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Y.K.SINHA
RAJALAKSHI ENGINEERING COLLEGE
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Why should we study properties of
atmosphere?
VariationofTemperature with Altitude
VariationofPressure with Altitude
VariationofDensity with Altitude
Tables ofStandard Atmosphere
TOPICS TO BE COVERED
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Why should we study
Atmospheric Properties Engineers designflight vehicles, turbine
engines and rockets that willoperate at various
altitudes.
They cannot design these unless the
atmospheric characteristics are not known.
For example,
SV
LCL
2
2
1
g
!
V
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What is a standard
atmosphere? Weather conditions vary around the globe,
from day today.
Taking all these variations intodesign is
impractical.
A standard atmosphere is therefore defined,
that relates fight tests, wind tunnel tests and
general airplane design to a commonreference.
This common reference is called a
standard atmosphere.
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International Standard Atmosphere
Standard Sea Level Conditions
Pressure 101325 Pa
Density 1.225 Kg/m3Temperature 15oC or 288 K
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Temperature vs. Altitude
Temperature, degreesAltitude,
km
. 6
km
6.66
km
47 km, T= .66
km
79 km
6 .66
9 km
Troposphere
tratosphere
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SYMMETRIC AND UNSYMMETRIC AIRFOIL
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CL VS ANGLE OF ATTACK CURVE
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Characteristic Curves
Available for
all classes of
standard
aerofoils.
Include plots
ofCD, CL, L/D, Example NACA 2421
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DRAG
DRAG IS THE RESOLVEDCOMPONENT OF THECOMPLETE AERODYNAMICFORCE WHICH IS PARALLEL TOTHE FLIGHT DIRECTION(OR
RELATIVE ONCOMINGAIRFLOW).
IT MUST ALWAYS ACT TOOPPOSETHE DIRECTION OFMOTION.
IT IS THE UNDESIRABLE
COMPONENT OF THEAERODYNAMIC FORCE WHILELIFT IS THE DESIRABLECOMPONENT
LIFT
DRAG
RESULTANT FORCE
C.P
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TYPES OF DRAG
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VARIATION OF DRAG WITH SPEED
Induceddrag decreases as V
increases, because we need less
values of CL at high speeds.
Otherdrag forces (form,
skin friction , interference)
increase.
Result: Drag first drops, thenrises.
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Minimum Drag & Power Speeds
This gives a simple theoretical relationshipbetween the flight speeds requiredforminimum drag and power conditions.
i.e. VP,min = (k2/3k1)1/4= 0. (k2/k1)
1/4
= % VD,min
Also, at minimum powerspeed,
3k1V2 = k2V
-2
@ 3CD0 = CL2 / (TAe)(orlift-induceddrag= 3 x parasite drag)
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Altitude Effects on PR v Airspeed
PR varies with 1/W (orVo /V). Minimum power required increases with
altitude but VP,min fixed ifplotted as
equivalent airspeeds. True airspeed
for minimum
power condition
increases withaltitude.
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Minimum Drag & Power Speeds
Since P = D x V,@ D = P /V so a single plotofP against V may be used todetermine
bothVP,min & VD,min.
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Available Thrust & Power (TA, PA)
Required thrust is determined byaerodynamics & weight considerations whileavailable thrust and power are functions ofthe propulsion system performance.
Bigdifferences between piston-props &turbojets so considered separately. Turbojets & fans have reasonably constant thrust
values sothrust-rated.
Piston-props arepower-rated. Both thrust & power reduce with increased
altitude (reduceddensity).
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Available Thrust & Power
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Maximum Velocity
May be determinedfrom plots ofeitherTR (or PR) and TA (or PA) against V.
Intersectionofcurves gives maximum
speed capability and possibly alsominimum speed capability (if
intersection is above stall speed).
Piston-props and turbojets/fans usually
considered separately.
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Maximum Velocityfor Piston-Prop
Most convenientlydeterminedfrom plots ofPR and PA against V.
Dashedlines give
curves atincreased altitude
- both minimum
and maximum
speeds affected inthis case.
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Maximum Velocityfor Jet/Fan
Most convenientlydeterminedfrom plots ofTR and TA against V.
Dashedlines give
curves atincreased altitude
- both minimum
and maximum
speeds againaffected in this
case.
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Breguet Formulae for
Piston-Prop A/CRange FormulaR = (L/sfc).(CL/CD).ln(W0/W1)
Where
W0 =gross aircraft weight, WF=fuel weight
W1 =W0 - WF, L = propeller efficiency
Endurance Formula
E = (L/sfc).(CL1.5
/CD). (2VS)(W1-0.5
- W0-0.5
)
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Range & Endurance Formulae
for Jet/Fan A/C
Endurance Formula
E = (1/tsfc).(CL/CD).ln (W0/W1)
Range Formula
R = 2(2/VS). (1/tsfc).(CL0.5/CD).(W1-0.5 - W0-0.5)
Note that range is altitude dependent while
endurance is not - opposite for piston-props.
However, tsfc also varies with altitude andeventually increases.
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Climbing
Consider aircraft in a steadyunacceleratedclimb with vertical climb speedofVc.
Force balance gives:cos c
L WK!
sinc
T D W K!
( ) /
sin /c c
W
V VK
@ !
!
( ) /c
V T D V W @ !
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Ceilings
Absolute ceiling- altitude forVc,max = 0
Service ceiling- altitude forVc,max = 100
ft/min
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Diving
Similar to the steadyunaccelerated climbcase.
Force balance fordive speedor sink rate
(Vd)gives:cos d
L WK!
sind
T D W K!
( ) /
sin /d c
D T W
V VK
@ !
!
( ) /d
V D T V W @ !
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AIRCRAFT STABILITY
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THANK YOU