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“Simple Aerodynamics"
Part 1
copyright 1984, 2004, Sublogic Corporation 

SmokeDog's Note: Much of this article is taken from a 1929 textbook. Some of the most clear and simple explanations were written in the early stages of the development of a field of study.

Most of this text can be absorbed by people ages 12 and up. If you are not ready to comprehend some of the math, don't worry. The verbal descriptions of properties of air will give you insights into the problems of traveling though the atmosphere.

Definition. Aerodynamics treats of the forces produced by air in motion, and is the basic subject in the study of the aeroplane. It is the purpose of this chapter to describe in detail the action of the wing in flight and the aerodynamic behavior of the other bodies that enter into the construction of the aeroplane. At present, aerodynamic data is almost entirely based on experimental investigations. The motions and reactions produced by disturbed air are so complex and involved that no complete mathematical theory has yet been advanced that permits of direct calculation.

Properties of Air. Air being a material substance, possesses the properties of volume, weight, viscosity and compressibility. It is a mechanical mixture of the two elementary gases, oxygen and nitrogen, in the proportion of 23 per cent of oxygen to 77 percent of nitrogen. It is the oxygen element that produces combustion, while the nitrogen is inert and does not readily enter into combination with other elements, its evident function being to act as a dilutant for the energetic oxygen.

Air is considered as a fluid since it is capable of flowing like water, but unlike water, it is highly compressible. Owing to the difference between air and water in regard to compressibility, they do not follow exactly the same laws, but at ordinary flight speeds and in the open air, the variations in the pressure are so slight as to cause little difference in the density. Hence for flight alone, air may be considered as incompressible. It should be noted that a compressible fluid is changed in density by variations in the pressure, that is, by applying pressure, the weight of a cubic foot of a compressible fluid is greater than the same fluid under a lighter pressure. This is an important consideration since the density of the air greatly affects the forces that set it in motion.

Every existing fluid resists the motion of a body, the opposition to the motion being commonly known as “resistance.” This is due to the cohesion between the fluid particles. The resistance is the actual force required to break them apart and make room for the moving body. Fluids exhibiting resistance are said to have “viscosity.” In early aerodynamic researches, and in the study of hydrodynamics, the mathematical theory is based on a “perfect fluid,” that is, on a theoretical fluid possessing no viscosity. Such theory would assume that a body could move in a fluid without encountering resistance, which in practice is, of course, impossible.

In regard to viscosity, it may be noted that air is highly viscuous—relatively much higher than water. Density for density, the viscosity of air is about 14 times that of water, and consequently the effects of viscosity in air are of the utmost importance in the calculation of resistance of moving parts.

Atmospheric air at sea level is about 1/800 of the density of water. Its density varies with the altitude and with various atmospheric conditions, and for this reason the density is usually specified “at sea level” as the sea level altitude gives a constant base of measurement for all parts of the world. As the density is also affected by changes in temperature, a standard temperature is also specified. Experimental results, whatever the pressure and temperature at which they were made, are reduced to the corresponding values at standard temperature and at the normal sea level pressure, in order that these results may be readily comparable with other data.

The normal (average) pressure at sea level is 14.7 pounds per square inch, or 2,119 pounds per square foot at a temperature of 60° Fahrenheit. At this temperature, 1 pound of air occupies a volume of 13.141 cubic feet. At 0° F. the volume shrinks to 11.58 cubic feet, the corresponding densities being 0.07610 at 60° and 0.08633 pounds per cubic foot at 0°, respectively. This refers to dry air only as the presence of water vapor makes a change in the density. With a reduction in temperature, the pressure decreases as the density increases so that the effect of heat is twofold.

With a constant temperature, the pressure and density both decrease as the altitude increases. For example, a density at sea level of 0.07610 pounds per cubic foot is reduced to 0.0357 pounds per cubic foot at an altitude of 20,000 feet. During this increase in altitude, the pressure drops from 14.7 pounds per square inch to 6.87 pounds per square inch. This variation, of course, greatly affects the performance of aeroplanes flying at different altitudes, and still more, affects the performance of the motor, since the latter cannot take in as much fuel-air mixture per stroke at high altitudes as at low. As a result the power is diminished as we gain in altitude.

The attached air table gives the properties of air through the usual range of flight altitudes. The pressures corresponding to the altitudes are given both in pounds per square inch and in inches of mercury so that barometer and pressure readings can be compared. In the fourth column is the percentage of the horsepower available at different altitudes, the horsepower at sea level being taken as unity (one). For example, if an engine develops 100 horsepower at sea level, it will develop 100 x 0.66 = 66 horsepower at an altitude of 10,000 feet above sea level. The barometric pressure in pounds per square inch can be obtained by multiplying the pressure, in inches of mercury, by the factor 0.4905, this being the weight of a mercury column 1 inch high.

In aerodynamic laboratory reports, the standard density of air is 0.07608 pounds per cubic foot at sea level, the temperature being 15 degrees Centigrade (59 degrees Fahrenheit). This standard density will be assumed throughout the book, and hence for any other altitude or density, the corresponding corrections must be made.

Air Pressure on Normal Flat Plates. When a flat plate or “plane” is held at right angles or “normal” to an air stream, it obstructs the flow and a force is produced that tends to move it with the stream. The stream divides, as shown in Fig. 1 and passes all around the edges of the plate (points P and R in the drawing), the stream reuniting at a point (M) far in the rear. Assuming the air flows from left to right, as in the figure, it will be noted that the rear of the plate at (H) is under a slight vacuum, and that it is filled with a complicated whirling mass of air. The general trend of the eddy paths are indicated by the arrows.

Figure 1. Air Travel about Normal Plate

At the front where the air current first strikes the plate there is a considerable pressure due to the impact of the air particles. In the figure, pressure above the atmospheric pressure is indicated by ++++ symbals, while the vacuous space at the rear is indicated by fine clots. As the pressure in front, and the vacuum in the rear, both tend to move the surface to the right in the direction of the air stream, the total force tending to move the plate will be the difference of pressure on the front and rear faces multiplied by the area of the plate. Thus if (F) is the force due to the impact pressure at the front, and (G) is the force due to the vacuum at the rear, then the total resistance (D) or “Drag” is the sum of the two forces.

Contrary to the common opinion, the vacuous (vacuum at the rear) part of the drag is by far the greater, say in the neighborhood of from 60 to 75 per cent of the total. When a body experiences pressure due to tile breaking up of an air stream, as in the present case, the pressure is said to be due to “turbulence,” and the body is said to produce “turbulent flow.” This is to distinguish the forces due to impact and suction, from the forces due to the frictional drag produced by the air stream rubbing over the surface.

Forces due to turbulent flow do not vary directly as the velocity of the air past the plate, but at a much higher rate. If the velocity is doubled, the plate not only meets with twice the volume of air, but it also meets it twice as fast. The total effect is four times as great as in the first place. The forces due to turbulent flow therefore vary as the square of the velocity, and the pressure increases very rapidly with a small increase in the velocity. The force exerted on a plate also increases directly with the area, and to a lesser extent, the drag is also affected by the shape and proportions. Expressed as a formula, the total resistance (D) becomes: D=KAVsqared where K = co-efficient of resistance determined by experiment, A = area of plate in square feet, and V = velocity in miles per hour. The value of K takes the shape and proportion of the plate into consideration, and also the air density.

Example. If the area of a flat plate is 6 square feet, the co-efficient K = 0.003, and the velocity is 60 miles per hour, what is the drag of the plate in pounds?
Solution: D = KAVsqared = 0.003 x 6 x (60 X 60) = 64.80 pounds drag.
For a square flat plate, the co-efficient K can he taken as 0.003.

SmokeDog's Note: In discussions of aerodynamics, we will often use the term "coefficient". A coefficient is a number often found through experimentation or observation, which allows you to compute results in convenient units (pounds, hours, dollars, etc.)

For example, you observe the results of cook times for a fully cooked turkey, given a variety of different trial weights of turkeys.

  Weight of Turkey Cook Time
Turkey #1 8 pounds 4 hours
Turkey #2 10 pounds 5 hours
Turkey #3 12 pounds 6 hours

You invent a coefficient, "cT" or "coefficient of turkey done time". For the Turkeys shown in the table, the coefficient cT=0.5.

Pounds of Turkey x cT = hours until cooked.

Different brands of turkeys may have different cT values.
Different aircraft parts may have different drag coefficients.
Next week we will explore the use of "streamlining' to produce a reduced drag coefficient.

(continued next week)

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“Simple Aerodynamics"
Part 1
copyright 1984, 2004, Sublogic Corporation