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Customer: Oleg Ostapenko E-mail: [e-mail] Customer: Oleg Ostapenko E-mail: [e-mail]

CHAPTER 3: LIFT

for the aerodynamic lift that the wing generates. Furthermore, Bernoulli’s Principle concerning the relationship between pressure variations and velocity changes in a fuid fow is ultimately derived from Newton’s Laws.

Though the advanced mathematical treatment of lift, which is required to fully explain this most important of forces in terms of the Principles of Flight, is beyond the scope of this book, it is important for all pilots who wish to understand the nature of lift to know that the Bernoulli and Newtonian predictions of the lift force measurable in a wind tunnel are both accurate.

A very concise explanation of the way the aerodynamic force generated by a wing is accounted for by both Bernoulli’s Principle and Newton’s Laws is given on the website of the National Aeronautics and Space Administration (NASA) of the United States of America. NASA writes that:

“Lift and drag are mechanical forces generated on the surface of an object as it interacts with a fuid. The net fuid force is generated by the pressure acting over the entire surface of a closed body [Bernoulli]. The pressure varies around a body in a moving fuid because it is related to the fuid momentum (mass × velocity). The velocity varies around the body because of the fow defection [Newton]…” (Our brackets.)

THE GENERAL LIFT EQUATION AND THE COEFFICIENT OF LIFT.

In our consideration of lift up to now, we have assumed that the speed of the free stream airfow is constant. Furthermore, one of our initial assumptions was that air fowing at low speeds typical of light aircraft fight is incompressible so, because we have not considered airfow at different altitudes and in different atmospheric conditions, we have taken density to be constant, too.

We have also discussed briefy that if the angle of attack remains constant, and the speed of the airfow increases, lift will increase.

The above are general observations, but if we wish to calculate the lift produced by any aerofoil in any conditions we have to take into account not only variations in angle of attack, airspeed and air density, we also have to consider the shape of the aerofoil, particularly the amount of camber on its upper surface. All these factors are taken into consideration by the Lift Formula:

Lift = CL ½ ρ v² S

The Lift Formula is one of the few formulae that you will be required to remember for the PPL theoretical knowledge examination. Lift, remember, is a force acting perpendicularly to the free-stream relative airfow. In the Lift Formula:

The formula for lift is given by the lift equation:

Lift = CL ½ ρv² S

CL	is the coeffcient of lift which takes account of the shape of the aerofoil
	and the aerofoil’s angle of attack with the relative airfow. CL has no units

½is a constant which is arrived at by experiment.

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Lift is directly proportional to air density.

Lift is directly proportional to

the square of the airspeed.

If airspeed is doubled, lift increases by a factor of 4.

ρis a Greek letter (pronounced “roe”) which represents the density of the air. ρ has the units kg/m³, if the lift force is to be measured in Newtons.

vis the velocity of the free-stream relative airfow which is the same as the true airspeed of the aircraft. Notice that lift varies according to the square of the velocity; v has the units m/sec, if the lift force is to be in Newtons.

S is the surface area of the wing. S has the units m² if the lift is in Newtons.

The Lift Equation reveals that the lift force produced by a wing is proportional to dynamic pressure, ½ ρv², to the area of the wing S and to the coeffcient of lift CL, which represents the shape of the wing and angle of attack of the wing to the relative airfow.

So what does the Lift Equation, Lift = CL ½ ρ v² S, tell us which is of practical use to the pilot?

Well, it tells him several things of varying degrees of usefulness:

•Lift is directly proportional to air density. This information is not very useful because a pilot can do nothing about air density, although he might deduce that the higher he fies, the lower will be the air density, and he might suspect that this fact might somehow affect the aircraft’s performance.

•Lift is directly proportional to wing area. That can be useful knowledge if an aircraft is ftted with Fowler Flaps which extend from the wing, and so increase area. The pilot might deduce, for instance, that with Fowler Flaps extended, he can generate the same lift at lower airspeeds.

•Lift is directly proportional to the square of the airspeed; so, if the aircraft fies twice as fast, the lift generated by the wings will increase fourfold. This is very useful information, because the pilot will see immediately that his ability to control the aircraft’s speed gives him direct control over the lift produced by the wings.

•Lift is directly proportional to the Coeffcient of Lift, CL. This is also very useful information. We have learnt that CL includes both the shape of the wing and the angle of attack of the wing with the free-stream relative airfow.

By increasing the angle of attack, the pilot can increase CL and so increase the lift produced by the wing, but not beyond the angle of attack for maximum lift. By selecting fap, the pilot can also modify the shape of his aircraft’s wing

and, therefore, also modify the value of CL. He will understand, therefore, that the selection or deselection of fap will affect the lift generated by the wing.

The Lift Equation also reveals a relationship between the speed of an aircraft and angle of attack. For any phase of straight, steady fight the aircraft’s weight must be exactly balanced by lift. Thus, assuming that air density, wing surface area, and wing shape are constant, we see that any change in airspeed, v, must require a corresponding change in CL if Lift is to remain constant and steady fight maintained.

Now, the only part of CL that the pilot can control is the angle of attack. So if airspeed, v, is increased, the angle of attack must be decreased and vice versa.

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CHAPTER 3: LIFT

From this fact, we may deduce that in conditions of steady fight, for each airspeed a specifc angle of attack and CL are required. This relationship reveals one of the fundamental principles of fying a light aircraft: that is, in steady, straight fight, airspeed is determined primarily by angle of attack. And, in steady, straight fight, the angle of attack is controlled by the pilot by selecting an appropriate pitch attitude with the control column or control wheel. At the same time, he uses the throttle to adjust engine power to maintain level fight, or a constant rate of descent or climb. Whether the pilot changes angle of attack frst, or engine power, when selecting a new airspeed, is something you will be taught by your fying instructor.

You will appreciate, then, that by referring to the Lift Equation, the pilot may at all times recall the fundamental relationships which affect the performance of his aircraft.

Variation of Coefficient of Lift with Angle of Attack

To bring this chapter on lift to a close let us examine a graph illustrating how the Coeffcient of Lift, CL, and so (because lift is directly proportional to CL), the total lift produced by any given wing varies with angle of attack.

Figure 3.23 The variation of CL with Angle of Attack.

Figure 3.23 shows the graph of CL against angle of attack for a typical aerofoil. The principal points to note from the graph are:

•As we are considering an aerofoil cross section, the wing will produce a net lift force even at 0º angle of attack, and even at a very small negative angles of attack. This is a property of most non-symmetrical aerofoils with a cambered upper surface. A fat plate and a symmetrical aerofoil would generate no lift at 0º angle of attack.

•The graph is a straight line between 0º and 12º, indicating a uniform increase in lift with increasing angle of attack.

•Beyond 12º angle of attack, the graph begins to curve over towards a maximum value of lift. In this region, there is only a small increase in lift with increasing angle of attack.

•Lift reaches a maximum at about 15º to 16º angle of attack. Above this angle, the graph begins to curve downwards indicating that the lift is decreasing.

The Coefficient

of Lift, CL, reaches a

maximum just

before the wing stalls.

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We see, therefore, that, for small angles of attack, any increase in the angle at which the wing meets the relative air fow leads to an increase in lift. But, after a given angle is reached (i.e. the angle of attack for maximum lift), any further increase in angle of attack will cause a relatively rapid decrease in lift, as shown by the sharp downturn in the graph. The angle at which lift begins to decrease is called the stalling angle of attack. You will learn more about stalling in a later chapter, but you should note here the important fact that a wing stalls at a given angle of attack, not at a given speed, although you will often come across the term stalling speed when considering stalling from straight and level fight.

SUMMARY.

In this chapter, we have attempted to explain the nature of the lift force generated by an aircraft wing and to investigate the factors which affect that lift force. When considering the motion of a wing through the air (remember, it is the relative motion of the air and the wing which is important), we have looked at the three very important scientifc principles of the Conservation of Mass, the Conservation of Momentum and the Conservation of Energy. We have seen how Newton’s Laws of Motion (conservation of momentum) and Bernoulli’s Principle (conservation of energy) both account for the generation of lift by a wing. Lift can be accounted for as a reaction to the downward turning of the airfow (Newton), and by the upwards acting pressure differential across the wing (Bernoulli). In some aeronautical circles you will fnd people who favour the Newtonian explanation and those who support the

Bernoulli explanation. Most aerodynamicists, however, treat the two accounts of lift generation as being two explanations of the same phenomenon, viewed from different perspectives.

For the pilot, the deep science is not of prime importance as long as he understands the basic nature of lift.

It is generally recognised that the Lift Equation, Lift = CL½ ρv²S, permits the pilot to keep the various factors affecting lift and airspeed clearly in mind. By committing the lift equation to memory and referring to it as required, the pilot may readily appreciate how lift is infuenced by angle of attack, the shape of the wing cross-section, the density of the air, airspeed and the area of the wings. The pilot should, therefore, have a good basic understanding of how the lift force is acting on his aircraft in fight, whatever manoeuvre he is performing.

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Customer: Oleg Ostapenko E-mail: [e-mail] CHAPTER 3: LIFT QUESTIONS

Representative PPL - type questions to test your theoretical knowledge of Lift.

1.Dynamic pressure equals:

a.total pressure plus static pressure

b.static pressure minus total pressure

c.total pressure divided by static pressure

d.total pressure minus static pressure

2.Relative airfow is _________ and ________ the movement of the aircraft.

a.	perpendicular to	opposite to
b.	parallel to	opposite to
c.	perpendicular to	in the same direction as
d.	parallel to	in the same direction as

3.In straight and level fight, the free stream airfow pressure compared to the pressure of the air fowing under the forward section of a wing is:

a.equal

b.higher

c.lower

d.of equal pressure but travelling faster

4.The velocity of air fowing over the upper surface of the wing of a typical training light-aircraft increases when compared to the velocity of the free airfow. Which of the options below best describes the pressure considerations of the air fowing over the wing:

a.its dynamic pressure will decrease and its static pressure increase

b.its dynamic pressure will remain constant and its static pressure will decrease

c.its dynamic pressure will increase and its static pressure decrease

d.its dynamic pressure will decrease and its static pressure remain constant

5.The air fow over the wing’s upper surface in straight and level fight, when compared with the airfow that is unaffected by the wing, will have:

a.a higher velocity

b.a higher density

c.a reduced velocity

d.the same velocity

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CHAPTER 3: LIFT QUESTIONS

6.Which of the four answer options most correctly completes the sentence? Increasing speed also increases lift because

a.lift is directly proportional to velocity

b.lift is directly proportional to the square of the airspeed

c.the increased velocity of the relative wind overcomes the increased drag

d.increasing speed decreases drag

7.1 - Air has mass

2 - Air is not compressible

3 - Air is able to fow or change its shape when subject to even small pressures

4 - The viscosity of air is very high

5 - Moving air has kinetic energy

The correct combination of true statements, from the above options, is:

a.1, 2, 3 and 5

b.2, 3 and 4

c.1 and 4

d.1, 3, and 5

8.A moving mass of air possesses kinetic energy. An object placed in the path of such a moving mass of air will be subject to:

a.static pressure and dynamic pressure

b.static pressure

c.dynamic pressure

d.dynamic pressure minus static pressure

9.The Principle of Continuity states that, in a Streamtube of decreasing crosssectional area, the speed of a subsonic and incompressible airfow will:

a.remain the same

b.decrease

c.increase

d.always become sonic

10.The angle of attack of an aerofoil is defned as:

a.the angle between the chord line of the aerofoil and the horizon

b.the angle between the chord line of the aerofoil and the relative airfow

c.the angle between the chord line of the aerofoil and the aircraft’s longitudinal axis

d.the angle between the mean camber line of the aerofoil and the relative airfow

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Customer: Oleg Ostapenko E-mail: [e-mail] CHAPTER 3: LIFT QUESTIONS

11.An aerofoil section is designed to produce lift resulting from a difference in the:

a.negative air pressure below and a vacuum above the surface

b.higher air pressure below the surface and lower air pressure above the surface

c.vacuum below the surface and greater air pressure above the surface

d.higher air pressure at the leading edge than at the trailing edge

12.Which of the sentences below makes the most correct statement about Lift?

a.Lift acts perpendicularly to the wing chord line

b.Lift acts parallel to the wing chord line

c.Lift acts perpendicularly to the wing mean camber line

d.Lift acts perpendicularly to the relative airfow

13.On an aerofoil section, the force of lift acts perpendicular to and the force of drag acts parallel to the:

a.relative airfow

b.longitudinal axis

c.chord line

d.aerofoil section upper surface

14.A positively cambered aerofoil starts to produce lift at an angle of attack of approximately:

a.4 to 6 degrees

b.0 degrees

c.minus 4 degrees

d.16 degrees

15.If the Angle of Attack and other factors remain constant, and the airspeed is doubled, lift will be:

a.doubled

b.one quarter of what it was

c.the same

d.quadrupled

16.Which of the answer options most correctly completes the sentence? The amount of lift a wing produces is directly proportional to:

a.the dynamic pressure minus the static pressure

b.the square root of the velocity of the air fowing over it

c.the air density

d.the air temperature

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CHAPTER 3: LIFT QUESTIONS

17.The centre of pressure is:

a.the force opposing gravity

b.the point through which the aircraft weight acts

c.the point through which total lift acts

d.the central point of the engine oil system

18.The total lift force is considered to act through which location in an aircraft’s wing?

a.The wing’s upper surface

b.Always forward of the Centre of Gravity (C of G)

c.The wing’s C of G

d.The Centre of Pressure

19.Static pressure acts:

a.parallel to airfow

b.parallel to dynamic pressure

c.in all directions

d.downwards

20.Which of the following statements is correct?

a.Lift acts perpendicular to the horizontal and drag parallel in a rearwards direction

b.Drag acts parallel to the chord and opposite to the direction of motion of the aircraft and lift acts perpendicular to the chord

c.Lift acts at right angles to the top surface of the wing and drag acts at right angles to lift

d.Drag acts parallel to the relative airfow, opposing the motion of the aircraft, and Lift acts perpendicularly to the relative airfow

21.In which of the conditions described below will the Coeffcient of Lift of a wing be at its maximum?

a.At the aircraft’s maximum rate of climb speed

b.At or just before the stall

c.In level fight at an angle of attack of between 4° and 6°

d.At the aircraft’s maximum angle of climb speed

22.The formula for lift is:

a.L = W

b.L = ½ ρV (CL)² S

c.L = CL ½ ρV² S

d.L = CL ½ ρ²V S

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Customer: Oleg Ostapenko E-mail: [e-mail] CHAPTER 3: LIFT QUESTIONS

23.Which of the following statements best accounts for how a lift force can be generated by a wing of aerofoil cross section whose upper surface is positively cambered and whose undersurface is uncambered?

a.The air fowing over the upper surface has a longer distance to travel than the air fowing under the wing

b.An upwards-acting reaction force is generated by the wing as it turns the airfow around it in a downwards direction

c.There is an upwards acting reaction to the airfow which bounces off the under surface of the wing as the airfow strikes the undersurface at a positive angle of attack

d.A wing of the aerofoil section described will naturally produce positive lift at any angle of attack

24.Which of the following statements best accounts for how the airfow around a wing of standard aerofoil cross section contributes to the lift force produced by the wing?

a.A wing of standard aerofoil cross-section acts like an inverted venturi tube

b.Because the total energy in the air passing above the wing is greater than the total energy in the air fowing beneath the wing

c.Lift is produced by the wing “skipping” over the airfow in the same way as a fat stone might skip over water

d.The downwards turning of the airfow by the wing produces a rate of change of momentum in the airfow, the reaction to which is a force acting on the wing in an upwards direction

Question	1	2	3	4	5	6	7	8	9	10	11	12
Answer
Question	13	14	15	16	17	18	19	20	21	22	23	24
Answer

The answers to these questions can be found at the end of this book.

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