
Bernoulli's Explanation of Lift
- The Bernoulli explanation of lift is based on the principle of energy conservation, which states that the total energy in a moving fluid remains constant.
- The total energy of a fluid consists of potential energy, kinetic energy, and energy due to pressure.
- According to Bernoulli's Principle, an increase in velocity (kinetic energy) causes a decrease in pressure, and vice versa.
Experiment to Illustrate Bernoulli's Principle
- An experiment with a water pipe connected to the mains and a small hole drilled in the side illustrates Bernoulli's Principle.
- When the tap is closed, the water in the pipe has no velocity, and all its energy is in the form of pressure energy.
- When the tap is opened, the water begins to flow, and its kinetic energy increases, causing its pressure energy to decrease.
- As the velocity of the water flow increases, the jet of water spurting from the hole gets shorter, demonstrating the inverse relationship between velocity and pressure.
Application of Bernoulli's Principle to Lift
- The measurement of steady, horizontal airflow around a wing shows that the air flowing over the upper surface increases in speed, while the air flowing under the lower surface decreases in speed.
- According to Bernoulli's Principle, the pressure at the upper surface is lower than at the lower surface, creating a pressure differential that generates a force acting in an upward direction.
- The lift force is proportional to the pressure differential across the wing multiplied by the surface area of the wing.
Comparison of Aerofoil and Flat-Plate Wings
- A wing of aerofoil cross-section is more efficient than a flat-plate wing in producing the downwards turning of the airflow, which leads to differences in velocity.
- As a result, the pressure differential across an aerofoil wing is greater, leading to a greater lift force and lower drag for the same wing surface area.
Centre of Pressure
- Total reaction and its components (lift and drag) originate from the Centre of Pressure.
- Defined as the point on a body where the total reaction of all aerodynamic forces affecting that body can be said to act.
- In cruising flight, the Centre of Pressure is located approximately 1/3 of the way back from the wing's leading edge.
- Angle of attack is small, around 4º, during cruising flight.
Important Distinction
- Centre of Pressure is not the same as the Centre of Gravity.
- Centre of Gravity is the point through which the total weight of the aircraft acts.
Low-Speed Airflow over a Wing
- Variations in velocity and pressure within a mass of air flowing around an aerofoil can account for the lift generated by a wing.
- Bernoulli's Principle applies to the flow of an ideal fluid, and air can be considered an ideal fluid as long as the velocity of the airflow over a wing is less than half the local speed of sound.
Understanding Bernoulli's Principle
- The principle states that the velocity of air is changing, which can be observed by the downwards turning (change in direction) of air flowing around a wing.
- To understand the equation that illustrates Bernoulli's Principle, we need to define two important terms used when describing fluid flow: streamlines and mass flow.
Key Concepts
- Streamlines: a concept used to describe fluid flow.
- Mass flow: a concept used to describe fluid flow.
Streamlines
- A streamline is an imaginary line within a steady flow of an ideal fluid.
- At every point on a streamline, the velocity of a fluid particle is always at a tangent to the line.
- In the steady flow of an ideal fluid, only one streamline can pass through any given point within the airflow.
- Streamlines cannot cross because, if they did, a fluid particle would be moving in two directions at once, which is impossible.
Stream Tube
- A stream tube is a region within a fluid flow containing a number of streamlines.
- Every fluid particle passing through a point on a streamline has a specific velocity.
- Example: fluid particles arriving at Point 1 have velocity v1, those at Point 2 have velocity v2, and those at Point 3 have velocity v3.
The Continuity Equation (Conservation of Mass)
- The Continuity Equation states that the rate of mass flow at Point 1 is the same as the rate of mass flow at Point 2 in a stream tube.
- Mass flow is considered as mass per unit time, and density (ρ) is equal to mass per unit volume.
- The equation for mass flow is: ρAv
- Since ρ is a constant for an incompressible fluid, the Continuity Equation can be simplified to: A1v1 = A2v2
- The product Av is constant for any region of flow of an ideal fluid.
Interpretation of the Continuity Equation
- If the cross-sectional area (A) of a stream tube increases, the velocity (v) of the fluid must decrease, and vice versa.
- Widely spaced streamlines indicate a lower flow velocity, while tightly packed streamlines indicate a higher velocity.
- An increase in cross-sectional area results in a decrease in velocity, and a decrease in cross-sectional area results in an increase in velocity.
Application to Airflow around an Aerofoil
- In the steady, horizontal flow of an ideal (incompressible) fluid, the internal pressure of the fluid is greatest where the speed of the airflow is lowest, and vice versa.
- The study of airflow around aerofoils is often conducted in a wind tunnel, and visible streamlines can be created using smoke.
- The streamlines around an aerofoil angled to the relative airflow at a small positive angle of attack show that the airflow speed is higher over the upper surface of the wing than underneath.
- The pressure differential across the wing generates a net force (pressure differential × wing area) acting in an upwards direction, resulting in lift force.
Bernoulli's Principle
- Bernoulli's Principle expresses the relationship between pressure variations and velocity changes in a fluid flow.
- It is derived from Newton's Laws and reveals a fundamental connection between pressure differential and rate of change of momentum.
Lift Generation
- The generation of lift by an aircraft wing involves three fundamental principles of Physics: Conservation of Momentum, Conservation of Mass, and Conservation of Energy.
- Bernoulli's Principle concentrates on the Conservation of Energy and is inevitably linked to the other two principles.
Conservation of Mass
- The Continuity Equation expresses the Conservation of Mass, stating that the rate of mass flow of an ideal fluid is constant at all points along a stream tube.
- The Continuity Equation indicates that where streamlines are widely spaced, a lower velocity of flow is present, and where streamlines are close together, a higher flow-velocity is present.
- The pressure of the fluid is greatest where the speed of flow is lowest, and vice versa.
Bernoulli's Principle and Energy
- Bernoulli's Principle states that the total energy within an ideal fluid flow is constant.
- For a horizontal flow of ideal fluid, the total energy in the airflow consists of the kinetic energy of airflow (due to its mass and velocity) and the airflow's pressure energy (due to the pressure of the air acting in all directions within the flow).
Dynamic and Static Pressure in Airflow
- When moving air is brought to rest, its kinetic energy does work on the object that brings it to rest, applying a force and exerting pressure due to its initial velocity, known as dynamic pressure.
- Dynamic pressure can be approximately registered by a flat plate attached to a wall by a spring, where the compression of the spring is due to the dynamic pressure alone.
- Dynamic pressure can be felt by holding a hand out of a moving car window with the palm perpendicular to the airflow.
Bernoulli's Principle and Static Pressure
- Bernoulli's Principle states that Total Pressure = Dynamic Pressure + Static Pressure = Constant.
- Static pressure refers to the pressure energy in an airflow that acts in all directions, not ambient atmospheric pressure.
- In airflow around an aircraft wing, static pressure varies, with the highest pressure at the stagnation point, just under the leading edge of the aerofoil.
Pressure Distribution around an Aerofoil
- Over the upper surface of the wing, where velocity increases, dynamic pressure increases and static pressure falls.
- Below the wing, where velocity decreases, static pressure increases and dynamic pressure falls.
- The pressure differential across the aerofoil accounts for the lift force that acts upwards from the area of higher pressure to the area of lower pressure.
Bernoulli's Equation
- Bernoulli's Principle can be expressed mathematically as an equation.
- The equation is derived for air of density ρ, flowing horizontally over an aircraft flying at a velocity v, under ideal fluid assumptions.
- The equation is: p + ½ ρv² = constant
- ½ ρv² represents the dynamic pressure of the air flow, also referred to as Q.
- p represents the static pressure in the airflow.
- The total pressure of the airflow, p + ½ ρv², is a constant.
Relationship between Velocity and Pressure
- An increase in velocity results in an increase in dynamic pressure.
- An increase in velocity results in a reduction in static pressure.
Bernoulli's Equation and Lift Force on a Wing
- A wing with an aerofoil cross-section in a wind tunnel with smoke introduced to visualize streamlines, with a small positive angle of attack (between +2° and +8°) between the wing and relative airflow.
- The wing's turning effect on the airflow causes a rate of change of momentum in the air mass, leading to variations in airflow velocity around the wing.
Streamlines and Airflow Velocity
- Streamlines are closer together above the wing's upper surface and farther apart below the wing's under surface.
- Widely spaced streamlines indicate lower air velocity, while closely spaced streamlines indicate higher air velocity.
Bernoulli's Equation and Pressure Variation
- Bernoulli's Equation (p + ½ ρv² = constant) shows that variations in airflow velocity result in corresponding variations in static and dynamic pressure.
- Where speed is highest, dynamic pressure is highest, and static pressure is lowest; conversely, where speed is lowest, dynamic pressure is lowest, and static pressure is highest.
Pressure Distribution and Lift Force
- The pattern of pressure distribution over the wing shows higher static pressure beneath the wing and lower static pressure above the wing, resulting in a pressure differential and lift force.
- The aerodynamic force acts from the higher static pressure beneath the wing to the lower static pressure above the wing.
- The pressure differential is not evenly distributed, with the greatest difference in pressure over the wing's forward section.
Relation between Airflow Speed and Lift Force
- As the speed of the free-stream airflow increases, the pressure differential across the wing increases, resulting in a greater lift force.
- The point on the wing where the total reaction of all aerodynamic forces acts is called the Centre of Pressure.
Variation of Lift and Pressure Distribution with Angle of Attack
- The pattern of lift and pressure distribution around a wing with an aerofoil cross-section changes with angle of attack.
- Angle of attack is the angle between the aerofoil's chord line and the relative (free stream) airflow, represented by the symbol α (Greek letter "alpha").
- At an angle of attack of about -5°, the stagnation point is on the upper surface of the wing, resulting in negative lift.
- At an angle of attack of around -2°, the upward and downward acting forces are equal, resulting in zero lift, but with a nose-down pitching moment.
- At 0° angle of attack, there is a net upward-acting lift force, but with a nose-down pitching moment.
- At 2° angle of attack, the stagnation point is on the lower surface of the wing, resulting in positive lift.
- During flight, the angle of attack is usually between 2° and 8°, but during stall recovery training, angles of attack of 16° and greater are experienced.
- As the angle of attack increases from 2° to 15°, the Centre of Pressure moves forward, and the resultant lift force increases in magnitude, reaching a typical stalling angle of attack around 16°.
- Beyond 16°, the lift force decreases abruptly, and the Centre of Pressure moves rearward due to airflow separation from the wing's upper surface.
- The gradual forward movement of the Centre of Pressure with increasing angle of attack can lead to instability, which is why conventional aircraft have tailplanes (horizontal stabilisers).
- The greater contribution to lift is made by the upper surface of the wing, especially at angles of attack from 2° to 15°.
- Keeping the upper surface of an aircraft wing free from contamination is critical.
Angle of Attack
- The angle of attack is the angle between the aerofoil's chord line and the relative (free stream) airflow.
- Do not confuse angle of attack with pitch attitude of the aircraft.
Angle of Attack vs. Pitch Attitude
- Pitch attitude is the angle of the aircraft's nose relative to the horizon.
- Pitch attitude is not a good indication of angle of attack, as the aircraft is rarely following the line of flight in which its nose is pointing.
Effect of Angle of Attack on Flight
- At a given aircraft weight, a given angle of attack corresponds to a particular airspeed.
- Increasing angle of attack (by raising the nose) allows the aircraft to fly slower.
- Decreasing angle of attack (by lowering the nose) allows the aircraft to fly faster.
Angle of Attack in Different Flight Scenarios
- The angle of attack remains the same at a given airspeed, regardless of whether the aircraft is descending, flying level, or climbing.
- Pitch attitude and power will differ in each scenario, despite the same airspeed and angle of attack.
The Nature of Lift
- Both Bernoulli and Newtonian explanations accurately predict the magnitude and direction of the resultant aerodynamic force acting on a wing.
- The aerodynamic lift generated by a wing is accounted for by two factors:
- The rate of change of momentum of the downwards deflected airflow over the wing (Newtonian explanation).
- The pressure differential across the wing (Bernoulli's explanation).
- Bernoulli's Principle is ultimately derived from Newton's Laws.
- Both Bernoulli and Newtonian predictions of the lift force are accurate and measurable in a wind tunnel.
NASA's Explanation of Lift
- Lift and drag are mechanical forces generated on the surface of an object as it interacts with a fluid.
- The net fluid force is generated by the pressure acting over the entire surface of a closed body (Bernoulli's Principle).
- Pressure varies around a body in a moving fluid because it is related to the fluid momentum (mass × velocity).
- Velocity varies around the body due to flow deflection (Newton's explanation).
The General Lift Equation
- The Lift Equation is a formula that takes into account the shape of the aerofoil, angle of attack, airspeed, air density, and wing surface area to calculate the lift produced by an aerofoil.
- The formula is: Lift = CL ½ ρ v² S, where CL is the coefficient of lift, ρ is air density, v is airspeed, and S is wing surface area.
Coefficient of Lift (CL)
- CL represents the shape of the aerofoil and its angle of attack with the relative airflow.
- CL has no units.
- By increasing the angle of attack, the pilot can increase CL and thus increase the lift produced by the wing, but not beyond the angle of attack for maximum lift.
Factors Affecting Lift
- Lift is directly proportional to air density, wing area, and the square of the airspeed.
- Lift is directly proportional to the Coefficient of Lift (CL), which represents the shape of the wing and angle of attack.
Practical Applications for Pilots
- The Lift Equation reveals that the pilot has direct control over the lift produced by the wings through control of airspeed.
- By increasing airspeed, the pilot can increase lift fourfold, and by decreasing airspeed, the pilot can reduce lift.
- The pilot can also modify the shape of the wing and thus the value of CL by selecting or deselecting flaps.
Relationship between Speed and Angle of Attack
- For any phase of straight, steady flight, the aircraft's weight must be exactly balanced by lift.
- Any change in airspeed requires a corresponding change in CL to maintain steady flight.
- The pilot can control the angle of attack to maintain steady flight.
- In steady, straight flight, airspeed is determined primarily by angle of attack.
Fundamental Principles of Flying
- The pilot controls angle of attack by selecting an appropriate pitch attitude with the control column or control wheel.
- The pilot uses the throttle to adjust engine power to maintain level flight, or a constant rate of descent or climb.
- The Lift Equation reveals the fundamental relationships that affect the performance of an aircraft.
Variation of Coefficient of Lift with Angle of Attack
- A wing with a non-symmetrical aerofoil cross-section produces a net lift force even at 0º angle of attack and small negative angles of attack.
- A flat plate and a symmetrical aerofoil would generate no lift at 0º angle of attack.
- The graph of Coefficient of Lift (CL) vs. angle of attack shows a uniform increase in lift between 0º and 12º angle of attack.
- Beyond 12º angle of attack, the graph curves over towards a maximum value of lift, with only a small increase in lift.
- Lift reaches a maximum at about 15º to 16º angle of attack.
- Above 15º to 16º angle of attack, the graph curves downwards, indicating a decrease in lift.
- A small increase in angle of attack leads to an increase in lift for small angles of attack.
- A further increase in angle of attack beyond the maximum lift angle causes a rapid decrease in lift.
- The angle at which lift begins to decrease is called the stalling angle of attack.
- A wing stalls at a given angle of attack, not at a given speed.
Lift Force Generation
- Lift force is generated by an aircraft wing due to the relative motion between the air and the wing.
- Three scientific principles are involved in the motion of a wing through the air: Conservation of Mass, Conservation of Momentum, and Conservation of Energy.
Newton's Laws and Bernoulli's Principle
- Newton's Laws of Motion (Conservation of Momentum) explain lift generation as a reaction to the downward turning of the airflow.
- Bernoulli's Principle (Conservation of Energy) explains lift generation as a result of the upward-acting pressure differential across the wing.
- Both explanations are valid and viewed as two perspectives of the same phenomenon.
The Lift Equation
- The Lift Equation is: Lift = CL½ ρv²S.
- This equation helps the pilot understand the factors affecting lift and airspeed.
- Factors influencing lift include:
- Angle of attack
- Wing cross-section shape
- Air density
- Airspeed
- Wing area
Importance for Pilots
- Understanding the basic nature of lift is essential for pilots.
- The pilot should have a good basic understanding of how the lift force is acting on the aircraft in flight, regardless of the maneuver being performed.
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Description
Learn about the fundamental forces acting on an aircraft in flight, including weight and lift. Discover how gravity and mass interact to affect an aircraft's motion.
