VCE Physics

Unit 2

Topic 3

Investigations: Aerospace

Unit OutlineApply the concept of forces, moments and equilibrium to balancing an aircraft;explain lift in terms of Bernoulli’s Equation and the rate of change of momentum model lift and Bernoulli’s concepts using a wind tunnel;explain drag, skin friction drag, pressure drag and principles of thrust;investigate experimentally the relationship between power and thrust;analyse aircraft performance including takeoff, climb and descent and cruise;investigate experimentally identified aspects of performance using a model.Use computer models to investigate phenomena associated with flightUse information sources to assess risk in the use and testing of flying models.Use safe and environmentally responsible practices in use and testing of flying models

Forces on Aircraft

Thrust Drag

Lift

Weight

All aircraft are subject to 4 forces which, in combination, determine their performance.These are:

1. Weight – the action of gravity on the total mass of the aircraft.

2. Lift – the aerodynamic force generated by the flight surfaces (mainly wings and horizontal tailplanes). Lift opposes weight

3. Thrust – the forward force produced by the power source (propeller or jet)

4. Drag – the frictional force resulting from the passage of the aircraft through the air. Drag opposes thrust

Aircraft Control - PitchAn aircraft must have the ability to move its nose upwards and downwards with respect to its tail in order to climb and descend.

This form of motion is called PITCH and is achieved by the ELEVATORS,control surfaces attached to the rear (trailing edge) of the horizontal sections of the tail.

Pitch occurs around a horizontal axis passing through the centre of mass

The pilot controls pitch by pulling back or pushing forward on the control column in the cockpit

Aircraft Control - RollAn aircraft must have the ability to lift one wing with respect to the other in order to help to change its heading (bank)

This form of motion is called ROLL and is achieved by AILERONS, control surfaces attached to the trailing edge near the wing tips

The pilot controls roll by moving the control column from side to side

Roll occurs around an axis running the length of the fuselage passing through the centre of mass

Aircraft Control - YawAn aircraft needs the ability to turn left and right.

This form of motion is called YAW and is achieved by the RUDDER, a control surface attached to the trailing edge of the Vertical Stabilizer on the tail.

The pilot controls the rudder with a pair of foot pedals in the cockpit. Yaw occurs around a vertical

axis through the centre of mass

Centre of Mass

In the vertical plane the weight acts through the “centre of mass” of the aircraft.

The Centre of Mass of any object with size is a point where all the object’s mass can be considered to be concentrated.

The position of the centre of mass can be altered by the way an aircraft’s payload (passengers, baggage and freight) are distributed within the craft.

Centre of Mass

For regularly shaped objects eg. squares or rectangles, cubes or spheres

The Centre of Mass is often called the Centre of Gravity of the aircraft.

the Centre of Mass of the object is in the geometric centre of the object

Centre of Mass

Torque

Objects that turn or twist do so because they are subject to a TORQUE.

Mathematically:Torque = Lever Arm x Force

= r F

The Lever Arm is the perpendicular distance between the pivot point and the point of application of the force.

F

r

Where:

= Torque (Nm)r = Lever Arm (m)

F = Force (N) Pivot Point

Torques act in all three directions of aircraft motion; Pitch, Roll and Yaw.At the Centre of Pressure the sum of the Rotational Torques is Zero

Torques are vectors whose direction is usually assigned as either clockwise or anticlockwise

Centre of PressureThe Centre of Pressure of an aircraft is that point around which it tends to rotate in response to lift forces.

The Centre of Pressure depends only on the SHAPE of the aircraft.

The relationship between the positions of the centre of mass and the centre of pressure decides whether an aircraft is able to maintain stable flight.

There is a different requirement for stability in each of the three axes of movement, pitch, roll and yaw

Centre of Pressure

Stable Flight

Pitch stability requires that the centre of vertical pressure (lift) fall behind the centre of mass.

Centre of Mass

Centre of Pressure

Roll stability requires that longitudinal roll axis of the airplane (lift) lie above at the centre of mass, as seen from the front (or tail) the airplane.

Yaw stability requires that the centre of pressure fall well behind the centre of mass as seen from the sides of the airplane.

Flight Stability

Centre of Mass(Weight)

Centre of Pressure(Lift)Let the Centre of Mass be the

point about which the aircraft pivots.

The torque exerted by the lift force tends to make the aircraft rotate in a clockwise direction and thus dive.

This tendency must countered if the aircraft is to fly straight and level.

The countering anticlockwise torque is generated by the horizontal stabilizers of the tail, generating downward “lift”.

Downward Lift

For an aircraft to be controllable the Centre of Pressure must be behind the Centre of Mass

Balancing Torques

Centre of Mass(Weight)

Centre of Pressure(Lift)

Downward Lift

300 kN

225 kN

? kN

18 m

6 m

Torque = Lever Arm x Force

= r F

For “balance” it is a requirement that Clockwise Torques = Anticlockwise Torques

Clkwise = (6)(225)

Anticlkwise = (18)(x)

Thus, (18)(x) = (6)(225) or x = 75 kN

Maximum Take Off Weight (MTOW) (really a misnomer) of a large commercial airliner is approximately 30,000 kg leading to a total weight of approx 300,000 N (300 kN)

Taking moments about the aircraft’s Centre of Mass and remembering:

Assume the Centre of Pressure is 6.0 m aft of the Centre of Mass with total lift forces of 225 kN

The centre of “lift” of the horizontal stabilizers 18 m behind the centre of mass.

What force is need for aircraft balance ?

75

Bernoulli’s Principle

Aerofoils produce lift because they obey the principle of conservation of energy, embodied in Bernoulli’s Principle.

Higher velocity means lower pressure, and vice versa (assuming constant mechanical energy).

Bernoulli’s principle takes account of the kinetic energy of moving air and the potential energy stored in the “springiness” of the air. (Energy is stored in pressurized air).

Moving air has kinetic energy just as any other moving object: Kinetic Energy per volume = ½ρv2 , where v is the local velocity, and ρ is the density, i.e. the mass per unit volume. Combining these, we conclude: P + ½ρv2 = Mechanical Energy per volume.Then, using the law of conservation of energy we conclude that a given air parcel’s mechanical energy remains constant as it flows past the wing.

Pressure, P, is (by definition) a force per unit area, which is equal to energy per unit volume: P = Potential Energy per volume    

Daniel Bernoulli1700 - 1782

Bernoulli’s Equation

The mathematical statement of this energy conservation is stated in the BERNOULLI EQUATION: P1 + ½ρv1

2 = P2 + ½ρv22

Remember:Energy per unit Volume before the wing passes through the air parcel = Energy per unit Volume after the wing passes through the air parcel.

v1 v2A1 A2

A1 > A2

v2 > v1

P2 < P1

P1 P2

Thus greater speed means lower pressure

AerofoilsThe surfaces on aircraft which provide lift are generally called AEROFOILS, or in America, airfoils.

There are a number of important terms associated with these structures:

The CHORD LINE is the straight line from the leading edge to the trailing edge of the airfoil.

The MEAN LINE of the airfoil is the line equidistant from the lower and upper surfaces, measured perpendicular to the chord line.

The CAMBER of the airfoil is the maximum distance between the chord line and the mean line.

Chord Line

Trailing Edge

Mean LineLeading Edge

Upper Surface

Lower Surface

Camber

Why Do Wings “Fly” ?This is not a simple question;There are two common explanations

1. Based loosely on the Bernoulli Principle, higher velocity means lower pressure.

The air travels a greater distance over the top of the wing.Therefore must travel faster. Therefore produces lower pressure.Therefore pressure difference produces a lift force.

This a a simplistic explanation of a wing’s operation and is just plain wrong !!!!!!!

This theory assumes that the air split by the leading edge must join up again at the trailing edge.

2. The second explanation is based on Newton’s 3rd law (action and reaction) and the law of conservation of momentum

Why Do Wings “Fly” ?

Different coloured dyes are introduced into the air steam at regular intervals.

Actual airflow around a wing.

The air moving over the top arrives at the trailing edge 10 to 15 ms EARLIER than that passing below the wing.

The “split” air has high and low velocities

Why Do Wings “Fly” ?The airflow produces upwash at the leading edge and downwash at the trailing edge

This results in setting up a circulation or VORTEX around the wing.

This wing shows the natural airflow with circulation included.The circulation adds to airflow above the wing and subtracts from it below.

Why Do Wings “Fly” ?This understanding of vortex production leads to the Newton’s 3rd Law explanation of “flight”

The fact that the air is forced downward clearly implies that there will be an upward force on the wing as a Newton's 3rd law reaction force.

From the conservation of momentum viewpoint, the air is given a downward component of momentum behind the airfoil, and to conserve momentum, something (the wing) must be given an equal upward momentum.

The idea of bound vortex and wake vortex may be easier to visualise when shown as above

Why Do Wings “Fly” ?

Each “cylinder of air” is given a downward component of momentum by the man “standing” on them.An upward component of momentum is imparted to the man in order to meet the law of conservation of momentum.Thus the man is supported and can “walk on air”

Wake vortices shed from this aircraft in flight can be clearly seen.

The conservation of momentum may be better understood by the walking on air analogy.

These vortices are extremely dangerous to following aircraft and take offs must be spaced to allow them to dissipate.

Angle of AttackAngle of attack is a term used in aerodynamics to describe the angle between the wing's chord and the direction of the relative wind (RW), effectively the direction in which the aircraft is currently moving. Angle of attack is often referred to as alpha (α)

RW

Angle of AttackThe amount of lift generated by a wing is directly related to the angle of attack, with greater angles generating more lift.

Stalled aerofoil

The Coefficient of Lift is a number associated with a particular shape of aerofoil, and is used to predict the lift force generated by a wing with this cross section.

The graph of Coefficient of Lift vs. Angle of Attack follows the same general shape for all aerofoils, but the particular numbers will vary.

This remains true up to the stall point, where lift starts to decrease again because of airflow separation.

STALL POINT

DragDrag is the resistance of the atmosphere to an aircraft pushing through it and depends upon:- (a)  the streamlining of the aircraft body (b)  the attachments to the airframe (c) turbulence at the junctions of structural components (d) the cooling airflow around the engine (e)  the roughness of the surface skin (f)  the density of the air   (g)  the velocity of the airflow (h)  the amount of lift being produced – which will increase as the angle of attack increases.

Drag

Airspeed

Parasite Drag

Induced Drag

Total Drag

Max RangeSpeed

The majority of the list (items a to g) are collectively known as PARASITE DRAG.They increase as speed increases until the total drag force equals the maximum thrust that can be produced.

Item (h), is the INDUCED DRAG, and is a consequence of lift generation, being very high, maybe 70% of the total drag, at the high AoA of the minimum controllable airspeed, but decreasing as speed increases being possibly less than 10% of the total at full throttle speed.

Total Drag is the sum of Parasite and Induced Drag

Flight – Take OffAt take off, an aircraft needs to produce large amounts of lift at relatively low speeds.

This is achieved by changing the shape of the wing (increasing its Camber) using FLAPS attached to the trailing edge of the wing. Large, heavily laden passenger aircraft may need to produce even more lift by the use of slats attached to the leading edge of the wing.

Angle of Attack

Coefficient of Lift (cL)

No Flaps

With Flaps

Flaps and Slats

For a given angle of attack, flaps give a greater cL than no flaps but reduce the stall point from about 170 to about 120.

Flaps and slats together increase both cL AND the stall point often to greater than 200.

Flight - Climbing

Generally, for an aircraft to climb Thrust MUST be greater than Drag and Lift greater than Weight

When an aircraft is climbing the 4 fundamental forces are not 900 apart as they are in level flight.

Weight always acts toward the centre of the earth and lift always acts at right angles to the long axis of the aircraft.

To maintain equilibrium in climb the following must be met: T = (D + W'') and L = W'

Weight can be broken up into components W’ opposing L and W” adding to Drag (D)

Flight - TurningObjects do not naturally travel in curved or circular paths. They must be forced to do so.The force required is called a Centripetal (centre seeking) Force labelled Fc.This force does not exist in its own right but must be supplied by something.

To maintain altitude in a level turn the vertical component of the lift must be equal to the weight of the airplane, so L' = W    The horizontal component of the lift is providing the Centripetal Force that makes the airplane turn.

As mentioned earlier lift always acts perpendicular to the wing. By banking an aircraft the lift is divided into two components, the vertical and horizontal components.

Here the centripetal force is supplied by the tension in the string

Flight - DescendingAn aircraft when it is descending is in a glide. It does so without engine power at a constant speed and rate of descent.

Weight (W) is again resolved into 2 components. The vertical component (W') is perpendicular to the horizontal component (W''). In absence of thrust, the horizontal component (W'') is providing a forward force.

To maintain equilibrium in glide the following must be met: W'' = D and W' = L

Generally, for an aircraft to descend Thrust MUST be less than Drag and Lift less than Weight

Speed of Sound

Aircraft travelling at greater than the speed of sound (about 340 ms-1 at sea level) are breaking the “sound barrier”.

As this happens the fall in pressure around the aircraft causes the water vapour in the air to condense, forming “clouds”.

Ollie Leitl 2004