Chapter

5

Lift

Aerodynamic Force Coefficient . . . . . . . . . . . . . . . . . . .	. .	. .	.	71
The Basic Lift Equation . . . . . . . . . . . . . . . . . . . . . .	. .	. .	.	72
Review: . . . . . . . . . . . . . . . . . . . . . . . . . . . .	. .	. .		.75
The Lift Curve . . . . . . . . . . . . . . . . . . . . . . . . . .	. .	. .		.76
Interpretation of the Lift Curve . . . . . . . . . . . . . . . . . . .	. .	. .	.	76
Velocity - Dynamic Pressure Relationship . . . . . . . . . . . . . . . .	. .	. .		.79
Density Altitude				79
Aerofoil Section Lift Characteristics . . . . . . . . . . . . . . . . . .	. .	. .		.79
Introduction to Drag Characteristics				80
Lift/Drag Ratio . . . . . . . . . . . . . . . . . . . . . . . . .	. .	. .	.	80
Effect of Aircraft Weight on Minimum Flight Speed . . . . . . . . . . . .	. .	. .		.82
Condition of the Surface . . . . . . . . . . . . . . . . . . . . . .	. .	. .		.82
Flight at High Lift Conditions				82
Three Dimensional Airflow				85
Wing Terminology . . . . . . . . . . . . . . . . . . . . . . . .	. .	. .		.85
Wing Tip Vortices . . . . . . . . . . . . . . . . . . . . . . . .	. .	. .	.	86
Wake Turbulence: (Ref: AIC P 072/2010) . . . . . . . . . . . . . . . .	. .	. .		.88
Ground Effect . . . . . . . . . . . . . . . . . . . . . . . . . .	. .	. .		.91
Conclusion				96
Summary				98
Answers from page 77 . . . . . . . . . . . . . . . . . . . . . .	. .	. .	.	99
Answers from page 78 . . . . . . . . . . . . . . . . . . . . . .	. .	. .	. 100
Questions . . . . . . . . . . . . . . . . . . . . . . . . . . .	. .	. .	101
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . .	. .	. .	108

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Lift 5

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Lift 5

Aerodynamic Force Coefficient

The aerodynamic forces of both lift and drag depend on the combined effect of many variables. The important factors are:

•	Airstream velocity (V)	} Dynamic Pressure ( ½ ρ V2)
•	Air density (ρ)
• Shape or profile of the surface			}	Pressure Distribution (CL or CD)
•	Angle of attack

•Surface area (S)

•Condition of the surface

•Compressibility effects (to be considered in later chapters)

Dynamic Pressure

The dynamic pressure (½ ρ V2) of the airflow is a common denominator of aerodynamic forces and is a major factor since the magnitude of a pressure distribution depends on the energy given to the airflow (KE = ½ m V2).

Pressure Distribution

Another major factor is the relative pressure distribution existing on the surface. The distribution of velocities, with resulting pressure distribution, is determined by the shape or profile of the surface and the angle of attack (CL or CD).

Surface Area

Since aerodynamic forces are the result of various pressures distributed on a surface, the surface area (S) is the remaining major factor - the larger the surface area for a given pressure differential, the greater the force generated.

Thus, any aerodynamic force can be represented as the product of three major factors:

•The dynamic pressure of the airflow (½ρ V2 )

•The coefficient of force determined by the relative pressure distribution (CL or CD),

and

• The surface area of the object (S)

The relationship of these three factors is expressed by the following equation:

F = Q CF S

where

F = aerodynamic force (Lift or Drag)

Q = dynamic pressure (½ρ V2)

CF = coefficient of aerodynamic force (CL or CD)

S = surface area

Lift 5

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The Basic Lift Equation

Lift is defined as the net force generated normal (at 90°) to the relative airflow or flight path of the aircraft.

The aerodynamic force of lift results from the pressure differential between the top and bottom surfaces of the wing. This lift force can be defined by the following equation:

L = 1/2 ρ V2 CL S

Correct interpretation of the lift formula is a key element in the complete understanding of Principles of Flight.

Figure 5.1

Note: For the sake of clarity; during this initial examination of the lift formula it is stated that CL is determined by angle of attack. This is true, but CL is also influenced by the shape or profile of the surface and other factors which will be amplified in later sections.

•An aircraft spends most of its time in straight and level flight.

•How much lift is required? The same as the weight.

•Consider that at any moment in time weight is constant, so lift must be constant.

•While generating the required lift force, the less drag the better because drag has to be balanced by thrust, and thrust costs money.

•The value of lift divided by drag is a measure of aerodynamic efficiency. This has a maximum value at one particular angle of attack. For a modern wing this is about 4°. If this “optimum” angle of attack is maintained, maximum aerodynamic efficiency will be achieved. Note: Maximum CL and minimum CD are not obtained at best L/D.

•Lift is generated by a pressure differential between the top and bottom surface of the wing. Pressure is reduced by the air accelerating over the top surface of the wing. The wing area must be big enough to generate the required lift force.

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Lift 5

•Air gets thinner as altitude increases. If the speed of the aircraft through the air is kept constant as altitude is increased, the amount of air flowing over the wing in a given time would decrease - and lift would decrease.

•For a constant lift force as altitude is increased, a constant mass flow must be maintained. As air density decreases with altitude, the speed of the wing through the air (the true airspeed (TAS) must be increased.

If you refer to the ICAO Standard Atmosphere chart on page 27, the air density at 40 000 ft is only one quarter of the sea level value. We can use this as an example to illustrate the relationship between the changes in TAS that are required as air density changes with altitude.

TO KEEP LIFT CONSTANT AT 40 000 ft,

TAS MUST BE DOUBLED

× 4

× 2

			KEEP CONSTANT TO
			MAINTAIN L/D MAX
L = ½	V2	CL S		FIXED AREA

CONSTANT

CONSTANT DYNAMIC PRESSURE (IAS)

1 4

Figure 5.2

For this example we will assume the optimum angle of attack of 4° is maintained for aerodynamic efficiency and that the wing area is constant.

At 40 000 ft the air density is 1/4 of the sea level value, so the speed of the aircraft through the air must be doubled to maintain dynamic pressure (hence lift) constant. TAS is squared because essentially we are considering the kinetic energy of the airflow (KE = ½ m V2).

Lift 5

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Lift 5

The lift formula can also be used to consider the relationship between speed and angle of attack at a constant altitude (air density).

IF SPEED IS DOUBLED, CL MUST BE REDUCED

TO ¼ OF ITS PREVIOUS VALUE

× 4	1
× 2		4

L = ½	V2	CL S	FIXED AREA
CONSTANT			DYNAMIC PRESSURE
			FOUR TIMES GREATER
CONSTANT			(IAS DOUBLED)
ALTITUDE

Figure 5.3

As speed is changed, angle of attack must be adjusted to keep lift constant.

As an example: if IAS is doubled, TAS will double, and the square function would increase dynamic pressure (hence lift) by a factor of four. As the aircraft is accelerated, the angle of attack must be decreased so that the CL reduces to one quarter of its previous value to maintain a constant lift force.

It is stated on page 27 that IAS will vary approximately as the square root of the dynamic pressure. The proportionality between IAS and dynamic pressure is:

I AS Q

For the sake of simplicity and to promote a general understanding of this basic principle (though no longer true when considering speeds above M 0.4), it can be said that TAS will change in proportion to IAS, at constant altitude, (double one, double the other, etc).

The lift formula can be transposed to calculate many variables which are of interest to a professional pilot. For example: if speed is increased in level flight by 30% from the minimum level flight speed, we can calculate the new CL as a percentage of CLMAX :

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