Basics Of Aerodynamics

1 Kutta-Joukowski Theorem

It refers to the lift generated by a rotating cylinder. It is an application of the
Magnus Effect which relates the pressure di erence created by a rotating and
translating motion of a cylinder through air (moving or still air with respect to
ground)
Their theorem for lift by a rotating cylinder is given as :
Lift per unit area (L)
L = rho GV (1)
Where:
rho = air density
G = Vortex Strength
G = rho omega R^2 (2)

2 Area Rule

As the plane approaches Mach 1 the air moves around it at the speed of sound.
the amount of air displaced depends on the cross-sectional area of the aircraft.
Now at diff erent point of the wing, the air is at diff erent Mach numbers. Once
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the air at Mach > 1 collides with air at Mach < 1 it create immense drag.
The area rule proposed by Whitcomb reduces this drag by tapering the fuselage
near the center of the wing-root. This helping to create larger space for air
to
ow and reducing the drag. Also by creating a wing sweep the change in
cross-section area of the aircraft reduces at each point making it airworthy at
transonic speeds.

3 Di fferent angle of attacks

This is to present wing-tip stalls.This is sometimes termed as wash-in. Here
the wing-root has a higher angle of attack then the wing-tip. So if the aircraft
stalls, the wing-root stalls rst and then the wing-tip. So once the wing-root
stalls the pilot would still have aileron control to present spinning and recover
from the stall.

4 Commercial flights at Transonic velocity

Pilot and airlines companies discourage
flight at transonic speed due to:
More fuel consumption - more prices
Higher instability
While crushing at altitude of 30000 the max speed to keep the aircraft
under control is at Mach < 1

5 Hyper Sonic Region

At Mach=5 the aircraft travels at speeds 5 times of sound. Here the sonic
cones of vacuum formed due to shock waves results in change in properties of
the air around it. this change is mainly due to viscosity of the air. There is a
sudden rise in temperature and reduction in pressure. As the velocity rises the
vacuum cone becomes narrower throwing it aircraft into projectile motion with
minimalistic lift.

6 Forces on an aircraft

6.1 Lift

It is the upward force created by the wing when moved laterally through the
air to create. A pressure di erence between the top surface and bottom surface
create lift.

6.2 Thrust

It is the forward force created by a propeller or get of an aircraft. The propeller
or the jet pushes the air backwards and by Newton's third law the aircraft moves
forward.

6.3 Weight

It is the force by created by the earth pulls an aircraft (Total mass) towards the
earth.

6.4 Drag

It is the force created by the oncoming air and trailing turbulence that pushes
the aircraft behind. It is analogues to frictional force generated when you push
a body on the ground.

7 Wing Design

7.1 Anhedral

This wing design is also called negative dihedral design. This is used in ghter
aircraft that require high rolling manoeuvring and sideways flight.

7.2 Dihedral

This looks like a shallow V or a V with lesser slopes. This is mostly used in commercial flights, where they require stable  flights. A dihedral air foil helps in turning and levelling o f flights. The two wings create forces perpendicular to their planes and thus provide torque when the aircraft recovers from a turn.

7.3 Polyhedral

This is like a dual dihedral air foil. This is mostly used in gliders and provides high and quick manoeuvring. The tilted wing tips help in recovering from a turn quickly.

8 Drag

8.1 Parasitic Drag

Parasitic drag is drag created by those parts of an aeroplane that do not con-
tribute to lifte.g., the tires, wind-shield, rivets, etc. There are, in turn, three
forms of parasitic dragform drag, skin-friction drag, and interference drag. Form
drag is caused by the frontal areas of the aeroplane, and is reduced by streamlin-
ing. Skin-friction drag is caused by the air passing over the aeroplane surfaces,
and is reduced by smoothing the surfaces (
ush riveting, smooth paints, and
waxing). Interference drag is caused by the interference of air
ow between parts
of an aeroplane (wings and fuselage) and is reduced by lleting interference ar-
eas.

8.2 Induced Drag

This type of drag is a result of the angle of attack of the wing required to gain
height. Thus, an aircraft achieves lift at the cost of induced drag.

9 Planforms

There are many wing planforms which carry their own advantages, disadvan-
tages and applications. Here I have written about a few wing planforms:

9.1 Rectangular

It is the most basic wing planform. It carries the main advantage of easy
manufacturing but is aerodynamically ine cient.

9.2 Elliptical

The elliptical planform is the most e cient planform due to its high lift and
lower induced drag capabilities. The major drawback of the elliptical design is
manufacturing. Due to a particular shape and producing perfect elliptical wings
is not possible.

9.3 Tapered

This is a modi cation to the rectangular wing planform. It has tapered wing-
tips. Easy manufacturing and good e ciency are its advantages, but it is not
as e cient as the elliptical wing and would have di erential drag during cruise
at transonic speeds.

9.4 Delta

It is a triangular design wing with very low aspect-ratio. The main advantage
is the it performs e ciently in all
ight regimes (subsonic,transonic and su-
personic). They also provide larger volume for fuel storage and they are quite
simple to build and maintain. Large induced drag due to low aspect-ratio and
higher angle of attacks during low speed are their major drawbacks.

10 Wing Sweep

It is angle between a line joining the center of the wing-root and wing-tip with
a line perpendicular to the air-foil. This idea was conceived while designing
aircraft which were created with Mach>1. The most common type of sweep
is sweep-back. When an aircraft reaches transonic speeds it creates a vacuum
cone under which there is immense drag. if the wing was straight then there
would be di fferential drag.

11 Washout

Washout is to twist the wings so that the wing-root and the wing-tip have
di fferent angle of attacks. This helps is stall warnings and recovery from a
stall. A stall occurs due to high induced drag created by higher angle of attacks
(> 15 ). Hence while stalling the the pilot still has control over the ailerons and
can recover from the stall.

12 Tapering

Tapering is to reduce the chord length from the wing-root to the wing-tip.
This is done to prevent tip-stalling. Due to the fact that the tip is narrower it
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produces lesser lift and lesser drag. Drag is the main reason behind stalling and
if the tip is able to reduce drag the pilot can have better control