Aircraft Performance - Drag Performance - Drag 1 o Classification of Drag Notes: ‘DragForce and...

Aircraft Performance - Drag

1

o Classification of Drag

Notes: ‘Drag Force and Drag Coefficient’

Drag is the enemy of flight and its cost. One of the primary functions of aerodynamicists and aircraft designers is to

reduce this coefficient

The drag coefficient (CD) is a non-dimensional parameter, but it takes into account every aerodynamic configuration

aspect of the aircraft including large components as wing, tail, fuselage engine, and landing gear; and small elements

such as rivets and antenna

This coefficient has two main parts

• lift-related drag coefficient or induced drag coefficient (CDi)

• zero-lift drag coefficient (CDo).

The calculation of the first one is not very hard, but it takes a long time and energy to determine the second part. In

large transport aircraft, this task is done by a group of engineers up to twenty engineers for a time period of up to six

months. This calculation is not only time consuming, but also is very sensitive, since it influences every aspect of

aircraft performance.


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A list of definitions of various types of drag is presented, and then a classification of all of these drag forces is

described

Induced Drag: The drag that results from the generation of a trailing vortex system downstream of a lifting

surface with a finite aspect ratio. In another word, this type of drag is induced by the lift force

Parasite Drag: The total drag of an airplane minus the induced drag. Thus, it is the drag not directly associated

with the production of lift. The parasite drag is composed of drag of various aerodynamic components


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o Parasite Drag

Skin Friction Drag: The drag on a body resulting from viscous shearing stresses (i.e., friction) over its contact

surface (i.e., skin)

This drag is a function of Reynolds number. There are mainly two cases where the flow in the boundary layer is

laminar or turbulent over the plate

A laminar boundary layer begins to develop at the leading edge and its thickness grows in downstream. At

some distance from the leading edge the laminar boundary becomes unstable and is unable to suppress

disturbances imposed on it by surface roughness or fluctuations in the free stream

In a distance the boundary layer usually undergoes a transition to a turbulent boundary layer


4

o Parasite Drag

Form Drag (sometimes called Pressure Drag): The drag on a body resulting from the integrated effect of the

static pressure acting normal to its surface resolved in the drag direction. Unlike the skin friction drag that

results from viscous shearing forces tangential to a body’s surface, form drag results from the distribution of

pressure normal to the body’s surface

Form drag is based on the projected frontal area


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o Parasite Drag

Interference Drag: The increment in drag resulting from bringing two bodies in proximity to each other. For

example, the total drag of a wing-fuselage combination will usually be greater than the sum of the wing drag

and fuselage drag independent of each other

Trim Drag: The increment in drag resulting from the (tail) aerodynamic forces required to trim the aircraft

about its center of gravity. Trim drag usually is a form of induced and form drag on the horizontal tail

Profile Drag: Usually taken to mean the total of the skin friction drag and form drag for a two-dimensional

airfoil section

Cooling Drag: The drag resulting from the momentum lost by the air that passes through the power plant

installation for the purpose of cooling the engine

Wave Drag: This drag; limited to supersonic flow; is a form of induced drag resulting from non-canceling

static pressure components to either side of a shock wave acting on the surface of the body from which the

wave is emanating


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• CD,0 is parasite drag coefficient at zero lift (aL=0)

• CD,i drag coefficient due to lift (induced drag)

• Oswald efficiency factor, e, includes all effects from airplane

• CD,0 and e are known aerodynamics quantities of airplane

iDDL

DD CCeAR

CCC ,0,

2

0,

Aircraft Performance – Drag Polar


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Drag Polar


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Aircraft Performance

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o 4 Forces Acting on Airplane

Model airplane as rigid body with four natural forces acting on it

Lift (L): Acts perpendicular to flight path (perpendicular to relative wind)

Drag (D): Acts parallel to flight path direction (parallel to relative wind)

Propulsive Thrust (T): For most airplanes propulsive thrust acts in flight path direction

Weight (W): Always acts vertically toward center of earth

Apply Newton’s Second Law (F=ma) to curvilinear flight path

• Force balance in direction parallel to flight path

• Force balance in direction perpendicular to flight path


11

o Static vs Dynamic Analyses

Static Performance: Zero Accelerations (dV/dt = 0)

• Maximum velocity

• Maximum rate of climb

• Maximum range

• Maximum endurance

Dynamic Performance: Accelerating Flight

• Take-off and landing characteristics

• Turning flight

• Accelerated flight and rate of climb


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o Level, Un-accelerated Flight

Equations of motion reduce to very simple expressions

• Aerodynamic drag is balanced by thrust of engine

• Aerodynamic lift is balanced by weight of airplane

WL

DT

L

D

L

D

C

C

W

T

SCVWL

SCVDT

WL

DT

2

2

2

1

2

1

D

L

W

CC

WT

D

L

R

• TR is thrust required to fly at a given velocity

in level, un-accelerated flight

• Notice that minimum TR is when airplane is at

maximum L/D

• Airplane’s power plant must produce a net

thrust which is equal to drag

o Level, Un-accelerated Flight



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o Thrust Requirement

TR for airplane at given altitude varies with velocity

Thrust required curve: TR vs V∞

• Select a flight speed V

• Calculate CL

SV

WCL

2

2

1

eAR

CCC L

DD

2

0,

D

L

R

CC

WT

• Calculate CD

• Calculate CL/CD

• Calculate TR

This is how much thrust engine must produce to fly at V∞


15

o Thrust Requirement

Different points on TR curve correspond to different angles of attack

D

LL

SCqD

SCqSCVWL

2

2

1

At a:

Large q∞

Small CL and a

D large

At b:

Small q∞

Large CL (CL2) and a (support W)

D large


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o Thrust Required vs Flight Velocity

eAR

CSqSCqT

CCSqSCqDT

LDR

iDDDR

2

0,

,0,

Zero-Lift TR

(Parasitic Drag)

Lift-Induced TR

(Induced Drag)

Zero-Lift TR ~ V2

(Parasitic Drag)

Lift-Induced TR ~ 1/V2

(Induced Drag)


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o Thrust Required vs Flight Velocity

Zero-Lift Drag = Induced Drag

At minimum TR and maximum L/D


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o Airplane Power Plants


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o Thrust vs Power

• Jets Engines (turbojets, turbofans for military and commercial applications) are usually rate in Thrust• Thrust is a Force with units (kg m/s2)

• Piston-Driven Engines are usually rated in terms of Power• Force*velocity with units (kg m/s2)*(m/s) = kg m2/s3 = Watts

• Usually rated in terms of horsepower (1 hp=550 ft lb/s = 746 W)

• Example:• Airplane is level, un-accelerated flight at a given altitude with speed V∞

• Power Required, PR=TR*V∞


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o Power Required

PR vs. V∞ qualitatively resembles TR vs. V∞


21

o Power Available


22

o Rate of Climb

Jet EnginePropeller Drive Engine

Maximum R/C Occurs when Maximum Excess Power


23

o Power Required

Aircraft Performance - Drag Performance - Drag 1 o Classification of Drag Notes: ‘DragForce and...

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Transcript of Aircraft Performance - Drag Performance - Drag 1 o Classification of Drag Notes: ‘DragForce and...