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Cha ter 3The Standard Atmosphere

.

Atmosphere is the air envelope surrounding the earth

,

represents (21%) ,Nitrogen (78%), and other gases

(1%) of the total volume.

Up to about 90 km altitude, composition of air is the

same (the homosphere)

Above about 90 km, composition varies with altitude(the heterosphere) as shown in figure.

Prof. Galal Bahgat SalemAerospace Dept., Cairo University

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The atmos here is divided into several la ersaccording to temperature variation with altitude

Why do we study the atmosphere?

For the design and performance determination of anyflying vehicle (airplane, missile, satellite,.etc),

,

temperature, and density of air is required.

The properties of the real atmosphere never remain

constant at any particular time or place.

Consequently, a hypothetical model is employed as an

approx ma on o w a may e expec e . s mo e sknown as the standard atmosphere.


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The Standard atmosphere depends on the measurement

o e mean va ue o empera ure w a u e com ne

with the hydrostatic equation which gives the variation of

p with the altitude .

2.The Hydrostatic Equation

of air at rest+ve hG

Force diagram for the hydrostatic equation


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the forces in any direction must be zero.

p(1)(1) (p+dp)(1)(1) (1)(1) g dhG = 0

Then - dp g dhG

= 0

Or dp/dhG = - g Hydrostatic equation

s equa on means a e pressuredecreases with the increase of height.


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What is the altitude?

1-Geometric Altitude hG is the height above sea-level.

2-Absolute Altitude ha is the height measured from thecen er o e ear .

ha = hG + R

=

The absolute altitude is important for space flight because

g varies with ha . ccor ng o ew on s aw o grav y,

g = go [R/ha ]2 = go [R/(R + hG) ]

2

where is at sea-level where3-Geopotential Altitude h is a fictitious (hypothetical)

altitude used to facilitate the calculations ( h hG )


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ha hG

Surface of earth(Sea level)

R

Definition of altitude

By definition : dp = - g dhG = - go dhThen : dh/dhG = g / go


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What is the relation between h & hG?

= + G

G

Integrate:0

h dh =0

hG R2/(R+hG)2 dhG G G

At hG = 6.5 km , h is less than hG by about 0.1% only.

At h = 65 km h is less than h b about 1% onl .

The Standard Atmosphere (SA)

It is defined in order to relate flight tests, wind-tunnel

,vehicle ( aircraft, missile, satellite,.etc ) to a common

reference.


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It gives mean values of p, T, , and other properties asunc on o a u e.

These values are obtained from experimental balloons

and soundin -rocket measurements with a mathematical

model of the atmosphere ( based on the equation ofstate and the hydrostatic equation).

evera erent stan ar atmosp eres ex st, ue to

using different experimental data in the models, but the

differences are insi nificant below 30 km 100,000 ft ,which is the domain of contemporary airplanes.

Definition Of The Standard Atmosphere (SA)

The standard atmosphere (SA) is defined by:1. Conditions at sea-level:


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= 1.01325 x 105

N/m2

= 2116.2 Ib/ft2

To = 288.16oK = 518.60 oR

o = 1.225 kg/m2 = 0.002377 slug/ft2

go = 9.807 m/s

2

= 32.17 ft/s

2

. e ne var a on o w a u e, ase on

experimental evidence, as shown in Figure.

= = =

determined by calculation.

# The atmospheric layers of the SA are either isothermal or

gra ent ayers, as s own n gure.


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Temperature distribution in the standard atmosphere


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Atmos heric ro erties variation of SA


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(A) Calculation in an Isothermal Layer:

, ,

Isothermal Layer

h1 T1,p1,1

From the hydrostatic equation: d p = - go dh

Substitute from the equation of state: p = RTdp/p = - (go/RT) dh (1)


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Integrate:p1

p

dp/p = -(go/RT) h1

h

dh

Hence, ln (p/p1) = -(go/RT) (h h1)

Or : (p/p1) = e

- go 1

= (/1) (2)

ecause , p p1 = 1 1 = 1from equation of state

and T = T1 (3)


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(B) Calculation in a Gradient Layer:

Base of layer h1T1,p1, 1

The temperature variation is linear,(T-T1)/(h-h1) = dT/dh = a

a is the temperature lapse rate ( +ve or ve)

= +

Then, dh = dT/a and substitute into Eqn.(1)

dp/p = - (go/aR) dT/T


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Inte rate:

p

d / = - /aR

T

dT/T

Hence, ln p/p1 = - (go/aR) ln T/T1

Then, p/p1 = (T/T1)-go/aR (5)

From equation of state:

1 1 1 1

Hence / = T/T1-[(go/aR)+1] 6

Where T is calculated from Eq.(4)


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With the Figure of variation of T with h and

Eqs.(2),(3),(4),(5), and (6) a Table of values for the

Standard Atmosphere is constructed and is given in

Engineering Units (see textbook Introduction to Flight,Anderson, pages 709-729)

. ressure u e p: e a t tu e n t e tan ar

Atmosphere corresponding to a particular static air

ressure.

5.Temperature Altitude hT :The altitude in the Standard

Atmosphere corresponding to a particular air

. 6.Density Altitude h

: The altitude in the Standard

Atmos here corres ondin to a articular air densit .


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