*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 per cent 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. In combustion, the oxygen enters into a chemical combination
with the fuel while the nitrogen passes off with the products of
combustion unchanged.
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, and for this reason the density (weight
per cubic foot) is always specified in a test.
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 and 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, and while this conception is an aid in studying
the reactions, the actual laboratory results are far from the computed
values. 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 this 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, while at 0° F. the volume
shrinks to 11.58 cubic feet, the corresponding densities being 0.07610
and 0.08633 pounds per cubic foot, 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 increases with the density
increase so that the effect of heat is twofold in its effect.
With a constant temperature, the pressure and density both decrease as
the altitude increases, 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 per stroke at
high altitudes as at low, and as a result the power is diminished as we
gain in altitude. The following table gives the power variations at
different heights above sea level.
This air table also 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. For example, if an engine
develops 100 horsepower at sea level, it will develop 100 × 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.
[Illustration: NOTE.-Densities marked * are interpolated from a graph,
but are close enough for all ordinary purposes.]
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. Owing to the fact
that the temperature decreases as we gain altitude, further corrections
must be made in the tabular values, but as the changes are rather
difficult to make and are relatively small we will not take the matter
up at this point.
[Illustration: Fig. 1. Air Flow About a Flat Normal Plate. Pressure Zone
at Front and .#. Turbulent Zone at Rear (H). Arrows Show Direction O
OW.]
*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 (P-R), the stream reuniting at a point (M) far in the rear.
Assuming the air flow 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. 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 is indicated by ***, while the vacuous space at the rear
is indicated by fine dots. 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 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 the 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 = KAV², 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 = KAV² = 0.003 × 6 × (60
X 60) = 64.80 pounds drag. For a square flat plate, the co-efficient K
can be taken as 0.003.
*Aspect Ratio*. The aspect ratio of a plate is the ratio of the length
to the width. Thus, with an aspect ratio of 2.0, we understand that the
plate is twice as long as it is wide. The ratio of the length to the
width has a very considerable influence of the resistance or drag, this
increasing as the ratio is made greater. If the resistance of a square
plate is taken as 1.00, the resistance of a plate with an aspect ratio
of 20 will be about 1.34 times as great. The following table will give
the effects of aspect ratio on the resistance of a flat plane.
EFFECTS OF ASPECT RATIO ON FLAT PLATES.
─────────────────────────────────────────────────────────────────
Aspect Ratio. Resistance K as a Multiple of a Square
Length/Width Plate.
─────────────────────────────────────────────────────────────────
1.00 (square) 1.00
─────────────────────────────────────────────────────────────────
1.50 1.04
─────────────────────────────────────────────────────────────────
2.00 1.05
─────────────────────────────────────────────────────────────────
3.00 1.07
─────────────────────────────────────────────────────────────────
4.00 1.08
─────────────────────────────────────────────────────────────────
5.00 1.09
─────────────────────────────────────────────────────────────────
6.00 1.10
─────────────────────────────────────────────────────────────────
7.00 1.12
─────────────────────────────────────────────────────────────────
9.00 1.14
─────────────────────────────────────────────────────────────────
10.00 1.15
─────────────────────────────────────────────────────────────────
15.00 1.26
─────────────────────────────────────────────────────────────────
20.00 1.34
─────────────────────────────────────────────────────────────────
30.00 1.40
─────────────────────────────────────────────────────────────────
To convert the values of a square plate into a flat plate of given
aspect ratio, multiply the resistance of the square plate by the factor
under the "K" heading. For example: The resistance of a certain square
plate is 20 pounds, find the resistance of a plate of the same area, but
with an aspect ratio of 15. *Solution*. The factor for a ratio of 15
will be found to be 1.26, hence the resistance of the required plate
will be 20 × 1.26=25.2 pounds.
[Illustration: Fig. 2. Air Flow About a Streamline Body Showing an
Almost Complete Absence of Turbulence Except at the Extreme Rear Edge.
Resistance Is Principally Due to Skin Friction.]
*Streamline 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 fishlike 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 negligible.
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 becomes partly
turbulent and partly frictional, with the resistance increasing rapidly
as the percentage of the turbulent region is increased.
The fact that the resistance is due 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 squared
while the frictional resistance only varies at the rate of V to the
1.86th power, 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 maximum 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.
An approximate formula showing the relation of fineness ratio and
resistance (curvature equal) was developed by A. E. Berriman, and
published in "Flight" Nov. 12, 1915. Let D = resistance of a flat plate
at a given speed, and R = resistance of a strut at the same speed and of
the same area, then the relation between the resistance of the flat
plate, and the strut will be expressed by the formula R/D=4L/300d, where
L = length of section and d = width as in Fig. 2. This can be transposed
for convenience, by assuming the drag of a flat plate as D = 0.003AV²,
where A = area in square feet, and V = velocity in miles per hour. The
ratio of the strut resistance to the flat plate resistance, given by
Berriman’s formula, can now be multiplied by the flat plate resistance,
or strut resistance = R = 0.003AV² X 4L/300d. = 0.012LAV²/300d. It
should be understood that the area mentioned above is the greatest area
presented to the wind in square feet, and hence is equal to the length
of the strut (not section) multiplied by the width (d).
[Illustration: Fig. 3. Imperfect Streamline Body with a Considerable
Turbulence Due to the Short, Stubby Form. Fig. 4 Shows the Flow About a
Circular Rod or Cylinder.]
Assuming the length (L) of the section as 7.5 inches, and the width (d)
as one inch, the fineness ratio will be 7.5. Using the Berriman formula
in its original form, the relative resistance of the strut and flat
plate of same area will be found as R/D=4L/3000 = 0.1, that is, the
resistance of a streamline form strut of above fineness ratio will be
about 0.1 of a flat plate of the same area. It should be understood that
this is only an approximate formula since even struts of the same
fineness vary among themselves according to the outline. Results
published 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 before 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.
*Resistance Calculations (Turbulency)*. In any plate or body where the
resistance is principally due to turbulent action, as in the flat plate,
sphere, cone, etc., the resistance can be computed from the formula R =
KAV², where R is the resistance in pounds and K, A, and V are as before.
The resistance co-efficient (K) depends upon the shape of the object
under standard air conditions, and differs greatly with flat plates,
cones, sphere, etc. The area (A) is the area presented to the wind, or
is the greatest area that faces the wind, and is taken at right angles
to its direction. The following table gives the value of K for the more
common forms of objects. See Figs. 4 to 12, inclusive:
There are almost an infinite number of different forms, but for the
present the above examples will fill our purpose. As an example in
showing how greatly the form of an object influences its resistance, we
will work out the resistance of a flat plate and a spherical ended cone,
both having the same presented diameter. The cone is placed so that the
spherical end will face the air stream. The area A of both objects will
be: 0.7854 × 2 × 2 = 3.1416 square feet. With an assumed wind velocity
of 100 miles per hour, the resistance of the circular flat disc will be:
R= KAV²=000282 × 3.1416 × (100×100) = 87.96 lbs. For the cone, R =
KAV²=0.000222 × 3.1416 × (100 × 100) = 6.97 lbs. From this calculation
it will be seen that it is advisable to surround the object with a
spherical cone shaped body rather than to present the flat surface to
the wind. In the above table the value of K is given for two positions
of the spherical based cone, the first is with the apex toward the wind,
and the second condition gives the value with the base to the wind. With
the blunt end forward, the resistance is about one-half that when the
pointed apex enters the air stream. This is due to the taper closing up
the stream without causing turbulence.
[Illustration: Figs. 4a-5-6-7-8-9-10-11-12. The Values of the Resistance
Co-efficient K for Different Forms and Positions of Solid Objects.
Arrows Indicate the Direction of the Relative Wind. (Eiffel.)]
With the apex forward there is nothing to fill up the vacuous space when
the air passes over the large diameter of the base as the curve of the
spherical end is too short to accomplish much in this direction.
*Skin Friction*. The air in rubbing over a surface experiences a
frictional resistance similar to water. At the present time the accepted
experiments are those of Dr. Zahm but these are still in some question
as to accuracy. It was found in these experiments that there was
practically no difference caused by the material of the surfaces, as
long as they were equally smooth. Linen or cotton gave the same results
as smooth wood or zinc as long as there was no nap or lint upon the
surface. With a fuzzy surface the friction increased rapidly. This is
undoubtedly due to a minute turbulence caused by the uneven surface, and
hence the increase was not purely frictional, but also due to
turbulence. In the tests, the air current was led parallel to the
surface in such a way that only the friction could move the surface. The
surface was freely suspended, and as the wind moved it edgewise, the
movement was measured by a sharp pointer. End shields prevented impact
of the air on the end of the test piece so that there was no error from
this source. The complete formula given by Dr. Zahm is rather
complicated for ordinary use, especially for those not used to
mathematical computations. If Rf = resistance due to friction on one
side of surface, L= length in direction of wind in feet, b = width of
surface in feet, and V= velocity in feet per second, then
Rf = 0.00000778L⁰.⁹³V¹.⁸⁶b.
It will be noted that the resistance increases at a lower rate than the
velocity squared, and at a less rate than the area. That is to say, that
doubling the area will not double the resistance, but will be less than
twice the amount. Giving the formula in terms of area and miles per hour
units, we have: Rf = 0.0000167A⁰.⁹³V¹.⁸⁶. Where A = area in square feet
and V = miles per hour. The area is for one side of the surface only. A
rough approximation to Zahm’s equation has been proposed by a writer in
"Flight," the intention being to avoid the complicated formula and yet
come close enough to the original for practical purposes. The latter
formula reads: Rf = 0.000009V² where Rf and V are as above. Up to 40
miles per hour the results are very close to Zahm’s formula, and are
fairly close from 60 to 90 miles per hour. This approximation is only
justified when the length in the direction of the wind is nearly equal
to the length. If the length is much greater, there is a serious error
introduced.
This formula is applied to surfaces parallel to the wind such as the
sides of the body, rudder, stabilizer, and elevator surfaces (when in
neutral). A second important feature of the friction formula is that it
illustrates the law of "similitude" or the results of a change in scale
and velocity, hence it outlines what we must expect when we compute a
full size aeroplane from the results of a model test.
*The Inclined Plane*. When a flat plate is inclined with the wind, the
resistance or drag will be broken up into two components, one at right
angles to the air stream, and one parallel to it. If the plate is
properly inclined, the right angled component can be utilized in
obtaining lift as with an aeroplane wing. This is shown in Fig. 13 where
L is the vertical lift force at right angles to the air stream and D is
the horizontal drag acting in the direction of the wind. As in the case
of the plate placed normal to the wind, there is pressure at the front
of the plate and a partial vacuum behind. The resultant force will be
determined by the difference in pressure between the front and the back
of the plate. The forces will vary as V² since the reaction is caused by
turbulent flow. Both the lift and drag will vary with the angle made
with the stream, and there will be a different value for the
co-efficient K for each change in the angle. The angle made with the air
stream is known as the "Angle of incidence" or the "Angle of attack."
The change of drag and lift does not vary at a regular rate with the
angle.
[Illustration: Fig. 13. Flow About, Inclined Plane and Forces Produced
by Stream. Fig. 14. Normal Plane with C.P. at center of Plate. Fig. 15..
C.P. Moves Toward Entering Edge When Plate Is Inclined to Wind.]
A line OR is the resultant of the lift and drag forces L and D, this
resultant being the force necessary to balance the two forces L-D. It is
on the point of application O that the plate balances, and this point is
sometimes known as the "Center of pressure." The center of pressure is
therefore the point at which the resultant intersects the surface of the
flat plate. The resultant OR is approximately at right angles to the
surface at small incident angles, and the point O is nearer the front or
"leading edge" (A) of the plane. The smaller the angle of incidence the
nearer will the point O approach the leading edge A. By drawing OL to
scale, representing the lift, and OD to scale representing the drag, we
can find the resultant OR by drawing LR parallel to the drag OD and DR
parallel to the lift line OL. All lines drawn through the intersection
of LR and DR will give the resultant OR to scale. All of the lines must
be started from the center of pressure at O.
The least resultant will, of course, occur when the plane is parallel to
the air stream. The maximum resultant will occur when the angle of
incidence is about 40 degrees, and on a further increase in the angle,
the value of the resultant will gradually decrease. When the plane is
parallel with the stream, the resultant is parallel to the plate, but
rapidly approaches a position at right angles at about an incidence of 6
to 10 degrees. Beyond 10 degrees incidence the angle of the resultant
increases past the normal.
The center of pressure (O), or the point where the resultant force
intersects the plane, moves forward as the angle of incidence is
decreased from 90°. When at right angles to the air current, the center
of pressure is exactly in the center of the plane as shown by Fig. 14.
In this case the drag (D) is the resultant, and acting in the center,
exactly balances the air forces. In Fig. 15 the angle of incidence is
reduced, consequently the center of pressure moves nearer the leading
edge (A). As the angle continues to decrease, the C. P. moves still
further forward until it lies directly on the front edge when the plate
becomes parallel with the air stream. The center of pressure movement is
due to the fact that more and more work is done by the front part of the
surface as the angle is decreased. Consequently the point of support, or
C. P., must move forward to come under the load. It should be understood
that the plane will balance about the C. P. if a knife edge bearing were
applied as at R in Fig. 15.
*Calculation of Inclined Planes*. We will now consider the inclined
plane as a lifting surface for an aeroplane, and make the elementary
calculations for such purpose. The lift will first be calculated for the
support of the given load, at the given velocity, and then the drag. For
several reasons, that will afterwards be explained, the flat plate or
plane is not used for the main lifting surfaces, but the experience
gained in computing the plate will be of great assistance when we start
calculating actual wings.
*Lift and Drag Co-efficients*. The lift component (L) of the inclined
flat plate depends on the velocity, area, aspect ratio and angle of
incidence. Instead of using the co-efficient (K) formerly used for the
total drag, we will use the lift co-efficient Ky. The formula for lift
now becomes: L = KyAV² where A = area in square feet, and V = velocity
in miles per hour. The lift co-efficient Ky, depends upon the angle of
incidence. The horizontal drag D will be calculated from the drag
co-efficient Kx, which is used in the same way as the co-efficient K in
the case of the normal plate. The subscript (x) is used to distinguish
it from the lift co-efficient. Both Ky and Kx must be corrected for
aspect ratio. The drag can be calculated from the formula: D = KxAV²
where the letters A and V are the same as above.
For the calculation of the drag, we will use a new expression—the
"Lift-Drag Ratio"—or as more commonly given, "L/D." This shows the
relation between the lift and drag, so that by knowing the lift and the
ratio for any particular case, we can compute the drag without the
necessity of going through the tedious calculation D = KxAV². The
lift-drag ratio for a flat plate varies with the angle of incidence, and
the aspect ratio, and hence a separate value must be used for every
inclination and change in aspect. To obtain the drag, divide the lift by
the lift-drag ratio. Hence if the lift is 1200 pounds, and the ratio
equals 6.00, the drag will be: 1200/6=200 pounds, or in other words, the
lift is 6 times the drag force. Changing the angle of incidence through
angles ranging from 1 degree to 7 degrees, the lift-drag ratio of a flat
plate will vary from 1.5 to 7.5. When the plane is parallel to the wind
stream and gives no lift, the drag is computed from Zahm’s skin friction
formula.
The following tables give the values of Ky, Kx, L/D, and center of
pressure movement for flat plates of various aspect ratios. The center
of pressure (C. P.) for each angle is given as a decimal fraction of its
distance from the leading edge, in terms of the width or "Chord."
[Illustration: Fig. 16. Plan View of Plate with Long Edge to Wind. Fig.
17. Plate with Narrow Edge to Wind, Showing Loss in Lift. 17a Shows
Effect of Raked Tips.]
Fig. 16 shows the top view or plan of a lifting surface, with the
direction of the wind stream indicated by the arrows w-w-w = w. The
longer side or "span" is indicated by S, while the width or chord is C.
Main lifting surfaces, or wings, have the long side at right angles to
the wind as shown. When in this position, the surface is said to be in
"Pterygoid Aspect," and when the narrow edge is presented to the wind,
the wing is in "Apteroid Aspect." The word "Pterygoid" means "Bird
like," and was chosen for the condition in Fig. 16, as this is the
method in which a bird’s wing meets the air. Contrary to the case with
true curved aeroplane wings, flat planes usually give better lift in
apteroid than in pterygoid aspect at high angles. The aspect ratio will
be the span (S) divided by the chord (C), or Aspect ratio = S/C.
It will be seen from the above that the lift coefficient Ky increases
with the aspect ratio, and that it generally declines after an angle of
30 degrees. The center of pressure moves steadily back with an increase
in angle.
*Example for Lifts*. A certain flat plane has an area of 200 square
feet, and moves at 50 miles per hour. The angle of incidence is 10
degrees, and the aspect ratio is 6. Find the total lift and the drag in
pounds. Also the location of the center of pressure in regard to the
leading edge, if the chord is 5.8 feet.
*Solution*. Under the table headed, "Aspect Ratio = 6" we find that Ky
at 10° = 0.00173, and that the lift drag ratio is 5.2. The center of
pressure is 0.333 of the chord from the front edge. The total lift then
becomes: L = KyAV² = 0.00173 x 200 x (50 x 50) = 865 pounds. Since the
lift drag ratio is 5.2, the drag = D = 865/5.2 = 166.3 pounds. The
center of pressure will be located 5.8 x 0.333 = 1.4 feet from the
leading edge.
Under the same conditions, but with an aspect ratio of 3, the lift will
become: L = KyAV² = 0.0014 x 200 x(50 x 50) = 700 pounds. In this case
the lift drag ratio is 5.1, so that the drag will be 137.8 pounds. Even
with the same area, the aspect ratio makes a difference of 865–700 = 165
pounds. If we were compelled to carry the original 865 pounds with
aspect 3 wing, we would also be compelled to increase the area, angle,
or speed. If the speed were to be kept constant, we would be limited to
a change in area or angle. In the latter case it would be preferable to
increase the area, since a sufficient increase in the angle would
greatly increase the drag. It will be noted that the lift-drag ratio
decreases rapidly with an increase in the angle.
[Illustration: Burgess Seaplane Scout.]
*Calculation of Area*: Let us assume that we are confined to the use of
an aspect ratio of 6, a speed of 50 miles per hour, weight = 2500
pounds, and wish to obtain the area that will give the most efficient
surface (Least lift-drag ratio.) The equation can be now transposed so
that the area = A = KyV². On examination of the table it will be seen
that the greatest lift-drag ratio is 6.4 at 5 degrees, and that the Ky
at this angle is 0.00103. Substituting these values in the equation for
area, we have A = L/KyV² = 2500/000103 x (50 x 50) = 971 square feet.
[Illustration: Wind Tunnel at Washington Navy Yard in Which the Air
Circulates Continuously Through a Closed Circuit]