Table 1: Direct Access to
the Sub-Disciplines of Aerospace Engineering
DESIGN-CENTERED INTRODUCTION TO
AEROSPACE ENGINEERING
6. EARTH'S ATMOSPHERE
Earth's radius is approximately 6.6357 x 106 meters.
This is approximately 4147 miles. Its slightly larger at the equator and
slightly smaller at the poles. Above the surface, there is about 0.9 x
105 meters of gaseous atmosphere. That's about 270,000 feet,
or 51 miles. We don't consider ourselves to have reached outer space until
we're about 100 miles up, but there is very little air above 51 miles.
Because of gravity, the air above presses down on the
air below. So as you come down towards the surface (i.e., towards the center
of the earth), the pressue gets higher. At the surface, the air pressure
(due to the 270,000 feet of air above) is enough to support a column of
mercury (Hg), 780 millimeters (mm) high. For a given base area, this column
of mercury weighs about the same as a column of air only 10,608 meters
high, if the density of the air in this column were the same as that at
the surface. So this means that most of the air is actualy within the bottom
layers of the atmosphere.
Hydrostatic equation
Although people at one time believed that the atmosphere
was like a jungle with huge, transparent monsters waiting to eat pilots
who flew too high, it is in fact like an ocean. While there are some non-uniformities
due to weather (and maybe due to pollution), the overall, average characteristics
of the atmosphere are surprisingly simple to calculate using physics and
chemistry, and a little bit of calculus. At a given height h above the
surface, let's say that pressure is p Newtons per square meter (N/m2,
or Pascals), and density is r kilograms
per cubic meter (kg/m3). The acceleration due to gravity is
g
meters per meters-per-second (m2/s). If you go up by a tiny
distance dh, the pressure decreases by a tiny amount dp.
. This is because you don't any longer have to support the weight of the
element dh of the air column that went below you.
Perfect Gas Law
The Perfect Gas Law is a relation between pressure, density,
temperature and composition of a gas.
The "perfection" refers to the fact that nothing inconvenient
happens over the range of the variables that we consider, like the composition
of the gas changing, etc. This is a good assumption at least over a range
of several hundred degrees Kelvin of temperature, or a change of a few
factors of 10 in pressure about any given "state". It is not adequate when
we consider the huge changes that occur to the air as it is slammed by,
say, the nose of a spacecraft re-entering the atmosphere at Mach 35 (35
times the speed of sound, typical speed of a re-entering Apollo space capsule),
or even a hypersonic missile going at Mach 8. So let's not worry about
those now, and safely assume that the gas is "perfect". Then, the quantity
R is a constant which depends only on the composition (i.e., the average
molecular weight) of the gas, i.e., air. The molecular weight of air is
easy to calculate, knowing that it is generally composed of 20% diatomic
oxygen (O2; molecular weight MW =32), 79% diatomic nitrogen (N2; MW =28),
and 1% argon (MW =44). Thus the average (or "mean") molecular weight of
air is (0.2*32 + 0.79*28 +0.01*44) = 28.96
The Universal Gas Constant is 8314 in SI units. Thus
the gas constant for air is R = 8314/28.96 = 287.04
Stratosphere
Differentiating the perfect gas law,
, or,
if T is constant. Thus in the "isothermal" regions of the atmosphere (where
temperature remains constant as altitude changes),
To see why
the density and pressure behave the same way, write the Perfect Gas law
for the two altitudes h1 and h2, and divide one by the other.
This holds in the Stratosphere, the region between 11,000
meters and 25,000 meters. In gradient regions, where T changes as altitude
changes, we will assume that this variation is linear,i.e.,
Troposphere
. In the Troposphere (the region below 11,000m), the constant a is approximately
-0.0065 deg. K per meter. thus, for a standard sea-level temperature of
288.12 Kelvin, the temperature in the troposphere is given by
T= 288.12 - 0.0065*h, where h is in meters. In this region,
the pressure and density variations can be found as follows:
Sea-Level
Standard Conditions
We all know that atmospheric conditions change from place
to place, season to season, day to day and even more frequently. If we
had one set of standard conditions, we could use those to do the calculations
of how an aircraft flies, and then modify those calculations for the specific
atmospheric conditions encountered at a given time. Thus the International
Standard Atmosphere has been developed. In this, the Sea-level Standard
conditions are as follows:
Temperature = 288.12 Kelvin, Pressure = 101,300 N/m2.
Using these, the density is: 1.225Kg/m3.
The variations with altitude as given according to the
formulae developed above. Now, on a given day, at a given point, let's
say we measue a certain pressure (because the pressure happens to be what
we can measure). We can express this as "so-many meters, Pressure Altitude",
meaning: "if this pressure were in the Standard Atmosphere, I would be
at this altitude". Similarly, we can express Density Altitude and Temperature
Alititude.
Regions of the Atmosphere
Below 500meters, we are in the Atmospheric Boundary Layer.
The winds in the atmosphere get obstructed by hills, buildings, and by
the friction of moving over the ground, and hence slow down, and also become
turbulent, in this region. This is where we see most of the gusts, tornadoes,
rain, snow, etc. Above this, and below 11,000 meters, is the Troposphere.
Most of the "weather" occurs in this region, through some thunderstorms
rise as high as 18,000 meters.
From about 11,000 meters to 25,000 meters is the Stratosphere,
where the temperature is constant at a cold 216.7 Kelvins.
From 25,000 meters to about 47,000 meters, the temperature
rises again, linearly, reaching 282.66K by 47,000 meters. Above that, the
temperature is again assumed to remain quite constant.
Click here for an "Atmosphere Calculator" from Professor Ilan Kroo's Web
Page at Stanford University, based on the 1976 Standard Atmosphere, upto
71000 meters.
http://aero.stanford.edu/StdAtm.html
Some sample values:
| Altitude, meters |
Temperature, K |
Density, kg/m^3 |
Pressure, N/m^2 |
Viscosity, Nsec/m^2 |
| 0 |
288.15 |
1.225 |
101,327 |
0.00001789 |
| 11,000 (end of troposphere) |
216.50 |
0.363925 |
22,633 |
0.00001421 |
| 25,000 (end of stratosphere) |
221.65 |
0.03946 |
2511.18 |
0.00001448 |
| 47,000 (end of linear temp. increase) |
270.648 |
0.00142 |
110.916 |
0.00001703 |
| 60,000 |
245.452 |
0.00028 |
20.3156 |
0.00001575 |
| 71,000 |
214.652 |
0.00006 |
3.95698 |
0.00001410 |
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Note, in summary:
1. It gets pretty cold and hard to breathe up there.
2. The "weather" is mostly below 11km.
3. Most flight occurs below 20,000 meters today.
4. High-altitude winds can reach 200mph.
5. The atmospheric boundary layer contains violent gusts
and changes in conditions.
