El Constructivismo y la Enseñanza de la Matemática

1. Density:

a. reduces as altitude increases b. is unaffected by temperature change c. increases with altitude increase d. reduces with temperature reduction 2. The presence of water vapour:

a. in air will increase its density

b. in the atmosphere will increase the power output of a piston engine c. in the atmosphere will increase the amount of lift generated by an

aircraft for a given true airspeed d. in air will reduce its density 3. Atmospheric pressure:

a. acts only vertically downwards

b. is measured in Pascals per square inch c. acts in all directions

d. increases with altitude

4. The air pressure that acts on anything immersed in it: a. is also known as Dynamic Pressure

b. is also known as Static Pressure c. is greater at altitude than at sea level d. is also known as Total Pressure

5. What properties of the Earth’s atmosphere most influence the performance of aircraft?

a. Its carbon dioxide content, temperature, pressure and humidity b. Its oxygen content, pressure, and water vapour content c. Its water vapour content, temperature, pressure and density d. Its nitrogen content, oxygen content, temperature and pressure 6. A piston engine aircraft flies in that layer of the atmosphere called:

a. the Stratosphere b. the Troposphere c. the Mesosphere d. the Tropopause

7. The respective percentages of the four most abundant gases that make up the atmosphere are?

a. Nitrogen 78% Oxygen 21% Argon 0.95% Carbon Dioxide 0.05% b. Oxygen 78% Nitrogen 21% Argon 0.95% Carbon Dioxide 0.05% c. Nitrogen 78% Oxygen 21% Argon 0.95% Carbon Monoxide 0.05% d. Oxygen 78% Nitrogen 21% Argon 0.95% Carbon Monoxide 0.05% 8. When considering the changes in density of the air with altitude, which of the

following four options is correct?

a. The temperature increase with increasing altitude causes density to increase

b. The reduction in pressure with increasing altitude causes density to reduce

c. The temperature reduction with increasing altitude causes density to increase

d. The increase in pressure with increasing altitude causes density to reduce

9. Assuming that the pressure at sea level is ISA, but the temperature is 10°C higher than ISA, the density will be:

a. as per ISA b. greater than ISA c. less than ISA d. unaffected

10. Which of the following options contains the main constituent gases of the Earth’s atmosphere?

a. Hydrogen, Carbon Dioxide and Helium b. Nitrogen, Oxygen and Water Vapour c. Nitrogen, Argon and Carbon Dioxide d. Helium, Nitrogen and Carbon Monoxide

11. Complete the following sentence to give the most correct statement. At constant air temperature and volume, if the pressure of the air increases: a. its density will decrease

b. its density will be unaffected because the volume remains constant c. its density will be unaffected because the temperature remains

constant

12. What is the definition of Relative Humidity?

a. The amount of water vapour present in a mass of air, at any temperature, expressed as a percentage of the maximum amount of water vapour that the air could support at the ISA sea-level temperature

b. The amount of water vapour present in a mass of air relative to the density of air

c. The amount of water vapour present in a mass of air expressed as a percentage of the maximum amount of water vapour that the air can support at the same temperature

d. The amount of water vapour present in a given volume of air expressed as a percentage of the total mass of the air

13. What will be the effect on air density of a reduction in air pressure while humidity and temperature remain constant?

a. The air density will decrease b. The air density will increase

c. The air density will remain unchanged

d. The density of the air is independent of pressure at constant volume

14. What is the equivalent temperature in Celsius of 77º Fahrenheit? a. 45º Celsius

b. 25º Celsius c. 60º Celsius d. 172º Celsius

15. If, on a given day, the actual outside air temperature at 3 000 feet is 12°C, what is the approximate difference between the actual and ISA temperature? a. 1° C b. 11° C c. 7° C d. 3° C Question 1 2 3 4 5 6 7 8 9 10 11 12 Answer Question 13 14 15 Answer

INTRODUCTION.

The first half of this book deals in some depth with the principal forces which act on an aircraft in flight. In this Chapter, we briefly introduce all four main forces and then go on to examine the nature of the force of lift, which is the force which sustains an aircraft in the air.

An aircraft, like any physical body, possesses mass. The Earth’s force of gravity acting on the aircraft’s mass gives the aircraft weight which acts vertically downwards towards the centre of the Earth. When an aeroplane has no forward speed, its weight keeps it firmly on the ground. (Unless the aeroplane is a Harrier, of course; but that is another story.)

In order that an aircraft may fly, its weight has to be counter-balanced by a force of equal magnitude to its weight and which acts in the opposite direction. This force is called lift. As we will learn, lift is generated as a result of the flow of air over the aircraft’s surfaces, principally its mainplanes or wings. In order to create this flow of air, the aircraft is propelled forwards through the air by a force to which we give the namethrust. But as soon as the aircraft begins to move under the influence of thrust, a force arises which opposes the thrust force, and acts against the direction of the aircraft’s motion. This force is called drag. The four forces we have just mentioned, weight, lift, thrust and drag, which act on any powered aircraft in flight, are illustrated in Figure 3.1. The diagram also depicts a force which is identified as the tailplane force. The tailplane force is not one of the principal flight forces; it is a balancing force. Do not concern yourself with it for the moment; you will meet tailplane force at the appropriate time.

The four principal forces acting on an aircraft in flight are inextricably interconnected. A pilot must have an adequate knowledge of the way in which these forces interact with one another in order to understand what governs his aircraft’s performance in any given phase of flight or in any particular manoeuvre.

The greater the weight of an aircraft, the more lift will be required to get the aircraft into the air and to maintain steady, straight flight, whether level, climbing or descending.

As the aircraft manoeuvres, it accelerates. Positive accelerations increase the aircraft’s effective weight and require more lift to be generated by the wings. An increase in lift inevitably causes drag to increase. As drag increases, more thrust must be applied to balance the greater drag; and so on.

You will find that you have to consider this interrelationship between the four principal flight forces quite often in your study of the Principles of Flight. But, for now, let us take a closer look at the first of the four forces: lift.

LIFT.

The Primary Cause of Lift.

Lift is the force which sustains an aircraft in the air and enables it to manoeuvre. But how does an aeroplane generate lift?

Well, one of the most important properties of air, you will recall, is that it possesses mass. For instance, the air which fills a typical living room in an average family home has a mass of around 60 kilograms (132 pounds). So when a solid body moves through air, the resulting displacement of the air mass causes an opposing force to be exerted on the body which is doing the displacing. The way in which this reaction force acts on the body (i.e. the magnitude and direction of the force) depends on the manner in which the body is moving and the shape and orientation of the body. First of all, let us consider the general case of how air might be displaced in order to produce lift when disturbed by a body which moves through it.

At this early stage in our consideration of lift, we do not want to look too closely at the fine detail of how lift is generated; that will come later. We just need to see the big picture for the moment. Let us, therefore, first of all consider how a body of undefined characteristics might affect the air through which it is moving.

The diagram in Figure 3.2, which we are viewing from “side-on” represents a screen behind which is concealed the “body of undefined characteristics” that we have mentioned. The body and the screen are moving together through the air, thereby

Figure 3.2 The undefined body behind the screen has exerted a force on the air to deflect the air downwards.

causing air to flow over the body. The arrows represent the direction of the relative motion of the free-stream airflow which, in the diagram, is seen passing behind the box. (Remember, in aerodynamics, it does not matter whether we are considering a body moving through the air, or moving air passing over a stationary body. The physical effects are the same.) At Point 1, we see that the flow of air is horizontal; but at Point 2 we observe that the airflow is inclined downwards. Consequently, because we know from Newton’s First Law of Motion (See Page 14) that any moving mass will continue to move at constant speed in a straight line (in other words, at constant velocity) unless acted on by a force, we can see that some kind of force, acting in a downwards direction, has been applied to the air mass as it passed behind the box. Well, the only object which is behind the box is our “body of undefined characteristics”; so it must have exerted a force on the air mass. We can see, then, from Newton’s Third Law of Motion (See Page 14) that the undefined body behind the screen which is exerting the downwards force on the air mass must, itself, be experiencing an equal reaction force acting in the opposite direction; that is, in an upwards direction.

Now, if we assume that the undefined body which is turning the air downwards is the wing of an aircraft, the upwards reaction force being experienced by the wing contributes to the force that aerodynamicists call lift. We will now go on to look at this upwards reaction force in more detail (see Figure 3.3).

The Nature of Lift - Newton and Bernoulli.

In describing the generation of lift by a moving fluid, we have to consider several laws of Physics. In fact, we must simultaneously consider the principle of the conservation of mass, the principle of the conservation of momentum, and the principle of the conservation of energy. (See Page 13) A complete discussion of the scientific theory of how a wing produces lift would be very complex, requiring us to be proficient in advanced mathematics, and would be well beyond the scope of this book. Such a formal treatment of lift would also be unnecessary for the average pilot, whether amateur or professional. However, in the remainder of this chapter we will be looking at lift-theory in enough detail to give what we trust is a convincing and comprehensive explanation of lift, which in no way misleads the student and which is of sufficient depth for the practical pilot.

Figure 3.3 A wing causing downwards turning of the airflow and experiencing an upwards- directed reaction force which contributes to lift.

A wing turns the airflow downwards. The reaction

force acting on the wing, in an upwards direction, contributes to lift.

Assumptions.

In the following explanations and discussions of the generation of lift by an aircraft’s wings, we consider the air as an ideal fluid. Consequently, we make three major assumptions about the physical properties of the airflow.

• The Compressibility of the Airflow. It is assumed throughout this book,

that the airflow over a wing is incompressible. Now, you will, of course, realise that air can be compressed very easily. Air in an inflated balloon is at higher than atmospheric pressure, as a child discovers when he releases a blown-up balloon and sees it propelled around a room as if it were an errant rocket. If you have ever inflated a bicycle tyre, you may have felt the heat generated in the end of the pump chamber as you do work on the air to compress it and force it into the tyre. And, of course, skin divers carry air bottles on their backs which contain what is actually called “compressed air”.

However, when air flows over the wing of an aircraft in flight, provided the speed is low and nowhere reaches a value of more than half the local speed of sound (Mach 0.5), the airflow is not compressed and, in any given atmospheric conditions, and at constant altitude, will maintain constant density. This assumption that air is incompressible works well for low- speed flight and simplifies the analysis of lift generation. The assumption is important for light aircraft pilots because if the speed of the airflow exceeds Mach 0.5, the compressibility of air does become an issue. But then we would be in the realms of high-speed flight and beyond the scope of this book. For your reference, the speed of sound, at sea-level, in the ICAO Standard Atmosphere, is about 662 knots (340.3 metres/sec or 1 116.4 feet/ sec); so a light aircraft will always be flying at far less than half that speed. • The Viscosity of the Airflow. When considering lift, we assume that air is

inviscid; that is, that air is of a viscosity approaching zero (See Page 9). In reality, air does possess a measurable amount of viscosity. However, the viscosity of air is very low, and air flowing around a wing does act as if it were inviscid, except in the very thin layers immediately next to the surface of the wing, which we call the boundary layer. We must note, though, that if air really were inviscid, we could not account for the force of drag. So, to sum up, our consideration of lift assumes that air has zero viscosity, but, in discussing drag, we must take the low viscosity of air into account.

• Steady Flow. In our treatment of lift, we assume that the airflow around the wing is steady. This means that the pattern of the airflow around the wing does not change with time. This does not mean that the velocity at all points in the flow is constant but it does mean that, at any given point in the airflow, velocity is constant.

The Flat-Plate Wing.

One of the simplest ways of changing the direction of a horizontal airflow, so that the air is directed downwards, is to move a flat plate through the air inclined at a small positive angle to the airflow (See Figure 3.4). You will probably be familiar with wings which have a “flat plate” cross-section from the simple type of wing used on model aircraft produced for children of all ages. Note that the angle between the plate and the undisturbed airflow, before the flow is modified by the wing, is called the angle of attack and is designated by the greek letter, a.

Though air is a gas that can be easily compressed, when air flows over a wing at speeds less than half the speed of sound, it is considered to be incompressible.

We depict the airflow in Figure 3.4 as being horizontal, but, of course, when an aircraft is in flight its direction of flight is often not horizontal. The angle of attack, then, must be understood as being the angle between the wing and what we will henceforth refer to as the relative airflow. A light aircraft in steady, cruising flight typically has an angle of attack of around 4º.

When a flat plate wing moves through the air, as shown in the diagram, it induces a small upwash in front of the plate followed by a small downturn or downwash in the air flowing over it. This “turning” of the air mass causes a reaction force to act on the flat plate wing directed both backwards and upwards (See Figure 3.5). In Principles of Flight, we call this reaction force the total reaction. You have doubtless felt this type of total reaction force if you have ever held you hand out of the window of a moving car, at an angle to the airflow, as illustrated in Figure 3.6.

Figure 3.5 The Flat Plate Wing, showing the Total Reaction Force.

Figure 3.6 Total Reaction.

Figure 3.4 The Flat Plate Wing.

The relative airflow flows parallel to the direction of

movement of the aircraft, but in the opposite direction.

The wing exerts a force on the air, and turns the air

downwards. In turn, the wing experiences a reaction force, acting upwards and rearwards, known as the Total Reaction.

The total reaction is just what its name suggests it to be. The total reaction has the magnitude and direction of the sum of the forces which act on the flat plate wing because of its motion through the air. Lift is the name that we give to 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.

(See Figure 3.7) Drag is the subject of Chapter 5. The Wing of Aerofoil Cross-section.

Following early experiments with wings of thin, flat, rectangular cross-section, pioneers of aviation soon discovered that greater lift could be produced for much lower drag by using a wing of curved cross section similar to the wing of a bird. This discovery led to the type of wing, with its distinctive aerofoil cross section, that is still used on light aircraft today (See Figure 3.8). As monoplanes replaced biplanes, it was also realised that the curved surfaces and depth of wings with aerofoil cross sections enabled wings to be built with the structural strength required by higher performance cantilever monoplane aircraft. (See Figure 3.8).

Figure 3.7 The Flat Plate Wing.

Figure 3.8 The Hurricane: a cantilever monoplane of legendary renown. Lift is the

name given to the component of the total reaction acting at right angles to the relative airflow.

Air flows over a wing of aerofoil cross section much more smoothly than over a flat plate wing, at equal angle of attack. Notice that, on the curved aerofoil, the angle of attack is measured as the angle between the undisturbed relative airflow and a straight line, called the chord line, joining the leading edge and the trailing edge of the wing. (See Chapter 4 for the terminology used in the description of aerofoils.) Much less turbulence is caused in the airflow over a wing of aerofoil cross section, and such a wing is much more efficient in producing the downwards turning of the airflow which is the key factor in the generation of lift.

In comparing the airflow over a flat plate wing and a wing of aerofoil cross section, notice, too, that the total reaction is less tilted back in the latter case than in the former, and that the ratio of the length of the lift vector to that of the drag vector