Pres2_Atmosphere.pdf

8/10/2019 Pres2_Atmosphere.pdf

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2. The Atmosphere

The first essential in the estimation (or measurement) of the performance of an aircraft

are:

- the knowledge of the state of the atmosphere in which the aircraft is flying (Ch 2)

- the ability to measure the relative motion between the aircraft and the

atmospheric air mass (Ch 3)

The state of the atmosphere is defined by its temperature (T) and pressure (p).

2.1. Characteristics of the atmosphere

The atmosphere consists of air, which is a mixture of the following gases:

- N (nitrogen) 78%- O (oxygen) 21%

- Ar (Argon) 0.9%

- CO2(carbon dioxide) 0.03%

- other inert gases rest

+ dust particles, water vapour & moisture

(little effect on gaseous properties)

99%


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2. The Atmosphere

Atmospheric air can be taken to behave as a neutral gas obeying the state equation:

p - pressure [N/m2]

- density [kg/m3]

T - temperature [K]

Rgas constant = 287.053 [Nm/kg/K]

2.2. Variation of properties

Temperature and pressure varies through the atmosphere, both along the surface ofthe Earth as well as vertically by altitude.

Surface variation of T

Temperature varies by: time - short term (day & night)

- long term (seasons)

location - along latitude (poles are cooler than equator)

- land mass distribution (deserts, mountains, etc.)

TRp ..


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2. The Atmosphere

Temperature variation by time and location: mean seasonal global temperature distribution.(Source: M.E. Eshelby: Aircraft Performance: Theory and Practice, AIAA Educational Series, 2000.)

Temporal

variation

Geographical variation

Latitude

Equator: - small seasonal variation

- high mean temperature

Poles: - large seasonal variation

- low mean temperature

North Pole: - warmer than South Pole, since

- lies at sea level, middle of an ocean(which acts as a heat sink)


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2. The Atmosphere

Surface variation of p

Pressure varies by: - time - air transportation from higher temperatureregions to lower ones leads to convection

currents.

These would normally take place along linesof longitude, but Coriolis forces due to theEarths rotation cause the flow to swirl andcreate a series of convection current cells, suchas:

CYCLONS (low pressure cells)

ANTI-CYCLONS (high pressure cells)

(Source: M.E. Eshelby: Aircraft Performance: Theory and Practice,

AIAA Educational Series, 2000.)

- location- land masses

Result:constantly changing complex pressure distribution over the Earths surface.

General global atmosphere pressure distribution.


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2. The Atmosphere

U.S.

South

WestEast

North

Intended

path

Real path

(curved towards

West)

Relative to the Earths surface

which means

Coriolis effect - creation of cyclons

U.S.

South

WestEast

North

Idealized

gunshot

towards A

A

U.S.

South

WestEast

NorthInstead of A,

it will land in

B due to the

rotation of

Earth

AB

Corioloisdeflection


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2. The Atmosphere

U.S.

NorthSouth airflows:

deflect WEST

in the NORTHERN HEMISPHERE:


SouthNorth airflows:

deflect EAST

WestEast airflows:

deflect SOUTH

EastWest airflows:

deflect NORTH

(assuming our path is in a plane going through

the centre of Earththe Great Circle route)


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2. The Atmosphere

U.S.

this forms a counter-clockwisesystem in a low pressure system:


Low

pressure

Note: this is valid ONLY for the Northern hemisphere. In the Southern hemisphere, the

opposite will be true, i.e. CLOCKWISE loops will be created there.

Hurricane Katrina in Aug 2005 was created in

the Northern Hemisphere, hence, she had a

COUNTER-CLOCKWISE rotation.

(Source: www.wikipedia.com)

U.S.


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2. The Atmosphere

HurricaneRitaNorthernHemisphere

17-26 September 2005


CycloneIngridSouthernHemisphere

6-17 March 2005


Australia (Queensland)

U.S.

MEXICO

CUBA

Papua-New Guinea


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2. The Atmosphere

Vertical variation of T

The Earths atmosphere is heated by radiation from the Sun. However,

- some of the energy is reflected back to the space by the atmosphere (~38%)

- some is absorbed by the atmosphere (~14%)

- rest passes through to the Earths surface (~48%)

Absorption is not uniformbut selectivein the different layersof the atmosphere,yielding a complex temperature-height profile.

0-11 [km]: TROPOSPHERE - water vapour and CO2 absorb radiation well,

creating a warm layer

11-50 [km]: STRATOSPHERE - little water vapour, little absorption, cool air layer


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2. The Atmosphere

Vertical temperature structure

Of the atmosphere.

(Source: M.E. Eshelby: Aircraft

Performance: Theory and

Practice, AIAA Educational

Series, 2000.)


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2. The Atmosphere

50-80 [km]: MESOSPHERE - large ozone (O3) content increases absorbivity ofthe ultraviolet spectrum of Suns radiation,leading to another warm layer, however, coolingdown with decreasing pressure (increasing H).

80-300 [km]: THERMOSPHERE - very few particles (hence very low pressure)

but this is another very warm layer, astemperature rises from 190 [K] (-83oC) to 1000 [K]. However, because of the thinness of

the air, this temperature would not be felt on thehuman body and is only a kinetic temperature,which governs the speed of the molecules in thethermosphere.

300 [km] - : EXOSPHERE - forms boundary with space

100 [km]von Krmn line, (imaginary boundary where aerodynamic forces becomeminimal) is defined as the boundary of the space by the US Air Force

Office of Aerospace Research.


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2. The Atmosphere

The thickness of these layers changes with latitude too:

Temperature-height

profiles measured at7 different latitude

locations.

Tropopause thickness

distribution reduced from

above data.


Performance: Theory and Practice,

AIAA Educational Series, 2000.)North Pole

Equator


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2. The Atmosphere

Conclusion:it is impossible to account for all the above variations of (T) and (p). Hence, amodel atmosphere has been introduced, which is called .

2.3. The International Standard Atmosphere (ISA)

with datum values at H=0 [m]:

p0 = 101,325 [N/m2]

= 1.225 [kg/m3]

T0 = 288.15 [K] = 15 [oC]

The temperature variation in any of the layers is defined as:

0 Mean seasonal sea-level

values at 45N latitude

)( iii HHLTT

Temperature lapse rate

(defined as in the following

graph)


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2. The Atmosphere

Temperature profile of the International Standard Atmosphere (ISA)(Source: M.E. Eshelby: Aircraft Performance: Theory and Practice, AIAA Educational Series, 2000.)


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2. The Atmosphere

This gives the temperature variation only. But since we have 3 variables in the state

equation (p, ,T), we need at least one more variable to define.

can be defined as:

since lower layers of air must support the weight of upper ones:

)(Hfp

dpdhgAdpgdhA

AdpApgVAp

AdppgmAp

F

..0.)...(

0.....

0).(..

0

gdh

dp.


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2. The Atmosphere

From the state equation:

Back-substituting:

Inserting for T yields:

Note: in the above equation, we assumed a constant g = g0, which represents the gravitational acceleration atthe Earth surface, g0 = 9.80665 m.s

-2. This is a further assumption we make for constructing the ISA

model atmosphere. In reality, gvaries with latitude for two reasons:

a) Earth radius is not constant: radius at poles is 20 km less than at Equator. Since gis

proportional to the distance from the centre of Earth, gat Equator will be less than at the

poles.

b) centrifugal acceleration due to the rotation of Earth is larger at the Equator. This further

reduces the value of gat the equator.

Nevertheless, assuming a constant g for ISA leads to less then 1% error below H = 65 km altitude.

TRp.

dh

TR

g

p

dp

gTR

p

dh

dp

.

.

)( iii HHLTT

dh

HHLTR

g

p

dp

iii )(

0


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2. The Atmosphere

20.

20

20

20

20

)(1LR

g

HHT

L

p

p

Upper STRATOSPHERE

And integrating in each layer yields:

1111

.

0

0

0

ln

10

HHRT

g

p

p

HT

L

p

p LRg

TROPOSPHERE

Lower STRATOSPHERE(using Li=0)

Thus, we have the variations of T=f(H)andp=f(H)and we can get from

the state equation.

)(Hf


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2. The Atmosphere

2.4. Relative properties

relative pressure

relative density

relative temperature

0

0

0

T

T

p

p

H [m]

11,000 22.3 % 36.4 %

20,000 5.4 % 8.8%


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2. The Atmosphere

Variation of relative properties in the ISA.


Performance: Theory and Practice,

AIAA Educational Series, 2000.)


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2. The Atmosphere

2.5. Off-standard and design atmospheres

The ISA is only a model atmosphere. The real atmosphere encountered at any given time

and place will generally not conform to the ISA model. Any atmosphere that does not conform

to the ISA profile is referred to as an

off-standard atmosphere.

It is often required to design an aircraft for, or to estimate the performance of an aircraft, in

off-standard conditions, such as for arctic or desert operations. The atmospheres which are

designed to cover the likely extreme variations in datum level temperatures are referred to as

design atmospheres.

These are most often T-H profiles parallel to the ISA model profile, displaced by an increment

in datum temperature. Examples of design atmospheres as defined by the European air-

worthiness codes of practice, JAR (Joint Aviation Regulations) are shown on the next

graphs.


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2. The Atmosphere

Design atmospheres in terms of

a) Pressure heights,

b) Geopotential heights,

according to JAR 25.


Performance: Theory and Practice,AIAA Educational Series, 2000.)


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2. The Atmosphere

Example: in the real(not the idealized ISA) atmosphere, the

following conditions (satisfying the state equation) were

measured at H=3,100 [m]:

which all correspond to a different ISA altitude:

h= 8,400 [m]

hp= 4,000 [m]

hT= 3,500 [m]

We usually use the geopotentialaltitude for aircraft & spacecraft performance

calculations.

][4.265

]/[61640

]/[809095.0

2

3

KT

mNp

mkg


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2. The Atmosphere

2.7. Units

Although the ISA is defined by reference to metric heights, international aircraft operations

are currently required to be flown by reference to altimeters calibrated inimperial units, i.e.

feet. Since the performance of aircraft is associated with practical operations, heights are

generally referred to in feet, rather than in meters, in performance analysis.

In this course, both metric and imperial units will be used for indicating height. Allother parameters (pressure, temperature, density, etc.) will be provided in metric units,

according to the basic definition of ISA.

2.8. Jet Streams

Jet streamsare fast flowing, confined air currents found in the atmosphere at around 12 km

above the surface of the Earth, just under the tropopause. They form at the boundaries of

adjacent air masses with significant differences in temperature, such as those of the polar

region and the warmer air at the South (the meridian temperature gradient). Because of the

effect of the Earth's rotation the streams flow West to East, propagating in a serpentine or

wave-like manner at lower speeds than that of the actual wind within the flow.


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2. The Atmosphere

Jet Stream fast facts:

Altitude: bottom at about 9.5 km (upper troposphere)

Thickness: 4-5 km

Width: ~500 km

Min.speed: 93 km/h

Average wind speed: ~150 km/h

Max.speed: ~480 km/h

Direction: East

Location of the jet stream at the time

of the Thursday lecture, Thu 5 Sep 2012

(Source: www.weather.ca).

Jet Stream


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2. The Atmosphere

There are two mainjet streams at polar latitudes, one in each hemisphere, and two minor

subtropical streams closer to the equator. In the Northern Hemisphere, the streams are

most commonly found between latitudes 30N and 70N for the polar jet stream, and between

latitude 20N and 50N for the subtropical stream. The wind speeds vary according to the

temperature gradient, averaging 55 km/h (35 mph) in summer and 120 km/h (75 mph) in

winter, although speeds of over 400 km/h (250 mph) are also known. Technically the wind

speed has to be higher than 90 km/h (55 mph) to be called a jet stream.

The location of the jet stream is an extremely important datum for airlines. In the United States

and Canada, for example, the time needed to fly East across the continent can be decreased

by about 30 minutes if an airplane can fly with the jet stream, or increased by the same amount

if it must fly West against it. On international flights, the difference is even greater, and it is

often actually faster flying Eastbound in the jet stream than taking the great circle route

between two points.

Jet streams were first discovered during World War II by Wiley Post and military pilots

flying bombers at high altitudes. The theory was explained by Erik Palmn and other

members of the so-called Chicago school of dynamical meteorologists. The first practical use

of jet streams was presumably the Japanese fire balloon attacks on the American mainland

later during the war.

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