Aerodynamics and Hydrostatic

 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:

 



P= ρRT

 

Aerodynamics and hydrostatic pressure





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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 Aerodynamics and hydrostatic pressure

 

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.