Several theories are used to describe the lifting force experienced when presenting an aerofoil to airflow at an angle of attack. Bernoulli’s theorem, Newton’s Laws, as well as Coanda effect and a number of others each have their use and limitations when applied to quantify lift. A purist would tend to rely on the more traditional circulation and lifting line theories, and these are still used to this day to accurately predict the lifting characteristics of aerofoil section in testing (i.e., wind tunnels). In accordance with the CAA AC-61 for CPL Principles of Flight, we are only required to divulge into one of these theories, Bernoulli’s theorem. Its limitations need no further digression within this manual. If you were to put your hand out the window of a car as it travels down the road, you would feel a pressure increase on the underside of your hand. Your hand would probably be forced upwards and rearwards. A fairly simple example, but serves to demonstrate the basic principles involved.
Factors Affecting Lift
Before we jump into the factors that affect lift, we need to look at the lift formula.
From the above image, we can see that the lift formula can be broken down into its components:
Coefficient of lift (CL): This is a measure of the efficiency or ability of the aerofoil to produce lift. This value will change with camber and angle of attack. The convention is to consider angle of attack as the most direct method of changing CL. The coefficient of lift has no unit of measure and may have a value of 1.5, for example. This can be plotted against the angle of attack on a graph, as shown below. This is known as the coefficient of lift curve.
Dynamic pressure (½ ρv2): For practical purposes, this equates to indicated airspeed (IAS).
Surface area: This includes the entire wing plan area, as illustrated below.
Factors Affecting Lift
Any increase in any one of these factors will give an increase in lift.
Generally, at a given angle of attack, the greater the camber or curvature of the upper surface, the greater the amount of lift obtained from a given wing; conversely, the flatter and the thinner the wing, the less is the lift. This difference is caused by the greater acceleration of air over a highly cambered surface, resulting in a larger reduction in pressure. The measure of the lifting effectiveness of a wing under a given set of conditions is its lift coefficient (CL). The CL is not constant and varies with the angle of attack. Furthermore, various aerodynamic aids can be used to raise the lifting effectiveness of the wing, i.e., flaps, slots, and slats.
Experimentation and aerodynamic testing find the value of the CL for any given aerofoil.
The higher the CL, the lower the minimum speed at which a given wing can produce the required lift. This would clearly be an advantage for agricultural operations or STOL aircraft that have lift requirements at low speeds. If the surface area of the wing is unchanged (i.e., flaps retracted) and if ½ r v2 remains constant, then any increase in the CL results in an increase in lift (and vice versa). All other factors remaining constant, lift increases in proportion to the square of the aircraft speed. The amount of lift being produced is determined by the CL at that angle of attack.
Coefficient of Lift Curve
We have already seen the coefficient of lift curve. We are now going to have an in-depth look at this graph.
If the lift coefficient of a wing is plotted versus angle of attack, the result would be a typical lift curve. This graph contains a number of important points. Here, we are isolating the effect angle of attack has on lift.
Line of Zero Lift
The angle of attack where no lift is obtained is where the aerodynamic reaction is ‘symmetric’, i.e., the airflow over the top and the bottom of the aerofoil has the same distance to travel. This means there will be no difference in the pressure created on the top and bottom surfaces and no net resultant force. This typically occurs at about –2° angle of attack on a cambered aerofoil. With a CL of zero, this angle is called the zero-lift angle.
The streamline pattern will be similar to the figure below.
Over the upper and lower surfaces of the aerofoil, the streamlines come closer together, which indicates an increase in velocity. This can be visualised by realizing that as air strikes the aerofoil, it parts so that some air flows over the aerofoil and some flows under it. At the leading edge, the velocity slows to zero and a stagnation point exists. The airflow then speeds up over the upper and lower surfaces until it peaks at or near the point of maximum camber. It then begins to gradually decrease until where the upper and lower flows meet and the velocity again slows to zero.
Effect of Flaps on CL
Lowering the flaps produces an increase in the lift coefficient at a given airspeed by increasing the camber of the aerofoil, which changes the lifting characteristics. Note on the graph below the zero-lift angle for an aerofoil with flap lowered.
Ice or Damage
Ice or damage to an aerofoil is not an ideal situation. It adversely affects the lifting capabilities. With ice or damage on the aerofoil, the airflow over the wing cannot adhere to the wing to remain a laminar flow. The airflow breaks away early and becomes turbulent, reducing the production of lift. Hence, any wing with ice or damage will have reduced lifting capabilities, i.e., a lower maximum coefficient of lift.
It is important to note the difference between geometric and effective angle of attack. Geometric angle of attack refers to the chord line compared to the ‘remote’ airflow ahead of the aircraft that has yet to be disturbed by the upwash of the aerofoil.
The effective angle of attack is the angle between the chord line and the ‘local’ airflow after it has been disturbed or affected by the upwash. An aircraft might always stall at about 15 degrees effective angle of attack. However, the geometric angle will be higher, and with the use of high-lift devices such as slots and slats, it will be much higher indeed. The graphs in this manual showing aerofoils with high lift devices such as slats are referring to the geometric angle of attack and not the effective angle of attack. (Note some textbooks may refer to effective angle as induced angle, for reasons that will become apparent later.)
Discuss the following questions in class now.