Properties of the s-shaped wing profile. Airplane wing profile: types, technical and aerodynamic characteristics, calculation method and maximum lift. Total aerodynamic force and its projections

I bring to your attention an article from the cycle of materials to help amateur designers of the ALS. Scientific consultant - Professor of the Department of Aircraft Engineering of the Moscow Aviation Institute, Doctor of Technical Sciences, laureate of the State Prize A.A. Badyagin. The article was published in the journal "Wings of the Motherland" # 2 for 1987.

Why, you ask, do we need an article about a profile for ultralight aircraft? I answer - the thoughts expressed in this article are directly applicable in aircraft modeling - the speeds are comparable, and, accordingly, the approach to design.

The best profile

Airplane design usually begins with the selection of the wing profile. After sitting for a week or two over directories and atlases, without fully understanding them, on the advice of a friend, he chooses the most suitable one and builds an airplane that flies well. The selected profile is declared the best. Another amateur chooses a completely different profile in the same way and his aircraft flies well. At the third, the plane barely takes off from the ground, and at first the seemingly most advantageous wing profile is considered no longer suitable.

Obviously, not everything depends on the profile configuration. Let's try to figure it out. Let's compare two wings with completely different profiles, for example, with the symmetrical Yak-55 and asymmetrical Clark YH - Yak-50. Let's define several conditions for comparison. First: wings with different profiles must have an aspect ratio (l).

l = I2 / S,
where I is the span, S is the area.

Second: since the angle of zero lift for the symmetric airfoil is equal to 00, we will shift its polar (see Fig. 1) to the left, which will physically correspond to the installation of the wing on an airplane with some positive spell angle.

Now, looking at the graph, you can easily draw an important conclusion: in the range of flight angles of attack, the characteristics of the wing are practically independent of the profile shape. Of course, we are talking about streamlined airfoils that do not have zones of intense flow separation in the range of flight angles of attack. The characteristics of the wing, however, can be significantly influenced by increasing the aspect ratio. For comparison, graph 1 shows wing polars with the same profiles, but with an aspect ratio of 10. As you can see, they went much steeper, or, as they say, the CU derivative with respect to a became higher (CU is the wing lift coefficient, a is the angle of attack). This means that with an increase in the elongation at the same angles of attack with practically the same drag coefficients Cx, higher bearing properties can be obtained.

Now let's talk about what depends on the shape of the profile.

First, the profiles have different maximum lift coefficient CU max. So, for symmetric wings, the lift coefficient of the wing is 1.2 - 1.4, ordinary asymmetric ones with a convex lower surface can have - up to 1.8, with a strong concavity of the lower surface it sometimes reaches 2. However, it must be remembered that profiles with a very high CU max usually have high Cx and mz - longitudinal moment coefficient. To balance an aircraft with such a profile, the tail unit must develop a lot of force. As a result, its aerodynamic resistance increases, and the overall gain obtained due to the high bearing profile is significantly reduced.

CU max significantly affects only the minimum aircraft speed - stall. It largely determines the simplicity of the technique of piloting the car. However, the influence of CU max on the stall speed is noticeably manifested at high specific loads on the wing G / S (G is the weight of the aircraft). At the same time, at loads typical for amateur aircraft, that is, 30 - 40 kg / m2, a large CU max is not significant. So its increase from 1.2 to 1.6 on an amateur aircraft can reduce the stall speed by no more than 10 km / h.

Secondly, the shape of the profile significantly affects the behavior of the aircraft at high angles of attack, that is, at low speeds during landing approach, in case of accidental "pulling the handle towards itself". At the same time, for thin profiles with a relatively sharp toe, a sharp stall of the flow is characteristic, which is accompanied by a rapid loss of lift and a sharp stall of the aircraft into a spin or on the nose. Thicker ones with a blunt toe are characterized by a "soft break" with a slow drop in lift. At the same time, the pilot always manages to understand that he is in a dangerous mode, and to bring the car to lower angles of attack, giving the handle away from him. A sharp stall is especially dangerous if the wing has a taper in plan and a thinner profile at the end of the wing. In this case, the flow stall occurs asymmetrically, the aircraft abruptly falls onto the wing and goes into a spin. It is this character that appears in the Yak-50 and Yak-52 aircraft, which have a very thin profile at the end of a strongly tapering wing (9% at the end and 14.5% at the root) with a very sharp toe - Clark YH. Here an important property of the profiles is revealed: the thinner ones have a lower Cy max and lower critical angles of attack, that is, the angles at which the flow stall occurs.

Wings with a constant relative profile thickness along the span have much better stall characteristics. For example, the Yak-55 with a moderately narrowed wing with a constant 18% profile along the span with a blunt toe, when reaching high angles of attack, smoothly lowers the nose and goes into a dive, since the flow stall occurs at the root of the wing, which does not create heeling moments. To obtain a root stall, it is better if the wing has no taper at all. It is these wings that are installed on most aircraft of the initial training. An early root stall can also be caused by installing an overflow on the wing, shown in Fig. 2. in this case, the root profile receives a smaller relative thickness and "less load-bearing shape". The installation of such an influx on the experimental Yak-50 once significantly changed the nature of the plane's stall: when reaching high angles of attack, it no longer fell on the wing, but lowered its nose and went into a dive.

The third parameter, which essentially depends on the shape of the profile, is the resistance coefficient Cx. However, as the practice of amateur aircraft construction shows, its reduction on an amateur aircraft with a specific load of 30-40 kg / m2, having a maximum speed of 200-250 km / h, practically does not affect flight characteristics. In this speed range, flight performance is practically unaffected by non-retractable landing gear, struts, braces, etc. Even the aerodynamic quality of a glider depends primarily on the wing lengthening. And only at the level of aerodynamic quality of 20-25 and l more than 15 due to the selection of the profile, the quality can be increased by 30-40%. While on an amateur aircraft with a quality of 10-12, due to the most successful profile, the quality can be increased by no more than 5-10%. It is much easier to achieve such an increase, if necessary, by selecting the wing geometry in the plan. Note one more feature: in the range of speeds of amateur aircraft, an increase in the relative thickness of the airfoil up to 18-20% has practically no effect on the aerodynamic drag of the wing, at the same time, the coefficient of lift of the wing increases significantly.

As you know, a significant increase in the wing bearing characteristics can be achieved through the use of flaps. It should be noted that one specific feature of the flap-equipped wings is that when deflected, the CU max depends little on which CU max had the initial profile, and is determined, in practice, only by the type of flap used. The simplest, most widely used on foreign light-engine aircraft and its characteristics are shown in Fig. 3.

The same flaps are used on the aircraft of our amateur P. Almurzin. Slotted, double-slotted and suspended flaps are more efficient. In fig. 4 shows the simplest of them and therefore are used more often.

CU max with a single-slotted flap can reach 2.3-2.4 and with a two-slotted flap - 2.6 - 2.7. In many textbooks of aerodynamics methods of geometric construction of the shape of the slot are given. But practice shows that the theoretically calculated gap still needs to be fine-tuned and fine-tuned in the wind tunnel, depending on the specific geometry of the profile, wing shape, etc. In this case, the slot either works, improving the characteristics of the flap, or does not work at all, and the probability that, theoretically, without blowing, it is possible to calculate and select the only possible shape of the slot is extremely small. Even professional aerodynamics, and even more so amateurs, rarely succeed in this. Therefore, in most cases on amateur aircraft, the slots on the flaps and ailerons, even if they are, do not give any effect, and a complex slotted flap works like the simplest. Of course, you can try them on amateur devices, but first you should think it over carefully, weighing all the pros and cons.

And a few more practical advice, which can be useful in the construction of amateur aircraft. It is desirable to maintain the wing profile very accurately from the nose to the point of maximum thickness. It is good if this part of the wing has a hard skin. The tail section can be wrapped around the canvas and, to simplify the technology, even straighten "under the ruler", as shown in Fig. 5. The curved tail section of the wing with the linen covering sagging between the ribs does not make more sense. The trailing edge of the wing does not have to be reduced to a sharp "knife". It can have a thickness of 10-15 mm, but not more than 1.5% of the chord (see Fig. 5). This does not affect the aerodynamic characteristics of the wing at all, but the efficiency of the ailerons somewhat increases, and simplifies the technology and design.

An important element of the profile is the shape of the aileron toe. The most common options are shown in Figure 6.

The profile formed by the "parabola 100" is used on ailerons and rudders that have axial aerodynamic compensation when the nose enters the stream, for example, on the Yak-55. Such a "blunt" shape of the toe with a very large value of axial aerodynamic compensation (20% and more) leads to a nonlinear increase in efforts on the control stick when the ailerons or rudders are deflected. The best in this respect are the "pointed" socks, like on the Su-26.

Symmetrical wing profiles are used for the empennage. Rudders, like ailerons, can be formed by straight bows with a blunt trailing edge. The tail with a thin flat profile, as on the American aerobatic aircraft "Pitts", "Laser" and others, has sufficient efficiency (see Fig. 7).

The rigidity and strength of the plumage is provided by the braces, it turns out to be very light and structurally simple. The relative thickness of the profile is less than 5%. With such a thickness, the characteristics of the plumage do not depend at all on the shape of the profile.

Here are the data on the profiles most suitable for amateur flying machines. Of course, other options are possible, but note that the best properties in the speed range of amateur aircraft are 15-18 percent with a blunt toe and with a maximum relative thickness located within 25% of the chord.

The recommended profiles have the following features: P-II and P-III were developed at TsAGI. They have high load-bearing properties and good performance at high angles of attack. They were widely used in the 30s-40s, and are still in use today.

NACA-23015 - the last two digits indicate the relative thickness in percent, the first is the batch number. The profile has a fairly high Cy max at low Cx, a low longitudinal moment coefficient Mz, which determines small balancing losses. The stall pattern for aircraft with this airfoil is "soft". NACA - 230 with a relative thickness of 12 - 18% is used on most light-engine, including amateur, US aircraft.

NACA - 2418 - for speeds less than 200 - 250 km / h is considered more profitable than NACA - 230. It is used on many aircraft, including the Czechoslovak Zlins.

GAW is a supercritical airfoil designed by American aerodynamicist Whitcomb for light aircraft. Profitable at speeds over 300 km / h. A "sharp" toe predetermines a sharp break at high angles of attack, a trailing edge "bent" downwards contributes to an increase in Cy max.

"Kri-Kri" - laminated glider profile, developed by the West German aerodynamicist Wortman and slightly modified by the designer of "Kri-Kri" French Colomban. The relative thickness of the profile is 21.7%, due to which high bearing characteristics are achieved. Like the GAW-1, this profile requires very high theoretical contour accuracy and High Quality wing surface finishes. We give the coordinates of the profile in mm, recalculated by the designer to the chord of the wing of the Kri-Kri aircraft, equal to 480 mm.

P-52 is a modern profile developed at TsAGI for light-engine aircraft. Has a blunt toe and a straight tail.

Yak-55 is a symmetrical profile for aerobatic sports aircraft. On the wing, the relative thickness is 12-18%, on the plumage - 15%. The stall pattern of the aircraft is very "soft" and smooth.

V-16 - French symmetrical profile, has a high Su max, is used on sports aircraft KAP-21, "Extra-230" and others.

Su-26 - 18%, Su-26 - 12% - special profiles for sports and aerobatic aircraft. Su-26-18% is used at the root of the wing of the Su-26, Su-26 - 12% - in the wing tip and on the tail. The profile has a "sharp" toe, which somewhat reduces the bearing properties, but allows you to achieve a very sensitive response of the machine to the deflection of the rudders. Although such an aircraft is difficult to fly for beginners, experienced athletes gain the ability to perform figures that are inaccessible to aircraft with a "soft" delayed reaction to the movement of the handle due to the blunt toe of the profile. The breakdown of an aircraft with a profile of the Su-26 type occurs quickly and abruptly, which is necessary when performing modern corkscrew figures. The second feature is the "compression" in the tail section, which increases the efficiency of the ailerons.

The wing of the Su-26 has large ailerons that occupy almost the entire trailing edge. If we "knock" the neutral of the ailerons (both at once) down by 10 °, the Su max will increase by about 0.2, approaching the Su max of a good asymmetrical profile. At the same time, Cx practically does not increase, and the aerodynamic quality does not decrease, the same is observed on other symmetrical airfoils. This is the basis of the use of ailerons, kinematically connected with the elevator, performing the functions of both ailerons and flaps at the same time, like flaps on a line model.

One of the important stages in the construction of an aircraft model is the calculation and design of the wings. In order to properly design a wing, several points must be taken into account: choose the right root and end profiles, choose them correctly based on the loads they provide, and also design the intermediate airfoils correctly.

Where does wing design begin?

At the beginning of the construction, a preliminary full-size sketch of the aircraft was made on tracing paper. During this stage, I decided on the scale of the model and the wingspan.

Determination of scope

Once the preliminary wingspan was approved, it was time to determine the weight. This part of the calculation was of particular importance. The original plan included a wingspan of 115 cm, however, preliminary calculation indicated that the load on the wings would be too high. So I scaled the model down to a span of 147 cm, excluding the wingtips. This design turned out to be more suitable from a technical point of view. After the calculation, it remains for me to make a weight table with the values ​​of the weights. I also added the average values ​​of the skin weight to my table, for example, the weight of the balsa skin of the aircraft was determined by me as the product of the wing area by two (for the bottom and top of the wing) by the weight of a square meter of balsa. The same was done for the tail and elevators. The weight of the fuselage was obtained by multiplying the area of ​​the side and the top of the fuselage by two and by the density per square meter of balsa.

As a result, I got the following data:

• Linden, 24 oz per cubic inch
• Balsa 1/32 '', 42 oz per square inch
• Balsa 1/16 '' 85 oz per square inch

Sustainability

After determining the weight, stability parameters were calculated in order to ensure that the aircraft would be stable and that all parts would be of adequate size.

For a stable flight, it was necessary to provide several conditions:

1. The first criterion is the mean aerodynamic chord (MAX) value. It can be found geometrically by adding the end chord to the root chord on both sides, and the root chord to the end chord on both sides, and then connect extreme points together. At the point of intersection, the center of the MAR will be located.
2. The aerodynamic focus of the wing is 0.25 of the MAC value.
3. This center must be found for both the wings and the elevators.
4. Next, the neutral point of the aircraft is determined: it shows the center of gravity of the aircraft, and is also calculated together with the center of pressure (center of lift).
5. Next, a static boundary is defined. This criterion evaluates the stability of an aircraft: the higher it is, the greater the stability. However, the more stable the aircraft is, the more maneuverable and less controllable it is. On the other hand, you cannot fly on a plane that is too unstable. The average value of this parameter is from 5 to 15%
6. Plumage ratios are also calculated. These coefficients are used to compare the aerodynamic efficiency of the elevator in terms of aspect ratio and distance to the wing.
7. The vertical tail ratio is usually between 0.35 and 0.8
8. The horizontal tail ratio is usually between 0.02 and 0.05

Choosing the right airfoil

Selecting the correct profile determines the correct behavior of the aircraft in the air. Below is a link to a simple and affordable tool for checking airfoils. As a basis for choosing the airfoils, I chose the concept that the chord at the wingtip is half the chord at the root. The best solution I found to avoid stalling the wing was to taper the wing abruptly at the tip without being able to maintain control of the aircraft until it reached a sufficient speed. I achieved this by turning the wing down at the tip and through careful selection of root and end profiles.

At the root, I chose the S8036 airfoil with a wing thickness of 16% of the chord length. This thickness made it possible to lay a spar of sufficient strength, as well as a retractable landing gear inside the wing. For the end part, the profile was chosen - S8037, which also has a thickness of 16% of the chord thickness. Such a wing will stall at a high lift coefficient, as well as at a higher angle of attack than the S8036 with the same Reynolds number (this term is used to compare profiles of different sizes: the larger the Reynolds number, the larger the chord). This means that with the same Reynolds number at the root of the wing, the stall will occur faster than at the tip, but control over the control will remain. However, even if the chord length of the root is twice the length of the ending chord, it has a Reynolds number twice, and increasing the number will delay the stall. That is why I turned the wingtip down, so that it will go into stall only after the root part.

Airfoil Resource: airfoiltools.com

Theory on the basics of wing design

The wing structure must provide sufficient lift for the weight of the aircraft and the additional stresses associated with maneuvering. This is mainly achieved through the use of a central spar, which has two belts, an upper and a lower one, a frame, and a thin skin. Despite the fact that the frame of the wing is thin, it provides the wings with sufficient flexural strength. Also, the design often includes additional side members to reduce drag at the front of the trailing edge. They are capable of taking both bending loads and increasing torsional stiffness. Finally, the leading edge can be pushed back behind the spar to form a closed transverse frame, called a D-shaped frame, and serves to absorb torsional loads. The figure shows the most common profiles.

1. The upper wing has an I-beam with the frame in the center and a leading edge with a skin called a D-tube. D-tube allows for increased torsional rigidity and can be added to any other side member designs, and can also be extended to the trailing edge to create a fully walled wing. For this wing, the rear spar is simply a vertical support. There is also a simple control plane, in other words, a flap, which is hinged at the top. This design is easy to reproduce.
2. The second wing has a C-spar, which has a reinforced main spar that is better suited to accommodate frontal loads. The wing is equipped with a center pivot that reduces the gap as well as drag compared to the top pivot.
3. The third profile has a spar in the form of a pipe, these are usually made of plastic tubes, they are convenient to make, but if the tubes are indirect or twisted, then twisting the wing can become a problem. Part of the problem can be solved by using an additional D - shaped tube. In addition, the spar is made of a C-shaped profile, which significantly increases the rigidity of the wing. The hinge is a rounded profile with a pivot point in the center of the rounded leading edge to reduce the buttonhole gap and for straight edges.
4. The fourth profile has a full box spar with a frame at both the front and rear. The clearance has the same feature as the previous profile and the same control plane. But it has fairings at the top and bottom to hide the gap.

All of these wing designs are typical for side members and for creating anchor loops for RC aircraft. These designs, without exception, are the only way to technically implement flaps and ailerons, and various other solutions can be tailored to them.

C - spar or box spar?

For my aircraft, I opted for a wooden C-spar with a strong leading edge and a simple vertical spar. The entire wing is sheathed in balsa for torsional rigidity and aesthetics.

Wood was chosen to replace the plastic tube as the aircraft is designed with a 2 degree internal angle and the plastic tube connection in the center of the wing will not be able to resist bending loads for long. The C-profile of the spar is also more favorable than the I-beam, as the full length of the slot must be made in the spar to fit into the grille. This added complexity is not at the expense of a noticeable increase in strength and spar weight ratio. The box spar was also rejected as it adds a lot of weight, however, it is not that difficult to build and is one of the best in terms of strength. A simple vertical spar combined with a looped fairing was the choice of wing design when the rest of the wing was sheathed and strong enough without any additional support.

• Spar. The wing spar is designed to absorb the bending load from the wing's lift. It is not designed to absorb the twisting force created by the aerodynamic forces of the wing, but the load is placed on the wing skin. This load distribution is suitable for light and very effective loading, as each part takes its place.
• The wing spar shelves are made of cast linden with dimensions ¼ x ½ x 24 ’’. Linden was chosen as a material because it handles well and has good strength for its weight. In addition, the ease of acquiring the right size blocks in specialized stores is captivating, since I did not have a woodworking machine for sawing boards at hand.
• The wing frame is made of a 1/32 ”thick linden sheet that attaches to the side member flanges at the top and bottom. Such a frame is a necessity because it dramatically improves the rigidity and strength of the wings, even at very low weight.
• The trailing edge / rear spar is made of 1/16 ”balsa sheet to help add torsional rigidity as well as unify the wing ribs and attach control planes to the rear of the ribs.

Rib design with AutoCAD

It turns out that making ribs for a trapezoidal wing can be an inspiring experience. There are several methods: the first method is based on cutting the wing profile using a stencil, first for the root part and then for the wingtip. It consists in joining both profiles together using bolts and drawing all the others along them. This method is especially good for making straight wings. The main limitation of the method is that it is only suitable for wings with a slight taper. Problems arise from the sharp increase in the angle between the airfoils with a significant difference between the tip chord and the wing root chord. In this case, during assembly, difficulties may arise due to the large waste of wood, sharp corners and edges of the ribs, which will need to be removed. So I used my own method: I made my own templates for each rib, and then processed them to get the perfect wing shape. The task turned out to be more difficult than I expected, since the pattern of the root part was fundamentally different from the tip, and all the profiles in between were a combination of the two previous ones, along with twisting and stretching. I used Autodesk AutoCAD 2012 Student Addition as my design program as I ate a dog on it when modeling RC airplanes in the past. The design of ribs takes place in several stages.

It all starts with importing data. The fastest way to import an airfoil (profiles can be found in the UIUC airfoil databases) into AutoCAD that I have found is to create an excel spreadsheet file as a table with columns of x and y profile points coordinates. The only thing to double-check is whether the first and last points correspond to each other: whether you get a closed loop. Then copy the received back to a txt file and save it. After this is done, you should go back and highlight all the information on the subject if you accidentally inserted the headings. Then AutoCAD runs spline and paste to mark the first point in the sketch. We press "enter" until the end of the process. The airfoil is basically processed in such a way that each chord becomes a separate element, which is very convenient for changing the scale and geometry.

Drawing and the relative position of the profiles in accordance with the plan. The leading edge and side members must be carefully brought to the desired size, while remembering the thickness of the skin. In the drawing, therefore, the side members should be drawn narrower than they really are. It is advisable to make the side members and the leading edge higher than they actually are, in order to make the drawing smoother. Also, the grooves on the side members should be located in such a way that the remaining part of the side member fits into the ribs, but remains square.

The figure shows the main airfoils before they are subdivided into intermediate ones.

The spar and the leading edge joint with it are connected together so that later they can be excluded from the construction.

The airfoils are mated together to form the wing shape with the spar and leading edge visible.

The spar and leading edge have been removed using the "subtract" operation, the rest of the wing is shown.

The wing is extended using the "solidedit" and "shell" functions. Further, the planes of the root part of the wing and the tip are selected alternately, removed, and what is obtained is the wing skin. Therefore, the inner part of the wing skin is the basis for the ribs.

The Section Plane function generates sketches of each profile.

After that, under the command "section plane", the creation of a section is selected. With this command, the created profiles at all points of the profile can be displayed. To help align the wing ribs, I strongly recommend creating a horizontal line on each section from the trailing edge of the wing to the leading edge. This will allow the wing to be properly aligned if it is built with torsion, and also to make it straight.

Since these templates are actually created with the wing skins in mind, the inner profile line is the correct line for the ribs.

Now that all ribs have been marked with the "text" command, they are ready to print. On each page with ribs, I placed a schematic box with a platform available for printing on a printer. Small ribs can be printed on thick paper, while for large airfoils, plain paper will work, which is then reinforced before cutting.

Complete set of parts

After designing the wing, analyzing and selecting all the parts necessary for making an aircraft model, a list of everything needed for construction was made.

Objective

Investigate the flow around the wing profile without taking into account its span, i.e. wings of infinite span. Find out how the pattern of the airfoil flow changes when the angle of attack changes. The study should be carried out for three modes - subsonic takeoff and landing, subsonic cruising and supersonic flights. Determine the lift and drag force acting on the wing. Build a wing polar.

BRIEF THEORY

Wing profile- section of the wing with a plane parallel to the plane of symmetry of the aircraft (section A-A). Sometimes a profile is understood as a section perpendicular to the leading or trailing edge of the wing (section BB).

Profile chord b - a segment connecting the most distant points of the profile.

Wingspan l - the distance between the planes parallel to the plane of symmetry and touching the ends of the wing.

Central (root) chordb 0 - chord in the plane of symmetry.

End chordb K - chord at the end section.

Sweep angle on the leading edgeχ PC - the angle between the tangent to the leading edge line and the plane perpendicular to the central chord.

As indicated in previous work, the total aerodynamic force is R decomposes into lifting force Y and the force of resistance X:

Lift force and drag force are determined using similar formulas:

where C Y and WITH X- coefficients of lift and resistance, respectively;

ρ - air density;

V- the speed of the body relative to the air;

S- effective body area.

Research is usually not dealt with by the forces themselves. Y and X, and with their coefficients C Y and C X .

Consider the air flow around a thin plate:

If the plate is installed along the flow (the angle of attack is zero), then the flow will be symmetrical. In this case, the air flow is not deflected by the plate and the lifting force Y is equal to zero. Resistance X minimal, but not zero. It will be created by the forces of friction of air molecules on the surface of the plate. Full aerodynamic force R is minimal and coincides with the resistance force X.

Let's start deflecting the plate a little at a time. Due to the mowing of the flow, the lifting force appears immediately. Y... Resistance X slightly increases due to the increase in the cross-section of the plate with respect to the flow.

As the angle of attack gradually increases and the flow slope increases, the lift increases. Obviously, resistance is also growing. It should be noted here that at low angles of attack, lift increases significantly faster than drag.

As the angle of attack increases, it becomes more difficult for the air stream to flow around the plate. Lift force, although it continues to increase, is slower than before. But the resistance is growing faster and faster, gradually overtaking the growth of lift. As a result, the total aerodynamic force R begins to lean back.

And then suddenly the picture changes dramatically. Air jets are unable to smoothly flow around the upper surface of the plate. A powerful vortex forms behind the plate. Lift drops sharply and drag increases. This phenomenon is called STOP in aerodynamics. The “torn off” wing ceases to be a wing. It stops flying and starts to fall

Let us show the dependence of the lift coefficients WITH Y and the forces of resistance WITH X from the angle of attack α on the charts.

Let's combine the resulting two graphs into one. Along the abscissa, we will postpone the values ​​of the resistance coefficient WITH X, and the ordinate is the lift coefficient WITH Y .

The resulting curve is called the WING POLARA - the main graph that characterizes the flight characteristics of the wing. Plotting on the coordinate axes the values ​​of the lift coefficients C Y and resistance C X, this graph shows the magnitude and direction of action of the total aerodynamic force R.

If we assume that the air flow moves along the axis C X from left to right, and the center of pressure (the point of application of the total aerodynamic force) is at the center of coordinates, then for each of the previously analyzed angles of attack, the vector of the total aerodynamic force will go from the origin to the polar point corresponding to the given angle of attack. Three characteristic points and the corresponding angles of attack can be easily marked on the polar: critical, economic and most advantageous.

Critical angle of attack- this is the angle of attack, when exceeded, the flow stall occurs. Wherein WITH Y maximum and the aircraft can be kept in the air at the lowest possible speed. This is useful when making an approach. See point (3) in the figures.

Economic angle of attack Is the angle of attack at which the aerodynamic drag of the wing is minimal. If you set the wing to an economic angle of attack, then it will be able to move at maximum speed.

Best angle of attack Is the angle of attack at which the ratio of the lift and drag coefficients C Y /C X maximum. In this case, the angle of deflection of the aerodynamic force from the direction of movement of the air flow is maximum. When the wing is set to the most advantageous angle of attack, it will fly the farthest.

Wing aerodynamic quality Is the ratio of the coefficients C Y /C X when setting the wing to the most advantageous angle of attack.

Work order

Wing profile selection:

An extensive library of aviation profiles can be found at the University of Illinois website: http://aerospace.illinois.edu/m-selig/ads/coord_database.html

Here is a base of approximately 1600 different wing profiles. Each profile has its picture (in * .gif format) and a table of coordinates of the upper and lower parts of the profile (in * .dat format). The database is freely available and constantly updated. In addition, this site contains links to other profile libraries.

Choose any profile and download the * .dat file to your computer.

Editing * .dat file with profile coordinates:

Before importing a file with profile coordinates into SW, it must be corrected in Microsoft Excel... But if you directly open this file in Excel, then all the coordinates will be in one column.

We need the coordinates X and Y profiles were in different columns.

Therefore, we first start Excel, and then open our * .dat file from it. In the drop-down list, indicate "All files". In the text wizard, we specify the data format - with the “Space” separator character.

Now X and Y coordinates each in its own column:

Now we delete line 1 with text, line 2 with extraneous data and empty line 3. Next, we look through all the coordinates and also delete empty lines, if any.

We also add a third column for the coordinate Z... In this column, fill all cells with zeros.

And we shift the entire table to the left.

The edited * .dat file should look something like this:

Save this file as a text file (tab delimited).

Creating a profile in SW:

Create a new part in SW.

Run the command "Curve through XYZ points" on the "Elements" tab.

A window will open:

Click OK and insert the wing profile curve into the document.

If you receive a warning that the curve is self-intersecting (this is possible for some profiles), then you need to manually edit the file in Excel to eliminate the self-intersection.

Now this curve needs to be converted to a sketch. To do this, create a sketch on the front plane:

Run the command "Transform Objects" on the "Sketch" tab and specify our profile curve as an element for transformation.

Since the initial curve is very small (the chord of the profile is only 1 mm!), Using the "Scale Objects" command we increase the profile a thousand times so that the values ​​of aerodynamic forces more or less correspond to the real ones.

Close the sketch and use the Extruded Boss / Base command to extrude the sketch into a solid 1000 mm long. You can actually extrude to any length, anyway we will solve the problem of two-dimensional flow.

Profile blowing in the Flow Simulation module:

It is necessary to blow the resulting profile in three speed modes: subsonic takeoff and landing (50 m / s), subsonic cruising (250 m / s) and supersonic (500 m / s) at different angles of attack: –5 °, 0 °, 10 °, 20 °, 30 °, 40 °.

In this case, it is necessary to build pictures in cross-section for each case and determine the lifting force and resistance force acting on the profile.

Thus, it is necessary to perform the calculation 18 times in Flow Simulation and fill in the following table:

Rotation of the wing in SW is performed using the Move / Copy Bodies command.

Common parameters of the project are: type of problem (external without taking into account closed cavities), type of fluid medium (air, laminar and turbulent flow, large Mach numbers for supersonic mode), velocity in the direction of the axis X V X= 50, 250 and 500 m / s. Leave the rest of the parameters by default.

In the properties of the computational domain, specify the type of problem - 2D modeling.

We indicate purpose of calculation- superficial, we put marks for average speeds on X and Y, as well as for forces on X and Y.

In conclusion, 6 graphs are built - the dependence of the lift Y and the forces of resistance X from the angle of attack α as well as 3 wing polars.

Control questions

What is a wing profile?

What is the angle of attack?

What is Wingspan?

How is a flow around a wing of a finite span different from a flow around a wing with an infinite span?

What is a wing chord?

What are the wing chords?

How to determine lift and drag force (formulas)?

What the dependency graphs look like C Y and C X from the angle of attack α ?

What is wing polar?

What are the characteristic points on the polar?

What is the aerodynamic quality of a wing?

Total aerodynamic force and its projections

When calculating the main flight performance of an aircraft, as well as its stability and controllability, it is necessary to know the forces and moments acting on the aircraft.

Aerodynamic forces acting on the surface of the aircraft (pressure and friction) can be reduced to the main vector of aerodynamic forces applied at the center of pressure (Fig. 1), and a pair of forces, the moment of which is equal to the main moment of aerodynamic forces relative to the center of mass of the aircraft.

Rice. 1. Total aerodynamic force and its projections in the two-dimensional (plane) case

Aerodynamic force is usually set by projections on the axes of the velocity coordinate system (GOST 20058-80). In this case, the projection onto the axis , taken with the opposite sign is called drag force , the projection on the axis - aerodynamic lift , projection on the axis - aerodynamic lateral force . These forces can be expressed in terms of dimensionless drag coefficients , lift and lateral force , respectively:

; ; ,

where is the high-speed head, N / m 2; - air speed, m / s; r is the mass density of air, kg / m 3; S - aircraft wing area, m 2. The main aerodynamic characteristics also include aerodynamic quality.

.

The aerodynamic characteristics of the wing,, depend on the geometric parameters of the airfoil and the wing, the orientation of the wing in the flow (angle of attack a and slip b), similarity parameters (Reynolds numbers Re and Mach), flight altitude H, as well as from other parameters . The Mach and Reynolds numbers are dimensionless and are determined by the expressions

where a Is the speed of sound, n is the kinematic coefficient of air viscosity in m 2 / s, is the characteristic size (as a rule, it is assumed, where is the average aerodynamic chord of the wing). To determine the aerodynamic characteristics of an aircraft, sometimes simpler, approximate methods are used. An aircraft is considered as a set of separate parts: wing, fuselage, empennage, engine nacelles, etc. The forces and moments acting on each of the individual parts are determined. In this case, the known results of analytical, numerical and experimental studies are used. The forces and moments acting on the plane are found as the sum of the corresponding forces and moments acting on each of its parts, taking into account their mutual influence.

According to the proposed method, the calculation of the aerodynamic characteristics of the wing is performed if some geometric and aerodynamic characteristics of the wing profile are specified.

Wing profile selection

The main geometric characteristics of the profile are set by the following parameters. The chord of a profile is a straight line segment connected to the two most distant points of the profile. The chord divides the profile into two parts: upper and lower. The largest segment perpendicular to the chord, enclosed between the upper and lower contours of the profile, is called profile thickness c (fig. 2). The line connecting the midpoints of the segments perpendicular to the chord and enclosed between the upper and lower contours of the profile is called middle line ... The largest segment perpendicular to the chord, enclosed between the chord and the midline of the profile, is called profile curvature f ... If, then the profile is called symmetrical .

Rice. 2. Wing profile

b- chord of the profile; c- profile thickness; f- curvature of the profile; - coordinate of the maximum thickness; - coordinate of maximum curvature

Thickness c and the curvature of the profile f, as well as coordinates and, as a rule, measured in relative units,,, or percentage , , , .

Wing profile selection is associated with satisfaction different requirements requirements for the aircraft (ensuring the required flight range, high fuel efficiency, cruising speed, ensuring safe takeoff and landing conditions, etc.). So, for light aircraft with simplified wing mechanization, special attention should be paid to ensuring the maximum value of the lift coefficient, especially during takeoff and landing. As a rule, such aircraft have a wing with a large value of the relative airfoil thickness% = 12 ¸ 15%.

For long-range aircraft with a high subsonic flight speed, in which an increase in takeoff and landing modes is achieved due to wing mechanization, the emphasis is on achieving best characteristics on cruising, in particular, to provide modes.

For low-speed aircraft, the choice of profiles is made from a series of standard (conventional) NACA or TsAGI profiles, which, if necessary, can be modified at the stage of the aircraft outline design.

For example, NACA profiles with four-digit designations can be used on light training aircraft, namely for wing and tail end sections. For example, profiles NACA2412 (relative thickness% = 12%, coordinate of maximum thickness% = 30%, relative curvature% = 2%, coordinate of maximum curvature% = 40%) and NACA4412 (% = 12%,% = 30%,% = 4%,% = 40%) have a fairly high value and smooth stall characteristics in the area of ​​the critical angle of attack.

NACA 5-digit profiles (230 series) have the highest lift of all standard series, but their breakout performance is less favorable.

NACA profiles with a six-digit designation ("laminar") have a low profile resistance in a narrow range of coefficient values. These profiles are very sensitive to surface roughness, dirt, build-up.

The classical (conventional) profiles used on airplanes with low subsonic speeds are distinguished by rather large local disturbances (discharges) on the upper surface and, accordingly, by small values ​​of the critical Mach number. The critical Mach number is an important parameter that determines the drag of the aircraft (for>, regions of local supersonic currents and additional wave drag appear on the surface of the aircraft).

An active search for ways to increase the cruising speed of flight (without increasing the resistance of the aircraft) has led to the need to find ways to further increase in comparison with classical speed profiles. This way of increasing is to reduce the curvature of the upper surface, which leads to a decrease in disturbances on a significant part of the upper surface. With a small curvature of the upper surface of the supercritical airfoil, the fraction of the lift generated by it decreases. To compensate for this phenomenon, the tail section of the profile is trimmed by smoothly bending it downward ("flap" effect). In this regard, the middle line of supercritical profiles has a characteristic S - figurative view, with a fold down of the tail section. Supercritical airfoils are usually characterized by negative curvature in the nose of the airfoil. In particular, at the MAKS 2007 air show in the exposition of JSC Tupolev, a model of the TU-204-100SM aircraft with a truncated wing was presented, which makes it possible to get an idea of ​​the geometric characteristics of the wing root section. The photo below (Fig. 3.) shows the presence of the ²belly ² profile and a rather flat upper part, typical of supercritical profiles. Supercritical profiles, in comparison with conventional velocity profiles, can increase by approximately = 0.05 ¸ 0.12 or increase the thickness by% = 2.5 ¸ 5%. The use of thickened profiles allows increasing the wing aspect ratio by = 2.5 ¸ 3 or decreasing the sweep angle from the wing by approximately = 5 ¸ 10 ° while storing the value .

Rice. 3. Wing profile of Tu-204-100SM aircraft

The use of supercritical airfoils in the arrangement of swept wings is one of the main directions for improving the aerodynamics of modern transport and passenger aircraft.

It should be noted that with the undoubted advantage of supercritical airfoils, in comparison with the usual ones, some of their disadvantages are an increase in the value of the dive torque coefficient and a thin tail section of the airfoil.

Basic geometric and aerodynamic characteristics of a finite span wing

Over the past 30 ¸ 40 years, the main wing type for subsonic long-haul aircraft has been a swept (c = 30 ¸ 35 °) wing with an aspect ratio, made with a narrowing h = 3 ¸ 4. The promising passenger aircraft presented at the MAKS - 20072 air show (Tu - 334, Sukhoy Superjet 100) had an aspect ratio. Progress in increasing wing aspect ratio has been achieved mainly through the use of composite materials in the wing structure.

Rice. 4. One-panel wing

The wing section in the plane of symmetry is called root profile , and its chord is root ; at the ends of the wing, respectively, end profile and terminal chord ... The distance from one end profile to another is called wingspan ... The chord of the wing profile can vary along its span. The ratio of the root chord to the trailing chord is called tapering of the wing h. The relationship is called wing lengthening ... Here S is the projection area of ​​the wing onto the plane perpendicular to the plane of symmetry of the wing and containing the root chord. If, during the flight, the ends are deflected relative to the root section, they speak of wing sweep ... In fig. 4 shows the angle between the perpendicular to the plane of symmetry and the leading edge of the wing, which determines leading edge sweep ... They also talk about coal sweep trailing edge , but most importantly - the angle (or just c) focus line , i.e. along a line connecting the foci of the wing profiles along its span. At zero sweep along the focus line for a wing with a non-zero taper, the wing edges are not perpendicular to the plane of symmetry of the wing. However, it is generally considered to be a straight wing rather than a swept wing. If the ends of the wing are deflected back relative to the root section, then they say about positive sweep if forward - about negative ... If the leading and trailing edges of the wing do not have kinks, then the sweep does not change along the span. Otherwise, sweep can change its meaning and even sign.

Modern swept wings with a sweep angle c = 35 ° of subsonic long-haul aircraft designed for cruising speeds corresponding to = 0.83 ¸ 0.85, have an average relative wing thickness% = 10 ¸ 11%, and supercritical wings with a sweep angle c = 28 ¸ 30 ° (for promising aircraft) about% = 11 ¸ 12%. The distribution of the thickness over the wingspan is determined from the conditions for realizing a given useful volume and the minimum wave drag. In order to realize the sliding effect in the side sections of swept wings, profiles with a "more forward" location of the point of maximum thickness are used in comparison with the rest of the wing.

Are not located in the same plane, then the wing has a geometric twist (Fig. 6), which characterizes the angle j.

Rice. 6. End and root wing profiles in the presence of geometric twist

Studies of aerodynamic models of aircraft have shown that the use of supercritical airfoils in combination with geometric twist makes it possible to provide. In this work, we use an approximate technique for determining the aerodynamic characteristics of the wing, based on the use of experimental data. The calculation of the aerodynamic coefficients and the wing is carried out in several stages. The initial data for the calculation are some geometric and aerodynamic characteristics of the airfoil. This data can be taken, in particular, from the atlas of profiles.

According to the results of calculating the aerodynamic coefficients, a dependence is constructed and a polar - dependence . A typical form of these dependences for low subsonic velocities is shown, respectively, in Fig. 7 and fig. eight.

The classic wing profile is as follows

The greatest thickness is located at about 40% of the chord.

In this case, the middle line changes in approximately the same way.

Such profiles were called supercritical (supercritical). They quickly evolved into 2nd generation supercritical profiles - the front end was approaching symmetrical, and the undercutting increased.

Moving the middle part of the profile down would bring additional advance in speed.

but further development stopped in this direction - even stronger undercut made the trailing edge too thin in terms of strength. Another disadvantage of the 2nd generation supercritical wing was the dive moment, which had to be parried by the load on the horizontal tail.

We decided: since you can't crop at the back, you need to crop in the front.

They write about the result:

“As you can imagine, this task was brilliantly solved. And the solution was just as ingenious as it was simple - we applied a cropping in the front lower part of the wing and reduced it in the rear. advantages of the supercritical profile.

Now engineers have a direct opportunity to increase flight speed by more than 10% without increasing engine power, or to increase the strength of the wing without increasing its mass.