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.
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.
article ended with illustrations of the term coefficient.
Lets repeat these concepts........
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
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.)
example, you observe the results of cook times for a
fully cooked turkey, given a variety of different trial
weights of turkeys.
invent a coefficient, "cT" or "coefficient
of turkey done time". For the Turkeys shown in
the table, the coefficient cT=0.5.
of Turkey x cT = hours until cooked.
brands of turkeys may have different cT values.
Different aircraft parts may have different drag coefficients.
cars have different drag coefficients.
we move on lets relate the coefficient of drag to modern automobiles.
The drag coefficient for autos is expressed in different units
that the traditional aircraft drag coefficient.
aircraft drag coefficients usually give a number to multiply
square feet of frontal area (the area of a structure or part
as seen from the front) in order to give drag in pounds of
automotive coefficient of drag, "Cd", appears to
be in units of square meters of frontal area with results
relating to horsepower required to push the car through the
air given the drag produced. (Actually the force units are
given in watts, but we know that 746 watts = 1 horsepower.)
of automobiles range from .25 to .5. The sleek, little Honda
Insight has a Cd of .25. The low coefficient of drag, multiplied
by a small frontal area, (multiplied again by velocity squared),
give it a gas mileage of over 60 miles per gallon (MPG) at
A low Cd
really helps gas mileage. The smallish Honda CRV sport utility
vehicle has a Cd of .5 and gives you 25 miles per gallon (MPG)
on the highway. The big Chrysler Town and Country family van
has a Cd of just .35 and gets 26 MPG, better than the smaller
read in the last article, a blunt, square-ish front end and
rear end contribute to a poor coefficient of drag. The rear
end contributes more than the front end.
with the 1929 text on aeronautics. Remember that this author
uses the terms:
coefficient of drag
D for pound of drag
A for square feet of frontal area
V for velocity in Miles Per Hour
Forms. When a body is of such form that it does not
cause turbulence when moved through the air, the drag is entirely
due to skin friction. Such a body is known as a “streamline
form” and approximations are used for the exposed structural
parts of aeroplanes in order to reduce the resistance. Streamline
bodies are fish-like or torpedo-shaped, as shown by Fig. 2,
and it will be noted that the air stream hangs closely to
the outline through nearly its entire length. The drag is
therefore entirely due to the friction of the air on the sides
of the body since there is no turbulence or “discontinuity.”
In practical bodies it is impossible to prevent the small
turbulence (I), but in well-designed forms its effect is almost
2. Air Flow Around Streamline Body.
In poor attempts
at streamline form, the flow discontinues its adherence to
the body at a point near the tail. The poorer the streamline,
and the higher the resistance, the sooner the stream starts
to break away from the body and cause a turbulent region.
The resistance now be comes partly turbulent and partly frictional,
with the resistance increasing rapidly as the percentage of
the turbulent region is increased.
3-4. Imperfect Streamline Bodies.
The fact that the
resistance is clue to two factors, makes the resistance of
an approximate streamline body very difficult to calculate,
as the frictional drag and the turbulent drag do not increase
at the same rate for different speeds. The drag due to turbulence
varies as V while the frictional resistance only varies at
the rate of V° hence the drag due to turbulence increases
much faster with the velocity than the frictional component.
If we could foretell the percentage of friction, it would
be fairly easy to calculate the total effect, but this percentage
is exactly what we do not know. The only sure method is to
take the results of a full size test.
Fig. 2 gives the
approximate section through a streamline strut such as used
in the interplane bracing of a biplane. The length is (L)
and the width is (d), the latter being measured at the widest
point. The relation of the length to the width is known as
the “fineness ratio” and in interplane struts
this may vary from 2.5 to 4.5, that is, the length of the
section ranges from 2.5 to 4.5 times the width. The ideal
streamline form has a ratio of from 5. to 5.75. Such large
ratios are difficult to obtain with economy on practical struts
as the small width would result in a weak strut unless the
weight were unduly increased. Interplane struts reach a maxi
mum fineness ratio at about 3.5 to 4.5. Fig. 3 shows the result
of a small fineness ratio, the short, stubby body causing
the stream to break away near the front and form a large turbulent
region in the rear.
by the National Physical Laboratory show streamline sections
giving 0.07 of the resistance of a flat plate of the same
area, with fineness ratio=6.5. In Fig. 4 the effects of flow
about a circular rod is shown, a case where the fineness ratio
is 1. The stream follows the body through less than one-half
of its circumference, and the turbulent region is very large;
almost as great as with the flat plate. A circular rod is
far from being even an approach to a perfect form.
In all the cases
shown, Figs. 1-2-3-4, it will be noticed that the air is affected
for a considerable distance in front of the plane, as it rises
to pass over the obstruction be fore it actually reaches it.
The front compression may be perceptible for 6 diameters of
the object. From the examination of several good low-resistance
streamline forms it seems that the best results are obtained
with the blunt nose forward and the thin end aft. The best
position for the point of greatest thickness lies from 0.25
to 0.33 per cent of the length from the front end. From the
thickest part it tapers out gradually to nothing at the rear
end. That portion to the rear of the maximum width is the
most important from the standpoint of resistance, for any
irregularity in this region causes the stream to break away
into a turbulent space. From experiments it has been found
that as much as one-half of the entering nose can be cut away
without materially increasing the resistance. The cut-off
nose may be left flat, and still the loss is only in the neighborhood
of 5 per cent.
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