Aerodynamic Lift and Drag and the Theory of Flight
The wings of birds were the original inspiration for the design of aerofoils however it was not until 1799 that engineer George Cayley carried out the first methodical study of the performance of aerofoils. His publication "On Aerial Navigation" in 1810, marked the beginning of the science of Aerodynamics. Since then, numerous fixed and variable aerofoil profiles have been developed, inspired by fish as well as birds, to optimise lift, drag and stalling characteristics over a wide range of speeds and through a variety of fluids.
Practical examples of the principles and basic forces involved are described below using the examples of Aircraft and Wind Turbines which both depend for their action on the flow of air around aerofoils.
Bernoulli's Theory of Flight
The Theory of Flight is often explained in terms Bernoulli's Equation which is a statement of the Conservation of Energy. It states that:
- For a non-viscous, incompressible fluid in steady flow, the sum of pressure, potential and kinetic energies per unit volume is constant at any point.
In other words, ignoring the potential energy due to altitude:
- When the velocity of a fluid increases, its pressure decreases by an equivalent amount to maintain the overall energy. This is known as Bernoulli's Principle
According to Bernoulli's Principle, the air passing over the top of an aerofoil or wing must travel further and hence faster that air the travelling the shorter distance under the wing in the same period but the energy associated with the air must remain the constant at all times. The consequence of this is that the air above the wing has a lower pressure than the air below below the wing and this pressure difference creates the lift.
Unfortunately Bernoulli's Principle does not explain how an aeroplane can fly upside down. Nor does it explain how aircraft and other structures with flat plate wings or even kites and paper aeroplanes can fly or remain airborne. This is where Newton's Laws come to the rescue. See below.
See also Daniel Bernoulli
Newton's Theory of Flight
Isaac Newton did not propose a theory of flight but he did provide Newton's Laws of Motion the physical laws which can be used to explain aerodynamic lift.
Newton's Second Law states that:
- The force on an object is equal to its mass times its acceleration or equivalently to its rate of change of momentum
F = M a = d/dt (M v)
In other words, whenever there is a change of momentum, there must be a force causing it. In this case, since momentum is a vector quantity, the change in direction of the airflow around the wing must be associated with a force on the volume of air involved.
Newton's Third Laws states that:
- To every action there is an equal and opposite reaction.
This means that the force of the aerofoil pushing the air downwards, creating the downwash, is accompanied by an equal and opposite force from the air pushing the aerofoil upwards and hence providing the aerodynamic lift.
It is thus the turning of the air flow which creates the lift.
See also Isaac Newton
Aircraft are kept in the air by the forward thrust of the wings or aerofoils, through the air. The thrust driving the wing forward is provided by an external source, in this case by propellers or jet engines.
The result of the movement of the wing through stationary air is a lift force perpendicular to the motion of the wing, which is greater than the downwards gravitational force on the wing and so keeps the aircraft airborne. The lift is accompanied by drag which represents the air resistance against the wing as it forces its way through the air. The drag is dependent on the effective area of the wing facing directly into the airflow as well as the shape of the aerofoil.
The magnitudes of the lift and drag are dependent on the angle of attack between the direction of the motion of the wing through the air and the chord line of the wing.
See more about the angle of attack and the theories of aerodynamic lift below.
See also details about the magnitude of Aerodynamic Lift and Drag and Missile Ballistics
Wind Turbine Blades
Wind Turbines extract energy from the force of the wind on an aerofoil, in this case a turbine blade. The relative motion between the air flow and the turbine blade, is the same as for the aircraft wing, but in this case the wind is in motion towards the turbine blades and the blades are passive so that the external thrust provided by the moving air flow is in the opposite direction to the thrust provided by the aircraft wing. The turbine blades thus experience lift and drag forces, similar to the aircraft wing, which set the blades in motion transferring the wind energy into the kinetic energy of the blades
The turbine blades are connected to a single rotor shaft and the force of the wind along the length of the blades creates a torque which turns the rotor.
As with aircraft wings, the magnitudes of the lift and drag on the turbine blade are dependent on the angle of attack between the apparent wind direction and the chord line of the blade.
See more deatils about Apparent Wind Direction
The dynamics of wind turbines is however slightly more complex than the dynamics of a simple wing because the direction of the gravitational force on the turbine blade changes with the rotation of the turbine rotor.
In a "theoretical" turbine with a single blade operating with a constant wind force, the magnitude and direction of the lift and drag with respect to the aerofoil profile will be constant throughout the full 360° rotation of the turbine rotor but the direction of the lift with respect to the ground will depend on the position of the rotor. The magnitude of the gravitational force on the blade will also be constant for any position of the rotor but the horizontal position of the centre of gravity of the blade with respect to the centre of the rotor will vary as the rotor turns. The net effect of these forces on the rotor torque depends on the position of the rotor.
- When the blade is horizontal and moving upwards it is moving against the force of gravity which is pulling the blade downwards so that the net lifting force on the blade and the resulting torque on the rotor is reduced.
- After 180° rotation of the rotor, the blade is once more horizontal but upside down and moving downwards so that the "lifting force" due to the wind is in the opposite direction and reinforces the downwards gravitational force so that the torque on the rotor is increased.
- When the blade is vertical, either at the top or the bottom of its cycle, the gravitational force is perpendicular to the lifting force and passes through the centre of the rotor shaft and hence has no effect on the torque which is purely due to lift.
Practical turbines however have multiple blades which balance each other, so that the gravitational effects cancel out and the torque on the rotor is constant.
See more details about Wind Power and Energy Conversion
The magnitude of the gravitational force on the aerofoil depends on the position and orientation of the turbine blade at any point during its 360° rotation and either augments or opposes the lift force. (See opposite)
Angle of Attack
The angle of attack of a turbine blade is the angle between the direction of the apparent or relative wind and the chord line of the blade. For an aircraft wing, it is the angle between the direction of motion of the wing and the chord line of the wing.
At very low angles of attack, the airflow over the aerofoil is essentially smooth and laminar with perhaps a small amount of turbulence occuring at the trailing edge of the aerofoil. The point at which laminar flow ceases and turbulence begins is known as the separation point.
Increasing the angle of attack increases the area of the aerofoil facing directly into the wind. This increases the lift but it also moves the separation point of laminar flow of the air above the aerofoil part way up towards the leading edge and the result of the increased turbulent flow above the aerofoil is an increase in the drag.
Maximum lift typically occurs when the angle of attack is around 15 degrees but this could be higher for specially designed aerofoils.
Above 15 degrees, the separation point moves right up to the leading edge of the aerofoil and laminar flow above the aerofoil is destroyed. The increased turbulence causes the rapid deterioration of the lift force while at the same time it dramatically increases the drag, resulting in a stall.
The graph opposite shows the lift and drag at different angles of attack experienced by a Clark Y aerofoil, a type widely used in general purpose aircraft designs. When moving through the air at constant speed, as the angle of attack is increased, both the lift and the drag increase until the aerofoil reaches a critical angle when the lift suddenly falls away and the aerofoil begins to stall, in this case, as the angle of attack approaches 20 degrees.
Since the lift generated by an aircraft wing is proportional to the angle of attack and also to the square of the aircraft speed, the same lift can be accomplished by flying at a higher speed with a lower angle of attack. Reducing the angle of attack also reduces the induced drag due to turbulence thus enabling greater aerodynamic efficiency. (See next)
Public Domain (Modified)
Aerodynamic Drag Components
Drag is the force experienced by an object representing the resistance to its movement through a fluid. Sometimes called wind resistance or fluid resistance, it acts in the opposite direction to the relative motion between the object and the fluid. The example opposite shows the aerodynamic drag forces experienced by an aerofoil or aircraft wing moving through the air with constant angle of attack as the air speed is increased..
The Total Aerodynamic Drag is the sum of the following components:
- Induced Drag - Due to the vortices and turbulence resulting from the turning of the air flow and the downwash associated with the generation of lift. Increases with the angle of attack. Inversely proportional to the square of the air speed. Decreases as aircraft speed increases and the angle of attack is reduced. Induced drag associated with the high angle of attack needed to maintain the lift is dominant at low air speeds.
- Form Drag or Pressure Drag - Due to the size and shape of the aerofoil. Increases with the square of air speed. Streamlined shapes designed to reduce form drag.
- Friction Drag - Arises from the friction of the air against the "skin" of the aerofoil moving through it. Increases with the surface area of the aerofoil and the square of air speed.
- Profile Drag or Viscous Drag- The sum of Friction Drag and the Form Drag.
- Parasitic Drag or Interference Drag - Incurred by the non-liftting parts of the aircraft such as the wheels, fuselage, tail fins, engines, handles and rivets. Increases with the square of air speed. Parasitic drag becomes dominant at higher air speeds.
- Wave Drag - Due to the presence of shock waves occurring on the blade tips of aircraft and projectiles. Associated with passing the sound barrier it is a sudden and dramatic increase in drag which only comes into play as the vehicle increases speed through transonic and supersonic speeds. Independent of viscous effects.
Sir George Cayley
The graph opposite is a modern day representation of results of experiments carried out by Sir George Cayley starting in 1799 and published in 1810.
It shows the superior lift characteristics and higher stall speed of aerofoils compared with a simple flat plate.
Cayley's aerofoils were based on the wings of birds.
His experiments were carried out many years before the advent of the wind tunnel and he used a Whirling Arm devised by John Smeaton in 1759 to provide a controlled airflow over his models.
See more about George Cayley and John Smeaton