AIRPLANE

Forces on an Airplane: (Basic)

• Thrust
1. This is the force obtained from the engines/propellers of the
aircraft that are responsible for longitudinal movement of
the aircraft.
2. It’s needed to overcome the force of drag.

• Drag
1. Any force that acts against the direction of motion of
aircraft is referred to as drag.
2. It is of two types - parasitic & induced.

• Weight
1. The force acting on an aircraft due to its mass is called
weight.
2. It’s always directed towards the Earth.

• Lift
1. The force acting perpendicular to the fuselage of the
aircraft is known as lift.
2. It basically balances the weight.
Elevator & Aileron:

• Their job is to vary lift.

• When they are lifted, the lift at that place reduces and that part of
the aircraft dips.
• When they are depressed the lift at that part increases and that
part of the plane rises.

Rudder:
• The job of the rudder is same as elevators but in vertical plane.
Slats:
• Spoilers are used to increase lift.
• They emerge outward and downward from the wings increasing
their curvature and hence increasing lift.
Flaps:
• Flaps do the same job except for the fact that they are at the back
of the wing.

Slats and Flaps:

• They are needed both while take-off and landing.
• While take-off they provide the excess lift if needed.
• While landing they can be used to increase drag and hence slow
down the aircraft.
Spoilers:
• They are needed to ensure that lift is minimized during landing.
• We can observe the spoilers are lifted up as soon as the plane
touches down.
• This prevents the plane from getting airborne due to high speed
during landing.

Airfoil:
• They wings of the aircraft are designed as an airfoil.
• An airfoil basically is a shape that causes the wind to pass across
it in such a way that the wind velocity over it is more than the
velocity below it.
• This causes a greater pressure under the wing as compared to the
pressure above it and hence the plane gets the upward lift.

• Chord line is the straight line that joins the leading and trailing
edges of the airfoil.
• Mean camber line refers to the line that bisects the airfoil into
equal areas.
 AIRFOILS

• Low speed aircrafts have highly curved airfoils i.e. long camber.
• In such a case lift is high and so is the drag.
Angle Of Attack (alpha):
• The angle between chord line and the direction of the free stream
velocity.
• It is always measured in RADIANS.
• It is almost linearly proportional to the lift generated for most of
the angles.

Forces in detail:(thrust and drag only)

Thrust:
The value of thrust determines the angle of attack for a leveled flight as
follows:
• When the thrust is high the airplane obviously exceeds drag and
gains speed. However, this increases lift as well and the aircraft
climbs. To maintain level the angle of attack is reduced and
hence lift is also reduces. The angle of attack in this case ideally
is 3 degrees.
• Similarly when the speed is low then the angle of attack is to be
increased to prevent decline of the aircraft. This increases the lift.
The angle in this case is 12 degrees.
• Cruise speed is the speed at which angle of attack is 6 degrees.

Drag:
Drag is basically of two types:
• Parasitic
• Induced
Parasitic:
It’s further of two types:
1. Form Drag
2. Skin Friction

Foam Drag:
This drag occurs due to disruption of streamline flow and can be easily
removed by making more streamline body.

Skin Friction:
• This type of drag is more difficult to be removes as every surface
does have some friction that results in drag.
• The effect can however be reduced by applying smooth surfaces
for the external body.

DRAG INCREASES WITH THE SQUARE OF VELOCITY AT

SPEEDS LESS THAN SUPERSONIC SPEEDS.

Induced:
Induced drag is unavoidable and occurs as follows:
• The pressure under the wing is greater than the same above the
wing and hence lift is generated.
• But this pressure tends to get neutralized as some wind escapes
from the underside of wing to above it from the tips of the wing.
• This reduces the pressure gradient by increasing the pressure
above the wing.
• This results in loss of lift and hence more thrust is needed to
compensate it resulting in greater exemption of fuel.
• This occurs in the form of vortices generated due to rotational
energy attained by wind at the vortex.
• Induced drag is directly proportional to angle of attack and
weight and inversely to length of wing and velocity.
 Wind Vortices

At low speeds the angle of attack required is higher and

hence the lift generated is higher and so is the induced
drag.
The induced drag reduces with increase in speed. t very
low speeds the aircraft stalls.

Drag v/s Speed

Aerodynamics in flight maneuvers

An aircraft can’t be steered like a car. Hence for changing the direction
of motion it has to be banked.
• Whenever a plane is banked, we can conveniently state that the
lift that balances the weight reduces although lift doesn’t reduce
as such.
• This happens as the lift’s vertical angle now is responsible to
balance the weight.
• The horizontal component now equals the centripetal force
generated when the aircraft is turning.

Angle of banking:
• Angle of bank is the angle b/w one of wings and the line
representing the centrifugal force.
• Greater the angle of banking, lesser the vertical lift and greater
the horizontal lift.
• It’s inversely proportional to the air-speed.

Aerodynamics during banking:

When banking is under effect,

• Lift balancing the weight is effectively reduced as a result of
which one has to increase the angle of attack in order to make the
vertical component of lift equal to the weight.
• But as angle of attack is increased the increment in lift can be
observed in the horizontal component as well. Hence we need
more centrifugal force to balance the excess lift for a leveled
flight. This now can be achieved by
1. Increasing the bank angle as this increases the horizontal lift or
2. Reducing speed.

• Now as the lift increases, drag also increases. When drag

increases then speed decreases. When speed decreases the aircraft
descends. To avoid this we need to increase lift which again can
be done either by:
1. Increasing the angle of attack or
2. Increasing air speed by increasing thrust or
3. Decreasing the angle of bank.

• By this we can conclude that:

1. Lift α drag.
2. Drag α 1/speed.
3. Speed α altitude.
4. Vertical lift α angle of bank.
5. Lift α angle of bank.
6. Lift α air speed.
For a slipping turn:
• Horizontal lift is greater than the centrifugal force.
• This is done by banking the aircraft too much for the rate of turn.
• The two forces can be balanced either by reducing the bank angle
or by increasing the rate of turn or a combination of both.

For a skidding turn:

• Centrifugal force is greater than horizontal lift.
• Here the rate of turn is too high for the angle of bank.
• The two forces can be balanced either by increasing the bank
angle or by decreasing the rate of turn or both.

Lift coefficient :( Cl)

Lift coefficient is given by:
Cl = L/PS.
Where L is lift and S is the wing area and
P = ½*p*(v^2).
P is the dynamic pressure on the wings from air being considered as
fluid.
v is the free stream velocity.
Drag coefficient :( Cd)
Cd = D/PS + (CL^2)/ (Pi*AR*e).

Here,

D/PS is the induced drag and rest is parasitic drag.

AR is the aspect ratio= ((Length of wing) ^2)/Area of wing.
e is Oswald efficiency factor= 0.75 on an average.

Lift by Drag ratio:

It’s always convenient to study lift and drag together.
L/D = Cl/Cd.
The variation w.r.t angle of attack is as shown:

At some particular angle L/D ratio is maximum (= 13). This is basically

to ensure higher lift and lower drag as lift is proportional to drag.
Now for a leveled flight it’s necessary that lift equals weight.
Hence, L=W=P*S*Cl.

And for an unaccelerated flight

T=D=P*S*Cd.

Therefore,
P*S=W/Cl

T=W/ (Cl*Cd).
Hence we can know the required thrust.
And power of engine needed is:

Pr = T*(v^2).

Stalling speed:
It’s the speed at which the aircraft will stall.

Vo = [{2W / (p*S*Cl)}] ^ 2.

Rate of climb: (R/C)

R/C is given by
(Thrust power – drag power)/W

= (Tp – Dp)/W

= (T*v – D*v)/W

= v sin C
Where C is the angle of climb. (C<20)

Time to climb is given by:

t = integral of dh/(R/C)
While banking,
The forces are as shown.
Therefore,

L cosQ = m (v^2)/R
And
L sinQ = W.

Hence,
Cos Q = [(1- (W/L) ^2)] ^1/2
Therefore,
L * [(1- (W/L) ^2)] ^1/2 = m (v^2)/R.
And,
1/R = {L * [(1- (W/L) ^2)] ^1/2} / m (v^2)
= {L * [(1- n^2)] ^ 1/2} / m (v^2).
Where n is the load factor i.e. L/W.
Hence,
R = (v^2)/ {g*{(n^2 – 1) ^1/2}}
Angular velocity (w)
w= (v^2)/R.
= (g*{(n^2 – 1) ^1/2}/v)
Pull Up/Down curves:
The curve is vertical and

For pull up-

R= (v^2)/ (g * (n-1))

And, for pull down,

R= (v^2)/ (g * (n+1))

For minimum radius,

v has to be minimum.
So,
We take the stalling velocity as
R= [2*(W/S)]/ [p*g*Cl, max].

And max rate of turn

wmax = g*{[(p*Cl, max*nmax) / (2*W/S)] ^1/2}.

nmax = [1/2*p*(v^2)*Cl, max]/ (W/S)