Flight InvestigationsTEXT BOOK CHAPTER 16 PAGE 362 - 377

Flight – the beginning The Wright Brothers

https://www.youtube.com/watch?v=VcqxI-OJ1mk

Failures / Early Attempts

https://www.youtube.com/watch?v=fw_C_sbfyx8

Newton’s laws of motionhttps://www.youtube.com/watch?v=iH48Lc7wq0U

Summary:

First Law The velocity of an object can change only if there is a non-zero net force acting on it.Second Law The relationship between the acceleration of an object, the net force acting on it, and the object’s mass can be expressed as Third Law When an object applies a force (action) to a second object, the second object applies an equal and opposite force (reaction) to the first object

Forces acting on an aircraftThe main forces acting on an aircraft in level flight can be identified as vertical and horizontal pairs.Vertical Pair – Lift and WeightHorizontal Pair – Thrust and Drag

Forces acting on an aircraftLift is the upward-

acting force created by a wing moving through

the air

Weight is the force applied to an object due to

gravity

Thrust is the forward force that drives an aircraft through the air

Drag is the rearward-acting force that resists the motion of an aircraft through

the air

Lift Force• Acts upwards, at right angles to the airflow direction.• Lift force is generated over the entire wing, although it is usually thought of as acting at one position along the wing.• This position is known as the centre of lift or the centre of pressure (CP).

Weight Force• The weight force is considered to act through the centre of gravity (COG) - This is the point where the mass of the aircraft is considered to be concentrated and is the point of balance.• If an aircraft were hung from a cable attached to its centre of gravity, it would hang level and perfectly balanced.• The location of an aircrafts COG depends on the load it carries (fuel, cargo, passengers etc)

In level flight the Lift Force and Weight Force are equal in size and opposite in direction.

Drag Force

• 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.

• There are several different types of drag forces that act on different parts of the aircraft when in flight. The arrow used to represent the drag, refers to the resultant of all the drag forces that act on every part of the aircraft.

Thrust Force• Causes an aircraft to move through the air.• Propeller blades or jet engines push the air backwards (an action).• The air pushed backwards therefore pushes the plane forwards with a force of equal magnitude (a reaction).• The magnitude of the thrust depends on the total Power delivered by engines of the aircraft.• 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:

Which for an aircraft can be related to the mechanical power output of the engines:

Forces acting on an aircraft Power (Watts, W) Force/Thrust (Newtons, N) Speed/Velocity (ms-1)

A jet travels at a constant speed of while it’s engine provides a total thrust of 10kN.

What is the Power output of the engines?

If in level flight, what is the total drag on the jet?In level flight, Thrust = Drag∴ Drag = 10,000 N

Forces acting on an aircraft If the net force acting on an aircraft in flight is zero, it maintains constant velocity.

If the net force acting on an aircraft is not zero, the magnitude and direction of the net force determines the magnitude and direction of the acceleration of the aircraft.

Describe the direction of the resulting motion (acceleration) if an aircraft has the following forces acting upon it in flight:

a) Lift = 5000 N, Drag = 800 N, Weight = 5000 N, Thrust = 1200 N Net Force 400 Forward – Plane accelerates Forward b) Lift = 6000 N, Drag = 900 N, Weight = 5000 N, Thrust = 900 N Net Force 1000 Upward – Plane accelerates Upward

Forces acting on an aircraft

The Aerodynamics of Flight

https://www.youtube.com/watch?v=5ltjFEei3AI&feature=related

Now Do Text Book - Chapter 16

Questions 1 – 3 Pg 376( Applying Newton’s laws to

Aircraft)

Moving through fluids Aeronautics is concerned with the motion of aircraft through gases – in particular, air.

To understand how lift in an aircraft occurs, we need to understand a little about movement through fluids.

All liquids and gases are fluids. Fluids, like solids, are composed of small particles.

Particles are packed less tightly in fluids than in solids, allowing movement of particles more freely.

Moving through fluids In the 1700’s Daniel Bernoulli developed the equation of continuity which stated,

“ All material that enters a pipe will leave the pipe” which can be expressed as:

Q = flow rate ( measured in cubic metres per second ) v = fluid speed ( measured in meters per second ) A = cross-sectional area of the pipe ( measured in square metres )

Moving through fluids

Q = flow rate ( measured in cubic metres per second )v = fluid speed ( measured in meters per second )A = cross-sectional area of the pipe ( measured in square metres )

eg1. In the diagram pictured, A1 is larger than A2. Using the equation of continuity, explain the difference in V1 and V2 in this scenario.

V1 < V2

Wider pipe, slower speed Narrower pipe, faster speed

Moving through fluids Q = flow rate ( measured in cubic metres per second )

v = fluid speed ( measured in meters per second )A = cross-sectional area of the pipe ( measured in square metres )eg2. Air flows through a pipe with a cross

sectional area of at a speed of . If the air exits the pipe at a speed , what is the cross sectional area of the end of the pipe?

eg3. Air flows through a pipe with radius of at a speed of . The end of the pipe has a radius of What is the velocity of the air travelling at the end of the pipe?

Q = flow rate ( measured in cubic metres per second )v = fluid speed ( measured in meters per second )A = cross-sectional area of the pipe ( measured in square metres )

𝐴𝑟𝑒𝑎𝑜𝑓 𝑎𝑐𝑖𝑟𝑐𝑙𝑒=𝜋𝑟 2

Now DoText Book - Chapter 16

Questions 4, 5, 6, 7a Pg 376( Moving through fluids and Bernoulli’s

Equation)

𝐴𝑟𝑒𝑎𝑜𝑓 𝑎𝑐𝑖𝑟𝑐𝑙𝑒=𝜋𝑟 2

𝑟𝑎𝑑𝑖𝑢𝑠=𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟2

Fluid Speed and Pressure – Bernoulli’s Principle

Applying the Law of Conservation of Energy to fluid flow, Bernoulli found that the total energy of fluid is constant throughout the flow. Regardless of the pressure/speed of the fluid in the system, the total energy stays the same.Using this principle, he derived an equation which states:

When dealing with aircraft travelling at high speeds, exceptions begin to occur due to friction on the wing of the aircraft, which causes heat. For aircraft, we refer to another version of this formula, developed by Leonhard Euler.

= fluid density ( ) = speed of the fluid ( ) = acceleration due to gravity ( ) = vertical displacement of the fluid ( ) = static pressure of the fluid ( )

(total pressure)

Euler found that an increase in speed, created when fluid flows through a narrow section of a pipe, produced a decrease in static pressure. He named this principle,the Bernoulli Principle which says, the pressure of fluid decreases as its velocity increases.For fluid at a constant height:

(total pressure)

= fluid density ( ) = speed of the fluid ( ) = vertical displacement of the fluid ( ) = static pressure of the fluid ( )

Dynamic Pressure (pressure

associated with movement)

Fluid Speed and Pressure – Bernoulli’s Principle

We can apply these principles to the wing of the aircraft.An aircraft’s wing has a curved top and a flat bottom – this shape is known as aerofoil.

The wing is shaped this way so that air travelling over the it’s top surface speeds up.This in turn reduces the air pressure above the wing to below normal pressure, resulting in an upward force known as the lift force.

Fluid Speed and Pressure – Bernoulli’s Principle

Newtonian Lift…..is the name given to the effect of the action reaction pair on the wing of an aircraft.

Newtonian Lift is the lift created in addition to the effects described by the Bernoulli principle. As Aerofoil passes through the air :• It pushes air below it downward (an action)

• Consequently, the air beneath the wing pushes upward (a reaction)

• The greater the amount of air that is deflected downwards by the wing, the greater the upward force, or the greater the Newtonian Lift.

Newtonian Lift only accounts for about 15% of the lift required for a

cruising aircraft.

Newtonian Lift• The downward flow of air caused by Newtonian Lift is called downwash

• The amount of downwash depends on the shape of the wing, the and the speed that the aircraft is travelling at.

• An effective wing design may involve trying to produce as much downwash as possible, without causing turbulence.

• The amount of downwash can change, due to the angle of the wing, called the angle of attack.

Angle of Attack• The position that the wing is angled at is called the angle of attack.• Increasing the angle of attack increases the lift• BUT, as the airflow experiences a greater disturbance, drag is increased, so more thrust must be produced by the engines to counteract the drag• If the angle of attack is increased significantly, the air is disturbed too much, increasing drag to the point of turbulence.

As the angle of attack increases, the planes lift increases, until the angle reaches the critical angle. At this point, lift drops, drag

increases and the plane stalls.

Now DoText Book - Chapter 16

Questions 12, 13, 14 Pg 376( Moving through fluids and Bernoulli’s

Equation)

ThenContinue on with your report

More on Thrust & Drag &

Drag Ratio

HOMEWORK• Read text book pages 368 – 370 ( up until the turning effect of a force section )• Answer questions 15 – 20• You should include of some the questions and your responses in your report, to support the concept / calculations

Glide RatioThe glide ratio of an aircraft is the ratio of the horizontal distance travelled (glide distance) to the loss of altitude while gliding (no power to the plane).

Its value is equal to the ratio of lift to drag.

Applying the equation:eg1. The engines of an aircraft fail while flying at an altitude of 500m , leaving the aircraft gliding to a safe landing 2 kms from the point of failure.

a) The glide ratio

b) The Lift to Drag Ratio

=

= the glide ratio =

Glide Ratioeg2. The engines of an aircraft fail while flying at an altitude of 800m. If the glide ratio is 6:1, calculate the horizontal distance travelled by the aircraft after the failure.

Using your paper planes from last lesson, estimate the glide ratio of your plane and compare with others in the class. Amend your plane to try and achieve a greater glide ratio.

Turning Effect of a forceSo we know that for an aircraft to maintain steady, level flight, the vertical pair and horizontal pair of forces must each be balanced.

Lift Force = Weight Force = Constant Altitude

Thrust Force = Drag Force = Constant Velocity

Turning Effect of a forceBut if we look closer, it’s not only the size of the forces that we need to take into account - we need to consider the distance between the line of action of the force and the centre of gravity of the aircraft.If lift is generated far back from the centre of gravity and weight far forward, the aircraft will not be balanced and will rotate due to the turning effect of the forces. This turning effect is called torque.

Torque = Force x distance

( N m ) (N) (m)

Turning Effect of a forceIn an aircraft, this may be considered in the example below.A plane has 4 engines each outputting a thrust force of 20,000N.The inner engines are 10 m from the centre, the outer engines are 5 m from the centre.The outer right engine cuts out. To keep the plane in astraight line, what force must the right engine output tocompensate for this loss?

𝜏=𝐹×𝑑

Eg2. A plane was loaded ready for flight, until 200kg of excess baggage was loaded onto the plane, located 5 m behind the centre of gravity of the plane. To ensure the plane remains in equilibrium, this weight must be balanced.This is done by adding fuel to a reserve tank 2 m in front of the centre of gravity of the plane. How much fuel must be added to maintain equilibrium?

𝜏=𝐹×𝑑

Now Do Text Book - Chapter 16

Questions 21, 23, 24 Pg 377( Torque & Equilibrium)