CHAPTER 18 How do heavy things fly? Contents Flight the beginning Forces acting on an aircraft Moving through fluids The Equation of Continuity Fluid speed and pressure Aerofoil characteristics Newton s Third Law More on thrust More on drag Lift-to-drag ratio Faster than sound Turning effect of a force Designing for lift and drag Controlling flight Stages of flight Wind tunnels Chapter review Summary Questions Note to students and teachers: This PDF has been provided as an offline solution for times when you do not have internet access or are experiencing connectivity issues. It is not intended to replace your ebook and its suite of resources. While we have tried our best to replicate the online experience offline, this document may not meet Jacaranda's high standards for published material. Please always refer to your ebook for the full and latest version of this title.
CHAPTER 18 How do heavy things fly? The Wright Flyer, 1903. The first controlled powered flight to carry a person REMEMBER Before beginning this chapter, you should be able to: recall that pressure is a measure of force per unit area recall that density is a measure of mass per unit volume describe motion in terms of distance, displacement, speed, velocity and acceleration explain how the action of forces changes the way an object moves Calculate the torque applied by force explain movement in terms of Newton s three laws of motion.
KEY IDEAS After completing this chapter, you should be able to: apply Newton s laws of motion to describe the action of forces on the motion of an aircraft identify factors that affect performance of an aircraft apply the concepts of torque and equilibrium to the motion of an aircraft relate the generation of lift to airspeed and pressure using Bernoulli s equation, and to the rate of change of momentum using Newton s laws of motion differentiate between induced drag and parasitic drag analyse the performance of an aircraft during take-off, climb, descent and cruise use a model to investigate aspects of the performance of an aircraft identify the effects of flying at very high speeds explain the operation of the elevator, rudder and ailerons in controlling a conventional aircraft apply aeronautical principles to the design of efficient cars and wind turbines. Flight the beginning The science and technology of flight originated over 000 years ago, when the Chinese began making and experimenting with kites. The idea of people taking to the air was just a dream until the early sixteenth century, when Leonardo Da Vinci produced detailed drawings of flying machines. However, his machines were not built or tested. The first recorded flight driven and controlled by an engine took place in 1903, with the Wright brothers of the USA. That first flight followed many experiments with gliders and using a wind tunnel. Weblink: Aviation milestones This chapter deals with the study of aeronautics the science of flight through the Earth s atmosphere. It includes the study of the forces that enable flight through the air, aircraft design and jet propulsion. Forces acting on an aircraft The main forces acting on an aircraft in level flight (shown in the figure below) can be identified as vertical and horizontal pairs. The vertical force pair is lift and force due to gravity. The horizontal force pair is thrust and drag. Lift acts upwards, and at right angles to airflow direction. The lift force is generated over the entire wing, although it can be modelle as acting at one position along a wing. This position is known as the centre of lift or the centre of pressure (CP).
The forces acting on an aircraft in level flight and with constant speed. For the sake of simplicity, all forces are shown as acting through the centre of gravity. REMEMBER THIS Newton s laws of motion 1. The velocity of an object can change only if there is a non-zero net force acting on it. This statement is an expression of Newton s First Law of Motion.. The relationship between the acceleration of an object, the net force acting on it, and the object s mass can be expressed as F net = ma. The relationship can also be expressed in terms of momentum. The net force mδv acting on an object is proportional to the time rate of change of momentum; that is, Fnet =. Δ t 3. When an object applies a force (an action) to a second object, the second object applies an equal and opposite force (called a reaction) to the first object. The wing is the primary source of lift on a conventional aircraft; however, the fuselage and tail also contribute to the total lift generated. In the figure below, the total lift force is represented as a single arrow. The force due to gravity force acting on an aircraft is considered to act though the centre of gravity. This is the point at which all the aircraft s mass can be considered to be concentrated. It is also the point of balance if an aircraft were hung from a cable attached to its centre of gravity, it would hang level and in perfect balance. The location of an aircraft s centre of gravity depends upon two factors: the load it carries (for example, fuel, passengers and cargo) and the positioning of the load within the aircraft. In steady level flight, the lift force and the force due to gravity are equal in size and opposite in direction. The thrust force that causes an aircraft to move through the air comes from the propeller blades or jet engines pushing the air backwards (an action). The air pushed backwards therefore pushes the plane forwards with a force of equal magnitude (a reaction). Digital doc: Investigation 18.1: Power and thrust Explore the relationship between power delivered to a propeller and the thrust it delivers.
As an aircraft moves through the air in flight, it experiences air friction or drag. The faster the aircraft moves, the greater the resultant drag force. In the figure on page XXX, the arrow drawn to represent drag is the resultant of all the drag forces that act on every part of the aircraft. There are several different types of drag force that act when an aircraft flies. If the net force acting on an aircraft in flight is zero, it maintains a constant velocity. If the net force acting on the aircraft is not zero, the magnitude and direction of the net force determine: the magnitude and direction of the acceleration of the aircraft the rate of change of momentum of the aircraft. Moving through fluids Aeronautics is principally concerned with the motion of aircraft through gases and, in particular, the air. All liquids and gases are fluids. Fluids, like solid objects, are composed of small particles. However, the particles that make up fluids do not behave in the same way as those that make up solid objects because they are able to move more freely. Daniel Bernoulli
The Equation of Continuity In the early 1700s, Swiss mathematician Daniel Bernoulli developed the Equation of Continuity, which stated: All material that enters a pipe will leave the pipe. This statement is based on Newton s mechanics, and the idea that mass can not be created or destroyed. The Equation of Continuity can be expressed as: Q = va 1 1 = va where Q = flow rate, measured in cubic metres per second (m 3 s 1 ) v = fluid speed, measured in metres per second (m s 1 ) A = cross-sectional area of the pipe, measured in square metres (m ). The location of an aircraft s centre of gravity depends upon two factors: the load it carries (for example, fuel, passengers and cargo) and the positioning of the load within the aircraft. If, as illustrated in the figure to the right, A is smaller than A 1, v must be greater than v 1. In order to increase the velocity of the fluid through the pipe, work must be done on the fluid travelling through the pipe to increase its kinetic energy. This can occur only if the pressure of the fluid entering the pipe is greater than the pressure of the fluid leaving the pipe. In short, it means that faster moving fluids have lower pressure. The flow of fluid through changing cross-sectional areas within a pipe SAMPLE PROBLEM 18.1 Air flows into a house through an open window. The airspeed is a gentle 30 cm s 1. It is a sliding window of dimensions 100 mm 400 mm. Inside the room, the far door is open by just 10 cm. The door is a standard height of 050 mm. What is the speed of the air as it flows through the door? Solution: Window area = A1 = 1. m 0.4 m = 0.48 m Fluid speed through the window = v = 1 0.30 m s 1
Door area = A = 0.10 m.05 m = 0.05 m The rate of air flow is a constant. flow rate in through the window = flow rate out through the door va 1 1 = va 1 0.30 m s 0.48m = 0.05 m v v = 1 0.70 m s The air flows through the door at a speed of 70 cm s 1. REVISION QUESTION 18.1 a. Water flows into one end of a pipe at a speed of 1.0 m s 1. The radius of the pipe at the point of entry is 5.0 cm. The pipe narrows so that the water leaves through an opening that is only.0 cm in radius. With what speed does the water flow out of the pipe? b. If a fluid flows at a speed of 1. m s 1 through a pipe of cross-sectional area 0.45 m, at what speed will it flow when the cross-sectional area: i. narrows to only 0.3 m ii. widens to 0.60 m? Fluid speed and pressure By applying the Law of Conservation of Energy to fluid flow, Bernoulli derived an equation that states: 1 ρ + ρ + = constant v gh P where ρ = the fluid density (measured in kg m 3 ) v = the speed of the fluid (measured in m s 1 ) g = acceleration due to gravity (measured in m s ) h = the vertical displacement of the fluid (measured in m) P = the static pressure of the fluid (in N m or Pa). According to this principle, the total energy of the fluid is constant throughout the flow. In simplest terms, this energy is comprised of: the kinetic energy due to motion, the gravitational potential energy due to changes in height, and the potential energy associated with the pressure of the fluid. This equation does not apply to aircraft moving at supersonic speeds due to changes in the behaviour of the fluid and significant heating of the wing. In 1738, the Swiss mathematician Leonhard Euler derived an equation that related the speed of a fluid to its static pressure. He found that an increase in speed, created when a liquid flows through a narrower section of a
pipe, produced a decrease in static pressure. Likewise, a decrease in speed (by enlarging the pipe) produced an increase in static pressure. The Bernoulli principle The statement that the pressure of a fluid decreases as its velocity increases is known as the Bernoulli principle, in honour of Euler s mentor, Daniel Bernoulli. Euler applied Bernoulli s equation to a fluid at a constant height, producing the equation: 1 ρ + = constant v P The cross-section of an aircraft wing forms a shape known as an aerofoil. This shape is designed so that air travelling over it will speed up. According to the Bernoulli principle, this reduces the air pressure above the wing. The opposite happens on the lower surface, with a lower speed resulting in an increased pressure. The result is an upwards force known as the lift force. How lift is developed by an aerofoil AS A MATTER OF FACT Digital doc: Investigation 18.: Bernoulli effects Explore how the Bernoulli principle applies to moving air. Formula One racing cars are fitted with aerofoils at the front and back, called the front and rear wings. They are actually inverted wing-shapes that help push the tyres onto the road and hence increase their grip. This also increases the drag force on the car, but the improved handling outweighs any detrimental effect. The descriptions of the movement of smooth surfaces in air can be extended to surfaces travelling through other fluids such as water. Ships must not pass within several metres of each other as they will be drawn together and may collide. Boats approaching a wharf may experience the same effect if they come in too fast. Aerofoils are not always used to provide lift. In racing cars, aerofoils are used to oppose lift and increase the car s grip on the track.
Aerofoil characteristics Weblink: Principles of flight The angle of attack is the angle between the wing of an aircraft and the direction of airflow. There are two key factors in the ability of an aerofoil to generate lift. The first is its shape. The front of the aerofoil is called the leading edge. This is usually quite rounded so it deflects the airflow above and below the wing. The rearmost point of the aerofoil is called the trailing edge. At the trailing edge, the upper and lower surfaces of the wing come to a sharp point to reintroduce the two airstreams with minimal disturbance. The theoretical line directly between the leading and trailing edge is called the chord line. Many simple aerofoils are symmetrical about the chord line. However, the majority of aerofoil shapes used today are not symmetrical and feature a curvature that is called camber, which is represented by the camber line. The second factor in an aerofoil s ability to generate lift is its orientation to the undisturbed airflow. This is known as the angle of attack and is measured as the angle between the undisturbed airflow and the chord line of the wing. Simple symmetrical aerofoils only generate lift when placed at an angle to the airflow, whereas a cambered aerofoil can generate lift at an angle of attack of zero degrees. As the angle of attack is increased from zero degrees, the difference between the pressure on the upper and lower surfaces increases and more lift is generated. This is accompanied by an increase in drag due to the greater disturbance in the airflow. At large angles of attack, the airflow on the top of the wing can separate and a swirling pattern of turbulence can be created. This reduces the lift and increases the drag and is commonly referred to as stall.
The effect of increasing the angle of attack; if the angle of attack becomes too great, turbulence is created, lift decreases, and the drag increases. PROOFS AS A MATTER OF FACT PAGE UNCORRECTED Newton s Third Law The mechanism by which aerofoils and wings generate lift can also be explained using Newton s Third Law. The overall effect of the movement of the wing through the air is to push the air downwards, creating what is called downwash. This can be thought of as an action, with the wing pushing the air Digital doc: downwards. The Newton s Third Law reaction pair of this is the air pushing the Investigation 18.3: wing upwards, or in other words the generation of lift. This is not an additional source of lift, but rather another approach to understanding the generation of Turbulence lift by a wing. Gliders and hang gliders rely on air heated by the land, rising and sending them soaring into the air. These upcurrents of air are known as thermals. Explore and describe turbulence effects in water.
More on thrust In order to move through the air, an aircraft must produce thrust. This is generally done with one or more propellers, or with jet engines. A propellerdriven aircraft is actually pulled through the air. The propeller itself is an aerofoil Weblink: turned by the engine and each blade of the propeller generates its own lift Forces on a wing in flight force. A large component of the lift force on the propellers is in the direction of applet motion of the aircraft and provides the thrust. As the aircraft moves through the air, air friction or drag occurs in the same way that drag occurs when you push your hand through water. The power output, P, when a force, F, is applied to an object causing the object to move with a speed, v, is given by the equation: P = Fv. The thrust and speed of an aircraft can be related to the mechanical power output of the engines by the same equation. Thus, for an aircraft: mechanical power output = thrust speed.
AS A MATTER OF FACT The design of a wind turbine is very similar to an aircraft propeller engine, but in reverse. The wind moves over the blades of the turbine, generating a force that causes the blades to rotate around the central hub. Within the hub this is rotation is transformed into electrical energy using a generator. More on drag There are several types of drag that are created when an aircraft moves through the air; the two main types induced drag and parasite drag. Induced drag Induced drag occurs due to the three-dimensional nature of an aircraft wing. At the tip of the wing the difference in pressure between the upper and lower surfaces draws air around the tip towards the upper surface, creating a large whirl of air called a vortex. This changes the effective angle of attack across a significant length of the wing span, resulting in a proportion of the lift force acting to oppose the forward motion of the aircraft. This component of the lift is called induced drag. AS A MATTER OF FACT Modern passenger aircraft commonly feature a vertical surface at the wing tip known as a winglet or wing tip fence. This is designed to decrease the interaction between the upper and lower surfaces, reducing the size of the vortex and in turn reducing the induced drag. This reduced drag leads to lower fuel consumption and decreased operating costs.
Parasite drag Parasite drag is the name given to the combined effect of skin friction drag and form drag. Neither of these forces, in contrast to induced drag, contributes towards the lift force, so they are given the vicious collective name of parasite drag. Skin friction drag is particularly relevant in cases of high speed and of well-streamlined shapes. It is a friction force caused by the contact between air and the surface of the aircraft, and it can be reduced by keeping the surface of the aircraft clean and polished. Form drag is the drag due to the shape or form of a surface. Improving the streamlining of an aircraft (or a car, truck or train) reduces the amount of form drag it experiences. Smooth covers called fairings are used to enclose, or partially enclose, shapes such as wheels or joints between different parts of an aircraft. Parasite drag increases roughly proportionally to the square of the speed. For example, if the airspeed is doubled, the parasite drag will increase by roughly a factor of four. It is therefore in the best interests of aircraft designers to create aircraft that are as aerodynamically streamlined as possible. Lift-to-drag ratio Weblink: The four forces of flight In the final analysis, it is the total drag on an aircraft that determines the necessary thrust required for it to achieve a given airspeed. If we try to get more lift from an aircraft by increasing its speed, for example, we usually get more drag. For every aircraft, there is a particular airspeed that generates the minimum drag, and this is also the airspeed that will produce the maximum lift-to-drag ratio. The higher the lift-to-drag ratio, the less power is required from the engine. The ratio of lift to drag can be found from the ratio of horizontal distance travelled (glide distance) to loss of altitude when gliding. This is known as the glide ratio. The glide ratio and the lift-to-drag ratio have the same value. A gliding aircraft with a glide ratio of 9:1 can fly 9 units of distance forward through the air for every 1 unit of height lost. Some modern gliders used for long distance racing have a glide ratio of more than 50:1. Large commercial passenger planes have glide ratios of about 10:1.
For a gliding aircraft, the lift-to-drag ratio is equal to the glide ratio. SAMPLE PROBLEM 18. After the engines of an aircraft fail, it glides in a straight line to a safe landing in a field 5.6 km from the point directly below where the engines failed. The glide ratio of the aircraft is 1:1. a. How much altitude is lost by the aircraft for every 1.0 km of ground distance covered? b. What was the altitude of the aircraft when its engines failed? Assume that the ground over which the aircraft glides is level and that there is insignificant thermal activity in the air. c. What is the lift-to-drag ratio while the aircraft is gliding? Solution: a. b. glide ratio loss of altitude loss of altitude = = = = glide distance loss of altitude glide distance glide ratio 1000 m 1 83m glide distance = glide ratio 3 5.6 10 m = 1 = 4.5 10 m The aircraft had an altitude of 450 m when its engines failed.
c. lift to drag = glide ratio = 1 :1 REVISION QUESTION 18. a. A glider loses 10 m in altitude over a ground distance of.5 km during an exhibition of straight line flight. i. What is the glide ratio of the glider? ii. What is the lift-to-drag ratio of the glider? b. During a safety drill, a pilot must glide a small plane in a straight line to a safe landing from an altitude of 500 m after the engines are switched off. The glide ratio of the plane is 4:1. What ground distance should the pilot allow for the landing after switching off the engines? The lift-to-drag ratio changes with the angle of attack. As the angle of attack increases from zero, the lift-to-drag ratio increases. Once the angle reaches about 15 0, turbulence occurs the lift decreases and the drag increases. When a plane slows down, the lift decreases. The pilot can restore the lift, and the lift-to-drag ratio, by slightly increasing the angle of attack. Faster than sound As an aircraft approaches the speed of sound, the behaviour of the airflow over the aircraft changes. The air becomes compressible, rendering the standard theories of fluid flow behaviour outlined in the preceding sections inadequate. At such high speeds, the rate at which the aircraft is disturbing the air forms shock waves. A shock wave is a propagating disturbance associated with abrupt changes in temperature, pressure and density. The formation of a shock wave on the surface of a wing creates significant turbulence in its wake, which leads to a dramatic increase in drag. The Mach number is the ratio of speed of an aircraft to the speed of sound. The speed of sound is approximately 343 m s 1 or 135 km h 1 ; an aircraft travelling at this speed is said to be moving at Mach 1.0. The speeds at which aircraft travel are broken into four broad regions: Subsonic speeds are significantly less than Mach 1.0. The effects of compressibility can be ignored. Transonic speeds are around Mach 0.8 to 1.0. The entire aircraft is moving slower than the speed of sound; however, as the air speeds up over the top of the wing it may exceed the speed of sound, causing shock waves to form and significantly increasing drag. Supersonic speeds of Mach 1.0 to 5.0. The majority of air interacting with the aircraft is travelling faster than the speed of sound. Shockwaves are present and drag is significantly increased. Heating becomes increasingly prominent at higher speeds. Hypersonic speeds of Mach 5.0 and above. In addition to the supersonic effects, it becomes necessary to consider the chemistry of the air molecules. The majority of passenger aircraft travel at subsonic speeds to avoid the significant increase in drag associated with speeds in the transonic region and above. Aircraft designed to travel at supersonic speeds require: a thinner and more swept back wing, significantly more thrust capability, carefully designed control surfaces, and specialised engine intakes and outlets. Supersonic travel remains elusive to the general public due primarily to much higher costs from higher fuel consumption and limited flight paths due to the disruption caused by sonic booms affecting populated areas. Turning effect of a force For an aircraft to maintain level, steady flight that is, constant speed at a constant altitude the vertical force pair of lift and weight must be balanced, and the horizontal force pair of thrust and drag must also be balanced.
This results in the whole aircraft being balanced or in equilibrium. However, it is not only the size of the forces that must be taken into account, but also the distance between the line of action of the force and centre of gravity of the aircraft. If the lift is far back from the centre of gravity and the weight far forward, the aircraft will tend to tip onto its nose and be nose heavy. This tendency for the aircraft to rotate is due to the turning effect of the forces. The turning effect of a force is called a torque or moment. In this chapter, the term torque will be used. The magnitude of the torque created by a force about a given pivot point can be calculated by: τ = F r where τ = magnitude of the torque, measured in units of newton metres (N m) F = magnitude of the force, measured in units of newton (N) d = perpendicular distance between the line of action of the force and the pivot or reference point, measured in metres (m). When an object is not rotating, it is said to be in rotational equilibrium. In order to achieve rotational equilibrium about an axis, the clockwise torques must be balanced by the anticlockwise torques. In other words, the net torque, τ net, must be zero. Imagine two girls sitting on opposite sides of a seesaw. If they want to be in rotational equilibrium they each must sit at a distance from the centre of the seesaw such that the net torque is zero. Thus τ clockwise = τ anticlockwise. They would normally find the right distances by trial and error, but if they felt inclined to use calculations they would take torques about the centre of the seesaw. The only forces that need to be considered are the respective force due to gravity on the girls. The normal reaction force applies no torque because it acts at the pivot point. So if girl 1 was 1.5 m from the centre the equation becomes: mg d = m1g 1.5m The distance d can be calculated as long as the weights are known. When an aircraft flies normally in a straight line, the net torque on it about any axis is zero. It is in rotational equilibrium. Although the forces on an aircraft are ideally kept in balance, it is always advisable to have an extra force available that can be called into action when required to correct any out-of-balance occurrence. In a conventional aircraft design this force is provided by the tail plane. The tail assembly of an aircraft comprises a vertical tail fin and a horizontal tail plane, called the vertical and horizontal stabilisers, respectively. The tail plane provides a downwards force called the tail lift. The balance of the aircraft can be corrected by adjustments to the tail plane to make the net torque equal zero.
SAMPLE PROBLEM 18.3 An aircraft in level flight has a total wing lift of 3.6 10 6 N. The centre of pressure is 1 m from the centre of gravity and the tail is a distance of 45 m from the centre of gravity as shown in the figure below. Calculate the tail lift. Solution: In normal, level flight there must be no rotation about the centre of gravity. Take torques about the centre of gravity. Recall that the centre of pressure is the point at which the lift is considered to be acting on the wings. τ net = 0 τclockwise = τ L d = L d anticlockwise T T w w where L w = wing lift and L T = tail lift. (The torque due to the weight is zero because the weight acts through the centre of gravity.) L T = 6 45 m 3.6 10 N 1 m 5 LT = 9.6 10 N The tail lift is equal to 9.6 10 5 N in a downwards direction. REVISION QUESTION 18.3 a. Calculate the tail lift required to balance the wing lift of 480 000 N for a light plane in which the wing distance d w is 3.0 m behind the centre of gravity and the tail distance d τ is 8.0 m behind the centre of gravity. The plane is in level flight. b. A tail lift of.0 10 5 N balances a wing lift of 6.5 10 5 N for a plane in level flight. The centre of pressure is 4.0 m behind the centre of mass. How far is the tail from the centre of mass? The load in an aircraft must be balanced to achieve level flight. When luggage is loaded into commercial aircraft the location of the total mass has been carefully considered. Luggage is weighed at passenger check-in to allow accurate calculation of location of baggage. The weight and location of the fuel for the flight must also be considered. It must be positioned so that it doesn t produce an unwanted turning effect. Digital doc: Investigation 18.4: Paper glider Build a simple dart glider and explore the forces of flight.
SAMPLE PROBLEM 18.4 Excess baggage of mass 10 kg is loaded into a plane. The turning effect of the excess baggage is balanced by loading extra fuel into a tank located.4 m in front of the centre of gravity of a plane before it takes off. The excess baggage has been loaded 1.6 m behind the centre of gravity. What mass of extra fuel must be added? Assume that g = 9.8 N kg 1. Solution: Take torques about the centre of gravity. m fuel τ net = 0 τfuel = τbaggage mfuelg dfuel = mbaggageg dbaggage 1 1 9.8N kg.4 m = 10 kg 9.8N kg 1.6 m 1 10kg 9.8N kg 1.6 m mfuel = 1 9.8N kg.4 m = 80kg A mass of 80 kg of extra fuel must be added to the tank. REVISION QUESTION 18.4 a. Unexpected cargo of mass 600 kg is loaded onto a plane in a hold.8 m in front of the centre of mass of the plane. In order to compensate for the turning effect of this cargo, the pilot loads extra fuel into a reserve tank located 4. m behind the centre of mass. What mass of extra fuel should the pilot add? b. Two containers of masses 000 kg and 3000 kg respectively must be loaded onto a cargo plane so that they have no net turning effect. The lighter container is placed 6.0 m in front of the centre of mass. Where must the heavier container be placed? Designing for lift and drag The lift coefficient (C L ) and drag coefficient (C D ) are used by aircraft designers to provide a comparable measure of the amount of lift and drag generated by a particular shape as it moves through the air. These coefficients are defined as follows: = F = F ρva ρva L D CL and CD 1 1 where C L = the lift coefficient C D = the drag coefficient F L = the lift force generated F D = the drag force generated ρ = the fluid density (measured in kg m 3 )
v = the speed of the fluid (measured in m s 1 ) A = the reference area in m (for lift this is the area of the wing viewed from above, for drag this is the area of the wing viewed from the front) The values of the lift and drag coefficients for different designs are determined by varying the shape, angle of attack and speed, and taking measurements of the forces generated. This can be done experimentally in a wind tunnel or using computer-based analysis tools. The lift and drag coefficient formulae can be rearranged to give the following formulae for calculating the lift and drag forces. 1 1 FL = CL ρv A and FD = CD = ρv A These relationships can be very useful for estimating the effect that a change in the design or configuration of an aircraft will have on the lift and drag forces produced. For example, it can be seen that doubling the velocity of the aircraft will quadruple the lift and drag force generated. AS A MATTER OF FACT Reducing the drag force is crucial for designing energy efficient cars. To minimise drag, it is necessary to design for the lowest value of drag coefficient multiplied by frontal area (commonly referred to as drag area) or C D A. The frontal area can be minimised by designing more compact vehicles, and the drag coefficient can be reduced by streamlining the vehicle shape to reduce disruption to the airflow. Modern vehicles have drag coefficients between 0.5 and 0.35, with the Tesla Model S setting the benchmark at 0.4. The drag area of the first massproduced electric car, the General Motors EV1, was 0.37 m compared to.47m for the Hummer H. The Tesla Model S has a drag area of 0.57 m. Controlling flight The motion of an aircraft is controlled by moving parts on its surface. These moving parts are called control surfaces. An aircraft in flight can move around three different axes:
the lateral (parallel with a line from wing tip to wing tip and through the centre of gravity) the vertical (perpendicular to the length of the plane and through the centre of gravity) the longitudinal (running along the length of the plane and through the centre of gravity). The primary control surfaces on an aircraft are called the elevator, rudder and ailerons. These components can be moved in either direction to change the camber and angle of attack of the aerofoil. This changes the size, and sometimes the direction, of the force generated, which in turn generates a torque that causes the aircraft to rotate in a particular direction. Movement around the lateral axis is known as pitch and is controlled by moveable areas on the rear edge of the horizontal tail plane called elevators. Raising the elevators decreases the camber of the tail, creating more downwards force, in turn raising the nose of the aircraft. Moving the elevators down produces the opposite effect. Pitch, yaw and roll Movement about the vertical axis is known as yaw and is controlled by a single moveable area along the rear edge of the vertical tail known as the rudder. This controls the direction, left or right, in which the aircraft is pointing. Movement about the longitudinal axis is known as roll, which is controlled by moveable areas on the trailing edges of both wings, known as ailerons. The ailerons work in opposite directions, one up and the other down. The aileron that moves up reduces the lift, so that wing will drop. The aileron that moves down causes more lift, so that wing will rise. The resultant turning effect causes the plane to roll, or bank. Weblink: Flight controls
Control surfaces on a small plane Stages of flight The typical flight of an aircraft contains a number of stages, each of which require a difference balance between the forces on the aircraft. During take-off the thrust must be significantly greater than the drag so that the aircraft will accelerate down the runway. Once the aircraft reaches the appropriate speed, the pilot will use the elevator to raise the nose, increasing the lift. Once the lift is greater than the force due to gravity the aircraft will accelerate upwards. During climb the aircraft will be flying upwards at an angle. As a consequence of this incline, a component of the force due to gravity acts to oppose the motion of the aircraft, requiring greater thrust to balance this out. Digital doc: Investigation 18.5: Investigating gliders Construct a simple glider and investigate the effects of design parameters on performance. The cruise stage is where aircraft are designed to spend most of their operating life. During this stage the forces are in balance; lift equals force due to gravity and thrust equals drag. Minimising drag in this configuration will minimise fuel consumption. When an aircraft makes a turn or manoeuvre to the left or right you ll notice that it also rolls into the turn. This is to re-orient the lift force so that a component of it provides the required force left or right to cause the aircraft to change direction. During the glide or descent phase of flight the nose of the aircraft is pointing slightly downwards. At this angle a component of the force due to gravity acts in the direction of motion of the aircraft, allowing the thrust to be reduced. In preparation for landing the pilot will decrease the speed of the aircraft by reducing the thrust. The required lift is maintained using moveable devices on the rear of the wing called flaps that increase the area and camber of the wing, producing more lift at a lower speed.
Forces during climb, turn and glide. Wind tunnels A great deal of research into the effects of airflow is done in wind tunnels. Models of aircraft (and cars, trucks, trains and so on) are fixed in the wind tunnel. A large fan creates an artificial airflow that is exactly the same as if
the air were still and the aircraft was moving. Sensors can be used to measure lift and drag and special cameras can detect variations in the airflow caused by changing the position or dimensions of the control surfaces. Wind tunnels can now be built, leased or even bought in kit form. Plans for building your own wind tunnel can be downloaded from the internet. Simulations of wind tunnel investigations are also available on the internet. A scale model is used in a wind tunnel to assist in aircraft design. Weblink: Online wind tunnel simulation Digital doc: Investigation 18.6: DIY wind tunnel Design and build a wind tunnel and use it to test wing sections.
AS A MATTER OF FACT The first wind tunnel was constructed by Orville and Wilbur Wright in 1898. Many of the features of the Wright brothers first powered plane were determined by experimental trial and error using their wind tunnel. A replica of the wind tunnel built and used by the Wright brothers in 1901 to help in the design of the gliders they built before their first powered flight in 1903. The data obtained from their 1901 wind tunnel was used in the design of the propellers for their powered Flyer. Chapter review Summary Lift and the force due to gravity are a force pair that acts on an aircraft in flight. Thrust and drag are a force pair that acts on an aircraft in flight. The force due to gravity acting on an aircraft is thought of as acting at one position, the centre of gravity. When a force acting on an aircraft in flight is drawn as an arrow, the arrow represents the resultant of all the component forces that contribute from various parts of the aircraft. The Equation of Continuity can be expressed as: Q = va = v A 1 1. The Bernoulli principle was expressed as an equation and states: 1 ρ + ρ + = constant. v gh P Another way to express the Bernoulli principle in the context of flight is that faster moving fluids have lower pressure. The generation of lift by a wing can also be explained using Newton s Third Law. The wing pushes the air downwards and the air pushes the wing upwards.
There are several types of drag that are created when an aircraft moves through the air. The two main types are induced drag and parasite drag. Parasite drag is the combined effect of skin friction drag and form drag. The total drag acting on an aircraft in flight determines the necessary thrust required for the aircraft to maintain a given airspeed. The behaviour of airflow changes when travelling at or beyond the speed of sound. This can lead to the formation of shockwaves and significant increases in drag. Torque is the turning effect of a force about a pivot or reference point. An aircraft in flight can move around three different axes: the lateral (known as pitch), the longitudinal (known as roll) and the vertical (known as yaw). The primary control surfaces on an aircraft are the elevator, rudder and ailerons. There are six main stages of flight: take-off, climb, cruise, turn, glide and landing. The balance of forces on the aircraft is different in each stage. Wind tunnels are used extensively to test the aerodynamics of aircraft designs. An aircraft s performance can be judged from its lift-to-drag ratio, also known as the glide ratio. Questions Applying Newton s laws to aircraft 1. Explain the difference between the centre of pressure and the centre of gravity.. Describe the resulting motion, if an aircraft has the following forces acting on it in flight: a. lift = 6000 N, drag = 500 N, weight = 5900 N, thrust = 500 N b. lift = 4000 N, drag = 600 N, weight = 4000 N, thrust = 500 N c. lift = 7000 N, drag = 300 N, weight = 6800 N, thrust = 310 N d. lift = 6600 N, drag = 450 N, weight = 6800 N, thrust = 460 N. 3. A business jet is travelling at a constant speed of 00 m s 1 while its engines provide a total thrust of 5 kn. a. If it is in level flight, what is the magnitude of the total drag on the jet? b. Assuming that all of the energy delivered by the engines is used to provide thrust, what is the power output of the engines? Moving through fluids and Bernoulli s equation 4. What basic difference between fluids and solids causes them to behave differently in terms of their motion? 5. If a fluid flows through a pipe of cross-sectional area 61 cm at a speed of 9.3 cm s 1, what must the crosssectional area be to make it speed up to 13 cm s 1? 6. If a fluid flows at a speed of.1 m s 1 through a pipe of diameter 0.15 m, what speed will it flow at when the pipe widens to a diameter of 0.45 m? 7. Air flows through a wind tunnel with a circular cross-section. a. How would you change the cross-sectional area of the wind tunnel in order to double the speed of the air passing through it? b. By what factor would the radius of the wind tunnel change to achieve the doubling of airspeed?
8. Assuming that everything else remains constant, what change in diameter of a wind tunnel would produce a 10-fold increase in the speed of the air moving through it? 9. Describe what happens to the pressure in a fluid as its speed increases. 10. Explain in terms of Bernoulli s principle how an aerofoil develops lift. 11. On the aerofoil below: a. draw and label an arrow to represent the lift force acting on the aerofoil b. draw and label the angle of attack c. label the trailing edge of the aerofoil. 1. The Airbus A380 has four jet engines, each capable of producing a maximum thrust of 370 kn. If the aircraft is travelling at 70 km h 1 and each engine is running at maximum thrust, what is the total mechanical power output of the aircraft? Lift and drag 13. What is the cause of wing-tip vortices? 14. The graph below shows how the parasite drag and induced drag acting on a particular aircraft change as the airspeed changes. a. On the graph, draw and label the curve representing the total drag (that is, the sum of the parasite and induced drags). b. At what airspeed does the maximum lift-to-drag ratio occur? c. Explain the importance of a high lift-to-drag ratio. d. Which region of the graph represents the conditions under which a stall is likely to occur? e. Explain what happens to the air around an aircraft wing when a stall occurs. 15. An aircraft has a glide ratio of 9:1 and is at an altitude of 100 m when its engine cuts out. a. How far could it travel before landing, assuming minimal thermal activity? b. What is the lift-to-drag ratio for this aircraft while it is gliding? 16. A glider loses 800 m in altitude while it covers a ground distance of 1 km. Calculate its: a. glide ratio b. lift-to-drag ratio. 17. A glider with a glide ratio of 40:1 glides in a straight path over a ground distance of 3.6 km to make a perfect landing. What was its initial altitude?
18. The lift equation is given as: 1 FL = CL ρv A What would be the overall effect of the lift produced by an aircraft in each of the following scenarios: a. decreasing the wing area by a factor of 1.5 by retracting the flaps b. increasing the aircraft speed by a factor of c. increasing the lift coefficient by a factor of by deploying the flaps d. halving the aircraft speed. Torque and equilibrium 19. An aircraft in level flight has a wing lift force of 15 000 N. The centre of pressure is 1.1 m behind the centre of gravity. The tail lift acts at a distance of 9.3 m from the centre of gravity. a. What is the size and direction of the tail lift? b. Why is it not necessary to know the mass of the plane to answer part (a) of this question? 0. If the tail lift in question 19 was reduced while the wing lift remained the same, the centre of gravity of the aircraft would need to be shifted. How can this be achieved? 1. A cargo plane is loaded with two large containers. The first container, which has a mass of 10 000 kg, is loaded into a hold located 1 m behind the plane s centre of gravity. The second container, which has a mass of 15 000 kg, is loaded so that it compensates for the torque applied by the first container. Where should the second container be located?. A passenger plane s rear fuel tank has been filled to allow for the usual amount of baggage in the rear hold, which is located 3.6 m behind the plane s centre of mass. The rear fuel tank is 4.0 m behind the centre of mass. However, an extra 00 kg of cargo has been placed in the hold. What mass of fuel must the pilot release from the rear tank before taking off to compensate for the turning effect of the extra baggage? Performance and control of an aircraft 3. Describe, without the aid of a diagram, the longitudinal, vertical and lateral axes of an aircraft. 4. Complete the following table. Type of motion roll Axis about which motion occurs vertical Aircraft control surface responsible for motion elevators