*Development of Modern Wings*. The first practical results obtained by
Wright Brothers, Montgomery, Chanute, Henson, Curtiss, Langley, and
others, were obtained by the use of cambered wings. The low value of the
lift-drag ratio, due to the flat planes used by the earlier
experimenters, was principally the cause of their failure to fly. The
Wrights chose wings of very heavy camber so that a maximum lift could be
obtained with a minimum speed. These early wings had the very fair
lift-drag ratio of 12 to 1. Modern wing sections have been developed
that give a lift-drag ratio of well over 20 to 1, although this is
attended by a considerable loss in the lift.
As before explained, the total lift of a wing surface depends on the
form of the wing, its area, and the speed upon which it moves in
relation to the air. Traveling at a low speed requires either a wing
with a high lift co-efficient or an increased area. With a constant
value for the lift-drag ratio, an increase in the lift value of the wing
section is preferable to an increase in area, since the larger area
necessitates heavier structural members, more exposed bracing, and
hence, more head resistance. Unfortunately, it is not always possible to
use the sections giving the heaviest lift, for the reason that such
sections usually have a poor lift-drag ratio. In the practical machine,
a compromise must be effected between the drag of the wings and the drag
or head resistance of the structural parts so that the combined or total
head resistance will be at a minimum. In making such a compromise, it
must be remembered that the head resistance of the structural parts
predominates at high speeds, while the drag of the wings is the most
important at low speeds.
In the early days of flying, the fact that an aeroplane left the ground
was a sufficient proof of its excellence, but nowadays the question of
efficiency under different conditions of flight (performance) is an
essential. Each new aeroplane is carefully tested for speed, rate of
climb, and loading. Speed range, or the relation between the lowest and
highest possible flight speeds, is also of increasing importance, the
most careful calculations being made to obtain this desirable quality.
*Performance*. To improve the performance of an aeroplane, the designer
must increase the ratio of the horsepower to the weight, or in other
words, must either use greater horsepower or decrease the weight carried
by a given power. This result may be obtained by improvements in the
motor, or by improvements in the machine itself. Improvements in the
aeroplane may be attained in several ways: (1) by cutting down the
structural weight; (2) by increasing the efficiency of the lifting
surfaces; (3) by decreasing the head resistance of the body and exposed
structural parts, and (4) by adjustment of the area or camber of the
wings so that the angle of incidence can be maintained at the point of
greatest plane efficiency. At present we are principally concerned with
item (2), although (4) follows as a directly related item.
Improvement in the wing characteristics is principally a subject for the
wind tunnel experimentalist, since with our present knowledge, it is
impossible to compute the performance of a wing by direct mathematical
methods. Having obtained the characteristics of a number of wing
sections from the aerodynamic laboratory, the designer is in a position
to proceed with the calculation of the areas, power, etc. At present
this is rather a matter of elimination, or "survival of the fittest," as
each wing is taken separately and computed through a certain range of
performance.
*Wing Loading*. The basic unit for wing lift is the load carried per
unit of area. In English units this is expressed as being the weight in
pounds carried by a square foot of the lifting surface. Practically,
this value is obtained by dividing the total loaded weight of the
machine by the wing area. Thus, if the weight of a machine is 2,500
pounds (loaded), and the area is 500 square feet, the "unit loading"
will be: w = 2,500/500 = 5 pounds per square foot. In the metric system
the unit loading is given in terms of kilogrammes per square meter.
Conversely, with the total weight and loading known, the area can be
computed by dividing the weight by the unit loading. The unit loading
adopted for a given machine depends upon the type of machine, its speed,
and the wing section adopted, this quantity varying from 3.5 to 10
pounds per square foot in usual practice. As will be seen, the loading
is higher for small fast machines than for the slower and larger types.
A very good series of wings has been developed, ranging from the low
resistance type carrying 5 pounds per square foot at 45 miles per hour,
to the high lift wing, which gives a lift of 7.5 pounds per square foot
at the same speed. The medium lift wing will be assumed to carry 6
pounds per square foot at 45 miles per hour. The wing carrying 7.5
pounds per square foot gives a great saving in area over the low lift
type at 5 pounds per square foot, and therefore a great saving in
weight. The weight saved is not due to the saving in area alone, but is
also due to the reduction in stress and the corresponding reduction in
the size and weight of the structural members. Further, the smaller area
requires a smaller tail surface and a shorter body. A rough
approximation gives a saving of 1.5 pounds per square foot in favor of
the 7.5 pound wing loading. This materially increases the horsepower
weight ratio in favor of the high lift wing, and with the reduction in
area and weight comes an improvement in the vision range of the pilot
and an increased ease in handling (except in dives). The high lift types
in a dive have a low limiting speed.
As an offset to these advantages, the drag of the high lift type of wing
is so great at small angles that as soon as the weight per horsepower is
increased beyond 18 pounds we find that the speed range of the low
resistance type increases far beyond that of the high lift wing.
According to Wing Commander Seddon, of the English Navy, a scout plane
of the future equipped with low resistance wings will have a speed range
of from 50 to 150 miles per hour. The same machine equipped with high
lift wings would have a range of only 50 to 100 miles per hour. An
excess of power is of value with low resistance wings, but is
increasingly wasteful as the lift co-efficient is increased. Landing
speeds have a great influence on the type of wing and the area, since
the low speeds necessary for the average machines require a high lift
wing, great area, or both. With the present wing sections, low flight
speeds are obtained with a sacrifice in the high speed values. In the
same way, high speed machines must land at dangerously high speeds. At
present, the best range that we can hope for with fixed areas is about
two to one; that is, the high speed is not much more than twice the
lowest speed. A machine with a low speed of 45 miles per hour cannot be
depended upon to safely develop a maximum speed of much over 90 miles
per hour, for at higher speeds the angle of incidence will be so
diminished as to come dangerously near to the position of no lift. In
any case, the travel of the center of pressure will be so great at
extreme wing angles as to cause considerable manipulation of the
elevator surface, resulting in a further increase in the resistance.
*Resistance and Power*. The horizontal drag (resistance) of a wing,
determines the power required for its support since this is the force
that must be overcome by the thrust of the propeller. The drag is a
component of the weight supported and therefore depends upon the loading
and upon the efficiency of the wing. The drag of the average modern
wing, structural resistance neglected, is about 1/16 of the weight
supported, although there are several sections that give a drag as low
as 1/23 of the weight. The denominators of these fractions, such as "16"
and "23," are the lift-drag ratios of the wing sections.
Drag in any wing section is a variable quantity, the drag varying with
the angle of incidence. In general, the drag is at a minimum at an angle
of about 4 degrees, the value increasing rapidly on a further increase
or decrease in the angle. Usually a high lift section has a greater drag
than the low lift type at small angles, and a smaller drag at large
angles, although this latter is not invariably the case.
*Power Requirements*. Power is the rate of doing work, or the rate at
which resistance is overcome. With a constant resistance the power will
be increased by an increase in the speed. With a constant speed, the
power will be increased by an increase in the resistance. Numerically,
the power is the product of the force and the velocity in feet per
second, feet per minute, miles per hour, or meters per second. The most
common English power unit is the "horsepower," which is obtained by
multiplying the resisting force in pounds by the velocity in feet per
minute, this product being divided by 33,000. If D is the horizontal
drag in pounds, and v = velocity of the wing in feet per minute, the
horsepower H will be expressed by:
H = Dv / 33,000
Since the speed of an aeroplane is seldom given in feet per minute, the
formula for horsepower can be given in terms of miles per hour by:
H = DV / 375
Where V = velocity in miles per hour, D and H remaining as before. The
total power for the entire machine would involve the sum of the wing and
structural drags, with D equal to the total resistance of the machine.
*Example*. The total weight of an aeroplane is found to be 3,000 pounds.
The lift-drag ratio of the wings is 15.00, and the speed is 90 miles per
hour. Find the power required for the wings alone.
*Solution*. The total drag of the wings will be: D = 3,000/15 = 200
pounds. The horsepower required: H = DV/375 = 200 × 90/375=48
horsepower. It should be remembered that this is the power absorbed by
the wings, the actual motor power being considerably greater owing to
losses in the propeller. With a propeller efficiency of 70 per cent, the
actual motor power will become: Hm = 48/0.70=68.57 for the wings alone.
To include the efficiency into our formula, we have:
H = DV/375E
where E = propeller efficiency expressed as a decimal. The greater the
propeller efficiency, the less will be the actual motor power, hence the
great necessity for an efficient propeller, especially in the case of
pusher type aeroplanes where the wings do not gain by the increased slip
stream.
The propeller thrust must be equal and opposite to the drag at the
various speeds, and hence the thrust varies with the plane loading, wing
section, and angle of incidence. Portions of the wing surfaces that lie
in the propeller slip stream have a greater lift than those lying
outside of this zone because of the greater velocity of the slip stream.
For accurate results, the area in the slip stream should be determined
and calculated for the increased velocity.
Oftentimes it is desirable to obtain the "Unit drag"; that is, the drag
per square foot of lifting surface. This can be obtained by dividing the
lift per square foot by the lift-drag ratio, care being taken to note
the angle at which the unit drag is required.
*Advantages of Cambered Sections Summarized*. Modern wing sections are
always of the cambered, double-surface type for the following reasons:
1. They give a better lift-drag ratio than the flat surface, and
therefore are more economical in the use of power.
2. In the majority of cases they give a better lift per square foot of
surface than the flat plate and require less area.
3. The cambered wings can be made thicker and will accommodate heavier
spars and structural members without excessive head resistance.
*Properties of Modern Wings*. The curvature of a wing surface can best
be seen by cutting out a section along a line perpendicular to the
length of the wing, and then viewing the cut portion from the end. It is
from this method of illustration that the different wing curves, or
types of wings, are known as "wing sections." In all modern wings the
top surface is well curved, and in the majority of cases the bottom
surface is also given a curvature, although this is very small in many
instances.
Fig. 1. shows a typical wing section with the names of the different
parts and the methods of dimensioning the curves. All measurements to
the top and bottom surfaces are taken from the straight "chordal line"
or "datum line" marked X-X. This line is drawn across the concave
undersurface in such a way as to touch the surface only at two points,
one at the front and one at the rear of the wing section. The
inclination of the wing with the direction of flight is always given as
the angle made by the line X-X with the wind. Thus, if a certain wing is
said to have an angle of incidence equal to 4 degrees, we know that the
chordal line X-X makes an angle of 4 degrees with the direction of
travel. This angle is generally designated by the letter (i), and is
also known as the "angle of attack." The distance from the extreme front
to the extreme rear edge (width of wing) is called the "chord width" or
more commonly "the chord."
In measuring the curve, the datum line X-X is divided into a number of
equal parts, usually 10, and the lines 1-2-3-4-5-6-7-8-9-10-11 are drawn
perpendicular to X-X. Each of the vertical numbered lines is called a
"station," the line No. 3 being called "Station 3," and so on. The
vertical distance measured from X-X to either of the curves along one of
the station lines is known as the "ordinate" of the curve at that point.
Thus, if we know the ordinates at each station, it is a simple matter to
draw the straight line X-X, divide it into 10 parts, and then lay off
the heights of the ordinates at the various stations. The distances from
datum to the upper curve are known as the "Upper ordinates," while the
same measurements to the under surface are known as the "Lower
ordinates." This method allows us to quickly draw any wing section from
a table that gives the upper and lower ordinates at the different
stations.
A common method of expressing the value of the depth of a wing section
in terms of the chord width is to give the "Camber," which is
numerically the result obtained by dividing the depth of the wing curve
at any point by the width of the chord. Usually the camber given for a
wing is taken to be the maximum camber; that is, the camber taken at the
point of greatest depth. Thus, if we hear that a certain wing has a
camber of 0.089, we take it for granted that this is the camber at the
deepest portion of the wing. The correct method would be to give 0.089
as the "maximum camber" in order to avoid confusion. To obtain the
maximum camber, divide the maximum ordinate by the chord.
[Illustration: Fig. 1. Section Through a Typical Aerofoil or Wing, the
Parts and Measurements Being Marked on the Section. The Horizontal Width
or "Chord" Is Divided Into 10 Equal Parts or "Stations," and the Height
of the Top and Bottom Curves Are Measured from the Chordal Line X-X at
Each Station. The Vertical Distance from the Chordal Line Is the
"Ordinate" at the Point of Measurement.]
*Example*. The maximum ordinate of a certain wing is 5 inches, and the
chord is 40 inches. What is the maximum camber? The maximum camber is
5/40 = 0.125. In other words, the maximum depth of this wing is 12.5 per
cent of the chord, and unless otherwise specified, is taken as being the
camber of the top surface.
The maximum camber of a modern wing is generally in the neighborhood of
0.08, although there are several Successful sections that are well below
this figure. Unfortunately, the camber is not a direct index to the
value of a wing, either in regard to lifting ability or efficiency. By
knowing the camber of a wing we cannot directly calculate the lift or
drag, for there are several examples of wings having widely different
cambers that give practically the same lift and drift. At the present
time, we can only determine the characteristics of a wing by experiment,
either on a full size wing or on a scale model.
In the best wing sections, the greatest thickness and camber occurs at a
point about 0.3 of the chord from the front edge, this edge being much
more blunt and abrupt than the portions near the trailing edge. An
efficient wing tapers very gradually from the point of maximum camber
towards the rear. This is usually a source of difficulty from a
structural standpoint since it is difficult to get an efficient depth of
wing beam at a point near the trailing edge. A number of experiments
performed by the National Physical Laboratory show that the position of
maximum ordinate or camber should be located at 33.2 per cent from the
leading edge. This location gives the greatest lift per square foot, and
also the least resistance for the weight lifted. Placing the maximum
ordinate further forward is worse than placing it to the rear.
Thickening the entering edge causes a proportionate loss in efficiency.
Thickening the rear edge also decreases the efficiency but does not
affect the weight lifting value to any great extent. The camber of the
under surface seems to have but little effect on the efficiency, but the
lift increases slightly with an increase in the camber of the lower
surface. Increasing the camber of the lower surface decreases the
thickness of the wing and hence decreases the strength of the supporting
members, particularly at points near the trailing edge. The increase of
lift due to increasing the under camber is so slight as to be hardly
worth the sacrifice in strength. Variations in the camber of the upper
surface are of much greater importance. It is on this surface that the
greater part of the lift takes places, hence a change in the depth of
this curve, or in its outline, will cause wider variations in the
characteristics of the wing than would be the case with the under
surface. Increasing the upper camber by about 60 per cent may double the
lift of the upper surface, but the relation of the lift to the drag is
increased. From this, it will be seen that direct calculations from the
outline would be most difficult, and in fact a practical impossibility
at the present time.
[Illustration: Fig. 2. (Upper). Shows a Slight "Reflex" or Upward Turn
of the Trailing Edge. Fig. 3. (Lower) Shows an Excessive Reflex Which
Greatly Reduces the C.P. Movement.]
By putting a reverse curve in the trailing edge of a wing, as shown by
Fig. 2, the stability of the wing may be increased to a surprising
degree, but the lift and efficiency are correspondingly reduced with
each increase in the amount of reverse curvature. In this way, stability
is attained at the expense of efficiency and lifting power. With the
rear edge raised about 0.037 of the chord, the N. P. L. found that the
center of pressure could be held stationary, but the loss of lift was
about 25 per cent and the loss of efficiency amounted practically 12 per
cent. With very slight reverse curvatures it has been possible to
maintain the lift and efficiency, and at the same time to keep the
center of pressure movement down to a reasonable extent. The New U.S.A.
sections and the Eiffel No. 32 section are examples of excellent
sections in which a slight reverse or "reflex" curvature is used. The
Eiffel 32 wing is efficient, and at the same the center of pressure
movement between incident angles of 0° and 10° is practically
negligible. This wing is thin in the neighborhood of the trailing edge,
and it is very difficult to obtain a strong rear spar.
*Wing Selection*. No single wing section is adapted to all purposes.
Some wings give a great lift but are inefficient at small angles and
with light loading. There are others that give a low lift but are very
efficient at the small angles used on high speed machines. As before
explained, there are very stable sections that give but poor results
when considered from the standpoint of lift and efficiency. The
selection of any one wing section depends upon the type of machine upon
which it is to be used, whether it is to be a small speed machine or a
heavy flying boat or bombing plane.
There are a multitude of wing sections, each possessing certain
admirable features and also certain faults. To list all of the wings
that have been tried or proposed would require a book many times the
size of this, and for this reason I have kept the list of wings confined
to those that have been most commonly employed on prominent machines, or
that have shown evidence of highly desirable and special qualities. This
selection has been made with a view of including wings of widely varying
characteristics so that the data can be applied to a wide range of
aeroplane types. Wings suitable for both speed and weight carrying
machines have been included.
The wings described are the U.S.A. Sections No. 1, 2, 3, 4, 5 and 6; the
R.A.F. Sections Nos. 3 and 6, and the well known Eiffel Wings No. 32, 36
and 37. The data given for these wings is obtained from wind tunnel
tests made at the Massachusetts Institute of Technology, the National
Physical Laboratory (England), and the Eiffel Laboratory in Paris. For
each of these sections the lift co-efficient (Ky), the lift-drift ratio
(L/D), and the drag co-efficient (Kx) are given in terms of miles per
hour and pounds per square foot. Since these are the results for model
wings, there are certain corrections to be made when the full size wing
is considered, these corrections being made necessary by the fact that
the drag does not vary at the same rate as the lift. This "Size" or
"Scale" correction is a function of the product of the wing span in feet
by the velocity of the wind in feet per second. A large value of the
product results in a better wing performance, or in other words, the
large wing will always give better lift-drag ratios than would be
indicated by the model tests. The lift co-efficient Ky is practically
unaffected by variations in the product. If the model tests are taken
without correction, the designer will always be on the safe side in
calculating the power. The method of making the scale corrections will
be taken up later.
Of all the sections described, the R.A.F.-6 is probably the best known.
The data on this wing is most complete, and in reality it is a sort of
standard by which the performance of other wings is compared. Data has
been published which describes the performance of the R.A.F.-6 used in
monoplane, biplane and triplane form; and with almost every conceivable
degree of stagger, sweep back, and decalage. In addition to the
laboratory data, the wing has also been used with great success on full
size machines, principally of the "Primary trainer" class where an "All
around" class of wing is particularly desirable. It is excellent from a
structural standpoint since the section is comparatively deep in the
vicinity of the trailing edge. The U.S.A. sections are of comparatively
recent development and are decided improvements on the R.A.F. and Eiffel
sections. The only objection is the limited amount of data that is
available on these wings—limited at least when the R.A.F. data is
considered—as we have only the figures for the monoplane arrangement.
*WING SELECTION.*
*(1) Lift-Drag Ratio*. The lift-drag ratio (L/D) of a wing is the
measure of wing efficiency. Numerically, this is equal to the lift
divided by the horizontal drag, both quantities being expressed in
pounds. The greater the weight supported by a given horizontal drag, the
less will be the power required for the propulsion of the aeroplane,
hence a high value of L/D indicates a desirable wing section—at least
from a power standpoint. In the expression L/D, L = lift in pounds, and
D = horizontal drag in pounds. Unfortunately, this is not the only
important factor, since a wing having a great lift-drag is usually
deficient in lift or is sometimes structurally weak.
The lift-drag ratio varies with the angle of incidence (i), reaching a
maximum at an angle of about 4° in the majority of wings. The angle of
incidence at which the lift-drag is a maximum is generally taken as the
angle of incidence for normal horizontal flight. At angles either
greater or less, the L/D falls off, generally at a very rapid rate, and
the power increases correspondingly. Very efficient wings may have a
ratio higher than L/D=20 at an angle of about 4°, while at 16° incidence
the value may be reduced to L/D = 4, or even less. The lift is generally
greatest at about 16°. The amount of variation in the lift, and
lift-drag, corresponding to changes in the incidence differs among the
different types of wings and must be determined by actual test.
After finding a wing with a good value of L/D, the value of the lift
co-efficient Ky should be determined at the angle of the maximum L/D.
With two wings having the same lift-drag ratio, the wing having the
greatest lift (Ky) at this point is the most desirable wing as the
greater lift will require less area and will therefore result in less
head resistance and less weight. Any increase in the area not only
increases the weight of the wing surface proper, but also increases the
wiring and weights of the structural members. With heavy machines, such
as seaplanes or bomb droppers, a high value of Ky is necessary if the
area is to be kept within practical limits. A small fast scouting plane
requires the best possible lift-drag ratio at small angles, but requires
only a small lift co-efficient. At speeds of over 100 miles per hour a
small increase in the resistance will cause a great increase in the
power.
*(2) Maximum Lift (Ky)*. With a given wing area and weight, the maximum
value of the lift co-efficient (Ky) determines the slow speed, or
landing speed, of the aeroplane. The greater the value of Ky, the slower
can be the landing speed. For safety, the landing speed should be as low
as possible.
In the majority of wings, the maximum lift occurs at about 16° of
incidence, and in several sections this maximum is fairly well sustained
over a considerable range of angle. The angle of maximum lift is
variously known as the "Stalling angle" or the "Burble point," since a
change of angle in either direction reduces the lift and tends to stall
the aeroplane. For safety, the angle range for maximum lift should be as
great as possible, for if the lift falls off very rapidly with an
increase in the angle of incidence, the pilot may easily increase the
angle too far and drop the machine. In the R.A.F.-3 wing, the lift is
little altered through an angle range of from 14° to 16.5°, the maximum
occurring at 15.7°, while with the R.A.F.-4, the lift drops very
suddenly on increasing the angle above 15°. The range of the stalling
angle in any of the wings can be increased by suitable biplane or
triplane arrangements. If large values of lift are accompanied by a
fairly good L/D value at large angles, the wing section will be suitable
for heavy machines.
*(3) Center of Pressure Movement*. The center of pressure movement with
varying angles of incidence is of the greatest importance, since it not
only determines the longitudinal stability but also has an important
effect upon the loading of the wing spars and ribs. With the majority of
wings a decrease in the angle of incidence causes the center of pressure
to move back toward the trailing edge and hence tends to cause nose
diving. When decreased beyond 0° the movement is very sharp and quick,
the C. P. moving nearly half the chord width in the change from 0° to
-1.5°. The smaller the angle, the more rapid will be the movement.
Between 6° and 16°, the center of pressure lies near a point 0.3 of the
chord from the entering edge in the majority of wing sections. Reducing
the angle from 6° to 2° moves the C. P. back to approximately 0.4 of the
chord from the entering edge.
There are wing sections, however, in which the C. P. movement is
exceedingly small, the Eiffel 32 being a notable example of this type.
This wing is exceedingly stable, as the C. P. remains at a trifle more
than 0.30 of the chord through nearly the total range of flight angles.
An aeroplane equipped with the Eiffel 32 wing could be provided with
exceedingly small tail surfaces without a tendency to dive. Should the
elevator become inoperative through accident, the machine could probably
be landed without danger. This wing has certain objectionable features,
however, that offset the advantages.
It will be noted that with the unstable wings the center of pressure
movement always tends to aggravate the wing attitude. If the machine is
diving, the decrease in angle causes the C. P. to move back and still
further increase the diving tendency. If the angle is suddenly
increased, the C. P. moves forward and increases the tendency toward
stalling.
If the center of pressure could be held stationary at one point, the
wing spars could be arranged so that each spar would take its proper
proportion of the load. As it is, either spar may be called upon to
carry anywhere from three-fourths of the load to entire load, since at
extreme angles the C. P. is likely to lie directly on either of the
spars. Since the rear spar is always shallow and inefficient, this is
most undesirable. This condition alone to a certain extent
counterbalances the structural disadvantage of the thin Eiffel 32
section. Although the spars in this wing must of necessity be shallow,
they can be arranged so that each spar will take its proper share of the
load and with the assurance that the loading will remain constant
throughout the range of flight angles. The comparatively deep front spar
could be moved back until it carried the greater part of the load, thus
relieving the rear spar.
With a good lift-drag ratio, and a comparatively high value of Ky, the
center of pressure movement should be an important consideration in the
selection of a wing. It should be remembered in this regard that the
stability effects of the C. P. movement can be offset to a considerable
extent by suitable biplane arrangements.
*(4) Structural Considerations*. For large, heavy machines, the
structural factor often ranks in importance with the lift-drag ratio and
the lift co-efficient. It is also of extreme importance in speed scouts
where the number of interplane struts are to be at a minimum and where
the bending moment on the wing spars is likely to be great in
consequence. A deep, thick wing section permits of deep strong wing
spars. The strength of a spar increases with the square of its depth,
but only in direct proportion to its width. Thus, doubling the depth of
the spar increases the strength four times, while doubling the width
only doubles the strength. The increase in weight would be the same in
both cases.
While very deep wings are not usually efficient, when considered from
the wing section tests alone, the total efficiency of the wing
construction when mounted on the machine is greater than would be
supposed. This is due to the lightness of the spars and to the reduction
in head resistance made possible by a greater spacing of the interplane
struts. Thus, the deep wing alone may have a low L/D in a model test,
but its structural advantages give a high total efficiency for the
machine assembled.
*Summary*. It will be seen from the foregoing matter that the selection
of a wing consists in making a series of compromises and that no single
wing section can be expected to fulfill all conditions. With the purpose
of the proposed aeroplane thoroughly in mind, the various sections are
taken up one by one, until a wing is found that most usefully
compromises with all of the conditions. Reducing this investigation to
its simplest elements we must follow the routine as described above: (1)
Lift-drift ratio and value of Ky at this ratio. (2) Maximum value of Ky
and L/D at this lift. (3) Center of pressure movement. (4) Depth of wing
and structural characteristics.
*Calculations for Lift and Area*. Although the principles of surface
calculations were described in the chapter on elementary aerodynamics,
it will probably simplify matters to review these calculations at this
point. The lift of a wing varies with the product of the area, and the
velocity squared, this result being multiplied by the co-efficient of
lift (Ky). The co-efficient varies with the wing section, and with the
angle of incidence. Stated as a formula: L = KyAV² where A = area in
square feet, and V = velocity of the wing in miles per hour. Assuming an
area of 200 square feet, a velocity of 80 miles per hour, and with K =
0.0025, the total life (L) becomes: L= KyAV² =0.0025 x 200 x (80 × 80) =
3,200 pounds. Assuming a lift-drag ratio of 16, the "drag" of the wing,
or its resistance to horizontal motion, will be expressed by D =
L/r=3,200/16=200 pounds, where r = lift-drag ratio. It is this
resistance of 200 pounds that the motor must overcome in driving the
wings through the air. The total resistance offered by the aeroplane
will be equal to the sum of the wing resistance and the head resistance
of the body, struts, wiring and other structural parts. In the present
instance we will consider only the resistance of the wings.
When the lift co-efficient, speed, and total lift are known, the area
can be found from A = L/KyV², the lift, of course, being taken as the
total weight of the machine. The area of the supporting surface for a
speed of 60 miles per hour, total weight of 2,400 pounds, and a lift
co-efficient of 0.002 is calculated as follows:
A = L/KyV² = 2,400/0.002 × (60 × 60) = 333 sq. ft.
A third variation in the formula is that used in finding the value of
the lift co-efficient for a particular wing loading. From the weight,
speed and area, we can find the co-efficient Ky, and with this value we
can find a wing that will correspond to the required co-efficient. This
method is particularly convenient when searching for the section with
the greatest lift-drag ratio. Ky = L/AV², or when the loading per square
foot is known, the co-efficient becomes Ky = L’/V². For example, let us
find the co-efficient for a wing loading of 5 pounds per square foot at
a velocity of 80 miles per hour. Inserting the numerical values into the
equation we have, Ky = L’/V² =5/(80 × 80) = 0.00078. Any wing, at any
angle that has a lift co-efficient equal to 0.00078 will support the
load at the given speed, although many of the wings would not give a
satisfactory lift-drag ratio with this co-efficient.
It should be noted in the above calculations that no correction has been
made for "Scale," aspect ratio or biplane interference. In other words,
we have assumed the figures as applying to model monoplanes. In the
following tables the lift, lift-drag and drag must be corrected, since
this data was obtained from model tests on monoplane sections. The
effects of biplane interference will be described in the chapter on
"Biplane and Triplane Arrangement," but it may be stated that
superposing the planes reduces both the lift co-efficient and the
liftdrag ratio, the amount of reduction depending upon the relative gap
between the surfaces. Thus with a gap equal to the chord, the lift of
the biplane surface will only be about 80 per cent of the lift of a
monoplane surface of the same area and section.
*Wing Test Data*. The data given in this chapter is the result of wind
tunnel tests made under standard conditions, the greater part of the
results being published by the Massachusetts Institute of Technology.
The tests were all made on the same size of model and at the same wind
speed so that an accurate comparison can be made between the different
sections. All values are for monoplane wings with an aspect ratio of 6,
the laboratory models being 18x3 inches. The exception to the above test
conditions will be found in the tables of the Eiffel 37 and 36 sections,
these figures being taken from the results of Eiffel’s laboratory. The
Eiffel models were 35.4x5.9 inches and were tested at wind velocities of
22.4, 44.8, and 67.2 miles per hour. The tests made at M. I. T. were all
made at a wind speed of 30 miles per hour. The lift co-efficient Ky is
practically independent of the wing size and wind velocity, but the drag
co-efficient Kx varies with both the size and wind velocity, and the
variation is not the same for the different wings. The results of the M.
I. T. tests were published in "Aviation and Aeronautical Engineering" by
Alexander Klemin and G. M. Denkinger.
*The R.A.F. Wing Sections*. These wings are probably the best known of
all wings, although they are inferior to the new U.S.A. sections. They
are of English origin, being developed by the Royal Aircraft Factory
(R.A.F.), with the tests performed by the National Physical Laboratory
at Teddington, England. The R.A.F.-6 is the nearest approach to the all
around wing, this section having a fairly high L/D ratio and a good
value of Ky for nearly all angles. It is by no means a speed wing nor is
it suitable for heavy machines, but it comprises well between these
limits and has been extensively used on medium size machines, such as
the Curtiss JN4–B, the London and Provincial, and others. The R.A.F-3
has a very high value for Ky, and a very good lift-drag ratio for the
high-lift values. It is suitable for seaplanes, bomb droppers and other
heavy machines of a like nature that fly at low or moderate speeds. The
outlines of these wings are shown by Figs. 7 and 8, and the camber
ordinates are marked as percentages of the chord. In laying out a wing
rib from these diagrams, the ordinate at any point is obtained by
multiplying the chord length in inches by the ordinate factor at that
point. Referring to the R.A.F.-3 diagram, Fig. 8, it will be seen that
the ordinate for the upper surface at the third station from the
entering edge is 0.064. If the chord of the wing is 60 inches, the
height of the upper curve measured above the datum line X-X at the third
station will be, 0.064 × 60 = 3.84 inches. At the same station, the
height of the lower curve will be, 0.016 × 60= 0.96 inch.
The chord is divided into 10 equal parts, and at the entering edge one
of the ten parts is subdivided so as to obtain a more accurate curve at
this point. In some wing sections it is absolutely necessary to
subdivide the first chord division as the curve changes very rapidly in
a short distance. The upper curve, especially at the entering edge, is
by far the most active part of the section and for this reason
particular care should be exercised in getting the correct outline at
this point.
[Illustration: Figs. 7-8. R.A.F. Wing Sections. Ordinates as Decimals of
the Chord.]
*Aerodynamic Properties of the R.A.F. Sections*. Table 1 gives the
values of Ky, Kx, L/D, and the center of pressure movement (C. P.) for
the R.A.F.-3 section through a range of angles varying from -2° to 20°.
The first column at the left gives the angles of incidence (i), the
corresponding values for the lift (Ky) and the drag (Kx) being given in
the second and third columns, respectively. The fourth column gives the
lift-drag ratio (L/D). The fifth and last column gives the location of
the center of pressure for each different angle of incidence, the figure
indicating the distance of the C. P. from the entering edge expressed as
a decimal part of the chord. As an example in the use of the table, let
it be required to find the lift and drag of the R.A.F.-3 section when
inclined at an angle of 6° and propelled at a speed of 90 miles per
hour. The assumed area will be 300 square feet. At 6° it will be found
that the lift co-efficient Ky is 0.002369. From our formulae, the lift
will be: L = KyAV² or numerically, L=0.002369 × 300 × (90 × 90) = 5,7567
lbs. At the same speed, but with the angle of incidence reduced to 2°,
the lift will be reduced to L = 0.001554 × 300 x (90 × 90) = 3,776.2
pounds, where 0.001554 is the lift co-efficient at 2°. It will be noted
that the maximum lift co-efficient occurs at 14° and continues at this
value to a little past 15°. The lift at the stalling angle is fairly
constant from 12° to 16°.
The value of the drag can be found in either of two ways: (1) by
dividing the total lift (L) by the lift-drag ratio, or (2) by figuring
its value by the formula D = KxAV². The first method is shorter and
preferable. By consulting the table, it will be seen that the L/D ratio
at 6° is 14.9. The total wing drag will then be equal to 5,756.7/149 =
386.4 lbs. Figured by the second method, the value of Ky at 6° is
0.000159, and the drag is therefore: D = KxAV² = 0.000159 × 300 × (90 ×
90) = 386.4. This checks exactly with the first method. The lift-drag
ratio is best at 4°, the figure being 15.6, while the lift at this point
is 0.001963. With the same area and speed, the total lift of the surface
at the angle of best lift-drift ratio will be 0001963 × 300 × (90 × 90)
= 4,770 lbs.
At 4° the center of pressure is 0.385 of the chord from the entering
edge. If the chord is 60 inches wide, the center of pressure will be
located at 0.385 × 60 = 23.1 inches from the entering edge. At 15°, the
center of pressure will be 0.29 × 60 = 17.4 inches from the entering
edge, or during the change from 4° to 15° the center of pressure will
have moved forward by 5.7 inches. At -2°, the pressure has moved over
three-quarters of the way toward the trailing edge -0.785 of the chord,
to be exact Through the ordinary flight angles of from 2° to 12°, the
travel of the center of pressure is not excessive.
The maximum lift co-efficient (Ky) is very high in the R.A.F.-3 section,
reaching a maximum of 0.003481 at an incidence of 14°. This is second to
only one other wing, the section U.S.A.-4. This makes it suitable for
heavy seaplanes.
Table 2 gives the aerodynamic properties of the R.A.F-6 wing, the table
being arranged in a manner similar to that of the R.A.F.-3. In glancing
down the column of lift co-efficients (Ky), and comparing the values
with those of the R.A.F.-3 section, it will be noted that the lift of
R.A.F.-6 is much lower at every angle of incidence, but that the
lift-drag ratio of the latter section is not always correspondingly
higher. At every angle below 2°, at 6°, and at angles above 14°, the L/D
ratio of the R.A.F.-3 is superior in spite of its greater lift. The
maximum L/D ratio of the R.A.F.-6 at 4° is 16.58, which is considerably
higher than the best L/D ratio of the R.A.F.-3. The best lift
co-efficient of the R.A.F.-6, 0003045, is very much lower than the
maximum Ky of the R.A.F.-3.
The fact that the L/D ratio of the R.A.F.-3 wing is much greater at high
lift co-efficients, and large angles of incidence, makes it very
valuable as at this point the greater L/D does not tend to stall the
plane at slow speed. A large L/D at great angles, together with a wide
stalling angle tends for safety in slow speed flying.
Both wing sections are structurally excellent, being very deep in the
region of the rear edge, the R.A.F.-6 being particularly deep at this
point. A good deep spar can be placed at almost any desirable point in
the R.A.F-6, and the trailing edge is deep enough to insure against rib
weakness even with a comparatively great overhang.
Scale corrections for the full size R.A.F. wings are very difficult to
make. According to the N. P. L. reports, the corrected value for the
maximum L/D of the R.A.F.-3 wing is 18.1, the model test indicating a
maximum value of 15.6. I believe that L/D = 17.5 would be a safe full
size value for this section. The same reports give the full size L/D for
the R.A.F.-6 as 18.5, which would be probably safe at 18.0 under the new
conditions.
*Properties of the Eiffel Sections (32-36-37)*. Three of the Eiffel
sections are shown by Figs. 10, 11 and 12, these Sections being selected
out of an enormous number tested in the Eiffel laboratories. They differ
widely, both aerodynamically and structurally, from the R.A.F.
aerocurves just illustrated.
[Illustration: Fig. 10-11-12 Ordinates for Three Eiffel Wing Sections]
Eiffel 32 is a very stable wing, as has already been pointed out, but
the value of the maximum L/D ratio is in doubt as this quantity is very
susceptible to changes in the wind velocity—much more than in the
average wing. Since Eiffel’s tests were carried out at much higher
velocity than at the M. I. T., his lift-drift values at the higher
speeds were naturally much better than those obtained by the American
Laboratory. When tested at 67.2 miles per hour the lift-drift ratio for
the Eiffel 32 was 184 while at 22.4 miles per hour, the ratio dropped to
13.4. This test alone will give an idea as to the variation possible
with changes in scale and wind velocity. The following table gives the
results of tests carried out at the Massachusetts laboratory, reported
by Alexander Klemin and G. M. Denkinger in "Aviation and Aeronautical
Engineering." Wind speed, 30 miles per hour.
The C. P. Travel in the Eiffel wing is very small, as will be seen from
Table 3. At -2° the C. P. is 0.33 of the chord from the leading edge and
only moves back to 0.378 at an angle of 20°, the intermediate changes
being very gradual, reaching a minimum of 0.304 at 6° incidence. The
maximum Ky of Eiffel 32 is 0.002908, while for the R.A.F.-6 wing, Ky =
0.003045 maximum, both co-efficients being a maximum at 16° incidence,
but the lift-drag at maximum Ky is much better for the R.A.F.-6.
Structurally, the Eiffel 32 is at a disadvantage when compared with the
R.A.F. sections since it is very narrow at points near the trailing
edge. This would necessitate moving the rear spar well up toward the
center with the front spar located very near the leading edge. This is
the type of wing used in a large number of German machines. It will also
be noted that there is a very pronounced reverse curve or "Reflex" in
the rear portion, the trailing edge actually curving up from the chord
line.
Eiffel 36 is a much thicker wing than either of the other Eiffel curves
shown, and is deficient in most aerodynamical respects. It has a low
value for Ky and a poor lift-drag ratio. It has, however, been used on
several American training machines, probably for the reason that it
permits of sturdy construction.
[Illustration: Fig. 13 Characteristic Curves for Eiffel Wings Sections]
Eiffel 37 is essentially a high-speed wing having a high L/D ratio and a
small lift co-efficient. The maximum lift-drag ratio of 20.4 is attained
at a negative angle -08°. The value of Ky at this point is 0.00086, an
extremely low figure. The maximum Ky is 0.00288 at 14.0°, the L/D ratio
being 4.0 at this angle. Structurally it is the worst wing that we have
yet discussed, being almost "paper thin" for a considerable distance
near the trailing edge. The under surface is deeply cambered, with the
maximum under camber about one-third from the trailing edge. It is
impossible to use this wing without a very long overhang in the rear of
the section, and like the Eiffel 32, the front spar must be very far
forward. For those desiring flexible trailing edges, this is an ideal
section. This wing is best adapted for speed scouts and racing machines
because of its great L/D, but as its lift is small and the center of
pressure movement rapid at the point of maximum lift-drag, it would be
necessary to fly at a small range of angles and land at an extremely
high speed. Any slight change in the angle of incidence causes the
lift-drag ratio to drop at a rapid rate, and hence the wing could only
be manipulated at its most efficient angle by an experienced pilot.
Again, the angle of maximum L/D is only a few degrees from the angle of
no lift.
*U.S.A. Wing Sections*. These wing sections were developed by the
Aviation Section of the Signal Corps, United States Army, and are
decided improvements on any wing sections yet published. The six U.S.A.
wings cover a wide range of application, varying as they do, from the
high speed sections to the heavy lift wings used on large machines. The
data was first published by Captains Edgar S. Gorrell and H. S. Martin,
U.S.A., by permission of Professor C. H. Peabody, Massachusetts
Institute of Technology. An abstract of the paper by Alexander Klemin
and T. H. Huff was afterwards printed in "Aviation and Aeronautical
Engineering." While several of the curves are modifications of the
R.A.F. sections already described, they are aerodynamically and
structurally superior to the originals, and especial attention is called
to the marked structural advantages.
U.S.A.-1 and U.S.A.-6 are essentially high speed sections with a very
high lift-drag ratio, these wings being suitable for speed scouts or
pursuit machines. The difference between the wings is very slight,
U.S.A.-1 with K-000318 giving a better landing speed, while U.S.A.-6 is
slightly more efficient at low angles and high speeds.
[Illustration: Fig. 14. U.S.A. Wing Sections Nos. 1-2-3-4-5-6, Showing
the Ordinates at the Various Štations Expressed as Decimals of the
Chord. U.S.A.-4 is a Heavy Lift Section, While U.S.A.-1 and U.S.A.-6.are
High Speed Wings. For Any Particular Duty, the Above Wings Are Very Deep
and Permit of Large Structural Members. The Center of Pressure Movement
Is Comparatively Slight.]
With 0° incidence, the ratio of U.S.A-1=11.0 while the lift-drag of
U.S.A.-6 at 0° incidence is 13.0. The maximum lift of U.S.A.-1 is
superior to that of Eiffel 32, and the maximum lift-drag ratio at equal
speeds is far superior, being 17.8 against 14.50 of the Eiffel 32.
Compared with the Eiffel 32 it will be seen that the U.S.A. sections are
far better from a structural point of view, especially in the case of
U.S.A.-1. The depth in the region of the rear spar is exceptionally
great, about the same as that of the R.A.F.-6. While neither of the
U.S.A. wings are as stable as the Eiffel 32, the motion of the C. P. is
not sudden nor extensive at ordinary flight angles.
Probably one of the most remarkable of the United States Army wings is
the U.S.A.-4 which has a higher maximum lift co-efficient (Ky) than even
the R.A.F.-3. The maximum Ky of the U.S.A.-4 is 0.00364 compared with
the R.A.F.-3 in which Ky (Maximum)=0.003481. Above 4° incidence, the
lift-drag ratio of the U.S.A.-4 is generally better than that of the
R.A.F.-3, the maximum L/D at 4° being considerably better. This is a
most excellent wing for a heavy seaplane or bomber. The U.S.A.-2 has an
upper surface similar to that of the R.A.F.-3, but the wing has been
thickened for structural reasons, thus causing a modification in the
lower surface. This results in no particular aerodynamic loss and it is
much better at points near the rear edge for the reception of a deep and
efficient rear spar.
U.S.A.-3 is a modification of U.S.A.-2, and like U.S.A.-2 would fall
under the head of "All around wings," a type similar, but superior to
R.A.F.-6. These wings are a compromise between the high speed and heavy
lift types—suitable for training schools or exhibition flyers. Both have
a fairly good L/D ratio and a corresponding value for Ky.
U.S.A.-5 has a very good maximum lift-drag ratio (16.21) and a good
lift-drag ratio at the maximum Ky. Its maximum Ky is superior to all
sections with the exception of U.S.A.-2 and 4. Structurally it is very
good, being deep both fore and aft.
In review of the U.S.A. sections, it may be said that they are all
remarkable in having a very heavy camber on both the upper and lower
surfaces, and at the same time are efficient and structurally excellent.
This rather contradicts the usual belief that a heavy camber will
produce a low lift-drag ratio, a belief that is also proven false by the
excellent performance of the Eiffel 37 section. The maximum Ky is also
well sustained at and above 0.003. There is no sharp drop of lift at the
"Stalling angle" and the working range of incidence is large.
*Curtiss Wing and Double Cambered Sections*. An old type of Curtiss wing
is shown by Fig. 15. It is very thick and an efficient wing for general
use. It will be noticed that there is a slight reflex curve at the
trailing edge of the under surface and that there is ample spar room at
almost any point along the section. The nose is very round and thick for
a wing possessing the L/D characteristics exhibited in the tests. The
conditions of the test were the same as for the preceding wing sections.
Fig. 16 shows a remarkable Curtiss section designed for use as a
stabilizing surface. It is double cambered, the top surface being
identical with the lower, and is therefore non-lifting with the chord
horizontal. The force exerted by the surface is equal with equal
positive or negative angles of incidence, a valuable feature in a
control surface. In spite of its great thickness, it is of excellent
stream line form and therefore has a very good lift-drag ratio. At 0°
angle of incidence the resistance is at a minimum, and is much less than
that of a thin, square edged, flat plate. This double cambered plane
reduces the stay bracing and head resistance necessary with the flat
type of stabilizer surface.
[Illustration: Fig. 15. Old Type of Curtiss Wing. 16. Curtiss Double
Camber for Control Surfaces.]
The Curtiss sections mentioned above were described in "Aviation and
Aeronautical Engineering" by Dr. Jerome C. Hunsaker, but the figures in
the above table were obtained by the author on a sliding test wire
arrangement that has been under development for some time. At the time
of writing several of the U.S.A. sections are under investigation on the
same device.
CORRECTION FACTORS FOR WING FORM AND SIZE.
*Aspect Ratio*. As previously explained, the aspect ratio is the
relation of the span to the chord, and this ratio has a considerable
effect upon the performance of a wing. In the practical full size
machine the aspect ratio may range from 5 in monoplanes, and small
biplanes, to 10 or 12 in the larger biplanes. The aspect in the case of
triplanes is even greater, some examples of the latter having aspects of
16 to 20. In general, the aspect ratio increases with the gross weight
of the machine. Control surfaces, such as the rudder and elevator,
usually have a much lower aspect ratio than the main lifting surfaces,
particularly when flat non-lifting control surfaces are used. The aspect
of elevator surfaces will range from unity to 3, while the vertical
rudders generally have an aspect of 1.
With a given wing area, the span increases directly with an increase in
the aspect ratio. The additional weight of the structural members due to
an increased span tend to offset the aerodynamic advantages gained by a
large aspect ratio, and the increased resistance due to the number and
size of the exposed bracing still further reduces the advantage.
*Effects of Aspect Ratio*. Variations in the aspect ratio do not give
the same results in all wing sections, and the lift co-efficient and L/D
ratio change in a very irregular manner with the angle of incidence. The
following tables give the results obtained by the N. P. L. on a Bleriot
wing section, the aspect ratio being plotted against the angle of
incidence. The figures are comparative, an aspect factor of unity
(1,000) being taken for an aspect ratio of 6 at each angle of incidence.
To obtain an approximation for any other wing section at any other
aspect ratio, multiply the model test (Aspect=6) by the factor that
corresponds to the given angle and aspect ratio. At the extreme right of
the table is a column of rough averages, taken without regard to the
angles.
The column of average values is not the average of the tabular values
but is the average of the results obtained by a number of investigators
on different wing sections. Through the small angles of 0° and 2° the
low aspect ratios give a maximum Ky greater than with the larger
aspects. The larger aspects increase the lift through a larger range of
angles but have a lower maximum value for Ky at small angles. Beyond 2°
the larger aspect ratios give a greater Ky.
*Aspect for Flat Plates*. For flat plates the results are different than
with cambered sections. The lift-drag ratios are not much improved with
an increase in aspect, but the highest maximum lift is obtained with a
small aspect ratio. For this reason, a small aspect ratio should be used
when a high lift is to be obtained at low speeds with a flat plate as in
the case of control surfaces. An aspect ratio of unity is satisfactory
for flat vertical rudders since a maximum effect is desirable when
taxi-ing over the ground at low speeds. The flat plate effects are not
important except for control surfaces, and even in this case the plates
are being superseded by double cambered sections.
*Reason for Aspect Improvement*. The air flows laterally toward the wing
tips causing a very decided drop in lift at the outer ends of the wings.
The lift-drag ratio is also reduced at this point. The center of
pressure moves back near the trailing edge as we approach the tips, the
maximum zone of suction on the upper surface being also near the
trailing edge. The lift-drag ratio at the center of the plane is between
4 or 5 times that at a point near the tips. All of the desirable
characteristics of the wing are exhibited at a point near the center.
When the aspect ratio is increased, the inefficient tips form a smaller
percentage of the total wing areas, and hence the losses at the tips are
of less importance than would be the case with a small aspect. The end
losses are not reduced by end shields or plates, and in attempts to
prevent lateral flow by curtains, the losses are actually often
increased. Proper design of the form of the wing tip, such as raking the
tips, or washing out the camber and incidence, can be relied upon to
increase the lift factor. This change in the tips causes the main wind
stream to enter the wings in a direction opposite to the lateral leakage
flow and therefore reduces the loss. Properly raked tips may increase
the lift by 20 per cent.
*Effects of Scale (Size and Velocity)*. In the chapter "Elementary
Aerodynamics" it was pointed out that the lift of a surface was obtained
by the motion of the air, or the "turbulence" caused by the entering of
the plane. It was also explained that the effect of the lift due to
turbulence varied as the square of the velocity and directly as the area
of the wings. This would indicate that the lift of a small wing (Model)
would be in a fixed proportion to a large wing of the same type. This
holds true in practice since nearly all laboratories have found by
experiment that the lift of a large wing could be computed directly from
the results obtained with the model without the use of correction
factors. That is to say, that the lift of a large wing with 40 times the
area of the model, would give 40 times the lift of the model at the same
air speed. In the same way, the lift would be proportional to the
squares of the velocities. If the span of the model is taken at "1"
feet, and the velocity as V feet per second, the product IV would
represent both the model and the full size machine. The lift is due to
aerodynamic forces strictly, and hence there should be no reason why the
"V²" law should be interfered with in a change from the model to the
full size machine.
In the case of drag the conditions are different, since the drag is
produced by two factors that vary at different rates. Part of the drag
is caused by turbulence or aerodynamic forces and part by skin friction,
the former varying as V² while the skin friction varies as V¹.⁸⁸. The
aerodynamic drag varies directly with the area or span while the skin
friction part of the drag varies as 1⁰.⁹³, where 1 is the span. From
considerations of the span and the speed, it will be seen that the
frictional resistance increases much slower than the aerodynamic
resistance, and consequently the large machine at high speed would give
less drag and a higher value of L/D than the small model. In other
words, the results of a model test must be corrected for drag and the
lift-drag ratio when applied to a full size machine. Such a correction
factor is sometimes known as the "Scale factor."
Eiffel gives the correction factor as 1.08, that is the liftdrag ratio
of the full size machine will be approximately 1.08 times as great as
the model.
A series of full size tests were made by the University of St. Cyr in
1912-1913 with the object of comparing full size aeroplane wings with
small scale models of the same wing section. The full size wings were
mounted on an electric trolley car and the tests were made in the open
air. Many differences were noted when the small reproductions of the
wings were tested in the wind tunnel, and no satisfactory conclusions
can be arrived at from these tests. According to the theory, and the
tests made by the N. P. L., the lift-drag ratio should increase with the
size but the St. Cyr tests showed that this was not always the case. In
at least three of the tests, the model showed better results than the
full size machine. There seemed to be no fixed relation between the
results obtained by the model and the large wing. The center of pressure
movement was always different in every comparison made.
One cause of such pronounced difference would probably be explained by
the difference in the materials used on the model and full size wing,
the model wing being absolutely smooth rigid wood while the full size
wing was of the usual fabric construction. The fabric would be likely to
change in form under different conditions of angle and speed, causing a
great departure from the true values. Again, the model being of small
size, would be a difficult object to machine to the exact outline. A
difference of 1/1000 inch from the true dimension would make a great
difference in the results obtained with a small surface.
*Plan Form*. Wings are made nearly rectangular in form, with the ends
more or less rounded, and very little is now known about the effect of
wings varying from this form. Raking the ends of the wing tips at a
slight angle increases both the lift-drag and lift by about 20 per cent,
the angle of the raked end being about 15 degrees. Raking is a widely
adopted practice in the United States, especially on large machines.
*Summary of Corrections*. We can now work out the total correction to be
made on the wind tunnel tests for a full size machine of any aspect
ratio. The lift co-efficient should be used as given by the model test
data, but the corrections can be applied to the lift-drag ratio and the
drag. The scale factor is taken at 1.08, the form factor due to rake is
1.2, and the aspect correction is taken from the foregoing table. The
total correction factor will be the product of all of the individual
factors.
*Example*. A certain wing section has a lift-drag ratio of 15.00, as
determined by a wind tunnel test on a model, the aspect of the test
plane being 6. The full size wing is to have an aspect ratio of 8, and
the wing tips are to be raked. What is the corrected lift-drag ratio of
the full size machine at 14°?
*Solution*. The total correction factor will be = 1.08 × 1.10 × 12 =
1.439. The lift-drag ratio of the full size modified wing becomes 15.00
x 1.439 = 21.585.
As a comparison, we will assume the same wing section with rectangular
tips and an aspect ratio of 3. The total correction factor for the new
arrangement is now 1.08 X 0.72 = 0.7776 where 0.72 is the relative
lift-drag due to an aspect of 3. The total lift-drag is now 15.00 X
0.7776 = 11.664.
Having a large aspect ratio and raked tips makes a very considerable
difference as will be seen from the above results, the rake and aspect
of 8 making the difference between 21.585 and 11.664 in the lift-drag.
Area for area, the drag of the first plane will be approximately
one-half of the drag due to an aspect ratio of three.
*Lift in Slip Stream*. The portions of a monoplane or tractor biplane
lying in the propeller slip stream are subjected to a much higher wind
velocity than the outlying parts of the wing. Since the lift is
proportional to the velocity squared, it will be seen that the lift in
the slip stream is far higher than on the surrounding area. Assuming for
example, that a certain propeller has a slip of 30 per cent at a
translational speed of 84 miles per hour, the relative velocity of the
slip stream will be 84/0.70 = 120 miles per hour. Assuming a lift factor
(Ky)=0.0022, the lift in the slip stream will be L = 0.0022 × 120 × 120
= 31.68 pounds per square foot. In the translational wind stream of 84
miles per hour, the lift becomes L = 0.0022 X 84 X 84 = 15.52 pounds per
square foot. In other words, the lift of the portion in the slip stream
is nearly double that of the rest of the wing with a propeller
efficiency of 70 per cent.