| SmokeDog's
Note: Some of Simple Aerodynamics, Part 1, 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.
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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.
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| 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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