Transcript VCE Physics Unit 2 Topic 3

VCE Physics
Unit 2
Topic 3
Investigations:
Aerospace
Unit Outline
Apply 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 flight
Use 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
All aircraft are
subject to 4
forces which, in
combination,
determine their
performance.
These are:
2. Lift – the aerodynamic force
generated by the flight
surfaces (mainly wings and
horizontal tailplanes). Lift
opposes weight
Lift
3. Thrust – the
forward force
produced by the
power source
(propeller or jet)
Thrust
Drag
Weight
1. Weight – the action of
gravity on the total mass
of the aircraft.
4. Drag – the frictional
force resulting from
the passage of the
aircraft through the air.
Drag opposes thrust
Aircraft Control - Pitch
An 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.
The pilot controls pitch by pulling
back or pushing forward on the
control column in the cockpit
Pitch occurs around a horizontal
axis passing through the centre
of mass
Aircraft Control - Roll
An 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 - Yaw
An 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
The Centre of Mass of any object
with size is a point where all the
object’s mass can be considered to
be concentrated.
For regularly shaped objects eg.
squares or rectangles, cubes or
spheres the Centre of Mass of the
object is in the geometric centre of
the object
Centre of Mass
In the vertical plane the weight acts
through the “centre of mass” of the
aircraft.
Centre of Mass
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.
The Centre of Mass is often called
the Centre of Gravity of the aircraft.
Torque
Objects that turn or twist do so
because they are subject to a
TORQUE.
The Lever Arm is the perpendicular
distance between the pivot point
and the point of application of the
force.
F
Mathematically:
Torque = Lever Arm x Force
r
=rF
Where:
 = Torque (Nm)
r = Lever Arm (m)
F = Force (N)
Torques are vectors whose
direction is usually assigned as
either clockwise or anticlockwise
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
Centre of Pressure
Centre of Pressure
The 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
Stable Flight
Centre of Pressure
Pitch stability requires that the centre
of vertical pressure (lift) fall behind the
centre of mass.
Centre of Mass
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 Pressure
(Lift)
Let the Centre of Mass be the
point about which the aircraft
pivots.
For an aircraft to be controllable
the Centre of Pressure must be
behind the Centre of Mass
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.
Downward
Lift
Centre of Mass
(Weight)
The countering anticlockwise
torque is generated by the
horizontal stabilizers of the tail,
generating downward “lift”.
Balancing Torques
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)
Assume the Centre of Pressure is
6.0 m aft of the Centre of Mass
with total lift forces of 225 kN
Taking moments about the
aircraft’s Centre of Mass and
remembering:
The centre of “lift” of the horizontal
stabilizers 18 m behind the centre of mass.
What force is need for aircraft balance ?
For “balance” it is a requirement that
Clockwise Torques = Anticlockwise Torques
225 kN
Centre of Pressure
(Lift)
6m
18 m
Torque = Lever Arm x Force
=rF
Clkwise  = (6)(225)
Anticlkwise  = (18)(x)
Thus, (18)(x) = (6)(225)
or x = 75 kN
Downward
Lift
75? kN
Centre of Mass
(Weight)
300 kN
Bernoulli’s Principle
Pressure, P, is (by definition) a force per unit
area, which is equal to energy per unit volume:
P = Potential Energy per volume
Moving air has kinetic energy just as any other
moving object:
Bernoulli’s
Kinetic Energy per volume = ½ρv2 , where v is
Aerofoils
principle takes the local velocity, and ρ is the density, i.e. the
produce lift
because they account of the mass per unit volume.
kinetic energy Combining these, we conclude:
obey the
of moving air P + ½ρv2 = Mechanical Energy per volume.
principle of
Then, using the law of conservation of energy
conservation and
the potential
we conclude that a given air parcel’s
of energy,
embodied in energy stored mechanical energy remains constant as it flows
in the
Bernoulli’s
past the wing.
“springiness”
Principle.
of the air.
Higher velocity means
(Energy is
lower pressure, and
stored in
vice versa (assuming
pressurized
constant mechanical
air).
energy).
Daniel Bernoulli
1700 - 1782
Bernoulli’s Equation
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.
P1
P2
v1
A
A2v2
A1 > A2
v2 > v1
P2 < P1
Thus greater speed
means lower pressure
The mathematical statement of this
energy conservation is stated in the
BERNOULLI EQUATION:
P1 + ½ρv12 = P2 + ½ρv22
Aerofoils
The CHORD LINE is the straight
line from the leading edge to the
trailing edge of the airfoil.
The 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 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.
Leading
Edge
Upper Surface
Mean Line
Trailing Edge
Camber
Lower Surface
Chord Line
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.
This a a simplistic explanation
of a wing’s operation and is
just plain wrong !!!!!!!
2. The second explanation is based
on Newton’s 3rd law (action and
reaction) and the law of
conservation of momentum
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 theory assumes that the air split
by the leading edge must join up again
at the trailing edge.
Why Do Wings “Fly” ?
Actual airflow around a wing.
The “split” air has high and low
velocities
Different coloured dyes are
introduced into the air steam at
regular intervals.
The air moving over the top
arrives at the trailing edge 10
to 15 ms EARLIER than that
passing below the wing.
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” ?
The conservation of momentum may be better
understood by the walking on air analogy.
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.
These vortices are extremely dangerous to
following aircraft and take offs must be
spaced to allow them to dissipate.
Angle of Attack
Angle 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 Attack
The amount of lift generated by a wing is
directly related to the angle of attack, with
greater angles generating more lift.
STALL
POINT
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.
Stalled aerofoil
Drag
Drag
Total
Drag
Parasite
Drag
Induced
Drag
Max
Range
Speed
Airspeed
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.
Total Drag is the sum of
Parasite and Induced Drag
Drag 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.
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.
Flight – Take Off
At take off, an aircraft needs to produce
large amounts of lift at relatively low speeds.
Coefficient
of Lift (cL)
With Flaps
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.
For a given angle of attack,
flaps give a greater cL than
no flaps but reduce the
Flaps and
Slats
stall point from about 170
to about 120.
No Flaps
Angle of Attack
Flaps and slats together
increase both cL AND
the stall point often to
greater than 200.
Flight - Climbing
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.
Generally, for an aircraft to
climb Thrust MUST be greater
than Drag and Lift greater
than Weight
Weight can be broken up into components
W’ opposing L and W” adding to Drag (D)
To maintain equilibrium in climb the following
must be met:
T = (D + W'') and L = W'
Flight - Turning
Objects 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.
Here the
centripetal
force is
supplied by
the tension
in the string
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.
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.
Flight - Descending
An 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.
Generally, for an aircraft to
descend Thrust MUST be less
than Drag and Lift less than
Weight
To maintain equilibrium in glide the
following must be met:
W'' = D and W' = L
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