*General Wing Requirements*. The performance of flat plates when used as
lifting surfaces is very poor compared with curved sections or wing
forms. It will be remembered that the greatest lift-drag ratio for the
flat plate was 6.4, and the best Ky was 0.00294. Modern wing sections
have a lift-drag ratio of over 20.0, and some sections have a lift
coefficient of Ky–0.00364, or about 60 per cent higher than the lift
obtained with a flat plate. In fact, this advantage made flight
possible. To Langley, above all other men, we owe a debt of gratitude
for his investigations into the value of curved wing surfaces.
*Air Flow About an Aerofoil*. To distinguish the curved wing from the
flat plane, we will use the term "Aerofoil." Such wings are variously
referred to as "Cambered surfaces," "Arched surfaces," etc., but the
term "Aerofoil" is more applicable to curved sections. The variety of
forms and curvatures is almost without limit, some aerofoils being
curved top and bottom, while others are curved only on the upper
surface. The curve on the bottom face may either be concave or convex,
an aerofoil of the latter type being generally known as "Double
cambered." The curves may be circular arcs, as in the Wright and
Nieuport wings, or an approximation to a parabolic curve as with many of
the modern wings.
Fig. 1-b shows the general trend of flow about an aerofoil at two
different angles of incidence, the flow in the upper view being
characteristic for angles up to about 6 degrees, while the lower view
represents the flow at angles approximating 16°. At greater angles the
air stream breaks away entirely from the top surface and produces a
turbulence that greatly resembles the disturbance produced by a flat
plate. It will be noted in the top figure (At small angles) that the
flow is very similar to the flow about a streamline body, and that the
air adheres very closely to the top surface. The flow at small angles is
very steady and a minimum of turbulence is produced at the trailing
edge.
[Illustration: Figs. 1a, 1b. Aerofoil Types and Flow at Different
Angles.]
When increased beyond 6°, turbulence begins, as shown in the lower
figure, and a considerable change takes place in the lift-drag ratio.
This is known as the "Lower Critical Angle." The turbulence, however, is
confined to the after part of the wing, and little or no disturbance
takes place in the locality of the lower surface. We observe that an
increase in angle and lift produces an increased turbulent flow about
the upper surface, and hence the upper surface is largely responsible
for the lift. Below 10° the trend of the upper portion of the stream is
still approximately parallel to the upper surface.
[Illustration: Fig. 2. Showing How Lift Is Obtained When an Aerofoil Is
Inclined at a Negative Angle, the Line of Flight Being Along X-X.]
From 16° to 18°, the stream suddenly breaks entirely away from the wing
surface, and produces an exceedingly turbulent flow and mass of eddies.
The lift falls off suddenly with the start of the discontinuous flow.
The angle at which this drop in lift takes place is known variously as
the "Second Critical Angle," the "Burble Point," or the "Stalling
Angle." Any further increase in angle over the stalling angle causes a
drop in lift as the discontinuity is increased. With the flat plane, the
burble point occurs in the neighborhood of 30° and movement beyond this
angle also decreases the lift. In flight, the burble point should not be
approached, for a slight increase in the angle when near this point is
likely to cause the machine to drop or "Stall." The fact that the
maximum lift occurs at the critical angle makes the drop in lift at a
slightly greater angle, doubly dangerous.
A peculiar feature of the aerofoil lies in the fact that lift is still
obtained with a zero angle of incidence, and even with a negative angle.
With the aerofoil shown in Fig. 2 there will be a considerable lift when
the flat bottom is parallel with the direction of travel, and some lift
will still be obtained with the front edge dipped down (Negative Angle).
The curved upper surface causes the air stream to rise toward the front
edge, as at E, hence the wing can be dipped down considerably in regard
to the line of motion X-X, without going below the actual air stream.
*Action in Producing Lift*. At comparatively high angles of incidence,
where there is turbulent flow, the lift and drag are due principally to
the difference in pressure between the upper and lower surfaces as in
the case of the flat plate.
There is a positive pressure below as in the front of a flat inclined
plane, and a vacuous region above the upper surface. The drag with the
plane below the burble point, and above the "Lower Critical Angle," is
due both to skin friction and turbulence—principally to the latter.
Below the first critical angle (6°), the skin friction effect increases,
owing to the closeness with which the air stream hangs to the upper
surface.
Since there is but little turbulence at the small angles below 6°, the
theory of the lift at this point is difficult to explain. The best
explanation of lift at small angles is given by Kutta’s Vortex
Hypothesis. This theory is based on the fact that a wing with a
practically streamline flow produces a series of whirling vortices
(Whirlpools) in the wake of the wings, and that the forward movement of
the plane produces the energy that is stored in the vortices. The
relation between these vortices is such, that when their motion is
destroyed, they give up their energy and produce a lifting reaction by
their downward momentum. The upward reaction on the wing is thus equal
and opposite to the downward momentum of the air vortices.
*Drag Components*. At large angles of incidence where turbulence exists,
the lift and also the drag are nearly proportional to the velocity
squared (V²). Where little turbulence exists, and where the air stream
hugs the surface closely, the drag is due largely to skin friction, and
consequently this part of the drag varies according to Zahm’s law of
friction (V²). For this reason it is difficult to estimate the
difference in drag produced by differences in velocity, since the two
drag components vary at different rates, and there is no fixed
proportion between them. Since the frictional drag does not increase in
proportion to the area, but as A⁰.⁹⁸, difficulty is also experienced in
estimating the drag of a full size wing from data furnished by model
tests.
*Incidence and Lift*. Up to the burble point the lift increases with an
increase in the angle; but not at a uniform rate for any one aerofoil,
nor at the same rate for different aerofoils. The drag also increases
with the angle, but more rapidly than the lift after an incidence of
about 4° is passed, hence the lift-drag ratio is less at angles greater
than 4°. Decreasing the angle below 4° also decreases the lift-drag, but
not so rapidly as with the larger angles. At the angle of "No Lift" the
drag is principally due to skin friction.
Fig. 3 shows a typical lift and incidence chart that gives the relation
between the angle of incidence Ɵ and the lift coefficient. This curve
varies greatly for different forms of aerofoils both in shape and
numerical value, and it is only given to show the general form of such a
graph. The curve lying to the left, and above the curve for the "Flat
plate," is the curve for the particular aerofoil shown above the chart.
The "Lift-Coefficients" at the left hand vertical edge correspond to the
coefficient Ky, although these must be multiplied by a factor to convert
them into values of Ky. As shown, they are in terms of the Absolute
units used by the National Physical Laboratory and to convert them into
the Ky unit they must be multiplied by 0.0051V² where V is in miles per
hour, or 0.00236v² where v = feet per second. The incidence angle is in
degrees.
[Illustration: Fig. 3. Chart Showing Relation Between Incidence And
Lift.]
It will be noted that the lift of the aerofoil is greater than that of
the plate at every angle as with nearly every practical aerofoil. The
aerofoil has a lift coefficient of 0.0025 at the negative angle of -3°,
while the lift of the flat plate of course becomes zero at 0°. As the
incidence of the aerofoil increases the lift coefficient also increases,
until it reaches a maximum at the burble point (Stalling angle) of about
11.5°. An increase of angle from this point causes the lift coefficient
to drop rapidly until it reaches a minimum lift coefficient of 0.46 at
17°. The flat plate as shown, reaches a maximum at the same angle, but
the lift of the plate does not drop off as rapidly. The maximum
coefficient of the aerofoil is 0.58 and of the plate 0.41. The rapid
drop in pressure, due to the air stream breaking away at the burble
point, is clearly shown by the sharp peak in the aerofoil curve. The
sharpness of the drop varies among different aerofoils, the peaks in
some forms being very flat and uniform for quite a distance in a
horizontal direction, while others are even sharper than that shown.
Everything else being equal, an aerofoil with a flat peak is the more
desirable as the lift does not drop off so rapidly in cases where the
aviator exceeds the critical angle, and hence the tendency to stall the
machine is not as great. This form of chart is probably the simplest
form to read. It contains only one quantity, the lift-coefficient, and
it shows the small variations more clearly than other types of graphs in
which the values of Kx, lift-drag, and the resultant force are all given
on a single sheet.
*Center of Pressure Movement*. As in the case of the flat plate the
center of pressure on an aerofoil surface varies with the angle of
incidence, but unlike the plate the center of pressure (C. P.) moves
backward with a decrease in angle. The rapidity of travel depends upon
the form of aerofoil, in some types the movement is very great with a
small change in the angle, while in others the movement is almost
negligible through a wide range. In general, aerofoils are inherently
unstable, since the C. P. moves toward the trailing edge with decreased
angles, and tends to aggravate a deficiency in the angle. If the angle
is too small, the backward movement tends to make it still smaller, and
with an increasing angle the forward movement of the center of pressure
tends to make the angle still greater.
Fig. 4 is a diagram showing the center of pressure movement for a
typical aerofoil with the aerofoil at the top of the chart. The left
side of the chart represents the leading edge of the aerofoil and the
right side is the trailing edge, while the movement in percentages of
the chord length is shown by the figures along the lower line. Thus
figure ".3" indicates that the center of pressure is located 0.3 of the
chord from the leading edge. In practice it is usual to measure the
distance of the C. P. from the leading edge in this way.
[Illustration: Fig. 4. Chart Giving Relation Between Incidence and C.P.
Movement.]
For an example in the use of the chart, let us find the location of the
C. P. at angles of 0°, 3° and 7°. Starting with the column of degrees at
the left hand edge of the chart, find 0°, and follow along the dotted
line to the right until the curve is reached. From this point follow
down to the lower row of figures. It will be found that at 0° the C. P.
lies about half way between 0.5 and 0.6, or more exactly at 0.55 of the
chord from the leading edge. Similarly at 3° the C. P. is at 0.37 of the
chord, and at 7° is at 0.3 of the chord. From 11° to 19°, the C. P. for
this particular aerofoil moves very little, remaining almost constant at
0.25 of the chord. Reducing the angle from 3° causes the C. P. to
retreat very rapidly to the rear, so that at –1° the C. P. is at 0.8 of
the chord, or very near the trailing edge of the wing.
*Other Forms of Charts*. The arrangement of wing performance charts
differs among the various investigators. Some charts show the lift,
drag, lift-drag ratio, angle of incidence, center of pressure movement,
and resultant pressure on a single curve. This is very convenient for
the experienced engineer, but is somewhat complicated for the beginner.
Whatever the form of chart, there should be an outline drawing of the
aerofoil described in the chart.
Fig. 5 shows a chart of the "Polar" variety in which four of the factors
are shown by a single curve. This type was originated by Eiffel and is
generally excellent, except that the changes at small angles are not
shown very clearly or sharply. The curve illustrates the properties of
the "Kauffman" wing, or better known as the "Eiffel No. 37." A more
complete description of this aerofoil will be found under the chapter
"Practical Wing Sections." A single curve is marked at different points
with the angle of incidence (0° to 12°). The column at the left gives
the lift-coefficient Ky, while the row at the bottom of the sheet gives
the drag-coefficients Kx. At the top of the chart are the lift-drag
ratios, each figure being at the end of a diagonal line. In this way the
lift, drag, liftdrag and angle of incidence are had from a single curve.
Take the characteristics at an angle of 10 degrees for example. Find the
angle of 10° on the curve, and follow horizontally to the left for Ky.
The lift-coefficient will be found to be 0.0026 in terms of miles per
hour and pounds per square foot. Following down from 10°, it will be
found that the drag-coefficient Kx = 0.00036. Note the diagonal lines,
and that the 10° point lies nearest to the diagonal headed 7 at the top
of the chart. (It is more nearly a lift-drag ratio of 7.33 than 7.) In
the same way it will be found that an angle of 8 degrees lies almost
exactly on the lift-drag diagonal marked 9. The best lift-drag is
reached at about 2 degrees at which point it is shown as 17.0. The best
lift-coefficient Ky is 0.00276 at 12 degrees.
[Illustration: Fig. 5. Polar Type Chart Originated By Eiffel.]
A third class of chart is shown by Fig. 6. This single chart shows three
of the factors by means of three curves; one for the lift-coefficient,
one for the drag-coefficient, and one for the C. P. movement. Follow the
solid curves only, for the dotted lines are for comparison with the
results obtained by another laboratory in checking the characteristics
of the wing. The curves refer to the R.A.F.-6 section described in the
chapter on "Practical Wing Sections." The lift-coefficients Ky will be
found at the right of the chart with the drag-coefficients Kx at the
left and in the lower column of figures. The upper column at the left is
for the C. P. movement and gives the C. P. location in terms of the
chord length. The angles of incidence will be found at the bottom.
Values are in terms of pounds per square foot, and miles per hour.
[Illustration: Fig. 6. Chart of R.A.F.-6 Wing Section with Three
Independent Curves.]
In using this chart, start with the angle of incidence at the bottom,
and follow up vertically to the lift or drag curves. If the value of Ky
is desired, proceed from the required incidence and up to the "Lift"
curve, then horizontally to the right. To obtain the drag, follow up
from the angle of incidence to the "drift" curve, and then horizontally
to the left. For the position of the C. P., trace up from angle until
the "Center of Pressure" curve is reached, and then across horizontally
to the left. If the angle of 8 degrees is assumed, the lift-coefficient
will be found as Ky = 0.0022, the drag Kx =0.00016, and the center of
pressure will be located at 0.32 of the chord from the leading edge.
This test was made with the air density at 0.07608 pounds per cubic
foot, and at a speed of 29.85 miles per hour. The peak at the burble
point is fairly flat, and gives a good range of angle before the lift
drops to a serious extent. The aerofoil R.A.F.-6 is a practical wing
form used in many machines, and this fact should make the chart of
special interest.
*Surface Calculations*. The calculation of lift and drag for an aerofoil
are the same as those for a flat plate, that is, the total lift is
expressed by the formula: L = KyAV² where A is the area in square feet,
and V is the velocity in miles per hour. From this primary equation, the
values of the area and velocity may be found by transposition.
A = L/KyV² and V = L/KyA.
The drag can be found from the old equation, D = KxAV², or by dividing
the lift by the lift-drag ratio as in the case of the flat plate.
*Example*: A wing of the R.A.F.-6 form has an area of 200 square feet,
and the speed is 60 miles per hour. What is the lift at 6° incidence?
*Solution*. From Chart No. 6 the lift coefficient Ky is 000185 at 6°,
hence the total lift is: L = KyAV² = 0.00185 x 200 x (60 x 60) = 1332
pounds. With an angle of 8 degrees, and with the same speed and area,
the lift becomes,
L = 0.0022 x 200 x (60 x 60) = 1584 pounds. The drag coefficient Kx at
an angle of 6° is 0.00012, and at 8° is 0.00016. The drag at 6° becomes
D = KxAV² = 0.00012 x 200 x (60 x 60) = 86.4 pounds. The lift-drag ratio
at this angle is L/D = 1332/864 = 15.4. The drag at 8° is D = KxAV² =
0.00016 x 200 x (60 x 60) = 115.2 pounds. The lift-drag at 8° is L/D =
1584/115.2 = 13.8.
*Forces Acting on Aerofoil*. Fig. 7 is a section through an aerofoil of
a usual type, with a concave under-surface In an aerofoil of this
character all measurements are made from the chordal line X-X which is a
straight line drawn across (and touching) the entering and trailing
edges of the aerofoil. The angle made by X-X with the horizontal is the
angle of incidence (i). The width of the section, measured from tip to
tip of the entering and trailing edges, is called the "Chord." In this
figure the entering edge is at the left. The direction of lift is "Up"
or as in the case of any aerofoil, acts away from the convex side.
In the position shown, with horizontal motion toward the left, the lift
force is indicated by L, and the horizontal drag force by D, the
direction of their action being indicated by the arrow heads. The force
that is the resultant of the lift and drag, lies between them, and is
shown by R. The point at which the line of the resultant force
intersects the chordal line X-X is called the "Center of Pressure" (C.
P.) The resultant is not always at right angles to the chordal line as
shown, but may lie to either side of this right angle line according to
the angle of incidence (i). A force equal to and in the same direction
as R, will hold the forces L and D in equilibrium if applied at the
center of pressure (C. P.) Owing to the difference in the relative
values of L and D at various angles of incidence, the angle made by R
with the chordal line must vary. The lift and drag are always at right
angles to one another. The resultant can be found by drawing both the
lines L and D through the C. P., and at right angles to one another, and
then closing up the parallelogram by drawing lines parallel to L and D
from the extreme ends of the latter. The resultant force in direction
and extent will be the diagonal R drawn across the corners of the
parallelogram.
[Illustration: Fig. 7. Forces Acting on an Aerofoil, Lift, Drag, and
Resultant. Relative Wind Is from Left to Right.]
The forces acting on the upper and lower surfaces are different, both in
direction and magnitude, owing to the fact that the upper and lower
surfaces do not contribute equally to the support of the aerofoil. The
upper surface contributes from 60 to 80 per cent of the total lift. A
change in the outline of the upper curved surface vitally affects both
the lift and lift-drag, but a change in the lower surface affects the
performance to an almost negligible amount.
In the case of thin circular arched plates the curvature has a much more
pronounced effect. When the curvature of a thin plate is increased, both
the upper and lower surfaces are increased in curvature, and this
undoubtedly is the cause of the great increase in the lift of the sheet
metal aerofoils tested by Eiffel.
The drag component of the front upper surface is "Negative," that is,
acts with the horizontal force instead of against it. The lower surface
drag component is of course opposed to the horizontal propelling force
by enough to wholly overcome the assisting negative drag force of the
front upper surface. The resultants vary from point to point along the
section of the aerofoil both in extent and direction. A resultant true
for the entering edge would be entirely different at a point near the
trailing edge.
*Distribution of Pressure*. To fully understand the relative pressures
and forces acting on different parts of the aerofoil we must refer to
the experimental results obtained by the Eiffel and the N. P. L.
laboratories. In these tests small holes were drilled over the aerofoil
surface at given intervals, each hole in turn being connected to a
manometer or pressure gauge, and the pressure at that point recorded.
While the reading was being taken, the wind was passed over the surface
so that the pressures corresponded to actual working conditions. It was
found that the pressure not only varied in moving from the entering to
trailing edge, but that it also varied from the center to the tips in
moving along the length of the plane. The rate of variation differed
among different aerofoils, and with the same aerofoil at different
angles of incidence.
On the upper surface, the suction or vacuum was generally very high in
the immediate vicinity of the entering edge. From this point it
decreased until sometimes the pressure was actually reversed near the
trailing edge and at the latter point there was actually a downward
pressure acting against the lift. The positive pressure on the under
surface reached a maximum more nearly at the center, and in many cases
there was a vacuum near the entering edge or at the trailing edge. With
nearly all aerofoils, an increase in the curvature resulted in a decided
increase in the vacuum on the upper surface, particularly with thin
aerofoils curved to a circular arc.
[Illustration: Fig. 8. Pressure Distribution for Thin Circular Section.
Fig. 9. Shows the Effect of Increasing the Camber. (Eiffel)]
By taking the sum of the pressures at the various parts of the surface,
it was found that the total corresponded to the lift of the entire
aerofoil, thus proving the correctness of the investigation. The sum of
the drag forces measured at the different openings gave a lower total
than the total drag measured by the balance, and this at once suggests
that the difference was due to the skin friction effect that of course
gave no pressure indication. The truth of this deduction is still
further proved by the fact that the drag values were more nearly equal
at large angles where the turbulence formed a greater percentage of the
total drag.
Figs. 8, 9, 10, 11, 12 are pressure distribution curves taken along the
section of several aerofoil surfaces. These are due to Eiffel. In Fig. 8
is the pressure curve for a thin circular aerofoil section, the depth of
the curve measured from the chordal line being 1/13.5 of the chord. The
vacuum distribution of the upper surface is indicated by the upper
dotted curve, while the pressure on the bottom surface is given by the
solid curve under the aerofoil. The pressures are given by the vertical
column of figures at the right and are in terms of inches of water, that
is, the pressure required for the support of a water column of the
specified height. Figures lying above 0 and marked (-), refer to a
vacuum or negative pressures, while the figures below zero are positive
pressures above the atmospheric. The entering edge is at the right, and
the angle of incidence in all cases is 6°.
It will be seen that the vacuum jumps up very suddenly to a maximum at
the leading edge, and again drops as suddenly to about one-half the
maximum. From this point it again gradually increases near the center,
and then declines toward the trailing edge. It will also be seen that
the pressure on the lower surface, given by the solid curve, is far less
than the pressure due to the upper surface. Since the lower pressure
curve crosses up, and over the zero line at a point near the trailing
edge, it is evident that the supper surface near the trailing edge is
under a positive pressure, or a pressure that acts down and against the
lift. The pressures in any case are very minute, the maximum suction
being 0.3546 inch of water, while the maximum pressure on the under
surface is only 0.085 inch.
Fig. 9 shows the effect of increasing the curvature or camber, the
aerofoil in this case having a depth equal to 1/7 the chord, or nearly
double the camber of the first. The sharp peak at the entering edge of
the pressure curve is slightly reduced, but the remaining suction
pressures over the rest of the surface are much increased, indicating a
marked increase in the total pressure. The pressure at the center is now
nearly equal to the front peak, and the pressure is generally more
evenly distributed. There is a vacuum over the entire upper surface and
a positive pressure over the lower. The general increase in pressure due
to the increased camber is the result of the greater downward deviation
of the air stream, and the corresponding greater change in the momentum
of the air. The speed at which the tests were made was 10 meters per
second, or 22.4 miles per hour. The curves are only true at the center
of the aerofoil length and for an aspect ratio of 6.
The average pressure over the entire surface in Fig. 8 is 1.202 pounds
per square foot, and that of Fig. 9 is 1.440 pounds, a difference of
0.238 pound per square foot due to the doubling camber (16.5 per cent).
Another aerofoil with a camber of only 1/27 gave an average pressure of
0.853 pound per square foot under the same conditions. A flat plane gave
0.546. Tabulation of these values will show the results more clearly.
──────────────────────────────────────────────────────────────────────
Camber of Av. Pres. Per Inc. in Pres. in Efficiency
Surface Sq. Ft. Lbs./Sq. Ft. ─────────────────
Top. Bottom.
──────────────────────────────────────────────────────────────────────
Flat Plane. 0.546 0.000 0.89 0.11
──────────────────────────────────────────────────────────────────────
1/27 0.853 0.307 0.72 0.28
──────────────────────────────────────────────────────────────────────
1/13.5 1.202 0.349 0.71 0.29
──────────────────────────────────────────────────────────────────────
1/7 1.440 0.238 0.59 0.41
──────────────────────────────────────────────────────────────────────
In this table, the "Efficiencies" are the relative lift efficiencies of
the top and bottom surfaces. For example, in the case of the 1/7 camber
the top surface lifts 59 per cent, and the bottom 41 per cent of the
total lift.
Fig. 10 is a thin aerofoil of parabolic form, while Fig. 11 is an
approximation to the comparatively thick wing of a bird. In both these
sections it will be noted that the front peak is not much greater than
the secondary peak, and that the latter is nearer the leading edge than
with the circular aerofoils. Also that the drop between the peaks is
small or entirely lacking. The lower surface of the trailing edge is
subjected to a greater down pressure in the case of the thin parabola,
and there is also a considerable down pressure on the upper leading
edge. The pressure in Fig. 10 is 1.00 pound per square foot, and that of
No. 11 is 1.205, while the efficiency of the top surfaces is
respectively 72 and 74 per cent.
[Illustration: Fig. 10. Thin Parabolic Aerofoil with Pressure
Distribution. Fig. 11. Pressure Distribution of Thick Bird’s Wing Type.
(Eiffel)]
Fig. 12 shows the effect of changing the angle of the bird wing from
zero to 8 degrees. The lift per square foot in each case is shown at the
upper left hand corner of the diagram while the percentages of the upper
and lower surface lifts are included above and below the wing. For these
curves I am indebted to E. R. Armstrong, formerly of "Aero and Hydro."
As the angle is increased, the suction of the upper surface is much
increased (0.541 to 1.370 pounds per square foot), and the pressure at
the leading edge increases from depression to a very long thin peak. The
maximum under pressure is not much increased by the angle, but its
distribution and average pressure are much altered. At 0° and 2° the
usual pressure is reduced to a vacuum over the front of the section as
shown by the lower curve crossing over the upper side of the wing, and
at this point the under surface sucks down and acts against the lift.
[Illustration: Fig. 12. Effect of Incidence Changes on the Pressure
Distribution of a Thick Bird’s Wing. (After Eiffel)]
*Distribution of Drag Forces*. The drag as well as the lift changes in
both direction and magnitude for different points on the wing. In the
front and upper portions the drag is "Negative," that is, instead of
producing head resistance to motion it really acts with the propelling
force. Hence on the upper and front portions the lift is obtained with
no expenditure of power, and in fact thrust is given up and added to
that of the propeller. The remaining drag elements at the rear, and on
the lower surface, of course more than overcome this desirable tendency
and give a positive drag for the total wing. The distribution is shown
by Fig 13 which gives the lift, drag and resultant forces at a number of
different points on two circular arc aerofoils having cambers of 1/13.5
and 1/7 respectively. In this figure, the horizontal drag forces are
marked D and d, and the direction of the drag is shown by the arrows.
The lift is shown by L and the resultant by R as in the Fig. 7.
As shown, the arrows pointing to the right are the "Negative" drag (d)
forces that assist in moving the plane forward, while the drag indicated
by arrows (D) pointing to the left are the drag forces that oppose or
resist the horizontal motion. With the smaller camber (1/13.5) the drag
forces are very much smaller than those with the heavier camber of 1/7,
and the negative drifts (d) are correspondingly smaller. All of the drag
due to the lower surface, point to the left (D), and hence produce head
resistance to flight. The drag to the rear of the center of the upper
surface are the same. In front of the upper center we have right hand,
or negative drifts (d), that aid the motion. These forward forces
obtained by experiment prove the correctness of Lilienthal’s "Forward
Tangential" theory advanced many years ago.
[Illustration: Fig. 13. Direction of Drag Over Different Portions of
Circular Arc - Aerofoils.]
[Illustration: Fig. 14a. Distribution for Wright Wing. (b) M. Farman
Wing. (c) Breguet Wing. (d) Bleriot Wing. (e) Bleriot 11-Bis.]
[Illustration: Fig. 15. Pressure Distribution at Various Points Along
the Length of a Nieuport Monoplane Wing.]
*Distribution on Practical Wings*. With the exception of the bird wing,
the distributions have been given for thin plates that are of little
value on an aeroplane. They do not permit of strong structural members
for carrying the load. The actual wing must have considerable thickness,
as shown by the aerofoils in Figs. 1, 2, 3, etc., and are of
approximately stream line form. Fig. 14 shows the distribution for
actual aeroplane wings: (a) Wright, (b) M. Farman, (c) Breguet, (d)
Bleriot 11.(d), (e) Bleriot 11-bis. The Wright wing is very blunt and
has an exceedingly high lift at the leading edge. The M. Farman, which
is slightly less blunt, has a similar but lower front peak. The Breguet
is of a more modern type with the maximum thickness about 25 per cent
from the leading edge. The latter shows a remarkably even distribution
of pressure, and is therefore a better type as will be seen from the
relative lifts of 0.916 and 0.986 pounds per square foot. The lift-drag
ratio of the Breguet is also better, owing to the greater predominance
of the negative drag components. Decreasing the thickness and the
undercamber of Bleriot 11, resulted in an unusual increase of 10 per
cent of the under pressure, and a decrease in the Suction, shown by
Bleriot 11-bis. The Bleriot has the sharpest entering edge and the least
upper pressure. In the above practical wing sections the aspect ratio is
variable, being the same in the test model as in the full-size machine.
The Bleriot being a monoplane has a lower aspect ratio (5), than the
biplanes (a), (b) and (c). The Breguet with an aspect of 8 has a lift of
0.986 pounds per square foot as against the 0.781 of the Bleriot, and
undoubtedly part of this difference is due to the aspect ratio. The
pressure falls off around the tips as shown by the successive sections
taken through a Nieuport monoplane wing in Fig. 15. Section (f) was
taken near the body and shows the greater lift. Section (g) is midway
between the tips and body, and (h) and (i) are progressively nearer the
tips. As we proceed toward the tips from the body the pressure falls off
as shown in the sections, this reducing from 1.07 to 0.55 pounds per
square foot. This wing also thins down toward the tips or "washes out,"
as it is called.
[Illustration: Fig. 16. Showing Pressure Distribution on the Plan View
of a Typical Wing, Leading Edge Along A-A, Trailing Edge D-C. Center of
Pressure. Marked "C.P." The Proportion Pressures Are Indicated by the
Shading on the Surface, the Pressure Being Negative at the Tips and Near
the Rear Edge.]