Air, Our Flight Environment
Airplanes operate in air, a gas made up of nitrogen,
oxygen, and several other constituents. The behavior of air, that is the way its properties like
temperature, pressure, and density relate to each other, can be described by
the Ideal or Perfect Gas
Equation of State:
Subscribe here to our Youtube Channel ... And you will have the advantage of asking questions specific to you and you get quick answers to your situations ....
where P is the barometric or hydrostatic pressure, ρ is the density, and T is the temperature. R is the gas constant for air. In this equation
the temperature and pressure must be given in absolute
values; in other words, temperature must
be in Kelvin or Rankine, not Celsius (Centigrade) or Fahrenheit. Of course the
units must all be consistent with those used in the gas constant:
Units of
This brings us to the
subject of units. It is important that all the units in the perfect gas
equation be compatible; i.e., all English units or all SI units, and that we be
careful if solving for, for example, pressure, to make sure that the units of
pressure come out as they should (pounds per square foot in the English system
or Pascals in SI). Unfortunately many of us don’t have a clue as to how to work
with units.
It is popular in U. S.
scientific circles to try to convince everyone that Americans are the only
people in the world who use “English” units and the only people in the world
who don’t know how to use SI units properly. Nothing could be further from the
truth. No one in the world actually uses SI units correctly in everyday life.
For example, the rest of the world commonly uses the Kilogram
as a unit of weight when it is actually
a unit of mass. They buy produce
in the grocery store in Kilograms, not Newtons. You would also be hard pressed to find anyone in the world, even in France, who knows that
a Pascal is a unit of pressure. Newtons and Pascals are simply not used in many
places outside of textbooks. In England the distances on highways are still
given in miles and speeds are given in mph even as the people measure shorter
distances in meters (or metres), and the government is still trying to get
people to stop weighing vegetables in pounds. There are many people in England
who still give their weight in “stones”.
As aerospace engineers we
will find that, despite what many of our textbooks say, most work in the
industry is done in the English system, not SI, and some of it is not even done in proper English units. Airplane speeds are measured in miles per hour or in knots, and distances are often quoted in nautical
miles. Pressures are given to pilots in inches
of mercury or in millibars. Pressures inside jet and rocket engines are
normally measured in pounds-per-square-inch (psi). Airplane altitudes are most
often quoted in feet. Engine power is given in horsepower and thrust in pounds.
We must be able to work in the real world,
as well as in the politically correct
world of the high school
or college physics
or chemistry or even engineering text.
It should be noted that what
we in America refer to as the “English” unit system, people in England call
“Imperial” units. This can get really confusing because
“imperial” liquid measures are different from “American” liquid measures. An “imperial” gallon is slightly larger than an American gallon and a “pint” of beer in Britain is not the same size as a “pint”
of beer in the U. S.
So, there are many possible
systems of units in use in our world. These include the SI system, the
pound-mass based English system, the “slug” based
English system, the cgs-metric system,
and others. We can discuss
all of these in terms of
a very familiar equation, Isaac Newton’s good old F = ma. Newton’s law relates units as well as physical
properties and we can use it
to look at several common unit systems.
Force = mass x
acceleration
1 Newton = 1 kg x 1 meter/sec2
1 pound-force = 1 pound-mass
x 32.17 ft/sec2
1 Dyne = 1 gram x 1 cm/sec2
1 pound-force = 1 slug x 1 ft/sec2
The first and last of the
above are the systems with which we need to be thoroughly familiar; the first
because it is the “ideal” system according to most in the scientific world, and
the last because it is the semi-official system of the world of aerospace
engineering.
In using any unit system there are three basic requirements:
1.
Always write units with any number that has units.
2.
Always work through
the units in equations at the same time that you work out the numbers.
3.
Always reduce the final units to their simplest form and
verify that they are the appropriate units for that number.
Following the above suggestions would eliminate about half of the
wrong answers found on most student homework and test papers.
In doing engineering problems one should
carry through the units as described above and make sure that the units make
sense for the answer and that the magnitude of the answer is reasonable. Good students do this
all the time while poor ones leave everything to chance.
The first part of this is
simple. If the units in an answer don’t make sense, for example, if the speed for an airplane is calculated to be 345 feet per pound or if we calculate a weight to be 1500 kilograms
per second, it should
be easy to recognize that something is wrong. A fundamental error has been made in following through
the problem with the units and this must be corrected.
The more difficult task is to recognize when the magnitude
of an answer is wrong; i.e., is not “in the right ballpark”. If we
are told that the speed
of a car is 92 meters/sec. or is 125 ft/sec. do we have any “feel”
for whether these
are reasonable or not? Is
this car speeding or not? Most of us don’t have a clue without doing some quick
calculations (these are 205 mph and 85 mph, respectively). Do any of us know our weight in Newtons?
What is a reasonable barometric pressure in the
atmosphere in any unit system?
So our second unit related
task is to develop some appreciation for the “normal” range of magnitudes for
the things we want to calculate in
our chosen units system(s). What is a reasonable range for a wing’s lift
coefficient or drag coefficient? Is it reasonable for cars to have 10 times the
drag coefficient of airplanes?
With these cautions in mind let’s go back and look at our “working medium”, the standard atmosphere.